Multi-point uniform pressure control system and method for low-stress clamping of thin-walled curved surface parts

Abstract

The application discloses a multi-point uniform pressure control system and method for low-stress clamping of thin-walled curved surface parts, relates to the technical field of industrial control systems, and comprises the following modules: a clamping area division and parameter acquisition module, which extracts part local structure stiffness and stress constraint parameters; a prior stiffness modeling module, which establishes a stiffness characterization model and determines a permissible stress boundary; a clamping stiffness online identification module, which accurately calculates the equivalent stiffness of each point by deducting the deformation of an actuator and a clamp structure; a force-deformation mapping module, which establishes a mapping relationship between clamping force and deformation and stress; a differential clamping force distribution module, which takes the consistent response of each point normal deformation as the goal, combines the permissible stress boundary and the cutting force constraint, and calculates the differential target clamping force of each point; and a loading execution and closed-loop control module, which loads and iteratively corrects based on deformation feedback and stress estimation. The above technical scheme improves the position stability of the part in the clamped state and the low-stress state control capability.

Description

Technical Field

[0001] This invention belongs to the field of industrial control system technology, specifically a multi-point pressure equalization control system and method for low-stress clamping of thin-walled curved parts. Background Technology

[0002] Thin-walled curved surface parts are widely used in aerospace, energy and power fields. Their structural characteristics include thin walls, complex curvature variations, and significant local stiffness differences. During the machining process, to ensure the positional stability and machining accuracy of the parts, a multi-point flexible clamping method is usually adopted. This involves setting multiple clamping units on the fixture according to the structural dimensions, curved surface shape, and machining area of ​​the part, and applying clamping forces to different positions of the part through hydraulic, pneumatic, or electric actuators.

[0003] In terms of clamping control, existing multi-point flexible clamping methods typically use the output pressure of the fixture actuator as the basis for judging the clamping state. Pressure sensors detect the output pressure of each clamping unit, and adjustments are made to each unit based on the detection results to ensure that each clamping point reaches a preset pressure value. When all clamping points reach the same or similar set pressure, the part is considered to be under relatively uniform stress, and the clamping process is complete. This strategy, which aims to make the output pressure at each clamping point consistent—i.e., multi-point pressure equalization control—is currently the most commonly used method in multi-point flexible clamping of thin-walled curved parts.

[0004] However, the aforementioned multi-point pressure equalization control strategy has shortcomings in practical applications. Thin-walled curved parts have low inherent stiffness, and different regions exhibit variations in wall thickness, curvature, and structural support conditions, resulting in varying resistance to external forces. When the same clamping force is applied to different locations, regions with higher stiffness experience less deformation, while regions with lower stiffness may experience larger localized deformations. Furthermore, due to machining errors, initial deformation, and clamping posture deviations in actual parts, the contact state between the part and the fixture may differ at different clamping positions, leading to inconsistent transmission of the clamping force within the part. Therefore, although the output pressure detected by the fixture may be the same, the actual degree of constraint, deformation response, and stress distribution in different regions of the part may still vary significantly, easily causing localized stress concentration or clamping deformation.

[0005] Furthermore, existing clamping control methods primarily focus on clamp-side state parameters such as hydraulic pressure, pneumatic pressure, or actuator displacement. However, the relationship between clamp-side parameters and the actual stress state of the part is influenced by multiple factors, including the part's structural characteristics, contact state, and changes in clamping conditions. Therefore, a simple linear correspondence does not exist between the two. Relying solely on the output pressure at the clamping point is insufficient to accurately determine whether a thin-walled curved surface part is under reasonable stress, nor can it guarantee the formation of a low-stress constraint state suitable for the part's structural characteristics across multiple clamping positions. Pressure equalization control focuses on the consistency of force values ​​at the clamping output end, rather than the uniformity of stress distribution on the part itself; there is a fundamental difference between the two.

[0006] Therefore, existing multi-clamping point force equalization control methods take the consistent output force of each actuator as the control objective, which fails to reflect the uneven distribution of actual stress in different areas of the part body caused by differences in stiffness and contact state. As a result, the force difference in different areas of the part during clamping is difficult to be effectively identified and compensated, which can easily cause local stress concentration and clamping deformation. Summary of the Invention

[0007] To address the above problems, this invention provides a multi-point pressure equalization control system and method for low-stress clamping of thin-walled curved parts, which solves the problems of local stress concentration and clamping deformation caused by differences in regional stiffness and contact state during multi-point clamping of thin-walled curved parts.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] The multi-point pressure equalization control system for low-stress clamping of thin-walled curved parts provided in this invention includes: a clamping area division and parameter acquisition module, used to divide the thin-walled part to be processed into multiple clamping areas according to the position of each clamping unit, and acquire the local structural stiffness parameters and stress constraint basic parameters of each clamping area; a priori stiffness modeling module, used to establish a priori stiffness characterization model of each clamping area according to the local structural stiffness parameters, and determine the allowable stress boundary of each clamping area according to the stress constraint basic parameters; and an online clamping stiffness identification module, used to control the actuator of each clamping unit to contact the surface of the part and apply a preset preload, and calculate the corresponding clamping stiffness of each clamping area according to the preload stage force data and displacement data collected by the force detection unit built into each clamping unit. The system includes a clamping equivalent stiffness module, which is determined based on the ratio of effective displacement data to force data after deducting the deformation contribution of the actuator itself and the deformation contribution of the fixture structure; a force-deformation mapping module, which establishes a mapping relationship between clamping force and normal deformation response and stress level of the part based on the clamping equivalent stiffness; a differentiated clamping force allocation module, which calculates the differentiated target clamping force of each clamping point based on the mapping relationship, with the goal of making the normal deformation response of each clamping point tend to be consistent, combined with allowable stress boundary and cutting force constraints; and a loading execution and closed-loop control module, which performs loading on each clamping unit according to the differentiated target clamping force, and iteratively corrects the clamping state based on the feedback of the normal deformation response of each point and the stress estimation based on the mapping relationship.

[0010] The multi-point pressure equalization control method for low-stress clamping of thin-walled curved parts provided in this invention includes the following steps: Step 1: Divide the thin-walled part to be processed into multiple clamping areas according to the position of each clamping unit, and obtain the local structural stiffness parameters and stress constraint basic parameters of each clamping area; Step 2: Establish a priori stiffness characterization model for each clamping area based on the local structural stiffness parameters, and determine the allowable stress boundary of each clamping area based on the stress constraint basic parameters; Step 3: Control the actuator of each clamping unit to contact the surface of the part and apply a preset preload, and calculate the stress on each clamping area based on the preload force data and displacement data collected by the force detection unit built into each clamping unit. The clamping equivalent stiffness of the corresponding clamping point is determined based on the ratio of effective displacement data to force data after deducting the deformation contribution of the actuator itself and the deformation contribution of the fixture structure; Step 4: Establish the mapping relationship between clamping force and normal deformation response and stress level of the part based on the clamping equivalent stiffness; Step 5: Based on the mapping relationship, with the normal deformation response of each clamping point tending to be consistent as the control target, and combined with allowable stress boundary and cutting force constraint, calculate the differentiated target clamping force of each clamping point; Step 6: Apply load to each clamping unit according to the differentiated target clamping force, and perform iterative correction of the clamping state based on the feedback of normal deformation response of each point and stress estimation based on the mapping relationship.

[0011] The beneficial effects achieved by the technical solutions provided in the embodiments of the present invention include at least the following:

[0012] (1) By establishing the uniformity of the normal deformation response of each clamping point as the control target of force distribution, and incorporating the allowable stress boundary and cutting force constraint as joint constraint conditions into the solution process of the target clamping force, it is helpful to take into account the deformation uniformity, stress safety and anti-cutting stability under multi-point clamping conditions. In the prior art, multi-point clamping usually adopts equal force distribution or simple distribution according to stiffness ratio, ignoring the inconsistency of effective pressing amount caused by the stiffness difference of each point, or it is easy to have excessive pressing in the area with weak stiffness or insufficient resistance of the clamping point in the direction of cutting force. The present invention incorporates the above three types of physical constraints into the same distribution framework for joint solution, which helps to alleviate the problem of mutual restraint between constraints under a single distribution criterion. Then, the constraint driving correction factor is formed by weighted combination of cutting load constraint component, deformation sensitivity constraint component and stress margin constraint component, and then compounded with the stiffness distribution weight determined based on the clamping equivalent stiffness ratio. This is conducive to more refined adaptive adjustment of the force value of each point on the stiffness balance benchmark. In the prior art, force distribution mostly relies on a single Stiffness weighting or uniform safety factors often make it difficult to distinguish the different requirements between points facing and away from the cutting force direction, and the ability to implement individual load reduction in local stress concentration areas is also relatively limited. In this invention, the three constraint components are independently weighted and respond independently, which helps to reduce the coupling interference of changes in one constraint component on the adjustment direction of the other components. Finally, when all constraint conditions are not activated, each constraint driving correction factor takes a preset reference value, and the normal deformation response of each point tends to be consistent. When any constraint condition is activated, that is, when the corresponding physical quantity exceeds the preset threshold, the correction factor of that point deviates from the reference value, resulting in a directional force value shift. The distribution results of the remaining inactive points are basically unaffected. In the prior art, constraint optimization often applies all constraints to the global solution at the same time. The activation of a certain local constraint is easily coupled to other clamping points through the solver, causing the force value of the unconstrained area to be reduced accordingly. This invention helps to control the constraint influence within the trigger point and its necessary range, so that the inactive area can maintain a relatively uniform deformation distribution state under most working conditions.

