A method for progressive sizing of a spherical bearing race

Abstract

The application relates to the technical field of bearing manufacturing, and discloses a gradual shaping method for a spherical bearing ring, which comprises the following steps: continuously pressing a spherical bearing outer ring blank and synchronously collecting pressure and displacement sequences, and performing spatial domain resampling; calculating the second derivative of stiffness according to the resampled point set, determining that rigid contact is generated and terminating the pressing when a mutation threshold is reached; entering an alternating pulsation forming stage, extracting quasi-static displacement and quasi-static forming force at the lower dead point; reconstructing a quasi-static envelope line model based on the extracted data, obtaining quasi-static envelope stiffness and the second derivative of quasi-static stiffness; respectively modulating the forward feeding step and the reverse retreat step of the next period according to the above stiffness parameters; and determining that the clearance forming is up to the standard when the quasi-static envelope stiffness reaches a preset target structure stiffness. The application excludes dynamic interference, prevents inner ring contact overload, converts the clearance into stiffness for online control, and improves the pressing and forming precision.

Description

Technical Field

[0001] This invention relates to the field of bearing manufacturing technology, specifically to a progressive shaping method for spherical bearing races. Background Technology

[0002] The assembly of spherical bearings typically requires the use of a mold to apply pressure to the outer ring blank, causing it to plastically deform and wrap around the inner ring, thereby creating a specific internal clearance between the inner and outer rings. The precision of controlling this clearance directly affects the rotational flexibility and service life of the spherical bearing.

[0003] In existing continuous compression molding processes, the pressure and displacement data collected by sensors are often mixed with high-frequency interference due to complex dynamic friction and mechanical chatter of the equipment. This makes it difficult for the system to accurately obtain the material's true resistance to deformation. As the pressing depth increases, the forming resistance changes drastically when the outer ring blank covers the inner ring to the critical point of rigid contact. Because existing technologies lack accurate identification and feedback braking methods for the characteristics of this resistance change, the equipment is prone to overpressure. This transient contact overload can easily lead to microcracks in the inner ring structure.

[0004] Furthermore, the internal clearance of spherical bearings during press fitting is a physical parameter enclosed within the mold and cannot be directly measured online during processing. Currently, conventional processes rely on setting fixed maximum pressure or final displacement thresholds to control press shutdown. This open-loop, fixed threshold control method cannot accommodate the slight differences in hardness and dimensions between different batches of raw materials. When material properties fluctuate, the bearing clearance pressed according to fixed parameters is often too large or too small, ultimately resulting in low clearance forming accuracy and poor finished product consistency. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a progressive forming method for spherical bearing races, which solves the problems in existing progressive forming and pressing processes for spherical bearings, such as data acquisition being susceptible to interference from mechanical chatter and dynamic friction, overload easily occurring during rigid contact leading to micro-cracks in the inner ring, and low forming accuracy due to the difficulty in online measurement of bearing internal clearance.

[0006] To address the above problems, the present invention provides the following technical solution: This invention provides a method for progressive shaping of spherical bearing rings, comprising the following steps: During the continuous pressing of the outer ring blank of the spherical bearing, the transient pressure sequence and the transient displacement sequence in the time domain are collected simultaneously. Spatial domain adaptive resampling is performed on the time-domain transient pressure sequence and the time-domain transient displacement sequence to obtain a discrete spatial sequence point set; The second derivative of stiffness is calculated based on the discrete spatial sequence point set. When the second derivative of stiffness reaches the preset curvature change trigger threshold, it is determined that the outer ring blank of the spherical bearing and the inner ring of the spherical bearing have reached the critical point of rigid contact, and the continuous pressing is terminated. Enter the alternating pulsating forming stage, which includes forward feed and reverse retraction, and extract quasi-static displacement data and quasi-static forming force at the bottom dead center of the pulsation cycle. Based on quasi-static displacement data and quasi-static forming force, the quasi-static envelope model is reconstructed and analytically differentiated to obtain the quasi-static envelope stiffness and the second derivative of the quasi-static stiffness. The forward feed step size of the next cycle is modulated according to the quasi-static envelope stiffness, and the reverse yield step size of the next cycle is modulated according to the second derivative of the quasi-static stiffness. When the quasi-static envelope stiffness is not less than the preset target structural stiffness, the clearance forming between the outer ring blank of the spherical bearing and the inner ring of the spherical bearing is deemed to have met the standard, and the alternating pulsating forming stage is terminated.

