Robot adaptive grinding and polishing processing method and system for complex surface

Abstract

The application belongs to the technical field of complex curved surface grinding and polishing processing, and particularly discloses a robot adaptive grinding and polishing processing method and system for complex curved surfaces. The method comprises the following steps: defining a workpiece boundary profile and a uniform coverage area according to the curvature of each cross section of the workpiece; based on a contact model, performing boundary force-position trajectory planning on the boundary profile to prevent overcutting, and performing surface force-position trajectory planning on the uniform coverage area to achieve uniform coverage; performing global planning on the grinding and polishing width and step length of the entire surface of the workpiece to meet the requirements of waviness, so as to obtain the grinding and polishing path and contact force of the entire surface of the workpiece; calculating the grinding and polishing speed based on the real-time grinding and polishing amount of the workpiece and the expected allowance; and performing conformable and collaborative grinding and polishing processing on the workpiece according to the grinding and polishing process parameters. The grinding and polishing force and grinding and polishing trajectory of the application take into account the profile fluctuation and processing efficiency, thereby ensuring the material removal consistency and better surface roughness value of the processed workpiece product, and realizing one-time forming of the grinding and polishing removal amount.

Description

Technical Field

[0001] This invention belongs to the field of complex surface grinding and polishing technology, and more specifically, relates to a robot adaptive grinding and polishing method and system for complex surfaces. Background Technology

[0002] Large, complex curved surface parts are key components in various fields, requiring high precision in their shape and position, as well as surface roughness, which are closely related to the lifespan and efficiency of equipment. Typical examples include aero-engine blades, wind turbine blades, turbine blades, and high-speed train bodies. Before being put into use, parts machined by machine tools must undergo one or more overall one-time finishing processes, namely, traditional grinding and polishing.

[0003] Currently, the main grinding and polishing methods used in China are manual grinding and polishing and gantry milling. Manual grinding and polishing requires a high level of experience from workers, resulting in inconsistent quality of parts produced by different workers. The positioning methods also vary, consuming significant manpower and exhibiting very low efficiency. Furthermore, the grinding and polishing process generates dust and noise, posing a significant health hazard to workers. While gantry milling frees up workers' hands, it is difficult to move and lacks flexibility. Workers also require a considerable amount of training to master its use. Its main drawback is its difficulty in efficiently and precisely machining the weakly rigid areas at the center and tail of parts. Robotic grinding and polishing, using mobile robots as the execution equipment, avoids the drawbacks of both manual and gantry milling. It is highly flexible, frees workers from tedious tasks, and avoids the harmful effects of dust, offering significant social benefits. However, robotic grinding and polishing is not a panacea, and its drawbacks are also apparent, particularly in the following aspects:

[0004] 1. The rigidity and low bandwidth of a robot's motion characteristics contradict the high rigidity and precision required for large, complex curved surface parts, resulting in severe force-position coupling problems and unknowable kinematic properties. 2. For a robot's end effector to successfully perform grinding and polishing, its interaction with the environment is crucial. In reality, due to manufacturing errors during the machining of large, complex curved surface parts, the complexity of the grinding and polishing environment, and the deformation of blades during clamping, the surface structure parameters cannot be accurately obtained. Furthermore, because large, complex curved surface parts themselves have characteristics such as large radial dimension variations, free-form surfaces, large dimensions, and weak rigidity, it is difficult to pre-define the contact force and machining trajectory for the robot during the grinding and polishing process. This easily leads to localized under-polishing or over-polishing, affecting surface accuracy, reducing efficiency, and extending equipment lifespan. 3. The removal allowance on complex curved surfaces is uneven, and because multiple parameters, including robot feed speed, tool speed, contact force, and workpiece curvature, are coupled and dynamically change during the grinding process, the grinding removal mechanism is unclear. Therefore, modeling the material removal depth is difficult in the grinding process of complex curved surfaces, which makes it impossible to reasonably plan and allocate grinding parameters to obtain the desired surface profile and roughness. Summary of the Invention

[0005] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a robotic adaptive grinding and polishing method and system for complex curved surfaces. Specifically, considering the characteristics of the complex curved surface workpiece and the features of its grinding and polishing process, a force-controlled robotic grinding and polishing device and its adaptive process parameter planning method are designed. Based on surface waviness, the grinding and polishing contact force and path width of the complex curved surface are planned, achieving a grinding and polishing force and trajectory that balances contour fluctuations and processing efficiency. The pose and contact force parameters of the workpiece boundary trajectory are optimized to avoid over-grinding at the edges. This ensures consistent material removal and good surface roughness values ​​for the processed workpiece, meeting the grinding and polishing requirements of blade-type parts. Furthermore, the grinding and polishing parameters can be adaptively generated based on the machining allowance, achieving one-time grinding and polishing removal, meeting the surface contour accuracy requirements, and possessing good efficiency.

[0006] To achieve the above objectives, according to one aspect of the present invention, a robotic adaptive grinding and polishing method for complex curved surfaces is proposed, comprising the following steps: Step 1: Defining the workpiece boundary contour and uniform coverage area based on the curvature of each section of the workpiece; Step 2: Based on the contact model, planning the boundary force-position trajectory to prevent overcutting for the boundary contour, and planning the surface force-position trajectory for uniform coverage for the uniform coverage area; Step 3: Globally planning the grinding and polishing path width and step size to meet the waviness requirements for the entire surface of the workpiece, thereby obtaining the grinding and polishing path and contact force for the entire workpiece surface; Step 4: Calculating the grinding and polishing speed based on the real-time grinding and polishing amount and the expected allowance of the workpiece; Step 5: Performing surface-compliant and collaboratively controlled grinding and polishing on the workpiece according to the above grinding and polishing process parameters.

[0007] As a further preferred embodiment, step two, which involves planning the boundary force-position trajectory to prevent overcutting of the boundary contour, specifically includes the following steps:

[0008] (11) Set the initial boundary trajectory and its initial contact force according to the workpiece boundary contour, and use it as the current force-position trajectory; (12) Calculate the contact boundary of the current force-position trajectory according to the contact model. If the contact boundary does not exceed the workpiece boundary, output the grinding and polishing path and contact force planning of the workpiece boundary. Otherwise, adjust the grinding and polishing contact force and tool position in sequence until the contact boundary does not exceed the workpiece boundary, and output the grinding and polishing path and contact force planning of the workpiece boundary.

[0009] As a further preferred embodiment, in step (12), the step of sequentially adjusting the polishing contact force and the tool position until the contact boundary does not exceed the workpiece boundary includes:

[0010] (121) Calculate the deformation of the grinding disc based on the initial contact force of the grinding point on the initial boundary trajectory; (122) Calculate the contact length, contact width and pressure distribution of the grinding disc contact area based on the deformation of the grinding disc; (123) Solve the distance δ1 between the grinding boundary of the current tool position and the preset boundary based on the contact width. If the distance δ1 is less than the preset allowable error, output the grinding path and contact force planning of the workpiece boundary. Otherwise, use the bisection method to optimize the value of the contact force so that the distance δ1 is less than the preset allowable error; (124) If the optimized contact force in step (123) is less than the working range of the grinding disc, adjust the tool position to obtain a boundary force-position trajectory that will not over-grind, and output the grinding path and contact force planning of the workpiece boundary at this time.

[0011] Preferably, the formula for calculating the deformation d of the grinding disc includes:

[0012]

[0013] In the formula, l0 is the thickness of the grinding disc, R1 and R2 are the principal radii of curvature of the gap between the workpiece and the grinding disc at the contact point, and F is the initial contact force. The equivalent elastic modulus of the elastic layer of the grinding disc;

[0014] Preferably, the calculation formulas for the contact length, contact width, and pressure distribution of the grinding disc contact area include:

[0015]

[0016]

[0017] In the formula, a and b are the major and minor axes of the elliptical contact region, respectively, and x and y are the coordinates in the local coordinate system of the contact region.