[0013] (2) By collecting the force change and the displacement change of the actuator during the pre-tightening stage, the deformation of the actuator itself and the deformation of the fixture structure are deducted by the product of the pre-calibrated actuator flexibility coefficient and the fixture structure flexibility and the force change, respectively. The clamping equivalent stiffness is determined according to the ratio between the force change and the effective pressing amount. This helps to more closely reflect the true contact stiffness of the part body. In the prior art, the ratio of force to the total displacement of the actuator is often used directly as the clamping stiffness. This usually includes the elastic deformation of the actuator screw, bearing and fixture base. Without deducting the system flexibility, the measured apparent flexibility will be too large and the apparent stiffness will be too small. If the stiffness is too low, the clamping force calculated accordingly may be too small, posing a risk of insufficient clamping in working conditions where cutting resistance is required. This invention separates the flexibility into two parts: the actuator and the fixture structure, calibrating and deducting them separately. This improves the accuracy of the identification results in reflecting the actual deformation characteristics of the part under its current contact state. Then, the equivalent stiffness of each clamping point is compared point-by-point with the equivalent stiffness characterization value output by the prior stiffness characterization model. Points below a preset ratio are marked as weak contact points. After applying a preset compensation amount to the actuator displacement, the data is re-collected and the stiffness is recalculated. This helps to identify and address issues such as false contact, localized pits, or other problems during the clamping stage. The system automatically detects and corrects abnormal contact conditions such as surface burrs. In existing technologies, contact quality abnormalities often only become apparent during processing due to increased vibration or workpiece micro-movements, by which time the workpiece may have already shifted to some extent. This invention verifies and corrects contact quality before formal loading, helping to reduce the probability of sudden loosening due to contact failure during processing. Finally, during the loading execution phase, a dual closed-loop coordinated control system of force loop and displacement loop is adopted. The force loop tracks the differentiated target clamping force, while the displacement loop monitors the displacement of each actuator point in real time with the maximum allowable indentation as the safety threshold. When the effective indentation at any point reaches the target value, the system automatically detects and corrects these abnormal contact conditions. When the displacement loop approaches or reaches the threshold, it gradually intervenes to limit the output of the force loop. If the actual clamping force at this point is lower than the target value, the force difference is calculated and redistributed among the remaining clamping points within a preset range around this point according to the equivalent stiffness ratio of each clamping point. In the prior art, when a single-loop force control encounters an over-limit displacement, it can usually only stop loading or trigger an alarm. The force gap at this point is often not compensated, and the uniformity of deformation across the entire field is easily affected. This invention enables the force gap at the over-limit point to be proportionally taken over by neighboring points with higher stiffness, which helps to reduce the risk of plastic crushing at the over-limit point while maintaining the relative uniformity of deformation distribution across the entire field and reducing the need for shutdown intervention.

[0014] It should be understood that the content described in this section is not intended to identify key or important features of the embodiments of the present invention, nor is it intended to limit the scope of the present invention. Attached Figure Description

[0015] Figure 1 A schematic diagram of a multi-point pressure equalization control system for low-stress clamping of thin-walled curved surface parts;

[0016] Figure 2 Flowchart for online identification of clamping stiffness;

[0017] Figure 3 The results of online stiffness identification during the clamping process;

[0018] Figure 4 The results were used to verify the mapping relationship between clamping force and part deformation response.

[0019] Figure 5 The results verify the consistency of forces and constraints for multi-point objectives;

[0020] Figure 6 A schematic diagram showing the dynamic signal response relationship under different cutting parameters;

[0021] Figure 7 The results show the time-domain and frequency-domain characteristics of multiple sensors under typical processing conditions;

[0022] Figure 8 The results of dynamic sensing and control adjustments during the processing;

[0023] Figure 9 A schematic diagram illustrating the analysis of cross-component control stability and test results;

[0024] Figure 10 The results show the graded unloading and residual deformation assessment after processing. Detailed Implementation

[0025] To enable those skilled in the art to better understand the technical solution, the present invention will be described in detail below with reference to embodiments. The description in this part is only exemplary and explanatory, and should not be used to limit the scope of protection of the present invention in any way.

[0026] Example 1: As Figure 1 The diagram shows a multi-point pressure equalization control system for low-stress clamping of thin-walled curved parts. The multi-point pressure equalization control system for low-stress clamping of thin-walled curved parts provided by this invention is used to realize multi-point collaborative clamping and stress constraint management of thin-walled curved parts in industrial control scenarios such as CNC machining or precision assembly. It includes: a clamping area division and parameter acquisition module, a priori stiffness modeling module, an online clamping stiffness identification module, a force-deformation mapping module, a differentiated clamping force distribution module, and a loading execution and closed-loop control module.

[0027] The clamping area division and parameter acquisition module is used to divide the thin-walled part to be processed into multiple clamping areas according to the position of each clamping unit. The division principle is: each clamping unit corresponds to one clamping area, and the range of the clamping area is determined by the center of the clamping unit's pressure head as the center and the radius is 1.5 to 3 times the radius of the circumcircle of the effective contact area of ​​the pressure head. The module acquires the local structural stiffness parameters and stress constraint basic parameters of each clamping area. The local structural stiffness parameters include the local wall thickness, principal curvature of the surface, the angle between the surface normal direction and the clamping load direction, the equivalent span of the clamping point neighborhood, and the distribution of adjacent reinforcing ribs and bosses. The stress constraint basic parameters include the yield strength of the part material, the effective contact area between the pressure head of each clamping unit and the part surface, and the process safety factor. The local wall thickness is the wall thickness of the part at the clamping area, in millimeters. For parts with variable wall thickness, the average wall thickness within the pressure head contact area is taken. The principal curvature of the surface is the two principal curvatures at the center of the clamping area, in millimeters. The clamping force can be extracted from the 3D model data of the part, or obtained through coordinate measuring machine (CMM) or laser scanning. The angle between the surface normal and the clamping load direction, i.e., the angle between the outward normal of the surface and the direction of the clamping force at the clamping area, is measured in radians. This angle determines the effective clamping component of the clamping force in the surface normal direction. The equivalent span of the clamping point neighborhood, i.e., the distance between the nearest supporting structures on both sides of the clamping point, such as reinforcing ribs, bosses, and part boundaries, is measured in millimeters. The equivalent span reflects the stress distribution within the clamping area. The degree of suspension during clamping is as follows: the larger the span, the lower the local stiffness; the distribution of adjacent reinforcing ribs and bosses, recording the position, cross-sectional dimensions, and distance from the clamping point of the nearest reinforcing rib or boss around the clamping area, as reinforcing ribs and bosses enhance local stiffness; the effective contact area between the pressure head of each clamping unit and the surface of the part is determined by the geometry of the pressure head, the curvature of the surface, and the preload state; the process safety factor, which is generally between 1.5 and 3.0, is determined according to the importance of the part and the machining accuracy requirements.

[0028] The prior stiffness modeling module is used to establish a prior stiffness characterization model for each clamping region based on the local structural stiffness parameters, and to determine the allowable stress boundary for each clamping region based on the stress constraint basic parameters.

[0029] Furthermore, the equivalent stiffness characterization value output by the prior stiffness characterization model has the same physical dimensions as the clamping equivalent stiffness. It is established based on a combination of material elastic modulus, local wall thickness, clamping point neighborhood span, and curvature correction factor, and mapped to force / displacement units through calibration coefficients. These calibration coefficients are obtained through pre-loading tests on standard specimens matching the material, thickness range, and surface type of the workpiece to be processed. They are used to correct the deviation between the theoretical stiffness model and the actual clamping boundary conditions. During actual processing, the calibration coefficients are periodically updated based on stiffness data from multiple clamping areas identified online, to reduce the impact of changes in processing conditions. The model bias is used to provide a priori reference for subsequent differentiated force allocation; the actual stiffness during the actual clamping process is obtained by the online identification module; it is determined by the local wall thickness, material elastic modulus and Poisson's ratio, equivalent span of the clamping point neighborhood, boundary condition correction coefficient and curvature correction factor. Specifically, the equivalent stiffness characterization value is proportional to the material elastic modulus, proportional to the wall thickness power exponent α of the local wall thickness, and inversely proportional to the span power exponent β of the equivalent span of the clamping point neighborhood, and is multiplied by the boundary condition correction coefficient, curvature correction factor and orientation correction factor in sequence; for example, for the thin plate bending problem, the wall thickness power exponent α is 3 and the span power exponent β is 2.

[0030] Specifically, the boundary condition correction coefficient is determined based on whether the edge of the clamping area is adjacent to the part boundary or supporting structure. For example, if there are supporting structures such as reinforcing ribs or bosses on all four sides of the clamping area, the correction coefficient is 1, indicating complete constraint. If one side of the clamping area is a free boundary, the correction coefficient is 0.6 to 1, and not 1. If both sides of the clamping area are free boundaries, the correction coefficient is 0.3 to 0.6, and not 0.6. If three or more sides of the clamping area are free boundaries, the correction coefficient is 0.1 to 0.3, and not 0.3. The specific value is determined by linear interpolation based on the distance between the free boundary and the clamping point.

[0031] Specifically, the curvature correction factor is determined based on the surface morphology of the clamping area. For example, when the absolute values ​​of the two principal curvatures of the clamping area are both less than the preset curvature determination threshold, a value of 10 is recommended. -4When the curvature is / mm, it is determined to be a flat plate region, and the curvature correction factor is 1, that is, no correction is performed; when the absolute values ​​of the two principal curvatures are not less than the preset curvature judgment threshold, it is determined to be a hyperbolic shell region, such as a spherical shell or a saddle-shaped shell. The curvature correction factor is determined according to the stiffness correction relationship of the two-way curvature in the thin shell bending theory. Specifically, the correction factor is equal to 1 plus an increment term. The increment term is proportional to the square of the wall thickness, proportional to the absolute value of the product of the two principal curvatures, and inversely proportional to the difference between 1 / 2 and the square of Poisson's ratio, and multiplied by the stiffness correction coefficient. This correction factor reflects the enhancement effect of the surface geometric constraint on the normal bearing capacity; for regions with local features such as stiffeners or bosses, the curvature correction factor is equal to 1 plus the ratio of the local stiffness of the stiffener or boss to the basic stiffness of the region without stiffeners. The local stiffness of the stiffener or boss is calculated according to the basic bending theory of beams or plates based on its section moment of inertia and length.

[0032] When the absolute value of only one of the two principal curvatures is not less than the preset curvature judgment threshold, it is judged as a single-curvature shell region, such as a cylindrical surface or a conical surface. The curvature correction factor is determined according to the stiffness correction relationship of unidirectional curvature in the thin shell bending theory. Specifically, the correction factor is equal to 1 plus an increment term. The increment term is proportional to the square of the wall thickness, proportional to the absolute value of the square of the non-zero principal curvature, and inversely proportional to the difference between 12 times 1 and the square of Poisson's ratio, and multiplied by the stiffness correction coefficient.