[0007] Preferably, spatial domain adaptive resampling is performed on the time-domain transient pressure sequence and the time-domain transient displacement sequence to obtain a discrete spatial sequence point set, specifically including: Set a minimum effective spatial step size and use the transient displacement in the time domain corresponding to the initial moment as the initial spatial anchor point; When the absolute value of the difference between the current transient displacement in the time domain and the spatial anchor point is not less than the minimum effective spatial step, and the sign of the difference is consistent with the positive direction set by the downward feed, the current transient pressure in the time domain and the transient displacement in the time domain are extracted into the discrete spatial sequence point set. The temporal transient displacement triggered by the extraction at the current moment is updated to a new spatial anchor point.

[0008] Preferably, the second derivative of stiffness is calculated based on a discrete spatial sequence of point sets, specifically including: Establish a computational sliding window and retrieve the latest preset number of discrete spatial sequence point sets and incorporate them into the computational sliding window; The displacement of the discrete spatial sequence point set within the calculation sliding window is taken as the independent variable, and the pressure of the discrete spatial sequence point set within the calculation sliding window is taken as the dependent variable. A second-order continuous polynomial model is established within the calculation sliding window using a local polynomial approximation algorithm. The second-order analytical derivative of the second-order continuous polynomial model is obtained by performing second-order analytical differentiation.

[0009] Preferably, quasi-static displacement data and quasi-static forming force are extracted at the bottom dead center of the pulsation cycle, specifically including: Real-time monitoring of actual spatial position and real-time feed rate; When the actual spatial position enters the position tolerance zone of the bottom dead center position, and the absolute value of the real-time feed speed drops to no more than the preset minimum speed threshold, the motion domain lock state is triggered. In the motion domain lock state, maintain a preset dwell time window at the current bottom dead center position; Collect continuous discrete pressure data within the dwell time window and perform arithmetic mean calculation to extract the quasi-static forming force, and use the current bottom dead center position as the quasi-static displacement data.

[0010] Preferably, the quasi-static envelope model is reconstructed based on quasi-static displacement data and quasi-static forming force, and analytical differentiation is performed to obtain the quasi-static envelope stiffness and the second derivative of the quasi-static stiffness, specifically including: The extracted quasi-static displacement data and quasi-static forming force are combined into feature data pairs and pressed into the quasi-static feature sequence; Establish a macroscopic sliding window, retrieve the latest number of feature data pairs pushed onto the stack in the quasi-static feature sequence, and establish a quasi-static envelope model; The quasi-static envelope stiffness is obtained by performing first-order analytical differentiation on the quasi-static envelope model, and the second-order analytical differentiation is obtained by performing second-order analytical differentiation on the quasi-static envelope model.

[0011] Preferably, the positive feed step size of the next cycle is modulated according to the quasi-static envelope stiffness, specifically including: A non-negativity check is performed on the quasi-static envelope stiffness. When the quasi-static envelope stiffness is non-negative, the target value of the positive feed step size for the next cycle is calculated using a nonlinear exponential decay function. Furthermore, the greater the quasi-static envelope stiffness, the smaller the calculated target value of the positive feed step size; Hard-limit safety protection is implemented on the calculated target value of the forward feed step, and its value is constrained between the preset maximum allowable feed step and the minimum safe feed step.

[0012] Preferably, the reverse backoff step size of the next cycle is modulated according to the second derivative of the quasi-static stiffness, specifically including: The target value of the reverse yield step size for the next cycle is calculated using a reverse modulation control law that is positively correlated with the second derivative of the quasi-static stiffness. Furthermore, as the second derivative of the quasi-static stiffness increases, the calculated target value of the reverse yield step size is increased. The calculated reverse yield step size target value is constrained between the preset maximum safe yield amplitude and the minimum basic yield amplitude.