[0018] As a further preferred option, step three includes the following steps: (31) planning the polishing trajectory with equal arc length and equal parameter step size for the entire surface of the workpiece; (32) based on the polishing trajectory planning, calculating the expected contact force of equal contact width point by point according to the workpiece curvature; (33) calculating the removal amount and waviness of the workpiece section based on the convolution material removal model; (34) if the waviness meets the requirements, output the polishing trajectory and contact force that meet the requirements; otherwise, adjust the path width and repeat steps (32) to (34) until the corresponding waviness meets the requirements, and output the polishing trajectory and contact force that meet the requirements.

[0019] Preferably, in step (33), the calculation formula for the convolutional material removal model includes:

[0020]

[0021] In the formula, P(u,v) is the pressure distribution near the tool position on the workpiece, V(x,y) is the ratio of the grinding disc linear velocity to the robot velocity, and k g It is the material removal factor of the convolution, which can be obtained through experimental calibration.

[0022] As a further preferred option, step four includes the following steps: (41) Based on the linearly simplified material removal model, complete the preliminary grinding and polishing speed planning; (42) Based on the real-time grinding and polishing amount and expected allowance of the workpiece, use the convolutional material removal model to perform material removal simulation and error calculation; (43) Correct the preliminary grinding and polishing speed according to the material removal error simulation results until the material removal error meets the requirements, and output the grinding and polishing speed.

[0023] Preferably, in step (41), the empirical formula for material removal includes:

[0024]

[0025] In the formula, Vw V represents the linear velocity of the polishing tool. f H represents the robot's feed rate. e It represents the desired removal depth distribution, F is the contact force planned in the previous step, and k F It is the material removal coefficient directly related to the contact force, and k g They were obtained together through experimental calibration;

[0026] Preferably, in step (43), the correction of the initial polishing speed includes:

[0027]

[0028] In the formula, H p It is a simulated value of the removal depth calculated based on the convolution material removal formula.

[0029] According to another aspect of the present invention, a robotic adaptive grinding and polishing system for complex curved surfaces is also provided, comprising: a main control module, used to define the workpiece boundary contour and uniform coverage area according to the curvature of each section of the workpiece, and based on a contact model, to perform boundary force-position trajectory planning to prevent overcutting on the boundary contour, to perform surface force-position trajectory planning for uniform coverage on the uniform coverage area, and to perform global planning of grinding and polishing path width and step length to meet the waviness requirements on the entire surface of the workpiece, thereby obtaining the grinding and polishing path and contact force of the entire workpiece surface, and calculating the grinding and polishing speed based on the real-time grinding and polishing amount and expected allowance of the workpiece; and a grinding and polishing device, used to perform surface conformal processing on the workpiece according to the workpiece grinding and polishing path and contact force.

[0030] As a further preferred embodiment, the polishing device includes a robot, a three-degree-of-freedom polishing flange located at the end of the robot, and a polishing disc module located on the three-degree-of-freedom polishing flange.

[0031] As a further preferred embodiment, the three-degree-of-freedom polishing flange includes a platform and a connecting module, as well as a support module. The platform and connecting module includes a moving platform and a fixed platform arranged at intervals. The support module includes three sets of telescopic adjustable linkage assemblies located between the moving platform and the fixed platform and arranged symmetrically about the center of the moving platform. One end of each telescopic adjustable linkage assembly is connected to the moving platform via a ball joint, and the other end is connected to the fixed platform via a revolute joint. In this way, by adjusting the length of the three sets of telescopic adjustable linkage assemblies, the moving platform can achieve translation along the z-axis or rotation along the x and y axes, respectively, achieving the three degrees of freedom.

[0032] As a further preferred embodiment, the telescopic adjustable linkage assembly includes a hinge component, a first drive component, a guide rail component, a slide plate, a rotary joint component, and a position sensing component. One end of the hinge component is connected to the moving platform, and the other end is fixedly connected to the first drive component. The power output shaft of the first drive component is connected to the slide plate. The slide plate moves along the guide rail component under the drive of the first drive component, and the bottom of the slide plate is connected to the fixed platform through the rotary joint component. In this way, the slide plate is driven by the first drive component to move along the guide rail component to adjust the distance and posture between the moving platform and the fixed platform. The position sensing component is used to identify the movement distance of the slide plate.

[0033] Preferably, the first driving component includes a telescopic drive motor, a synchronous pulley, and a lead screw component. The power output shaft of the telescopic drive motor is connected to the synchronous pulley. The synchronous pulley includes a driving pulley, a driven pulley, and a belt wound around the driving pulley and the driven pulley. The driven pulley is connected to the lead screw component, and the lead screw component is fixedly connected to the slide plate.

[0034] Preferably, the position sensing component includes a sensor fixing strip, a sensing sheet, and a sensing sensor arranged along the direction of movement of the skateboard. The sensor fixing strip is fixedly connected to the guide rail component. One end of the sensing sheet is slidably connected to the sensor fixing strip, and the other end moves synchronously with the skateboard. The sensing sensor includes two sensors, which are respectively arranged on both sides of the sensing sheet along the direction of movement of the skateboard, and the distance between the two sensing sensors at least covers the maximum movement distance of the sensing sheet.

[0035] Preferably, the top surface of the moving platform is further provided with a grinding and polishing module. The grinding and polishing module includes a grinding and polishing motor, a one-dimensional force sensor, a sensor connecting plate, a coupling, a bearing, and a grinding disc. One end of the grinding and polishing motor is fixedly connected to the moving platform, and the other end is connected to the sensor connecting plate. Multiple one-dimensional force sensors are evenly arrayed along the circumference of the grinding and polishing motor, and the one-dimensional force sensors are located between the moving platform and the sensor connecting plate. The power output shaft of the grinding and polishing motor is connected to the coupling. One end of the coupling is connected to the sensor connecting plate, and the other end passes through the bearing and is connected to the grinding disc.

[0036] As a further preferred embodiment, the actual processing space area of ​​the three-degree-of-freedom polishing flange is:

[0037] l min ≤l i ≤l max

[0038] φ min ≤φ i ≤φ max

[0039] Among them, l min The minimum length of the telescopic adjustable linkage assembly is represented by l. max φ represents the maximum length of the telescopic adjustable linkage assembly, li represents the actual length of the telescopic adjustable linkage assembly, and φ represents the maximum length of the telescopic adjustable linkage assembly. min φ is the minimum rotation angle of the ball joint. max φ is the maximum rotation angle of the ball joint. i The actual rotation angle of the ball joint;

[0040] Preferably, the rotation angle expression of the ball joint on the upper platform is:

[0041]

[0042] Where, n i This is the reference vector for installing the ball joint.

[0043] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages:

[0044] 1. This invention proposes a computational tool—a calculation method for complex surface grinding and polishing contact problems—that can concisely and accurately calculate the contact range and pressure distribution at any tool point during grinding and polishing. Based on this, a convolutional method for calculating material removal depth is proposed, which can accurately predict the distribution of material removal depth under a set of grinding and polishing parameters.

[0045] 2. The method of the present invention proposes a grinding and polishing boundary definition method based on cross-sectional curvature normalization. On this basis, the pose and contact force parameters of the workpiece boundary trajectory are optimized, which can avoid the occurrence of edge over-grinding.

[0046] 3. The method of this invention plans the grinding and polishing contact force and path width for complex curved surfaces based on surface waviness, thereby obtaining grinding and polishing force and trajectory that balance contour fluctuations and processing efficiency. This ensures consistent material removal and good surface roughness values ​​for the processed workpiece, meeting the grinding and polishing requirements of blade-type parts.