[0033] In another implementation, the equivalent stiffness characterization value is further corrected according to the angle between the surface normal direction and the clamping load direction. That is, when there is an angle between the clamping force direction and the surface normal direction, if the clamping equivalent stiffness characterization value is calculated with the actuator axial force as the numerator and the normal indentation as the denominator, it needs to be multiplied by a direction correction factor. In this case, the direction correction factor is the cosine of the angle, thus converting it into normal stiffness. If the clamping equivalent stiffness characterization value is calculated with the normal force component as the numerator, the direction correction factor is 1, and no further correction is made. When the angle is zero, the correction factor is 1, and no correction is made.

[0034] Specifically, the stiffness correction factor is a dimensionless coefficient whose value depends on the shell type and diameter-to-thickness ratio. It is used to characterize the amplification or weakening effect of different shell geometries on the normal bearing stiffness. The specific value selection rules are as follows:

[0035] For spherical shells, when the diameter-to-thickness ratio is not greater than 50, the stiffness correction factor is taken as 1.15 to 1.25; when the diameter-to-thickness ratio is greater than 50 and not greater than 200, the stiffness correction factor is determined by linear interpolation of the diameter-to-thickness ratio between 1.25 and 1.05; when the diameter-to-thickness ratio is greater than 200, the stiffness correction factor approaches the asymptotic value of 1.0.

[0036] For cylindrical shells, when the diameter-to-thickness ratio is not greater than 80, the stiffness correction factor is between 0.95 and 1.05; when the diameter-to-thickness ratio is greater than 80 but not greater than 300, the stiffness correction factor is determined by linear interpolation of the diameter-to-thickness ratio between 1.05 and 0.90; when the diameter-to-thickness ratio is greater than 300, the stiffness correction factor approaches the asymptotic value of 0.90.

[0037] For saddle-shaped shells, the diameter-to-thickness ratio corresponding to the smaller of the two principal radii of curvature is used as the equivalent diameter-to-thickness ratio. When the equivalent diameter-to-thickness ratio is not greater than 60, the stiffness correction factor is taken as 0.75 to 0.85. When the equivalent diameter-to-thickness ratio is greater than 60 and not greater than 250, the stiffness correction factor is determined by linear interpolation of the equivalent diameter-to-thickness ratio between 0.85 and 0.70. When the equivalent diameter-to-thickness ratio is greater than 250, the stiffness correction factor approaches the asymptotic value of 0.70.

[0038] The above numerical range and asymptotic values ​​are determined by comparison and verification between the analytical solution of thin shell theory and the finite element calibration results. When the diameter-to-thickness ratio of the actual part exceeds the above range, those skilled in the art can extrapolate to determine the diameter-to-thickness ratio according to the same calibration method, or take the diameter-to-thickness ratio as the asymptotic value of the corresponding type as a conservative estimate.

[0039] In addition, based on the calculation results of the equivalent stiffness characterization values ​​of each region, each clamping region is divided into high stiffness region, medium stiffness region and low stiffness region to form a priori stiffness distribution map, which serves as a comparison benchmark for subsequent online identification and an initial reference for differentiated force allocation.

[0040] The online clamping stiffness identification module is used to control the actuators of each clamping unit to contact the surface of the part and apply a preset preload. Based on the force and displacement data collected by the force detection unit built into each clamping unit during the preload stage, the equivalent clamping stiffness of the clamping point corresponding to each clamping area is calculated. The equivalent clamping stiffness is determined based on the ratio of the effective displacement data after deducting the deformation contribution of the actuator itself to the force data.

[0041] like Figure 2 The flowchart shown illustrates the online clamping stiffness identification process. Further, the specific process by which the online clamping stiffness identification module calculates the equivalent clamping stiffness includes:

[0042] Each clamping unit actuator is controlled to approach the part surface at a preset low speed, such as 0.5-2 mm / s. When the reading of the force detection unit, such as a piezoelectric force sensor or strain gauge force sensor, exceeds the preset contact judgment threshold for the first time, the pressure head is determined to be in initial contact with the part surface, and the current displacement value of the actuator at that point is recorded as the initial contact zero point. The principle for setting the preset contact judgment threshold is that it should be greater than the sensor noise level, usually 3 to 5 times the noise peak value, and less than the minimum force value that produces measurable elastic deformation of the part, with 0.5 to 5 Newtons recommended. At the same time, the deviation between the initial contact zero points of each point is calculated. If the deviation between the initial contact zero points of each point exceeds the preset gap threshold, such as 0.05-0.5 mm, it is determined that there is an initial gap at that point, which is marked as a point to be compensated. In subsequent loading, the displacement compensation amount is added to ensure that effective contact is established before applying the target clamping force.

[0043] After initial contact is established at each point, the force value corresponding to the preset contact judgment threshold is applied to the preset preload, and the force change and the displacement change of the actuator are collected. The preset preload can be set to 10%-30% of the final target clamping force to ensure that the part is in the pure elastic response range. The loading rate can be set to 1 to 10 Newtons per second to avoid the dynamic effect affecting the static stiffness identification accuracy.

[0044] The deformation of the actuator itself is equal to the actuator's compliance coefficient multiplied by the force change. The compliance coefficient is obtained beforehand through no-load calibration, i.e., applying a known force to the actuator and measuring its deformation. The deformation of the fixture structure is equal to the fixture structure compliance coefficient multiplied by the force change. The fixture structure compliance coefficient is obtained through pre-calibration, i.e., installing a rigid standard block as a substitute part on the fixture, applying a known force, and measuring the fixture deformation. The effective pressing amount is equal to the measured displacement change minus the sum of the actuator deformation and the fixture structure deformation. The clamping equivalent stiffness is equal to the force change divided by the effective pressing amount. The clamping equivalent stiffness characterizes the combined stiffness of the contact interface-part structure after deducting the flexibility of the actuator itself and the flexibility of the fixture structure. Specifically, it includes two series stiffness components: the stiffness of the fixture-part contact interface and the stiffness of the part's local structure. The stiffness of the fixture-part contact interface is the stiffness corresponding to the contact deformation between the pressure head and the part surface. The stiffness of the part's local structure is the stiffness corresponding to the local bending and membrane deformation of the part's clamping area under normal load. The flexibility of the actuator itself and the flexibility of the fixture structure are excluded through the above deduction process and are not included in the clamping equivalent stiffness.

[0045] In this embodiment, when calculating the normal deformation response of the part in subsequent modules, the following unified relationship is adopted: the normal deformation response of the part is equal to the current displacement of the actuator minus the initial contact zero point displacement value, and then minus the sum of the actuator compliance coefficient and the fixture structure compliance coefficient multiplied by the current clamping force.

[0046] like Figure 3 The results of online stiffness identification during the clamping process are shown, intuitively demonstrating the effectiveness of this process. Figure (a) shows the relationship between the loading force and the effective pressing amount at multiple sampling points. By collecting force-displacement data corresponding to different loading stages and deducting the influence of the actuator's own flexibility and the fixture's structural flexibility, the effective deformation response under the contact state between the part and the fixture is obtained. The data at each sampling point show an approximately linear trend with small residuals, indicating that the part is in the elastic response range during the pre-tightening stage, thus verifying the stability of the stiffness identification based on the force-displacement ratio. Figure (b) reflects the identification stiffness distribution corresponding to different part models. Different structural parameters lead to differences in the stiffness of the clamping area. The stiffness distribution obtained through online identification can reflect the actual clamping state and complement the prior stiffness model, enabling the subsequent clamping force distribution to be transformed from theoretical prediction to dynamic adjustment based on the actual state. The equivalent stiffness of each clamping point is compared with the equivalent stiffness characterization value output by the prior stiffness characterization model. If the equivalent stiffness of any point is lower than the preset equivalent stiffness characterization value (i.e., the product of the equivalent stiffness characterization value and a preset ratio, such as 0.5), then the point is marked as a low stiffness point to be confirmed. The force response increment at this point under the preset compensation displacement is further detected. If the force response increment is lower than the preset contact effectiveness threshold, it is confirmed as a weak contact point and compensation is performed. A preset compensation amount, such as 0.01-0.1 mm, is applied to the actuator displacement at this point to further align the pressure head with the zero point. The surface of the component is examined, and then the equivalent stiffness of the clamping is recalculated. If the force response increment is normal, it is confirmed as a low-stiffness area caused by the structure itself. The target clamping force at the corresponding clamping point is reduced according to the structural bearing capacity of the area. At the same time, the reduced clamping force is redistributed to other clamping points according to the stiffness distribution weight of the remaining clamping points. The causes of weak contact points include local pits on the curved surface causing the pressure head to not fully fit, local burrs causing virtual contact, and excessive deviation between the normal of the curved surface and the clamping direction. The preset compensation displacement is dynamically determined based on the online identification stiffness of the current area and the maximum allowable indentation.

[0047] In addition, if the ratio of the equivalent stiffness of adjacent clamping points exceeds the preset non-uniformity threshold, such as 3-6 times, the contact state is determined to be severely non-uniform, and the cause needs to be investigated.

[0048] The force-deformation mapping module is used to establish a mapping relationship between clamping force and the normal deformation response and stress level of the part based on the clamping equivalent stiffness. For example... Figure 4The figures show the verification results of the mapping relationship between clamping force and part deformation response. Figure (a) shows the relationship between the target clamping force and the actual clamping force during the graded loading process. As the loading level increases, the actual clamping force can gradually increase along with the target clamping force. Figure (b) shows the change of the closed-loop error between the target force and the actual force during the loading process. The error always remains within the preset range, indicating that the force loop control can achieve stable loading. Figure (c) shows the change of displacement response corresponding to each loading stage. As the loading level increases, the displacement of the actuator shows a continuous changing trend, verifying the effectiveness of establishing the loading level-actuator displacement mapping relationship based on online stiffness identification. Figure (d) shows the mapping relationship between deformation and stress utilization rate. As the normal deformation increases, the stress utilization rate increases synchronously, but never exceeds the allowable stress boundary, indicating that the established force-deformation-stress constraint relationship can be used for clamping force safety control.