[0013] Preferably, determining that the clearance forming between the outer ring blank of the spherical bearing and the inner ring of the spherical bearing meets the standard specifically includes: The difference between the target structure stiffness and the quasi-static envelope stiffness of the current period is calculated to obtain the stiffness approximation deviation; When the stiffness approach deviation remains no greater than zero within a preset number of consecutive pulsation cycles, an internal trigger signal is output indicating that the forming endpoint has been reached, thus determining that the clearance forming between the outer ring blank of the spherical bearing and the inner ring of the spherical bearing has met the standard.

[0014] Preferably, after determining that the clearance forming between the outer ring blank and the inner ring of the spherical bearing has met the standard and terminating the alternating pulsating forming stage, the process further includes: At the final determined forming depth, the pressure holding stage begins and the pressure holding time is accumulated. During the pressure holding phase, the pressure value is continuously monitored. If the pressure value drops by more than the set pressure drop percentage threshold, it is determined that an abnormal pressure drop has occurred and an abnormal shutdown is triggered. If the pressure holding time reaches the preset time parameter of the process and no abnormal pressure drop occurs, then reverse zeroing is executed to return to the safe avoidance position.

[0015] Preferably, after performing the reverse zero return to the safe avoidance position, the quasi-static envelope stiffness finally reached in the current forming process, the total accumulated positive feed displacement, and the pressure decay curve of the holding stage are packaged and uploaded to a non-volatile storage medium, and the historical feature data is cleared and the state machine parameters are reset.

[0016] This invention provides a method for progressive shaping of spherical bearing rings. It has the following beneficial effects: 1. This invention converts time-domain acquisition into spatial-domain resampling based on displacement dimension, filters out overlapping data generated by mechanical flutter, and uses a local polynomial approximation algorithm to calculate the second derivative of stiffness. This process quantifies the curvature change of the forming resistance curve, thereby achieving accurate identification of the critical point of rigid contact between the inner and outer rings and timely termination of pressing down, preventing the inner ring from cracking due to contact overload.

[0017] 2. This invention employs alternating pulsating forming motions that include forward feeding and reverse retraction to release local residual stress. Simultaneously, a motion domain lock-in mechanism is set at the bottom dead center for dwell extraction. Through this step, the interference of the mechanical motion inertia of the equipment and the dynamic friction of the contact surface on the pressure sensor is eliminated, thereby obtaining the true quasi-static forming force parameters and providing a reliable data basis for subsequent stiffness calculations.

[0018] 3. This invention reconstructs the envelope model based on the extracted quasi-static data to obtain the quasi-static envelope stiffness, and transforms the internal clearance of the bearing, which cannot be directly measured online, into a structural stiffness parameter for evaluation; based on this, the forming step size of subsequent cycles is dynamically modulated, and the forming endpoint is determined by comparing it with the target stiffness, thus avoiding the control error caused by the traditional fixed threshold press-fitting method and improving the clearance forming accuracy. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the progressive shaping system architecture for spherical bearing rings according to the present invention; Figure 2 This is a flowchart of the progressive shaping method for spherical bearing rings according to the present invention; Figure 3 This is a diagram illustrating the spatial domain adaptive resampling and smoothing denoising effects of the present invention. Figure 4 This is a diagram showing the evolution of the second derivative of stiffness and the state machine switching triggering method of the present invention. Figure 5 This is a diagram of the variable parameter alternating pulsating spatial displacement trajectory of the present invention; Figure 6 This is the quasi-static envelope reconstruction and target equivalent control chart of the present invention. Detailed Implementation

[0020] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] See attached document Figure 1 and attached Figure 2 , Figure 1 This is a schematic diagram of a progressive shaping system architecture for spherical bearing races according to an embodiment of the present invention; Figure 2 This is a flowchart of a progressive shaping method for spherical bearing races according to an embodiment of the present invention. Figure 1 As shown, the present invention provides a progressive shaping system for spherical bearing rings, which may include: a precision servo electric press mechanism, a high-frequency optical grating ruler, a dynamic force sensor, and an industrial computer.