[0047] 4. This invention uses the convolution principle and iterative optimization algorithm to collaboratively plan the contact force, trajectory, tool rotation speed, and robot feed speed for grinding and polishing complex curved surfaces. It can adaptively generate grinding and polishing parameters based on the machining allowance, achieving one-time grinding and polishing removal, meeting the surface contour accuracy requirements, and possessing good efficiency.

[0048] 5. Based on the constructed grinding and polishing parameters, the present invention proposes a force-controlled end effector that connects with a robotic arm, namely a parallel surface-compliant three-degree-of-freedom grinding and polishing flange. The parallel mechanism provides high stiffness, good inertia, and a compact structure, effectively improving bandwidth. Simultaneously, the surface compliance achieved through force control and impedance control strategies ensures adaptive adjustment of the end flange's posture, guaranteeing consistency with the normal direction of the surface during grinding and polishing, and ensuring constant-force grinding and polishing. This significantly improves processing quality, enhances the surface accuracy of large and complex curved parts, and increases work efficiency. Attached Figure Description

[0049] Figure 1 This is a flowchart of a robot-adaptive grinding and polishing method for complex curved surfaces, according to an embodiment of the present invention.

[0050] Figure 2 In the figure, (a) represents the relative positional relationship between the coordinate systems of the robot, tool, and workpiece. Figure 2 (b) in the figure represents the positional relationship between the polishing point and the workpiece;

[0051] Figure 3 A flowchart for planning the workpiece boundary polishing trajectory and its contact force;

[0052] Figure 4 (a) in the diagram is a schematic diagram of section division and curvature calculation. Figure 4 (b) in the diagram is a schematic diagram of boundary trajectory generation in boundary trajectory planning;

[0053] Figure 5 This is the surface force trajectory planning process for uniform coverage involved in the embodiments of the present invention;

[0054] Figure 6 This is a schematic diagram of the force-position trajectory planning results involved in an embodiment of the present invention;

[0055] Figure 7 This is the grinding and polishing speed planning process involved in the embodiments of the present invention;

[0056] Figure 8 This is a schematic diagram of the three-degree-of-freedom grinding and polishing flange structure involved in the present invention;

[0057] Figure 9 This is an exploded view of the flange grinding and polishing module assembly involved in this invention;

[0058] Figure 10 This is an exploded view of the flange branch module assembly of the present invention;

[0059] Figure 11 This is an exploded view of the flange platform and connecting components involved in the present invention;

[0060] Figure 12This is a simplified diagram of the parallel curved surface compliant three-degree-of-freedom grinding and polishing flange mechanism involved in this invention;

[0061] Figure 13 This is a simplified diagram of the 3-RPS mechanism involved in this invention;

[0062] Figure 14 This is a diagram of the branch motion spiral in a 3-RPS mechanism;

[0063] Figure 15 This is a 3-PRS spiral motion analysis diagram;

[0064] Figure 16 This is a schematic diagram of a typical cross-section of a ball joint according to an embodiment of the present invention;

[0065] Figure 17 This is a schematic diagram showing the position of the ball joint relative to the moving platform;

[0066] Figure 18 This is a schematic diagram of the impedance controller involved in an embodiment of the present invention;

[0067] Figure 19 (a) in the diagram is a schematic diagram of the variable impedance using the hyperbolic tangent function. Figure 19 (b) in the diagram is a schematic diagram of the variable impedance using the hyperbolic secant function.

[0068] In all the accompanying drawings, the same reference numerals denote the same technical features, specifically: A-grinding and polishing module, B-branching module, C-platform and connecting module, 1-grinding disc, 2-bearing, 3-coupling, 4-sensor connecting plate, 5-one-dimensional force sensor, 6-grinding and polishing motor, 7-lead screw component, 8-lead screw, 9-cross roller linear guide, 10-lead screw nut, 11-slide plate, 12-sensor protective plate, 13-new sensing plate, 14-sensor fixing strip, 15-sensor, 16-telescopic drive motor, 17-synchronous pulley, 18-moving platform, 19-transition plate, 20-fixed platform, 21-hinge, 22-copper column, 23-universal ball joint. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0070] like Figure 1 As shown in the figure, an embodiment of the present invention provides a robot-adaptive grinding and polishing method for complex curved surfaces, comprising the following steps:

[0071] (1) Before operation, the model of the six-axis industrial robot and its grinding and polishing tools need to be initialized and defined. For example... Figure 2 As shown, the coordinate systems of the robot, tool, and workpiece are calibrated to ensure the relative positional relationships between the components of the polishing system. The basic principle of polishing trajectory planning is:

[0072]

[0073] in, It is the transformation matrix of the six-axis end-effector coordinate system relative to the robot's base coordinate system. This matrix is ​​usually read by the robot teach pendant or communication interface. Representation of the tool coordinate system relative to the six-axis end-effector coordinate system. This represents the workpiece coordinate system relative to the robot's base coordinate system. It needs to be calibrated, typically through methods such as the four-point method, external measuring instruments, or installation positioning, which will not be elaborated upon here. The contribution of this invention lies in planning a series of grinding and polishing points on the workpiece. W P CCi And its corresponding grinding and polishing parameters.

[0074] (2) Define the workpiece boundary contour and uniform coverage area based on the curvature of each section of the workpiece. Specifically, the boundary force-position trajectory planning to prevent overcutting of the boundary contour includes the following steps:

[0075] (21) Set the initial boundary trajectory and its initial contact force according to the workpiece boundary contour, and use it as the current force-position trajectory. In this step, the step of sequentially adjusting the grinding and polishing contact force and the tool position point until the contact boundary does not exceed the workpiece boundary includes:

[0076] The deformation of the grinding disc is calculated based on the initial contact force at the grinding and polishing points on the initial boundary trajectory.

[0077] Calculate the contact length, contact width, and pressure distribution of the grinding disc contact area based on the deformation of the grinding disc;

[0078] The distance δ1 between the grinding and polishing boundary of the current tool position and the preset boundary is calculated based on the contact width. If the distance δ1 is less than the preset allowable error, the grinding and polishing path and contact force planning of the workpiece boundary are output. Otherwise, the contact force value is optimized by the bisection method so that the distance δ1 is less than the preset allowable error.

[0079] If the optimized contact force is less than the working range of the grinding disc, the tool position point is adjusted to obtain a boundary force-position trajectory that will not over-grind, and the grinding and polishing path and contact force planning of the workpiece boundary at this time are output.

[0080] (22) Calculate the contact boundary of the current force-position trajectory according to the contact model. If the contact boundary does not exceed the workpiece boundary, output the grinding and polishing path and contact force planning of the workpiece boundary. Otherwise, adjust the grinding and polishing contact force and tool position in sequence until the contact boundary does not exceed the workpiece boundary, and output the grinding and polishing path and contact force planning of the workpiece boundary.

[0081] More specifically, in an optional preferred embodiment of the present invention, during the grinding and polishing process of complex curved surface parts, over-grinding is prone to occur in the area near the edge. This is because the contact wheel (grinding disc) of the grinding and polishing tool experiences stress concentration due to edge contact pressure near the edge, resulting in an excessive amount of material removed in that area. Conventional trajectory planning methods typically use the u and v parameters of the freeform surface model as a reference. However, if this method is also used to plan the boundary region, it will lead to uncontrollable distance between the grinding and polishing trajectory and the workpiece boundary. Therefore, this embodiment proposes a grinding and polishing boundary trajectory planning method based on the definition of the boundary contour line and the contact model. First, as Figure 4 As shown, firstly, the cross-sectional profile of the workpiece is obtained based on the model or measurement results, and the curvature of each cross-section is calculated. The curvature value of each cross-section is then normalized using the maximum curvature as a reference. This allows setting the global curvature radius R0 corresponding to the boundary trajectory, thus obtaining... Figure 4 The initial boundary profile is shown in (b) of the diagram.