[0049] Furthermore, the force-deformation mapping module adopts a hierarchical computational architecture of single-point mapping and multi-point coupled correction, specifically including:

[0050] Based on the preset preload, apply a preset standard test force to each clamping point, such as 20%-50% of the preset preload, and obtain the normal deformation response of each point in its neighborhood caused by the test force. The neighborhood is defined as all other clamping points except the clamping point itself, which are within the range centered on the clamping point and with a preset coupling radius as the distance. It is recommended that the preset coupling radius be 0.5 to 1.5 times the maximum local span of the part.

[0051] The coupling coefficient of a clamping point is defined as the ratio of the maximum absolute value of the normal deformation response increment of all clamping points in the neighborhood other than the clamping point currently applying the test force, to the absolute value of the normal deformation response increment of that clamping point itself under the test force.

[0052] If the coupling coefficient of all clamping points is less than the preset coupling threshold, for example, 0.1 to 0.2, it is determined to be a weak coupling state. At this time, the normal deformation response of each clamping point is determined according to the ratio of the clamping force at that point to the equivalent clamping stiffness at that point.

[0053] If the coupling coefficient of any clamping point is not less than the preset coupling threshold, it is determined to be a strong coupling state. At this time, by applying a unit test force to each clamping point in sequence and recording the normal deformation response of each point in the whole field, a compliance matrix with the deformation response of each point as the element is constructed. The global stiffness matrix is ​​obtained by inverting the compliance matrix. The deformation distribution vector of the whole field is obtained by applying a force vector to the global stiffness matrix.

[0054] For weak coupling, the following comprehensive conditions can be used to help determine whether multi-point coupling correction needs to be enabled: the ratio of the distance between adjacent clamping points to the length of the local stiffness attenuation characteristic of the part, whether the measured deformation response increment of the neighboring point exceeds the product of the deformation response increment of the point itself and the preset ratio when a single point is loaded, and the ratio of the overall stiffness of the part to the local stiffness. When the above judgments indicate that the coupling effect cannot be ignored, multi-point coupling correction is enabled.

[0055] Furthermore, based on the clamping force and geometric parameters at each clamping point, the stress level of each clamping area is estimated. The contact stress is equal to the clamping force at each clamping point divided by the effective contact area. For the case of spherical indenter contacting curved surface, the effective contact area can be determined according to Hertz contact theory, that is, the contact area is proportional to the square of the normal load, the square of the equivalent radius of curvature, and the square of the negative third of the equivalent elastic modulus. For simplified engineering calculations, when the contact area does not change significantly, the measured contact imprint area under preload can be taken as a constant approximation. The bending stress is estimated based on the relationship between the clamping force at that point, the equivalent span, and the section modulus. Specifically, the moment-stress relationship of simply supported or fixed plates under concentrated load in classical plate bending theory can be referred to. The stress utilization rate is the larger of the ratio of the contact stress at that point to the allowable contact stress and the ratio of the bending stress to the allowable bending stress.

[0056] It should be noted that stress estimation is an engineering approximation. Its purpose is not to obtain precise stress values, but to establish a comparative relationship between the relative stress levels of each clamping point, identify stress concentration risk points, and determine whether the stress at each point is close to the allowable boundary in order to provide a safety warning. Since the allowable stress boundary itself includes a process safety factor, even if there is a certain error in the stress estimation, as long as the estimation error does not exceed the margin range covered by the safety factor, the effectiveness of the stress constraint can be guaranteed.

[0057] The safety margin equals the allowable stress boundary divided by the estimated stress value at the current clamping point, then subtracted by 1. The upper bound of the relative error of the stress estimation is determined by taking the uncertainties of each input parameter in the prior stiffness characterization model as input. These input parameters include local wall thickness measurement tolerance, material elastic modulus tolerance, equivalent span calculation deviation, the width of the boundary condition correction coefficient range, and the curvature correction factor lookup accuracy. The maximum relative deviation of the estimated stress value is obtained by linearly superimposing the first-order partial derivatives or by Monte Carlo sampling according to the power relationship of the parameters in the stress estimation equation. This upper bound of the error is the maximum relative deviation of the estimated stress value. When the upper bound of the relative error of the stress estimation is less than or equal to the safety margin, the current safety factor is considered sufficient to cover the estimation error. If the constraint is effective, when the upper bound of the relative error of stress estimation is greater than the safety margin, the safety factor is increased to make the safety margin no less than the upper bound of the error, or the stress calculation is switched to the force-stress accurate mapping table established by finite element pre-analysis until the condition that the upper bound of the error does not exceed the safety margin is met, or the safety factor and the stress calculation are switched to the force-stress accurate mapping table established by finite element pre-analysis at the same time so that both meet the condition. For situations where the accuracy of stress estimation is required, such as when the part material is a brittle material, the force-stress accurate mapping table of each clamping area can be established by finite element pre-analysis during the clamping area division and parameter acquisition stage to replace the above analytical estimation.

[0058] The differentiated clamping force allocation module is used to calculate the differentiated target clamping force for each clamping point based on the mapping relationship, with the goal of ensuring that the normal deformation response of each clamping point tends to be consistent. This is done in conjunction with allowable stress boundaries and cutting force constraints. For example... Figure 5 The figures show the results of the consistency verification of multi-point target force and constraint. Figure (a) shows the distribution of differentiated target clamping forces at multiple clamping points. As can be seen from the figure, the target clamping forces at different clamping points are not evenly distributed, but are adjusted according to the local stiffness, constraint state, and stress boundary of each clamping area. This allows areas with higher stiffness to bear larger clamping forces, while areas with lower stiffness have reduced clamping loads, thus avoiding excessive local pressing in thin-walled areas. Figure (b) shows the consistency relationship between the target clamping force and the actual clamping force. The horizontal axis represents the target clamping force, and the vertical axis represents the actual applied clamping force. The scattered points are distributed as a whole. The fact that the load execution module is positioned near the theoretical consistency reference line indicates that it can achieve stable tracking according to the differentiated target clamping force. Figure (c) shows the change in springback clearance during the loading process of each clamping point. As the differentiated clamping force is adjusted, the residual clearance of each clamping point is maintained within the allowable range, indicating that after online stiffness identification and pre-tightening compensation, each clamping area can establish an effective contact state. Figure (d) shows the change in stress utilization rate under clamping force constraint. As can be seen from the figure, the stress utilization rate of each clamping point is lower than the preset allowable boundary, indicating that the determined differentiated target clamping force can simultaneously meet the requirements of positioning reliability and low stress constraint.

[0059] Specifically, the allowable stress boundary includes allowable contact stress and allowable bending stress. Allowable contact stress equals the yield strength of the part material divided by the process safety factor. Allowable bending stress equals the yield strength of the part material multiplied by the thin-wall stability reduction factor, then divided by the process safety factor. The thin-wall stability reduction factor is determined based on the theory of critical buckling stress in thin plates, calculated according to the ratio between wall thickness, stability constant, and the equivalent span in the vicinity of the clamping point. That is, the critical buckling stress is directly proportional to the material's elastic modulus and the square of the wall thickness, and inversely proportional to the square of the span. It depends on the stability constant corresponding to the boundary constraint form. This coefficient reflects the decrease in structural bearing capacity when the wall thickness is smaller and the span is larger. Its value is between 0 and 1, and the value of the thin-wall stability reduction coefficient does not exceed the preset reference value. The stability constant is selected according to the boundary constraint form of the clamping area: 4.0 when four sides are simply supported, 6.5 to 7.5 when four sides are fixed, 0.4 to 1.5 when three sides are simply supported and one side is free, and 0.2 to 0.5 when two sides are simply supported and two sides are free. When the calculated reduction coefficient is greater than 1.0, it is taken as 1.0.

[0060] Specifically, the allowable clamping force at each point is calculated from the allowable stress boundary. The allowable clamping force for contact is equal to the allowable contact stress multiplied by the effective contact area. The allowable clamping force for bending is equal to the allowable bending stress multiplied by the section modulus and then divided by the equivalent span. The smaller of the two values ​​is taken as the final allowable clamping force at that point. The cutting force constraint is the tangential anti-slip bearing capacity of each clamping point, which is determined by the normal clamping force, the contact friction coefficient at that point, and the angle between the clamping force direction and the local normal. It is not less than the cutting force at that point multiplied by a preset safety factor.

[0061] Furthermore, the differentiated clamping force distribution module adopts a stiffness constraint weight correction distribution method, specifically including:

[0062] The differentiated target clamping force at each clamping point is obtained by modifying the reference clamping force through a constraint-driven correction factor and a stiffness distribution weight. That is, the differentiated target clamping force at each clamping point is equal to the reference clamping force multiplied by the stiffness distribution weight and then multiplied by the constraint-driven correction factor. The reference clamping force is the basic force value uniformly distributed at each point without considering stiffness differences and constraint conditions. It is equal to the total clamping force requirement divided by the total number of clamping points. The total clamping force requirement is determined by the maximum cutting force, the friction coefficient, and the safety factor. The stiffness distribution weight is equal to the ratio of the equivalent clamping stiffness at that point to the arithmetic mean of the equivalent clamping stiffness at all points. Points with higher stiffness are assigned a larger force, and points with lower stiffness are assigned a smaller force. When the stiffness distribution index γ is between 0.4 and 0.7, the difference in normal deformation response at each point is significantly reduced relative to the equal force distribution. When the stiffness distribution index γ is 1, the normal deformation response at each point tends to be consistent under weak coupling conditions. In another implementation, a stiffness distribution index can be introduced, with a value ranging from 0 to 1. The stiffness distribution weight is expressed as the ratio of the equivalent stiffness of the clamping point to the average stiffness raised to the power of γ. When γ is 0, it degenerates into equal force distribution, and when it is 1, it is a fully proportional stiffness distribution. It is recommended to take a value of 0.4 to 0.7.

[0063] The constraint-driven correction factor is used to reflect the deviation of the constraint conditions from the pure stiffness equilibrium distribution. It is determined by a weighted combination of the cutting load constraint component, the deformation sensitivity constraint component, and the stress margin constraint component. That is, the constraint-driven correction factor is equal to the cutting load constraint component multiplied by the first weighting coefficient, plus the deformation sensitivity constraint component multiplied by the second weighting coefficient, plus the stress margin constraint component multiplied by the third weighting coefficient. The sum of the weighting coefficients of each component is equal to 1. For example, the first weighting coefficient is 0.3 to 0.5, the second weighting coefficient is 0.2 to 0.4, the third weighting coefficient is 0.2 to 0.4, and the preset reference value is 1.0.