[0022] The precision servo electric press mechanism is equipped with a direct drive servo motor and a ball screw transmission assembly.

[0023] The direct-drive servo motor is connected to the press slide via a ball screw transmission assembly, and is used to drive the press slide to perform linear feed motion and alternating pulsation.

[0024] The forming mold is located below the press slide and is used to place the blank of the outer ring of the spherical bearing, which is equipped with the inner ring of the spherical bearing.

[0025] A high-frequency optical grating ruler is installed on the side of the precision servo electric press mechanism to collect displacement data of the press slide.

[0026] The dynamic force sensor is installed in the force transmission path between the press slide and the forming die to collect axial forming pressure data.

[0027] The industrial computer establishes communication connections with direct-drive servo motors, high-frequency optical grating rulers, and dynamic force sensors.

[0028] The industrial computer is equipped with low-level position and torque dual closed-loop control logic, which is used to receive sensor signals and output drive commands to the actuator.

[0029] Reference Figure 2 The present invention also provides a method for progressively shaping spherical bearing rings based on the above-mentioned progressive shaping system for spherical bearing rings, the method specifically including the following steps: In S100, the industrial computer sends a constant-speed pressing command to the direct-drive servo motor, driving the press slide to move the forming die downwards at a set base speed, forcing the spherical bearing outer ring blank to undergo free plastic rheology. During this process, the industrial computer synchronously receives the time-domain transient pressure sequence and time-domain transient displacement sequence transmitted back by the high-frequency grating ruler and dynamic force sensor at a set sampling frequency.

[0030] In S200, the industrial computer performs spatial domain adaptive resampling on the received time-domain transient pressure and displacement sequences. Using a preset minimum effective spatial step size as a threshold, the industrial computer extracts a set of discrete spatial sequence points that satisfy the displacement increment condition, constructing a spatial domain feature analysis queue.

[0031] The S300 industrial computer applies a local polynomial approximation algorithm to the data points in the spatial domain feature analysis queue to calculate the transient tangential stiffness and the second derivative of stiffness. The industrial computer monitors the numerical evolution of the second derivative of stiffness in real time. When the second derivative of stiffness reaches the preset curvature change trigger threshold, it determines that the outer ring blank of the spherical bearing and the inner ring of the spherical bearing have reached the rigid contact critical point, and generates a braking command to terminate continuous downward pressure.

[0032] In S400, the industrial computer sends variable-parameter alternating pulse commands to the direct-drive servo motor, controlling the press slide to enter a pulse forming stage that includes forward feed and reverse retraction. During this stage, the industrial computer monitors the transient speed of the press slide, triggers data latching at the bottom dead center of each pulse cycle, and extracts quasi-static displacement and quasi-static pressure data.

[0033] The S500 industrial computer reconstructs the quasi-static envelope based on continuously extracted quasi-static displacement and pressure data, and performs analytical differentiation on the quasi-static envelope to obtain the quasi-static tangential stiffness and the second derivative of the quasi-static stiffness for the current pulsation cycle. The industrial computer modulates the forward feed step size for the next cycle based on the quasi-static tangential stiffness, and modulates the reverse yield step size for the next cycle based on the second derivative of the quasi-static stiffness.

[0034] In S600, the industrial computer compares the real-time updated quasi-static tangential stiffness with the preset target structural stiffness. When the quasi-static tangential stiffness is greater than or equal to the target structural stiffness, the clearance forming is deemed satisfactory. The industrial computer then terminates the variable parameter alternating pulsation command, controls the press slide to maintain a closed-circuit pressure state at the current coordinate position, and then returns to the initial origin.