[0082] Based on the initial boundary profile, the initial contact force at the grinding and polishing points is preset to be F according to experience. The deformation d of the grinding disc can be obtained according to the following formula (1).

[0083]

[0084] Where l0 is the thickness of the grinding disc, R1 and R2 are the principal radii of curvature of the gap between the workpiece and the grinding disc at the contact point, and F is the initial contact force. for

[0085] The equivalent elastic modulus of the grinding disc's elastic layer. This yields the length and width of the contact area as follows:

[0086]

[0087] Meanwhile, the pressure distribution in the contact area is as follows:

[0088]

[0089] The preset allowable error is δ0. Based on the calculated contact width, the distance δ1 between the current tool position point's grinding / polishing boundary and the preset boundary is determined. The contact force value is optimized using a bisection method, ensuring that 0 < δ1 < δ0. This ensures that the grinding / polishing contact area falls completely within the curved surface, preventing over-grinding. If the optimized contact force is less than the working range of the grinding head, the tool position point is adjusted inward to obtain a set of boundary force trajectory that prevents over-grinding.

[0090] (3) Globally plan the polishing path width and step length to meet the waviness requirements for the entire workpiece surface, thereby obtaining the polishing path and contact force for the entire workpiece surface. Specifically:

[0091] (31) Plan the polishing trajectory with equal arc length, row width and equal parameter step size for the entire surface of the workpiece.

[0092] (32) Based on the polishing trajectory planning, calculate the expected contact force of equal contact width point by point according to the workpiece curvature;

[0093] (33) Calculate the removal amount and waviness of the workpiece cross section based on the convolution material removal model;

[0094] (34) If the waviness meets the requirements, output the polishing trajectory and contact force that meet the requirements; otherwise, adjust the path width and repeat steps (32) to (34) until the corresponding waviness meets the requirements and output the polishing trajectory and contact force that meet the requirements.

[0095] More specifically, in one embodiment of the present invention, after completing the force and potential trajectory planning of the grinding and polishing boundary, it is necessary to perform global planning of the entire surface force and potential trajectory and its grinding and polishing parameters, such as... Figure 5 As shown. According to the grinding and polishing accuracy requirements, a slightly larger line width parameter is first preset, and trajectory planning with equal arc length line width and equal parameter step size is carried out. In order to obtain a more uniform part surface, the contact force is planned according to formulas (1) and (2) at different positions and under different curvatures, so that the contact width b is equal.

[0096] Specifically, the convolution principle for calculating the material removal depth based on convolution in this embodiment is shown in formula (4), which indicates that the material removal depth on the workpiece surface is the convolution of the pressure and velocity on the surface.

[0097]

[0098] Where P(u,v) is the pressure distribution near the tool position on the workpiece, which can be obtained using formula (3), and V(x,y) is the ratio of the grinding head linear velocity to the robot velocity. The corresponding numerical calculation method is shown in formula (5), which means that the removal depth at any point on the surface is equal to the sum of the products of pressure and velocity at all moments when it is in contact with the surface.

[0099]

[0100] Because the removal depth of a single toolpath is higher in the middle and lower at the edges, and there needs to be some overlap between adjacent toolpaths, a certain degree of ripples will form on the cross-section and contour. In principle, the smaller the line width, the denser the toolpaths, and the smaller the ripples, but at the same time, the efficiency is also lower. Therefore, the line width needs to be optimized with the ripple requirement as a constraint. The iterative formula for line width optimization is as follows (6).

[0101]

[0102] Among them, W a W is the waviness of the material removal distribution corresponding to the simulation of the material removal depth for the current line width. e This is the desired waviness, generally set to 90% of the part's requirement. w is the current row width, and w' is the row width after iteration. Formula (6) is executed iteratively until w' - w < Δ. This completes the force trajectory planning for the entire workpiece surface, as shown below. Figure 6 As shown.

[0103] (4) Calculate the polishing speed based on the real-time polishing allowance and expected margin of the workpiece. For example... Figure 7 As shown, the specific items include:

[0104] (41) Based on the linearly simplified material removal model, the initial grinding and polishing speed is planned; (42) Based on the real-time grinding and polishing amount and expected allowance of the workpiece, the convolutional material removal model is used to perform material removal simulation and error calculation; (43) The initial grinding and polishing speed is corrected according to the material removal error simulation results until the material removal error meets the requirements, and the grinding and polishing speed is output. More specifically, in a preferred embodiment of the present invention, the initial grinding and polishing speed is planned first according to the linearly simplified material removal empirical formula (7). Wherein V w V represents the linear velocity of the polishing tool. f H represents the robot's feed rate. e This represents the desired removal depth distribution, and F is the contact force planned in the previous step. Since the robot's speed needs to be obtained online, the ratio of the polishing tool speed to the robot speed is planned here. This yields an initial set of forces, positions, polishing tool rotation speed, and robot feed speed.

[0105]

[0106] Formula (5) can be used to simulate the corresponding removal depth distribution, yielding a more accurate predicted value for the removal depth of the convolutional material. Based on this simulation result, the parameters of the initial planning are corrected:

[0107]

[0108] After correction using formula (8), the new grinding and polishing parameters are resubmitted into formula (7) for simulation and error calculation until the root mean square error (RMSE) of the depth is removed. p -H e Less than the permissible value H for the contour error a Up to this point. In practical applications, the robot speed V is obtained online based on the planned speed ratio. fa This will give you the rotational speed that should be sent to the polishing tool:

[0109]

[0110] This completes the planning of the polishing trajectory, contact force, and speed for the entire curved surface.

[0111] According to another aspect of the present invention, a robotic adaptive grinding and polishing system for complex curved surfaces is also provided, comprising: a main control module, used to define the workpiece boundary contour and uniform coverage area according to the curvature of each section of the workpiece, and based on a contact model, to perform boundary force-position trajectory planning to prevent overcutting on the boundary contour, to perform surface force-position trajectory planning for uniform coverage on the uniform coverage area, and to perform global planning of grinding and polishing path width and step length to meet the waviness requirements on the entire surface of the workpiece, thereby obtaining the grinding and polishing path and contact force of the entire workpiece surface, and calculating the grinding and polishing speed based on the real-time grinding and polishing amount and expected allowance of the workpiece; and a grinding and polishing device, used to perform surface conformal processing on the workpiece according to the workpiece grinding and polishing path and contact force.

[0112] Based on any combination of the above embodiments, in this embodiment, the polishing device includes a robot, a three-degree-of-freedom polishing flange disposed at the end of the robot, and a polishing disc module disposed on the three-degree-of-freedom polishing flange.