[0064] The cutting load constraint component is determined based on the ratio of the minimum cutting force requirement at the clamping point to the average of the minimum cutting force requirements at all points. The minimum cutting force requirement is a preset multiple of the cutting force at the clamping point, such as 1.2-2 times. The component of the clamping point facing the cutting force direction is greater than 1, and the component of the clamping point facing away from the cutting force direction is less than 1.

[0065] The deformation sensitivity constraint component is determined based on the sensitivity of the normal deformation response at that point to the change in unit clamping force. For weak coupling, the sensitivity is equal to the reciprocal of the clamping equivalent stiffness at that point. For strong coupling, the sensitivity is equal to the diagonal element at the corresponding position in the inverse of the global stiffness matrix. If the sensitivity is higher than the preset sensitivity threshold, the component takes a value less than 1, such as 0.7 to 0.9, to reduce the force distribution and avoid excessive deformation. If the sensitivity is lower than the preset sensitivity threshold, the component takes a value greater than or equal to 1, such as 1.0 to 1.3, to appropriately increase the force distribution to compensate for the reduction at other points. The preset sensitivity threshold can be 1.5 to 2.5 times the reciprocal of the average stiffness.

[0066] The stress margin constraint component is determined based on the stress utilization rate at that point; when the current stress utilization rate is lower than the preset margin threshold, the value is greater than or equal to 1, for example, 1.0 to 1.2; when the current stress utilization rate is higher than the preset margin threshold, the value is less than 1, for example, 0.5 to 0.9. The stress utilization rate of each clamping point is defined as the ratio of the current estimated stress at that point to the corresponding allowable stress boundary; the preset margin threshold can be 0.6 to 0.8.

[0067] In the weakly coupled state, when all constraints are not activated (i.e., the cutting force demand at all points does not exceed a preset multiple of the average value, the deformation sensitivity at all points does not exceed a preset sensitivity threshold, and the stress utilization rate at all points does not exceed a preset margin threshold), the constraint-driven correction factor takes a preset reference value. At this time, the differentiated target clamping force at each clamping point is determined by the product of the reference clamping force and the stiffness allocation weight, so that the normal deformation response at each point is equal. In the strongly coupled state, when all constraints are not activated, the target clamping force is solved according to the global stiffness matrix and the target deformation vector.

[0068] When any constraint condition is activated, the constraint-driven correction factor of the corresponding clamping point deviates from the preset reference value, and the differential target clamping force at that point shifts relative to the stiffness balance distribution value; whereby, constraint condition activation means that the physical quantity corresponding to the constraint condition exceeds the preset threshold.

[0069] In addition, the constraints of the differentiated clamping force distribution module also include global torque balance constraints and maximum deformation constraints. The global torque balance constraint is that the sum of the torque vectors of the clamping forces at each clamping point about the center of mass of the part and the torque vectors of the cutting forces about the center of mass of the part does not exceed the preset torque allowable value. The maximum deformation constraint is that the maximum value in the normal deformation response of each clamping point does not exceed the preset deformation upper limit. The preset deformation upper limit is the maximum clamping deformation allowed by the process, which can be set to one-fifth to one-third of the machining tolerance.

[0070] The solution process of the differentiated clamping force allocation module is as follows: the differentiated target clamping force obtained by the joint correction of constraint-driven correction factor and stiffness allocation weight is used as the initial value of the iteration. The root mean square value of the difference between the normal deformation response of each clamping point and the average normal deformation response of the whole field is used as the objective function. The allowable stress boundary, cutting force constraint, global moment balance constraint and maximum deformation constraint are used as inequality constraints. The clamping force of each clamping point is not less than the preset lower limit is used as the boundary constraint. The final differentiated target clamping force of each clamping point is determined by the constraint optimization algorithm such as sequential quadratic programming or interior point method.

[0071] If a constraint is active in the solution, meaning it equals the optimal solution, the dual information corresponding to that constraint, i.e., the Lagrange multiplier value, is added as an additional correction to the constraint-driven correction factor to correct the force distribution in the next iteration. If a feasible solution that satisfies all constraints exists but has not converged, the current best feasible solution is output and an optimization incomplete convergence message is generated. If no feasible solution that satisfies all constraints exists, the clamping force is stopped from being increased further, and the abnormal handling process is initiated, including reducing the machining load, readjusting the clamping position, or replanning the clamping force distribution scheme.

[0072] The Lagrange multiplier values ​​corresponding to the activation constraints are normalized and then added as additional correction increments to the constraint-driven correction factor. Specifically, the process is as follows: First, before establishing the optimization problem, each constraint function is divided by its corresponding reference eigenvalue to achieve dimensionlessness. The maximum deformation constraint uses the allowable deformation, the maximum stress constraint uses the allowable stress boundary, and the non-negative contact force constraint uses the preset preload as the reference eigenvalue. Before establishing the optimization problem, the objective function is divided by the allowable deformation, and each constraint function is divided by its corresponding reference eigenvalue to achieve uniform dimensionlessness, ensuring that the objective function, constraint functions, and corresponding Lagrange multipliers are all dimensionless and do not change with unit selection. Second, it is uniformly stipulated that the multiplier takes a positive value when the constraint exceeds the allowable boundary and a zero value when it does not. This sign convention remains unchanged during iteration. Then, the dimensionless multiplier is multiplied by a preset feedback gain coefficient to obtain the correction factor increment. The increment is a dimensionless constant greater than 0 and less than 1, ranging from 0.01 to 0.1, used to limit the correction amplitude in a single round to prevent oscillation. A saturation limiting process is then applied to this increment, ensuring the absolute value of the increment does not exceed 0.2, keeping the correction factor within a reasonable range of 0.5 to 1.5. Simultaneously, the total change in the correction factor between adjacent iterations is controlled to not exceed the step size limit of 0.1; any excess is truncated and reserved for the next round, ensuring a smooth transition in force distribution. Finally, convergence is determined and the result is output when the dimensionless violation of all active constraints and the maximum change in the correction factor between rounds are both less than the convergence tolerance of 0.01. If convergence is not achieved after the maximum number of iterations (50), the current result is output and a safety warning is triggered. After the above processing, the increment of the correction factor and the correction factor itself have the same dimensions and can be directly superimposed. The correction result does not change with the constraint unit, and the iteration process is monotonically approaching under the dual constraints of gain and saturation.

[0073] In addition, after calculating the differentiated target clamping force, it is necessary to verify whether the coefficient of variation of the deformation response at each point, i.e., the ratio of the standard deviation to the mean, does not exceed the preset allowable threshold for deformation uniformity, such as 15% to 25%. If it does, the following convergence adjustment is performed: if the constraint driving correction factor at each point is too large, driven by the cutting load constraint, under the premise of meeting the minimum force requirement at that point, the cutting load weight is reduced or the reference clamping force is increased to make the force distribution tend to be uniform; if the constraint driving correction factor at each point is too small, driven by the stress constraint, check whether the stress constraint at that point can be relieved by increasing the contact area, such as replacing the pressure head or reducing the stiffness distribution index, and recalculate after adjustment until the deformation uniformity meets the requirements.

[0074] The loading execution and closed-loop control module is used to load each clamping unit according to the differentiated target clamping force, and to iteratively correct the clamping state based on the feedback of the normal deformation response at each point and the stress estimation based on the mapping relationship.

[0075] Furthermore, the iterative correction in the loading execution and closed-loop control module adopts an incremental iterative approach with coordinated dual closed-loop control of force loop and displacement loop, specifically including:

[0076] The force ring uses a differentiated target clamping force as the tracking target and adjusts the output force of the actuator through a closed-loop feedback controller, such as a proportional-integral-derivative controller or an impedance controller, so that the actual clamping force tracks the target value. The force ring control cycle is recommended to be 1-10ms. The force ring ensures clamping reliability and provides sufficient anti-cutting force constraints.

[0077] The displacement ring uses the maximum allowable indentation as a threshold to monitor the displacement of each actuator point in real time. The displacement ring ensures the safety of the parts and prevents any single-point deformation from exceeding the limit. The maximum allowable indentation is determined based on the ultimate normal deformation response corresponding to the allowable bending stress. Specifically, it can refer to the relationship between allowable stress and maximum deflection in the classical beam or plate bending theory. It is directly proportional to the square of the equivalent span and inversely proportional to the material's elastic modulus and wall thickness. It is then multiplied by the bending coefficient determined according to the boundary conditions. The maximum allowable indentation can be taken as 0.05 to 0.2 mm.

[0078] To avoid impact and over-constraint caused by applying the target clamping force all at once, the loading process is divided into preset levels, such as three to ten levels, increasing progressively. The loading amount for each level is the differentiated target clamping force divided by the level number. After each level of loading is completed, a preset time is maintained, such as 1-10 seconds, and force and displacement data at each point are collected. The increment of the normal deformation response at each point is checked to see if it does not exceed a preset multiple of the predicted value based on the mapping relationship, such as 1.5-2 times. If it does, loading is paused and iterative correction begins. For parts with symmetrical structures, symmetrical points are loaded synchronously to avoid generating additional bending moments. For asymmetrical structures, loading is performed in order of stiffness from high to low. First, the main positioning constraint in the high stiffness region is established, and then the auxiliary constraint in the low stiffness region is applied.

[0079] Furthermore, the dual closed-loop coordination rule is as follows: a preset warning ratio can be set to 0.7 to 0.9. When the effective pressing amount at each point is lower than the preset warning ratio of the maximum allowable pressing amount, the force loop controls the loading process, and the displacement loop does not output control commands but only records displacement data. When the effective pressing amount at any point reaches the preset warning ratio, the displacement loop triggers a warning signal, and the force loop reduces the loading rate at that point to the product of the original rate and the preset ratio, such as 20% to 50%. When the effective pressing amount at any point reaches or exceeds the maximum allowable pressing amount, the displacement loop forcibly intervenes, limits the clamping force from continuing to increase, and performs load reduction adjustment according to the displacement recovery situation until the effective pressing amount falls back to below the sum of the maximum allowable pressing amount and the preset safety hysteresis, and then re-participates in the target clamping force optimization calculation.