[0035] The spherical bearing ring progressive forming method provided by this invention executes high-frequency time-domain synchronous sampling logic in the initial stage to obtain basic data characterizing the physical state of the forming process. The specific operation of this stage includes the following sub-steps: S101, after receiving the system start signal, the industrial computer initializes and configures the internal control parameters. In this embodiment, the industrial computer sets the basic pressing rate of the press slide. and the system sampling frequency of the underlying data acquisition hardware. For the base downpressure rate The specific numerical settings and matching rules can be determined by those skilled in the art through conventional process tests based on the material yield strength, wall thickness, and taper of the forming die of the spherical bearing outer ring blank being processed. This calibration process is well-known in the field and will not be elaborated upon here. As a preferred method, the industrial computer will set the system sampling frequency... Configured in high-frequency mode, the specific value is usually determined by taking into account the control cycle of the actuator and the data refresh rate of the sensor. For example, it can be set between 1kHz and 10kHz so that when the material undergoes micro-lattice slip or stiffness abrupt change, the system can capture enough discrete data points to support the subsequent analytical algorithm.

[0036] S102, the low-level position control module of the industrial computer outputs position tracking commands to the direct-drive servo motor. Based on these commands, the direct-drive servo motor responds and drives the press slide via the ball screw transmission assembly at a set base pressing rate. It moves downwards at a constant speed. During this process, the press slide transmits axial thrust to the forming die, which forces the metal material of the outer ring blank of the spherical bearing to undergo free plastic flow in the area not constrained by the inner ring, and gradually shrinks and conforms radially towards the spherical contour of the inner ring of the spherical bearing.

[0037] S103, during the period when the press slide maintains a continuous downward pressing action, the industrial computer's real-time kernel is based on the system sampling frequency. A periodic hardware interrupt mechanism is triggered. During each hardware interrupt-triggered control cycle, the industrial computer reads the current pulse count value of the high-frequency grating ruler and the current analog voltage or digital communication value of the dynamic force sensor in parallel. To ensure data synchronization and the accuracy of subsequent processing, the industrial computer converts the read pulse count value into physical displacement, converts the force feedback signal into an absolute pressure value, and appends a timestamp generated by the current hardware clock to each set of data.

[0038] Considering the large amount of monitoring data generated during the forming process, the industrial computer sequentially pushes the displacement and pressure data, along with timestamps, into a memory buffer, forming a continuous one-dimensional time-domain data sequence. A cyclic overwrite or block-based transfer mechanism can be configured to prevent memory overflow. The discrete sampling time point sequence of the system operation is defined as follows: ,in This is a positive integer index number on the time axis. The interval between two adjacent sampling time points is determined by the system sampling frequency; that is, the difference between adjacent time points is equal to the reciprocal of the system sampling frequency.

[0039] At any given sampling time point At this point, the transient displacement in the time domain acquired and recorded by the system is denoted as... The time-domain transient pressure acquired and recorded synchronously is denoted as The time-domain transient displacement and time-domain transient pressure sequences generated by the aforementioned continuous acquisition actions can serve as the basic data source for characterizing the macroscopic mechanical evolution process of the progressive shaping of the spherical bearing raceway, and can also help provide underlying input data support for subsequent removal of high-frequency mechanical vibration interference and prevention of computational singularities.

[0040] In this embodiment, although high-frequency time-domain sampling can capture rich process states, under conditions where the press is at extremely low speed or faces significant forming resistance resulting in extremely slow press slide feed, there may be no effective displacement increment between consecutively acquired adjacent time points. If the discrete difference derivative is directly performed on this time-domain data, a singularity with the denominator approaching zero can easily occur because the displacement increment is less than the physical resolution of the high-frequency grating ruler. To address the aforementioned potential data processing defects, the industrial computer is equipped with a spatial domain adaptive resampling algorithm, which converts the original time-driven logic into displacement spatial-driven logic. The specific operation of this algorithm includes the following sub-steps: S201, Before performing the data resampling operation, the industrial computer determines the minimum effective spatial step size to trigger spatial recording. The minimum effective step size The specific value is usually related to the physical limits of the underlying location acquisition hardware. As a preferred setting, the system reads the physical resolution value of the high-frequency grating ruler and sets the minimum effective spatial step size. The value is set to a specific positive integer multiple of the physical resolution, for example, between 10 and 50 times the resolution. For the sensor resolution calibration and hardware frequency multiplication parameter reading and configuration, those skilled in the art can refer to conventional electrical interface manuals for instructions; the parameter reading and configuration methods are well-known in the field and will not be elaborated upon here. After the settings are complete, the system reads the data point corresponding to the initial time of the time-domain sampling sequence as the initial spatial anchor point. and the spatial domain sequence index number Initialize to 1.