[0113] Any combination based on the above embodiments, such as Figures 8 to 17As shown in this embodiment, the three-degree-of-freedom polishing flange includes a platform and a connecting module, as well as a support module. The platform and connecting module includes a movable platform 18 and a fixed platform 20 arranged at intervals. The support module includes three sets of telescopic adjustable linkage assemblies located between the movable platform 18 and the fixed platform 20 and arranged symmetrically about the center of the movable platform 18. One end of each telescopic adjustable linkage assembly is connected to the movable platform 18 via a ball joint, and the other end is connected to the fixed platform 20 via a revolute joint. In this way, by adjusting the length of the three sets of telescopic adjustable linkage assemblies, the movable platform 18 can achieve the three degrees of freedom of translation along the z-axis or rotation along the x and y axes respectively. More specifically, the telescopic adjustable linkage assembly includes a hinge component, a first drive component, a guide rail component, a slide plate 11, a rotary joint component, and a position sensing component. One end of the hinge component is connected to the moving platform 18, and the other end is fixedly connected to the first drive component. The power output shaft of the first drive component is connected to the slide plate 11. The slide plate 11 moves along the guide rail component under the drive of the first drive component, and the bottom of the slide plate 11 is connected to the fixed platform 20 through the rotary joint component. In this way, the slide plate 11 is driven by the first drive component to move along the guide rail component to adjust the distance and posture between the moving platform 18 and the fixed platform 20. The position sensing component is used to identify the movement distance of the slide plate 11. The first driving component includes a telescopic drive motor 16, a synchronous pulley 17, and a lead screw component. The power output shaft of the telescopic drive motor 16 is connected to the synchronous pulley 17. The synchronous pulley 17 includes a driving pulley, a driven pulley, and a belt wound around the driving pulley and the driven pulley. The driven pulley is connected to the lead screw component, and the lead screw component is fixedly connected to the slide plate 11. The position sensing component includes a sensor fixing strip 14, a sensing plate 13, and sensing sensors 15 arranged along the movement direction of the slide plate 11. The sensor fixing strip 14 is fixedly connected to the guide rail component. One end of the sensing plate 13 is slidably connected to the sensor fixing strip 14, and the other end moves synchronously with the slide plate 11. There are two sensing sensors 15, respectively arranged on both sides of the sensing plate 13 along the movement direction of the slide plate 11, and the distance between the two sensing sensors 15 at least covers the maximum movement distance of the sensing plate 13. The top surface of the moving platform 18 is also provided with a grinding and polishing module. The grinding and polishing module includes a grinding and polishing motor 6, a one-dimensional force sensor 5, a sensor connecting plate 4, a coupling 3, a bearing 2, and a grinding disc 1. One end of the grinding and polishing motor 6 is fixedly connected to the moving platform 18, and the other end is connected to the sensor connecting plate 4. Multiple one-dimensional force sensors 5 are evenly arranged in an array around the circumference of the grinding and polishing motor 6, and the one-dimensional force sensors 5 are located between the moving platform 18 and the sensor connecting plate 4. The power output shaft of the grinding and polishing motor 6 is connected to the coupling 3. One end of the coupling 3 is connected to the sensor connecting plate 4, and the other end passes through the bearing 2 and is connected to the grinding disc 1.

[0114] like Figure 9 As shown, in a preferred embodiment of the present invention, the flange as a whole comprises an upper (moving) platform for mounting a drive mechanism, three telescopic connecting rods (sliding pairs), and a base (fixed platform). The upper platform is connected to the connecting rods via three ball joints (spherical pairs). The three ball joints are evenly distributed on a circle with radius r centered on the upper platform. The lines connecting the three ball joints to the center of the circle are mutually 120°, i.e., B1, B2, and B3 form equilateral triangles, and the circle with radius r centered on the upper platform is its circumcircle. The other end of the connecting rods is connected to the base via equidistant pin joints (rotating pairs). Similarly, P1, P2, and P3 are also equilateral triangles, and the circle with radius R centered on the base is its circumcircle. By changing the length of the connecting rods, the movement of the upper platform relative to the base can be manipulated. Three of the connecting rods are constrained by the pin pair, so they can only rotate around points P1, P2, and P3 in three planes that are perpendicular to the base and pass through B1P1, B2P2, and B3P3, respectively. Therefore, once the lengths of the three connecting rods are determined, the position of the upper platform can be uniquely determined. Based on the above analysis, the polishing flange mechanism designed in this invention can perform three degrees of freedom: translation along the z-axis and rotation along the x and y axes. Structurally, the flange can be divided into three parts, from top to bottom: A. Grinding disc polishing module, B. Branch chain module, and C. Platform and connecting module, with a total height of 270mm. In the process of structural design and selection of key components, the principles of compact structure and ease of processing and assembly were followed. Standard parts were used as much as possible, and the parameters of non-standard parts were designed based on the parameters of standard parts, significantly reducing processing and assembly time and facilitating later component replacement and optimization upgrades. Figure 3 As shown, the grinding and polishing module includes a grinding disc 1, an RU42 crossed roller bearing, a coupling 3, a sensor connection plate 4, a one-dimensional force sensor 5, and a Yaskawa servo motor. The grinding disc 1 has a diameter of 120mm and a thickness of 5mm. The diameter of the grinding disc 1 is half the diameter of the moving platform, which is both aesthetically pleasing and practical. Its overall dimensions are consistent with the sensor connection plate 4, forming a symmetrical structure. Both the grinding disc 1 and the sensor connection plate 4 have threaded holes. The threaded hole in the grinding disc 1 mates with the inner ring of the RU42 crossed roller bearing to fix the grinding disc 1 and the bearing 2 together. The threaded hole on the sensor connection plate 4 is used to fix the one-dimensional force sensor 5 together with the moving platform. The grinding and polishing motor is a Yaskawa servo motor 6. The motor output shaft is connected to the coupling 3, which is fixed to the inner ring of the RU42 crossed roller bearing 2 through mounting holes. This allows the motor 6 to rotate, driving the grinding disc 1 to rotate, ensuring the grinding and polishing quality. Figure 11As shown, the entire chain consists of four parts: a motor section, a transmission section, a position sensing section, and a guide rail section. The motor 16 in the motor section is the same type as the motor 6 in the A grinding and polishing section. The output shaft of motor 16 is connected to a synchronous pulley 17, driving the synchronous pulley 17 to rotate. The transmission section uses a synchronous pulley drive, allowing the motor to control the movement of the lead screw 8 via the belt. The position sensing section consists of a sensor protective plate 12, two LU-L24 sensors 15, a new sensor plate 13, and a sensor fixing strip 14. The sensor protective plate 12 isolates the sensor from the external environment, preventing dust and other contaminants from damaging the components. The new sensor plate 13 is fixed to the sensor fixing strip 14 and can slide along the guide rail. The two LU-L24 sensors 15 are evenly distributed on the sensor fixing strip 14, allowing them to detect the position of the new sensor plate 13 (i.e., the guide rail) at any time. This position information is transmitted to the PC, enabling online monitoring of the guide rail's position and thus obtaining the real-time attitude of the moving platform. The guide rail works by using a synchronous pulley 17 to drive the lead screw 8 to rotate. The rotation of the lead screw 8 causes the lead screw nut 10 to move, which in turn moves the slide plate 11, achieving a variable linkage length, i.e., a sliding pair. As can be seen from the internal structure diagram of the guide rail, the slide plate 11 is fixed to four crossed roller linear guide rails 9 to achieve free sliding. Meanwhile, the upper end of the lead screw 8 has two 635 bearings 7, a lead screw locking nut, bearing caps, and other fixing parts to increase the load-bearing capacity of the lead screw 8 and achieve higher precision.

[0115] like Figure 12 As shown, the entire polishing flange has two platforms: a fixed platform 20 and a moving platform 18. The fixed platform 20 is connected to the robotic arm, and the moving platform 18 is connected to the polishing section for polishing. The moving platform 18 and the fixed platform 20 have the same diameter of 240mm and a thickness of 8mm. Corresponding threaded holes are drilled on the two platforms for connection and fixation based on the positional distribution of the flange at the end of the robotic arm and the threaded holes of the one-dimensional force sensor. The connecting parts are mainly standard components, namely the universal ball joint damping hinge 23 (ball joint), hinge 21 (rotary joint), copper column 22, and transition plate 19. The installation connections between standard components use carbon fiber plates of appropriate thickness to achieve high rigidity and strength while minimizing weight. Some key connecting parts use machined aluminum alloy parts to simplify the structure and ensure the required strength. The universal ball joint damping hinge 23 can swing in any direction and the torque is adjustable. It has a long service life and is easy to disassemble. The hinge 21 is selected for its high precision, which can effectively reduce the flange space and save raw materials. The copper column 22 and the transition plate 19 can be used to connect the moving pair to the moving platform 18 and the fixed platform 20 respectively.