[0080] Furthermore, if any point enters the force-holding mode due to excessive displacement, resulting in the actual clamping force being lower than the differentiated target clamping force, the force difference at that point is calculated, which is the difference between the target clamping force and the actual clamping force. The force difference is then redistributed among the remaining clamping points in the neighborhood of that point that have not entered the force-holding mode according to their equivalent clamping stiffness ratio. After redistribution, the displacement of the receiving point is checked simultaneously to ensure that the global torque balance and minimum cutting force constraint are met. If any constraint check fails, the constraint optimization calculation is re-entered.

[0081] Incremental iterative correction is specifically as follows: The normal deformation response of the part is determined jointly by the actuator displacement, the initial contact zero-point displacement value, and the system compliance compensation amount. Specifically, it equals the current actuator displacement minus the initial contact zero-point displacement value, then minus the sum of the actuator compliance coefficient and the fixture structure compliance coefficient multiplied by the current clamping force. The initial contact zero-point displacement value is the contact start displacement value recorded by the online clamping stiffness identification module. The system compliance compensation amount is determined by multiplying the sum of the actuator compliance coefficient and the fixture structure compliance coefficient by the change in force of the current clamping force relative to the initial contact zero-point. The force adjustment amount is based on the normal deformation response at each point and the normal deformation at each clamping point. The target clamping force is determined by the deviation between the arithmetic mean of the response and the deviation between the stress utilization rate at each point and the preset upper limit. Specifically, for points with large deformation (i.e., stiffness lower than the identification value), the target clamping force is reduced; for points with small deformation (i.e., stiffness higher than the identification value), the target clamping force is increased; and for points with high stress utilization rate, the target clamping force is reduced, transferring the force difference to neighboring points with lower stress utilization rate. The differentiated target clamping force in the current iteration is equal to the target clamping force in the previous iteration plus the relaxation factor multiplied by the force adjustment. The relaxation factor is a decay coefficient greater than zero and not exceeding 1.0, which can be taken as 0.3 to 0.6. If the relaxation factor is too small, the convergence is slow; if it is too large, oscillations will occur.

[0082] It should be noted that when the measured normal deformation response at a certain point is greater than the predicted value based on the identified stiffness and the current force value, it is determined that the actual stiffness at that point is lower than the identified value, and the target clamping force at that point should be reduced; when the measured normal deformation response at a certain point is less than the predicted value, it is determined that the actual stiffness at that point is higher than the identified value, and the target clamping force at that point can be increased; for points with high stress utilization, the target clamping force should be reduced, and the force difference should be transferred to neighboring points with lower stress utilization.

[0083] The iteration termination condition is that the root mean square value of the difference between the normal deformation response of each clamping point and the average normal deformation response of the whole field is less than the preset uniformity threshold, the stress utilization rate of all clamping points does not exceed the preset stress upper limit, and the differential target clamping force change between two adjacent iterations is less than the preset convergence threshold. The preset uniformity threshold can be 1%-5% of the target deformation value, the preset stress upper limit can be 0.85-0.95, and the preset convergence threshold can be 0.5%-2% of the target clamping force value. If the number of iterations for incremental iterative correction reaches the preset upper limit, such as 20-50 times and the termination condition is still not met, the current optimal solution is output and a manual intervention prompt is issued.

[0084] In addition, after all clamping points have been loaded and undergone closed-loop correction, a comprehensive judgment of the clamping status is performed: if the deformation uniformity index does not exceed the corresponding preset threshold, and the comprehensive stress utilization rate of all points does not exceed the preset upper limit, and there are no displacement exceeding the limit, then the clamping is deemed qualified, and the clamping is locked to enter the processing stage; if the deformation uniformity index exceeds the corresponding preset threshold, the deformation distribution is deemed unreasonable, and deformation equalization correction continues to be performed; if there are stress utilization rate exceeding the limit, it is deemed that there is a risk of stress concentration, and stress constraint correction is performed; if there are displacement exceeding the limit, the clamping is deemed unqualified, the point is unloaded, the contact surface is checked, and the entire process from online identification to loading control is re-executed.

[0085] The multi-point pressure equalization control method for low-stress clamping of thin-walled curved surface parts provided in this embodiment of the invention includes the following steps:

[0086] Step 1: Divide the thin-walled part to be processed into multiple clamping areas according to the position of each clamping unit, and obtain the local structural stiffness parameters and stress constraint basic parameters of each clamping area.

[0087] Step 2: Establish a priori stiffness characterization model for each clamping region based on the local structural stiffness parameters, and determine the allowable stress boundary for each clamping region based on the stress constraint foundation parameters.

[0088] Step 3: Control the actuators of each clamping unit to contact the surface of the part and apply a preset preload. Calculate the clamping equivalent stiffness of the clamping point corresponding to each clamping area based on the force and displacement data collected by the force detection unit built into each clamping unit during the preload stage. The clamping equivalent stiffness is determined based on the ratio of the effective displacement data to the force data after deducting the deformation contribution of the actuator itself and the deformation contribution of the fixture structure.

[0089] Step 4: Establish the mapping relationship between clamping force, normal deformation response of part, and stress level based on the clamping equivalent stiffness.

[0090] Step 5: Based on the mapping relationship, with the goal of making the normal deformation response of each clamping point as consistent, and in combination with the allowable stress boundary and cutting force constraint, calculate the differentiated target clamping force of each clamping point.

[0091] Step 6: Apply load to each clamping unit according to the differentiated target clamping force, and perform iterative correction of the clamping state based on the feedback of the normal deformation response at each point and the stress estimation based on the mapping relationship.

[0092] Example 2: Based on Example 1, the present invention also includes a machining process dynamic monitoring and stiffness degradation compensation module, which is used to continuously and dynamically monitor and adaptively compensate the clamping state during the machining process.

[0093] Specifically, during the machining process, clamping force, actuator displacement, spindle load signal, workpiece vibration signal obtained by accelerometer, and cutting force signal derived from force gauge or spindle current are continuously collected at each point. The stress utilization rate at each point is continuously updated according to the mapping relationship. The stress utilization rate is the ratio of the current estimated stress at that point to the corresponding allowable stress boundary. The current estimated stress is the larger value between contact stress and bending stress, that is, the stress utilization rate is the larger value between the ratio of contact stress to allowable contact stress and the ratio of bending stress to allowable bending stress at that point.

[0094] During the cutting process, the dynamic changes in external loads directly affect the clamping stability, such as... Figure 6 Figure 1 shows a schematic diagram of the dynamic signal response relationship under different cutting parameters, used to analyze the influence of cutting parameter changes on the stability of the clamping state during machining. Figure 2(a) shows the relationship between cutting force response and radial cutting width and axial cutting depth. As can be seen from the figure, with the increase of cutting depth and cutting width, the material removal increases, and the cutting force generally shows an upward trend, forming a high load concentration area in the large cutting parameter region. This result indicates that changes in machining load directly change the external disturbance force borne by the clamping area. Therefore, it is necessary to dynamically evaluate the clamping state in conjunction with real-time cutting force changes. Figure 3(b) shows the distribution of the synthesized vibration force response. It can be seen that with the increase of cutting parameters, the vibration amplitude increases synchronously. The increase in the amount of cutting load and the presence of enhanced vibration in some parameter combinations indicate that a large cutting load may lead to a decrease in the local constraint stiffness of thin-walled parts, resulting in a reduction in dynamic stability. Figure (c) shows the variation law of the spindle current response. Since there is a corresponding relationship between the spindle current and the cutting load, the trend of machining load variation can be indirectly obtained by collecting the spindle current variation, and it can be used as a cutting state sensing signal without an additional force measuring device. Figure (d) shows the correlation between the amount of material removed and the cutting force, vibration, and current characteristics. As can be seen from the figure, as the amount of material removed increases, each dynamic response parameter shows a certain correlation trend. Therefore, the stiffness degradation of the clamping state can be judged based on the multi-parameter fusion results.

[0095] To accurately identify stiffness degradation, in-depth time-frequency domain analysis was performed on multi-sensor signals, such as... Figure 7As shown, the results of multi-sensor time-domain and frequency-domain characteristic analysis under typical machining conditions are presented. Figure (a) shows the time-domain variation curve of cutting force, and Figure (b) shows the time-domain variation curve of vibration signal. As can be seen from the figures, during the stable machining stage, both cutting force and vibration signal remain within a certain fluctuation range. When the local clamping stiffness decreases or machining disturbance increases, the amplitude of the time-domain signal will show abnormal fluctuations, which can be used as a preliminary basis for judging stiffness degradation. Figure (c) shows the frequency-domain characteristics of cutting force, and Figure (d) shows the frequency-domain characteristics of vibration signal. Through frequency-domain analysis, the corresponding main frequency change and abnormal frequency components during machining can be obtained. When the vibration main frequency shifts relative to the initial stable state, it indicates that the dynamic stiffness of the part-fixture system has changed. Therefore, this embodiment achieves a comprehensive judgment of the clamping state change during machining by simultaneously acquiring cutting force, vibration, and spindle load signals, and combining the time-domain amplitude change and frequency-domain characteristic change.

[0096] The stiffness degradation warning indicator is triggered when any of the following four conditions occur: the displacement of any actuator continues to increase under constant clamping force and the rate of increase exceeds the preset drift threshold; the frequency corresponding to the main frequency component in the workpiece vibration signal shifts downward relative to the initial value by more than a preset proportion; the cutting force signal exhibits periodic abrupt changes and the amplitude of the abrupt changes exceeds the preset cutting force fluctuation threshold; the rate of increase of the stress utilization rate at any point under constant clamping force exceeds the preset stress drift threshold. The preset drift threshold can be 0.001 to 0.01 mm / min, the preset proportion can be 5% to 15%, the preset cutting force fluctuation threshold can be 10% to 30% of the average cutting force, and the preset stress drift threshold can be 0.01 to 0.05 mm / min.

[0097] When the stiffness degradation warning sign is triggered, a preset test force increment is applied to re-identify the online stiffness. Stiffness degradation is confirmed only when the online stiffness decreases more than the preset degradation threshold relative to the reference value, triggering the stiffness degradation criterion. The preset test force increment is determined based on the current clamping force at the clamping point, the allowable additional load on the part, and the adjustment resolution of the actuator, so that the additional deformation generated during the application of the preset test force increment is within the elastic deformation range.

[0098] When the stiffness degradation criterion is triggered, the following adjustments are made sequentially based on the current state of the point. If multiple conditions are met simultaneously, the adjustment corresponding to the earlier condition is executed in the order of the four conditions: If the current normal deformation response of the point reaches or exceeds the product of the maximum allowable pressing amount and the preset ratio, the clamping force at the point is reduced; if the current normal deformation response of the point is lower than the product of the maximum allowable pressing amount and the preset ratio and the cutting force direction is positive towards the point, the clamping force at the point is maintained or increased; if the current normal deformation response of the point is lower than the product of the maximum allowable pressing amount and the preset ratio and the cutting force direction is not positive towards the point, the current clamping force is maintained unchanged; if the stress utilization rate of the point reaches the preset stress threshold, the clamping force at the point is reduced. The preset stress threshold is 0.7 to 0.9 times the allowable stress boundary.

[0099] For adjacent clamping points in the degraded region, the clamping force is adjusted according to the torque balance requirement of the clamping force at each clamping point on the center of mass of the part. This is to compensate for the constraint changes caused by the force changes at the degraded points. The stress utilization rate and normal deformation response of each adjacent point after adjustment are verified to not exceed the corresponding limits. The priority is to maintain the global constraint balance and the stability of the part positioning, rather than simply reducing or increasing the force value at a certain point. If the vibration signal triggers a chatter warning, the cutting parameters are adjusted first. At the same time, the direction of clamping force adjustment is determined based on the rate of change of vibration response after a small trial adjustment. If increasing the clamping force reduces the vibration amplitude, the force is increased; otherwise, the force is decreased. If the direction cannot be determined, the lower limit of safe clamping is maintained, and the clamping force is restored after the vibration is eliminated.

[0100] After each processing area is completed or a preset amount of material is removed (e.g., 5% to 20% of the total removal amount), or when the wall thickness change exceeds 10%, processing is paused. A preset small force increment is applied to each point based on the current clamping force (e.g., 5% to 10% of the current clamping force). The clamping equivalent stiffness is updated according to the ratio of this force increment to the corresponding displacement increment, and the mapping relationship and differentiated target clamping force distribution scheme are updated accordingly.

[0101] For time-varying characteristics during the processing, such as Figure 8As shown, the results of dynamic sensing and control adjustment during the processing are illustrated. The horizontal axis represents the processing time. Figure (a) shows the changes in actual stiffness and clamping force during processing, while the vertical axis represents the relative initial values ​​of the online stiffness median and clamping force. The relative initial value of the online stiffness median is the normalized result of the online stiffness median relative to the initial processing state stiffness, and the relative initial value of the clamping force is the normalized result of the clamping force relative to the initial processing state clamping force. As processing progresses, continuous monitoring can promptly detect stiffness degradation. Figure (b) shows the changes in deformation response and stress utilization rate during processing, with the vertical axis representing deformation uniformity and stress utilization rate. Deformation uniformity is an index of the uniformity of normal deformation at each clamping point. As processing progresses, the stress in the clamping area increases, but it remains below 1, indicating no risk of instability. The green curve remains close to 0. The clamping force distribution strategy can maintain uniform deformation. Figure (c) shows the machining dynamic response. The vertical axis represents the relative initial value, indicating the normalized results of different dynamic signals relative to the initial state, including spindle load and synthetic vibration. As shown in the figure, the cutting load is generally stable during machining. As machining progresses, the stiffness of the thin-walled structure decreases and the cutting excitation increases, leading to an increase in vibration response. In addition, although there are fluctuations in vibration, the spindle load does not show obvious abnormalities, indicating that a single load signal cannot fully reflect the clamping state and that multi-source data needs to be integrated for comprehensive analysis. Figure (d) shows the control action time distribution corresponding to different stages. The vertical axis represents the control action state, indicating the control strategy adopted based on the monitoring results. As machining progresses, when stiffness degradation or constraint state changes are detected, control actions such as cutting parameter adjustment and stiffness compensation are executed to achieve adaptive clamping and holding during machining.

[0102] To verify the universality of this method, statistical analysis was conducted on the control effects on different types of parts, such as... Figure 9 The diagram shows the cross-part control stability and inspection result analysis, used to verify the adaptability of the dynamic monitoring and stiffness degradation compensation method proposed in this embodiment under different part conditions. Figure (a) shows the cross-part deformation uniformity distribution corresponding to different part models. As can be seen from the figure, the deformation response of each part differs under different structural parameters and stiffness distribution conditions. However, after online stiffness identification and dynamic compensation, the deformation uniformity of each part is improved, indicating that the method can reduce the impact of part structural differences on the clamping effect. Figure (b) shows the statistical results of inspection status and control intervention. As can be seen from the figure, after implementing dynamic monitoring and compensation, most parts are in a qualified state, and some parts with initial risks are transformed into a qualified state after dynamic adjustment, verifying that the closed-loop correction mechanism based on state feedback can improve the stability of the clamping process.

[0103] Example 3: Based on Example 1, the present invention also includes a graded unloading and springback control module for orderly unloading and residual deformation assessment after processing.

[0104] After processing, the clamping force at each point is reduced in stages in the reverse order of loading. It is recommended that the number of unloading stages be the same as the number of loading stages. After each unloading stage, the workpiece is held for a preset time and the springback displacement of the workpiece is monitored during the holding period. The force-displacement change path at each point is recorded to assess whether there is a risk of residual deformation.

[0105] After unloading, record the final springback amount at each point. Compare the final springback amount with the effective indentation amount at each point during the loading stage to calculate the residual deformation amount at each point. The residual deformation amount at each point is equal to the effective indentation amount at that point during the loading stage minus the springback amount at that point after unloading. If the residual deformation amount at any point exceeds the preset residual deformation threshold, such as 0.005 to 0.02 mm, it is marked as a point with abnormal residual deformation pending confirmation. After confirmation by re-executing the graded unloading and springback control module, the point with abnormal residual deformation pending confirmation is marked as a plastic deformation point, and its location and deformation amount are recorded. The location and deformation amount are used as the reference correction input for subsequent processes to compensate for geometric deviations caused by plastic deformation. At the same time, this information can be used as the basis for correcting the clamping scheme of subsequent parts in the same batch. Figure 10 As shown, the results of graded unloading and residual deformation evaluation after processing are presented. Figure (a) shows the change in springback response during the loading-unloading process. By comparing the effective indentation during the loading stage with the actual springback during the unloading stage, the residual deformation of each clamping area can be obtained. Figure (b) shows the residual deformation distribution corresponding to different part models. Different structural stiffnesses lead to differences in the residual response after unloading. By statistically analyzing the residual deformation, potential plastic deformation areas can be identified, providing data for optimizing clamping parameters of similar parts in the future. Figure 10 It can be seen that the graded unloading method can reduce the structural abrupt changes caused by the one-time release of clamping force, and at the same time realize the quantitative evaluation of the unloading springback behavior of thin-walled curved parts.

[0106] It should be noted that, in this document, the terms "comprising," "including," and any other variations are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Specific examples have been used in this document to illustrate the principles and implementation methods of the present invention. These examples are merely for the purpose of helping to understand the method and core ideas of the present invention. The above are only preferred embodiments of the present invention. It should be pointed out that, due to the limitations of written expression and the objective existence of infinite specific structures, those skilled in the art can make several improvements, modifications, or variations without departing from the principles of the present invention, and can also combine the above technical features in an appropriate manner. These improvements, modifications, variations, or combinations, or the direct application of the concept and technical solution of the present invention to other situations without modification, should all be considered within the scope of protection of the present invention.

Claims

1. A multi-point pressure equalization control system for low-stress clamping of thin-walled curved surface parts, characterized in that, include: The clamping area division and parameter acquisition module is used to divide the thin-walled part to be processed into multiple clamping areas according to the position of each clamping unit, and to acquire the local structural stiffness parameters and stress constraint basic parameters of each clamping area. The prior stiffness modeling module is used to establish a prior stiffness characterization model for each clamping region based on the local structural stiffness parameters, and to determine the allowable stress boundary for each clamping region based on the stress constraint basic parameters. The clamping stiffness online identification module is used to control the actuator of each clamping unit to contact the surface of the part and apply a preset preload. It calculates the clamping equivalent stiffness of the clamping point corresponding to each clamping area based on the force data and displacement data collected by the force detection unit built into each clamping unit during the preload stage. The clamping equivalent stiffness is determined based on the ratio of the effective displacement data to the force data after deducting the deformation contribution of the actuator itself and the deformation contribution of the fixture structure. The force-deformation mapping module is used to establish a mapping relationship between clamping force and part normal deformation response and stress level based on clamping equivalent stiffness. The differentiated clamping force distribution module is used to calculate the differentiated target clamping force of each clamping point based on the mapping relationship, with the goal of making the normal deformation response of each clamping point tend to be consistent, and in combination with the allowable stress boundary and cutting force constraint. The loading execution and closed-loop control module is used to load each clamping unit according to the differentiated target clamping force, and to iteratively correct the clamping state based on the feedback of the normal deformation response at each point and the stress estimation based on the mapping relationship.

2. The multi-point pressure equalization control system for low-stress clamping of thin-walled curved surface parts according to claim 1, characterized in that, The equivalent stiffness characterization value output by the prior stiffness characterization model is determined by the local wall thickness of each clamping region, the equivalent span of the clamping point neighborhood, the surface shape, and the boundary constraint conditions. The equivalent stiffness characterization value is also corrected in direction based on the angle between the surface normal direction and the clamping load direction; The allowable stress boundary includes allowable contact stress and allowable bending stress. The allowable bending stress is determined by reducing the material yield strength according to the thin-wall stability reduction factor. The thin-wall stability reduction factor is determined according to the ratio of wall thickness to the equivalent span of the clamping point neighborhood and the boundary constraint form of the clamping area.