[0116] like Figure 13As shown, in this embodiment of the invention, in the three-degree-of-freedom polishing flange (3-RPS) mechanism, R is a revolute joint, P is a prismatic joint, and S is a ball joint. Based on helical theory, the helical system of the branch motion is:

[0117]

[0118] like Figure 14 As shown, the constraint screw system is:

[0119] $ r =(1 0 0; 0 f -e) (11)

[0120] Therefore, the other two branches are similarly parallel to the first revolute joint and pass through the center of their respective branch spherical joints. Meanwhile, the three constraint forces are linearly independent, restricting the platform's three degrees of freedom. The restricted motions include the platform's translation in the X and Y directions and its rotation in the Z direction.

[0121] Calculated according to the modified GK formula:

[0122]

[0123] In the formula: M represents the number of degrees of freedom of the polished flange; n represents the number of components of the polished flange; g represents the number of kinematic pairs in the polished flange; f i represents the number of degrees of freedom of the i-th kinematic pair of the polished flange; v represents the parallel redundant constraint.

[0124] Therefore, it can be concluded that the 3-RPS mechanism can achieve two rotations and one transfer with full circumference.

[0125] In this invention, the working space of the 3-RPS parallel mechanism refers to the actual processing space area that the center point C of the upper platform can reach, which can largely reflect the performance of the parallel mechanism.

[0126] In reality, many factors can affect the workspace of a parallel mechanism, primarily physical constraints such as the length of the drive rod, the ball joint constraint, and the interference constraints between links. Since the invented 3-RPS parallel mechanism has three independent degrees of freedom, determining the workspace requires calculating these three translational degrees of freedom, i.e., X. C Y C Z C The coordinates of the three translation variables require solving equations with one translation and two rotation coordinates as independent variables. Since these three equations are highly nonlinear, they will inevitably bring great difficulties to the solution. This invention solves the equations for the above three constraints to obtain the actual workspace. This makes the solution method for the workspace relatively simple and reliable, and also convenient for practical application.

[0127] Discussion of drive rod length constraints:

[0128] The invented 3-RPS parallel grinding and polishing flange has three drive rods, which are distributed at 120° along the circumference. The length of each rod can be determined by the coordinates of two points. Because the sliding pair has a stroke limitation, the length of the drive rods is limited, expressed as l. min The minimum length of a rod is represented by l. max Let represent the maximum length of the member. Then, the length of the member can be constrained by the following formula:

[0129] l min ≤l i ≤l max (13)

[0130] Discussion of ball joint constraints: Let the rotation angle of the ball joint be φ. i Its range is determined by the angle between the z-axis of the fixed coordinate system and the Z-vector of the ball joint, such as... Figure 16 As shown. The Z-axis reference vector of the i-th ball joint on the upper platform is represented by n. i If we express the value, then the expression for the ball joint rotation angle of the upper platform is: Where i = 1, 2, 3. Its rotation constraints are:

[0131] φ min ≤φ i ≤φ max (14)

[0132] In the formula n i φ is the reference vector for installing the ball joint. min φ is the minimum rotation angle of the ball joint. max This is the maximum rotation angle of the ball joint.

[0133] The following derivation aims to express φ i Let the normal vector N of the plane c-xyz be:

[0134] N = a1I + b1J + c1K (15)

[0135] a1, b1, and c1 are constant term coefficients, I is the x-axis unit vector, J is the y-axis unit vector, and K is the z-axis unit vector;

[0136] The corresponding plane equation is:

[0137] Ax + By + Cz = d (16)

[0138] A, B, and C are constant coefficients, d is a constant term, and x, y, and z are the coordinate axes of the corresponding plane.

[0139] Depend on Figure 13 It can be known that:

[0140]

[0141] Where B1B2 and B2B3 are the line vectors pointing from B1 to B2 and B2 to B3 respectively, the components of the normal vector N can be determined:

[0142]

[0143]

[0144]

[0145] Because the ball joint is firmly fixed to the upper platform, such as Figure 10 As shown, the axis of symmetry of each ball hinge intersects the normal to the upper platform at point m, and extends along the normal through point (x). c ,y c ,z c The equation of the straight line is:

[0146]

[0147] By defining the unit vector component, we can obtain:

[0148]

[0149]

[0150]

[0151] Therefore, the Cartesian coordinates of point m can be obtained as follows:

[0152] x m =x c +AD m

[0153] y m =y c +BD m

[0154] z m =z c +CD m (twenty one)

[0155] Similarly, the equation of the connecting rod in a straight line is:

[0156]

[0157] Angle φ can be obtained i The expression is as follows:

[0158]

[0159] Where i = 1, 2, 3 and 0 < φ i <φ max / 2..

[0160] Due to the inherent characteristics of the mechanism, interference between the links is not allowed. At this point, all constraints have been discussed.

[0161] Through the above embodiments, the expressions for the virtual rod length and the rotation angle of the ball hinge are now known. Due to the special nature of the polished flange structure, interference between rods will not occur; therefore, only the two constraints of rod length and rotation angle range need to be considered. The principle of the boundary numerical limit search method is to search for points in space. If both the rod length and rotation angle of the desired point are within the specified limit range, then the point is within the working space of the mechanism. If neither of the specified conditions is met, then the point is outside the working space of the mechanism. Finally, by finding all points that meet the constraints and drawing them as surfaces, the complete working space of the mechanism can be obtained. By using parallel planes to divide the working space into infinitesimal elements with a thickness of ΔZ, finding the boundaries of the working space in each plane, and connecting them to form surfaces, the three-dimensional working space of the mechanism can be obtained.

[0162] More specifically, first initialize the parameters of the flange mechanism: l min The minimum length of the rod, l max R is the maximum length of the rod, R is the diameter of the fixed platform, r is the diameter of the moving platform, and Z is the maximum length of the rod. min The minimum height that the center point of the moving platform can reach, Z max The maximum height achievable by the center point of the moving platform, α, and β are Euler angles; initial values ​​are set according to the designed grinding and polishing flange dimensions: for example, l min =170mm, l max =240mm, R=120mm, r=120mm, Z0=160mm;

[0163] Calculate the length of each telescopic rod of the flange and the corresponding rotation angle of the flange; determine whether the corresponding rotation angle of the flange meets the constraint requirements. If it does, record the corresponding parameters and draw the working space boundary of the flange. If it does not meet the requirements, adjust the parameters ΔZ, α, and β, and recalculate the length of each telescopic rod of the flange and the corresponding rotation angle of the flange until the corresponding rotation angle of the flange meets the constraint requirements, thus drawing the working space boundary of the flange. After simulating the mechanism in the working space using a boundary numerical limit search method written in MATLAB software, the boundary diagram of the working space is obtained.

[0164] Due to the inherent contradiction between the rigidity and low bandwidth of a robot's motion characteristics and the high rigidity and precision required for large, complex curved surfaces, coupled with severe force-position coupling issues and unknown kinematic properties, the robot's end effector must possess a certain degree of compliance during machining to reduce processing errors. To achieve compliance in the contact force and attitude of the flexible flange end, a corresponding force control algorithm is needed for real-time control of the contact force. This invention employs an impedance control algorithm, gravity compensation using a six-dimensional force sensor, and a corresponding impedance controller to achieve the surface compliance of the polished flange.

[0165] Furthermore, based on any of the above embodiments or combinations thereof, in this embodiment, the mechanical impedance is generated by the mechanical system itself and characterized by the mass matrix M, damping matrix D, and stiffness matrix K. Impedance control establishes the dynamic relationship between force and position, resulting in the ideal impedance control model for the polished flange:

[0166]

[0167] Where x d with f d Let M be the desired pose and desired force of the polishing flange, respectively. x(t) and f(t) are the current pose and current contact force of the polishing flange detected by the sensor in real time, respectively. Δx and its first and second derivatives represent the deviations between the desired and current pose, velocity, and acceleration of the polishing flange. The impedance control of the polishing flange is achieved by adjusting parameter M. d D d With K d This is to achieve control over the force and position at the flange end.