3. The multi-point pressure equalization control system for low-stress clamping of thin-walled curved surface parts according to claim 1, characterized in that, The specific process by which the online clamping stiffness identification module calculates the equivalent clamping stiffness includes: Control the contact of each clamping unit actuator with the part surface, determine the initial contact zero point of each point, apply the preset preload from the initial contact zero point, and collect the force change and the displacement change of the actuator. The deformation of the actuator itself and the deformation of the fixture structure are determined based on the product relationship between the pre-calibrated compliance coefficient of the actuator and the compliance coefficient of the fixture structure and the force change, respectively. The effective pressing amount is obtained by subtracting the deformation of the actuator itself and the deformation of the fixture structure from the displacement change of the actuator. The clamping equivalent stiffness is determined based on the ratio between the force change and the effective pressing amount. The clamping equivalent stiffness of each point is compared with the equivalent stiffness characterization value output by the prior stiffness characterization model. If the clamping equivalent stiffness of any point is lower than the preset equivalent stiffness characterization value, then the point is marked as a low stiffness point to be confirmed. The force response increment of the low stiffness point to be confirmed under the preset compensation displacement is detected. If the force response increment is lower than the preset contact effectiveness threshold, it is confirmed as a weak contact point and compensation is performed. After applying the preset compensation amount to the displacement of the actuator at the point, the clamping equivalent stiffness is recalculated. Otherwise, it is confirmed as a low stiffness area caused by the structure itself, and a structural stiffness constraint identifier is generated. The structural stiffness constraint identifier is fed back to the target clamping force optimization module to limit the upper limit of the clamping force in the area and recalculate the target clamping force of each clamping point.

4. The multi-point pressure equalization control system for low-stress clamping of thin-walled curved surface parts according to claim 1, characterized in that, The force-deformation mapping module adopts a hierarchical computational architecture of single-point mapping and multi-point coupled correction, specifically including: Based on the preset preload, a preset standard test force increment is applied to each clamping point to obtain the normal deformation response increment caused by the test force increment at each point in its neighborhood. The ratio of the maximum value of the normal deformation response increment of all clamping points in the neighborhood other than the clamping point currently applying the test force to the normal deformation response increment of the clamping point itself under the test force is defined as the coupling coefficient of the clamping point. If the coupling coefficient of all clamping points is less than the preset coupling threshold, it is determined to be a weak coupling state. The normal deformation response of each clamping point is determined according to the ratio of the clamping force at that point to the equivalent clamping stiffness at that point. If the coupling coefficient of any clamping point is greater than or equal to the preset coupling threshold, it is determined to be a strong coupling state. A global stiffness matrix with each clamping point as a node is established, and the deformation distribution vector of the whole field is obtained by solving the global stiffness equation.

5. The multi-point pressure equalization control system for low-stress clamping of thin-walled curved surface parts according to claim 4, characterized in that, The differentiated clamping force distribution module adopts a stiffness constraint weight correction distribution method, specifically including: The differentiated target clamping force at each clamping point is obtained by modifying the reference clamping force through a constraint-driven correction factor and stiffness allocation weight. The stiffness distribution weight is determined based on the ratio of the equivalent stiffness of the clamping point to the average value of the equivalent stiffness of clamping points. The reference clamping force is the basic force value that is uniformly distributed at each point without considering stiffness differences and constraint conditions. The constraint-driven correction factor is determined by a weighted combination of the cutting load constraint component, the deformation sensitivity constraint component, and the stress margin constraint component. In the weakly coupled state, when all constraints are not activated, each constraint-driven correction factor takes a preset reference value. At this time, the differentiated target clamping force of each clamping point is determined by the product of the reference clamping force and the stiffness distribution weight. In the strongly coupled state, when all constraints are not activated, the target clamping force is solved according to the global stiffness matrix and the target deformation vector. When any constraint condition is activated, the constraint-driven correction factor at the corresponding clamping point deviates from the preset reference value, and the differential target clamping force at that point shifts relative to the stiffness balance distribution value.

6. The multi-point pressure equalization control system for low-stress clamping of thin-walled curved surface parts according to claim 5, characterized in that, The differentiated clamping force distribution also includes global torque balance constraints and maximum deformation constraints; The differentiated clamping force allocation module uses the differentiated target clamping force obtained by the joint correction of constraint-driven correction factor and stiffness allocation weight as the initial value of the iteration, takes the uniformity of the normal deformation response of each clamping point as the objective function, takes the allowable stress boundary, cutting force constraint, global moment balance constraint and maximum deformation constraint as inequality constraints, and takes the clamping force of each clamping point not being less than the preset lower limit as the boundary constraint. The final differentiated target clamping force of each clamping point is determined by constraint optimization solution. If a constraint is active in the solution, the dual information of that constraint is fed back as an additional correction to the constraint-driven correction factor to correct the force allocation in the next round of force allocation optimization iteration.

7. The multi-point pressure equalization control system for low-stress clamping of thin-walled curved surface parts according to claim 1, characterized in that, The iterative correction in the loading execution and closed-loop control module adopts an incremental iterative approach with coordinated dual closed-loop control of force loop and displacement loop, specifically including: The force loop performs closed-loop control with the differentiated target clamping force as the tracking target; The displacement ring uses the maximum allowable pressing amount as a safety threshold and monitors the displacement of each actuator in real time. When the effective pressing amount at any point approaches or reaches the maximum allowable pressing amount, the displacement ring gradually intervenes to limit the force ring output at that point. If any point is restricted by the displacement ring due to excessive displacement, resulting in the actual clamping force being lower than the differentiated target clamping force, calculate the force difference at that point, and redistribute the force difference among the remaining clamping points within a preset range around that point according to their clamping equivalent stiffness ratio. The incremental iteration is specifically as follows: the normal deformation response of the part is determined by the initial contact zero displacement value of each point determined by the actuator displacement and the clamping stiffness online identification module, as well as the system flexibility compensation amount. The system flexibility compensation amount is determined by the actuator flexibility coefficient, the fixture structure flexibility and the current clamping force. The differentiated target clamping force of the current iteration is superimposed with the force adjustment amount adjusted by the relaxation factor on the basis of the previous iteration. The iteration terminates when the deformation uniformity, stress safety, and convergence simultaneously meet the preset conditions.

8. The multi-point pressure equalization control system for low-stress clamping of thin-walled curved surface parts according to claim 7, characterized in that, It also includes a processing dynamic monitoring and stiffness degradation compensation module, used for: During the processing, clamping status signals and processing signals at each point are continuously collected, and the stress utilization rate at each point is continuously updated according to the mapping relationship. The stress utilization rate is the larger of the ratio of the contact stress to the allowable contact stress and the ratio of the bending stress to the allowable bending stress at that point. The stiffness degradation warning indicator is triggered when any of the following four situations occur: the displacement of the actuator at any point continues to increase under the condition of constant clamping force and the rate of increase exceeds the preset drift threshold; the frequency corresponding to the main frequency component in the workpiece vibration signal shifts down relative to the initial value by more than a preset ratio; the cutting force signal exhibits periodic abrupt changes and the amplitude of the abrupt changes exceeds the preset cutting force fluctuation threshold; the rate of increase of the stress utilization rate at any point under the condition of constant clamping force exceeds the preset stress drift threshold. When the stiffness degradation warning sign is triggered, a preset trial force increment is applied to re-identify the online stiffness. Only when the online stiffness decreases more than the preset degradation threshold relative to the reference value is it confirmed as stiffness degradation and the stiffness degradation criterion is triggered. When the stiffness degradation criterion is triggered, the adjustment direction of the clamping force at the point is determined based on the relationship between the current normal deformation response at the point and the maximum allowable indentation, as well as the relationship between the stress utilization rate at the point and the allowable stress boundary. The torque balance coordination adjustment is then performed on the adjacent clamping points in the degradation region. During the processing, a preset small force increment is applied to each point according to a preset cycle based on the current clamping force. The clamping equivalent stiffness is updated according to the ratio of the force increment to the corresponding displacement increment, and the mapping relationship and differentiated target clamping force distribution scheme are updated accordingly.

9. The multi-point pressure equalization control system for low-stress clamping of thin-walled curved surface parts according to claim 7, characterized in that, It also includes a graded unloading and rebound control module, used for: After processing, the clamping force at each point is reduced in stages in the reverse order of loading. After each stage of unloading, the workpiece is held for a preset time and the springback displacement of the workpiece is monitored during the holding period. The force-displacement change path at each point is recorded. After unloading, record the final springback amount at each point, compare the final springback amount with the effective indentation amount at each point during the loading stage, and calculate the residual deformation amount at each point. Check the residual deformation amount point by point. If the residual deformation amount exceeds the preset residual deformation threshold, mark it as a point with abnormal residual deformation that needs to be confirmed. After confirming the staged unloading and springback control module again, the residual deformation anomaly points to be confirmed are marked as plastic deformation points and their positions and deformation amounts are recorded. The positions and deformation amounts of the plastic deformation points are used as the reference correction inputs for subsequent processes.

10. A multi-point pressure equalization control method for low-stress clamping of thin-walled curved surface parts, characterized in that, Includes the following steps: Step 1: Divide the thin-walled part to be processed into multiple clamping areas according to the position of each clamping unit, and obtain the local structural stiffness parameters and stress constraint basic parameters of each clamping area. Step 2: Establish a priori stiffness characterization model for each clamping region based on the local structural stiffness parameters, and determine the allowable stress boundary for each clamping region based on the stress constraint foundation parameters. Step 3: Control the actuator of each clamping unit to contact the surface of the part and apply a preset preload. Calculate the clamping equivalent stiffness of the clamping point corresponding to each clamping area based on the force and displacement data collected by the force detection unit built into each clamping unit during the preload stage. The clamping equivalent stiffness is determined based on the ratio of the effective displacement data to the force data after deducting the deformation contribution of the actuator itself and the deformation contribution of the fixture structure. Step 4: Establish the mapping relationship between clamping force, normal deformation response of part, and stress level based on the clamping equivalent stiffness; Step 5: Based on the mapping relationship, with the goal of making the normal deformation response of each clamping point as consistent, and in combination with the allowable stress boundary and cutting force constraints, calculate the differentiated target clamping force of each clamping point. Step 6: Apply load to each clamping unit according to the differentiated target clamping force, and perform iterative correction of the clamping state based on the feedback of the normal deformation response at each point and the stress estimation based on the mapping relationship.

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