[0168] By ensuring that the reference trajectory satisfies:

[0169]

[0170] In theory, accurate tracking of the desired force is possible. However, in real-world scenarios, environmental location and stiffness parameters often deviate from their true values. By analyzing the impedance model, the force error equation can be obtained:

[0171]

[0172] Considering the error δx e and δk e The steady-state force error equation is:

[0173]

[0174] Variable impedance control based on bounded functions:

[0175] When the environmental stiffness is known but the location information is inaccurate and there are unknown changes, i.e. By analyzing the impedance control force error equation, we obtain:

[0176]

[0177] Due to environmental stiffness k e Since the force tracking error is relatively large, even a small position error can lead to a large force tracking error. Therefore, a variable impedance strategy with bounded impedance parameters is proposed when the environment is unknown and changes, which reduces the steady-state force error and improves the system robustness.

[0178] Assume the variable impedance model is as follows:

[0179]

[0180] Where b(t) is the time-varying damping coefficient, k(t) is the time-varying stiffness coefficient, and the conformation trajectory is equal to the actual trajectory x. c =x, and The proposed law governing the variation of impedance parameters is as follows:

[0181]

[0182] In the above formula, b0 is the initial value of damping, and k b Here, k is the damping adjustment coefficient, k0 is the initial stiffness value, and φ(t) is a function related to force error.

[0183]

[0184] The variable impedance used is mediated by bounded functions y = tanh(x) and y = sech(x), respectively, whose graphs are shown below. Figure 19 As shown in the figure. The actual damping variation range can be seen from the function graph as [b0-k]. b ,b0+k b The stiffness adaptively varies within the range (0, k0], where parentheses indicate the range does not include the boundary, and square brackets indicate the range includes the boundary. Clearly, when the system is stable, the stiffness and damping parameters are bounded: stiffness k(t) → 0, b(t) → b0 - k(b), and e... fss →0.

[0185] Furthermore, based on any of the above embodiments or combinations thereof, in this embodiment, gravity compensation calculation for the flange is also performed. This invention uses ZYZ Euler angles to describe the attitude of the grinding and polishing flange, where α, β, and γ are the rotation coefficients of the cubic coordinate transformation. Let the gravity of the grinding and polishing module be G, then the vector representation of the gravity of the grinding and polishing module in the coordinate system O-XYZ is: In the coordinate system c-xyz, the gravity of the grinding and polishing module depends not only on the magnitude of G, but also on α, β, and γ. To achieve this... In the coordinate system c-xyz, this is reflected by left multiplying by the inverse of the rotation matrix [T].

[0186]

[0187] The vector of gravity in the basic coordinate system O-XYZ is represented as: The cosine of the angle between gravity and the x-axis in the workpiece coordinate system c-xyz is:

[0188]

[0189] The component of the gravity of the grinding and polishing module along the x-axis in the workpiece coordinate system c-xyz is:

[0190] G x =G×cosψ=r 31 G (35)

[0191] Similarly, the components of the gravity of the grinding and polishing module on the three coordinate axes of the workpiece coordinate system c-xyz are:

[0192] {G x G y G z}={r 31 G,r 32 G,r 33 G} (36)

[0193] Furthermore, based on any of the above embodiments or combinations thereof, this embodiment also includes a torque compensation calculation for the flange.

[0194] The torque signals measured on each coordinate axis of the sensor are related not only to the components of the grinding and polishing module's gravity in the other two coordinate systems, but also to the position of the grinding and polishing module's center of mass in the workpiece coordinate system. Assume the torque components of the grinding and polishing module's gravity on the three coordinate axes in the workpiece coordinate system are {M}. x M y M z The coordinates of the center of gravity of the grinding and polishing module in the workpiece coordinate system are {L}. x ,L y ,L z Previously, the components of the gravity of the grinding and polishing module on the three coordinate axes in the workpiece coordinate system c-xyz were obtained as {G}. x G y G z Based on the relationship between force and torque, the following expression can be obtained:

[0195]

[0196] When the center of mass of the grinding and polishing module falls on the Z-axis of the sensor, at this time L x =L y =0, the above expression can be simplified to:

[0197]

[0198] In the actual measurement process, in addition to the influence of the gravity of the grinding and polishing module mentioned above on the measurement results, the initial value setting of the sensor itself will also have a great impact on the measurement results. Therefore, the initial value must be obtained and compensated before the actual measurement.

[0199] Assume the initial value of the six-dimensional force sensor is set to {F}. x0 ,F y0 ,F z0 ,T x0 ,T y0 ,T z0 The actual value measured by the sensor is {F}. ex ,F ey ,F ez ,T ex ,T ey ,T ez},but:

[0200]

[0201] Then, based on the six specific poses, a simultaneous solution can be obtained for {F}. x0 ,F y0 ,F z0 ,T x0 ,T y0 ,T z0 The size and position of the center of gravity of the grinding and polishing module. Furthermore, in this embodiment, the principle of the designed impedance controller is as follows: Figure 18 As shown, by setting the corresponding control parameter M d D d With K d The environmental impedance parameters, obtained through estimation or online learning, allow the input to be the target position of the polishing flange and the output to be the contact force at the end of the polishing flange. Adjusting these parameters can improve the controller's performance.

[0202] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A robotic adaptive grinding and polishing method for complex curved surfaces, characterized in that, Includes the following steps: Step 1: Define the workpiece boundary contour and uniform coverage area based on the curvature of each section of the workpiece. Step 2: Based on the contact model, perform boundary force-potential trajectory planning to prevent overcutting of the boundary contour, and perform surface force-potential trajectory planning for uniform coverage of the uniformly covered area. Step 3: Perform global planning of the polishing path width and step length to meet the waviness requirements for the entire surface of the workpiece, thereby obtaining the polishing path and contact force for the entire surface of the workpiece. Step 4: Calculate the polishing speed based on the real-time polishing amount and expected allowance of the workpiece; Step 5: Perform surface-compliant and coordinated grinding and polishing on the workpiece according to the above grinding and polishing process parameters; Step two, specifically the boundary force-position trajectory planning for preventing overcutting of the boundary profile, includes the following steps: (11) Set the initial boundary trajectory and its initial contact force according to the workpiece boundary contour, and use it as the current force-position trajectory; (12) Calculate the contact boundary of the current force-position trajectory according to the contact model. If the contact boundary does not exceed the workpiece boundary, output the grinding and polishing path and contact force planning of the workpiece boundary. Otherwise, adjust the grinding and polishing contact force and tool position in sequence until the contact boundary does not exceed the workpiece boundary, and output the grinding and polishing path and contact force planning of the workpiece boundary. In step (12), the step of sequentially adjusting the grinding and polishing contact force and the tool position until the contact boundary does not exceed the workpiece boundary includes: (121) Calculate the deformation of the grinding disc based on the initial contact force at the grinding and polishing point on the initial boundary trajectory; (122) Calculate the contact length, contact width and pressure distribution of the contact area of ​​the grinding disc based on the deformation of the grinding disc; (123) Calculate the distance δ1 between the grinding and polishing boundary of the current tool position and the preset boundary based on the contact width. If the distance δ1 is less than the preset allowable error, output the grinding and polishing path and contact force planning of the workpiece boundary. Otherwise, use the bisection method to optimize the value of the contact force so that the distance δ1 is less than the preset allowable error. (124) If the optimized contact force in step (123) is less than the working range of the grinding disc, the tool position point is adjusted to obtain the boundary force-position trajectory that will not be over-grinded, and the grinding and polishing path and contact force planning of the workpiece boundary at this time are output. The formula for calculating the deformation d of the grinding disc includes: ， In the formula, l0 is the thickness of the grinding disc, R1 and R2 are the principal radii of curvature of the gap between the workpiece and the grinding disc at the contact point, and F is the initial contact force. The equivalent elastic modulus of the elastic layer of the grinding disc; The formulas for calculating the contact length, contact width, and pressure distribution of the grinding disc contact area include: ， ， In the formula, a、b These are the major and minor axes of the elliptical contact region, respectively. x, y These are the coordinates in the local coordinate system of the contact area.

2. The robot-adaptive grinding and polishing method for complex curved surfaces according to claim 1, characterized in that, Step three includes the following steps: (31) Plan the polishing trajectory with equal arc length, line width and equal parameter step size for the entire surface of the workpiece; (32) Based on the polishing trajectory planning, calculate the expected contact force of the equal contact width point by point according to the workpiece curvature; (33) Calculate the amount of material removed from the workpiece cross section and the waviness based on the convolution material removal model; (34) If the waviness meets the requirements, output the polishing trajectory and contact force that meet the requirements; otherwise, adjust the path width and repeat steps (32) to (34) until the corresponding waviness meets the requirements and output the polishing trajectory and contact force that meet the requirements.

3. The robot adaptive grinding and polishing method for complex curved surfaces according to claim 2, characterized in that, In step (33), the calculation formula for the convolutional material removal model includes: ， In the formula, It refers to the pressure distribution near the tool position on the workpiece. It is the ratio of the millstone's linear velocity to the robot's velocity. It is the material removal factor of the convolution.

4. The robot-adaptive grinding and polishing method for complex curved surfaces according to claim 1, characterized in that, Step four includes the following steps: (41) Based on the linearly simplified material removal model, the preliminary grinding and polishing speed planning was completed; (42) Based on the real-time grinding and polishing amount and the expected allowance of the workpiece, the convolutional material removal model is used to simulate material removal and calculate errors; (43) Correct the initial polishing speed according to the simulation results of material removal error until the material removal error meets the requirements, and output the polishing speed.

5. The robot adaptive grinding and polishing method for complex curved surfaces according to claim 4, characterized in that, In step (41), the empirical formula for material removal includes: ， In the formula, This indicates the linear velocity of the polishing tool. This indicates the robot's feed rate. It is the distribution of the desired removal depth. It is the contact force that was planned in the previous step. It is the material removal coefficient.

6. The robot adaptive grinding and polishing method for complex curved surfaces according to claim 5, characterized in that, In step (43), the correction of the initial polishing speed includes: ， In the formula, It is a simulated value of the removal depth calculated based on the convolution material removal formula.

7. A robotic adaptive grinding and polishing system for complex curved surfaces, used to implement the robotic adaptive grinding and polishing method for complex curved surfaces as described in any one of claims 1-6, characterized in that, include: The main control module is used to define the workpiece boundary contour and uniform coverage area according to the curvature of each section of the workpiece. Based on the contact model, it performs boundary force-position trajectory planning to prevent overcutting on the boundary contour, surface force-position trajectory planning to uniformly cover the uniform coverage area, and global planning of the polishing line width and step length to meet the waviness requirements on the entire surface of the workpiece. In this way, the polishing path and contact force of the entire workpiece surface are obtained, and the polishing speed is calculated based on the real-time polishing amount and expected allowance of the workpiece. A polishing device is used to perform surface conformal processing on a workpiece according to the polishing path and contact force.

8. The robotic adaptive grinding and polishing system for complex curved surfaces according to claim 7, characterized in that, The polishing device includes a robot, a three-degree-of-freedom polishing flange located at the end of the robot, and a polishing disc module located on the three-degree-of-freedom polishing flange.

9. The robotic adaptive grinding and polishing system for complex curved surfaces according to claim 8, characterized in that, The three-degree-of-freedom polishing flange includes a platform and a connecting module as well as a support module. The platform and connecting module includes a moving platform (18) and a fixed platform (20) arranged at intervals. The support module includes three sets of telescopic adjustable linkage assemblies arranged symmetrically about the center of the moving platform (18) between the moving platform (18) and the fixed platform (20). One end of the telescopic adjustable linkage assembly is connected to the moving platform (18) through a ball joint, and the other end is connected to the fixed platform (20) through a revolute joint. In this way, by adjusting the length of the three sets of telescopic adjustable linkage assemblies, the moving platform (18) can move along the z-axis or rotate along the x and y axes respectively, achieving the three degrees of freedom of movement.

10. The robotic adaptive grinding and polishing system for complex curved surfaces according to claim 9, characterized in that, The telescopic adjustable linkage assembly includes a hinge component, a first drive component, a guide rail component, a slide plate (11), a rotary joint component, and a position sensing component. One end of the hinge component is connected to the moving platform (18), and the other end is fixedly connected to the first drive component. The power output shaft of the first drive component is connected to the slide plate (11). The slide plate (11) moves along the guide rail component under the drive of the first drive component, and the bottom of the slide plate (11) is connected to the fixed platform (20) through the rotary joint component. In this way, the slide plate (11) is driven by the first drive component to move along the guide rail component to adjust the distance and posture between the moving platform (18) and the fixed platform (20). The position sensing component is used to identify the movement distance of the slide plate (11).

11. The robotic adaptive grinding and polishing system for complex curved surfaces according to claim 10, characterized in that, The first driving component includes a telescopic drive motor (16), a synchronous pulley (17), and a lead screw component. The power output shaft of the telescopic drive motor (16) is connected to the synchronous pulley (17). The synchronous pulley (17) includes a driving pulley, a driven pulley, and a belt wrapped around the driving pulley and the driven pulley. The driven pulley is connected to the lead screw component, and the lead screw component is fixedly connected to the slide plate (11).

12. The robotic adaptive grinding and polishing system for complex curved surfaces according to claim 11, characterized in that, The position sensing component includes a sensor fixing strip (14), a sensing plate (13), and a sensing sensor (15) arranged along the movement direction of the slide plate (11). The sensor fixing strip (14) is fixedly connected to the guide rail component. One end of the sensing plate (13) is slidably connected to the sensor fixing strip (14), and the other end moves synchronously with the slide plate (11). There are two sensing sensors (15), which are respectively arranged on both sides of the sensing plate (13) along the movement direction of the slide plate (11), and the distance between the two sensing sensors (15) covers at least the maximum movement distance of the sensing plate (13).

13. The robotic adaptive grinding and polishing system for complex curved surfaces according to claim 12, characterized in that, The top surface of the moving platform (18) is also provided with a grinding and polishing module. The grinding and polishing module includes a grinding and polishing motor (6), a one-dimensional force sensor (5), a sensor connecting plate (4), a coupling (3), a bearing (2), and a grinding disc (1). One end of the grinding and polishing motor (6) is fixedly connected to the moving platform (18), and the other end is connected to the sensor connecting plate (4). Multiple one-dimensional force sensors (5) are evenly arranged in an array along the circumference of the grinding and polishing motor (6), and the one-dimensional force sensor (5) is located between the moving platform (18) and the sensor connecting plate (4). The power output shaft of the grinding and polishing motor (6) is connected to the coupling (3). One end of the coupling (3) is connected to the sensor connecting plate (4), and the other end passes through the bearing (2) and is connected to the grinding disc (1).

14. The robotic adaptive grinding and polishing system for complex curved surfaces according to claim 13, characterized in that, The actual processing space area of ​​the three-degree-of-freedom polishing flange is: ， ， Among them, using For the minimum length of the telescopic adjustable linkage assembly, use This is the maximum length of the telescopic adjustable linkage assembly. This refers to the actual length of the telescopic adjustable linkage assembly. The minimum rotation angle of the ball joint. The maximum rotation angle of the ball pair, This is the actual rotation angle of the ball.

15. The robotic adaptive grinding and polishing system for complex curved surfaces according to claim 14, characterized in that, The rotation angle expression of the ball joint of the moving platform is: ， in, This is the reference vector for installing the ball joint.

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