[0041] S202, as high-frequency sampling in the time domain continues, the industrial computer's processing units traverse the timestamped data point by point. Transient displacement in the time domain The computing unit calculates the current transient displacement in the time domain in real time. With the recorded spatial anchor point The difference between them. Considering that high-frequency mechanical chatter in the forming environment may cause reciprocating pseudo-displacements near the origin, the system not only evaluates the displacement span when calculating the difference, but also performs sign verification for the feed direction. The specific triggering condition is set as: the current transient displacement in the time domain. With spatial anchor point The absolute value of the difference is greater than or equal to the minimum effective step size in space. Furthermore, the sign of this difference must be consistent with the positive direction set for the slider's downward feed.

[0042] The system activates the data push logic only if the current time domain data point meets the above judgment conditions; otherwise, if the spatial span threshold is not reached or the direction rebounds abnormally, the system determines that the current time domain point is in the motion stagnation or invalid flutter interval, and the computing unit directly discards it or uses it only for display purposes, thereby filtering out redundant and overlapping data that cause operational singularities at the underlying level.

[0043] S203, when the decision condition is triggered, the industrial computer will immediately... Corresponding time-domain transient displacement With time-domain transient pressure The data is extracted synchronously and pushed into a spatial domain feature analysis queue constructed from internal registers. The pushed data is then redefined as a discrete spatial sequence point set; specifically, the system denotes the currently extracted time-domain transient displacement as the [number missing]. Spatial displacement The extracted time-domain transient pressure is simultaneously denoted as the first... Space pressure .

[0044] After completing the push operation on the current data pair, the system needs to provide a new baseline for the next spatial step determination. The industrial computer updates the current transient displacement that just triggered the push operation to the new spatial anchor point, i.e., it performs an assignment operation. At the same time, let the spatial domain sequence index number Perform an increment operation of 1.

[0045] Through the aforementioned iterative resampling mapping mechanism, the system dynamically generates a set of sequential features in the memory of an industrial computer, distributed either strictly equidistantly or non-equidistantly as needed by spatial physical displacement. This resampling algorithm can adaptively shield against stagnation interference in the time dimension, providing a smooth and reliable data source that meets analytical continuity requirements for subsequent local polynomial fitting and higher-order derivative calculations, while helping to preserve the forming mechanical features.

[0046] After obtaining the discrete spatial sequence point set after the aforementioned resampling processing, if the control system directly uses the method of discrete difference between adjacent points to calculate stiffness and curvature, the inherent white noise in the sensor acquisition link and high-frequency mechanical vibration interference in the environment are often amplified during the second difference process, which may lead to the inaccurate identification of the true mechanical abrupt changes. To overcome this deficiency at the data processing level, industrial computers introduce a sliding window mechanism and a local polynomial approximation algorithm to achieve smooth filtering and continuous reconstruction of the underlying discrete data. The specific process of this processing stage includes the following sub-steps: S301, In this embodiment, the industrial computer allocates a fixed-length circular buffer within its memory region to construct a computational sliding window. The system retrieves the latest features from the spatial domain feature analysis queue in real time. Each pair of spatial sequence data is incorporated into the current sliding window. The sliding window capacity is... The specific numerical setting can be configured by those skilled in the art based on the electromagnetic noise distribution level under actual working conditions and the computing power of the microprocessor. Typically, this capacity setting needs to be combined with a preset minimum effective spatial step size so that the overall displacement span covered can encompass the expected contact critical zone characteristics; for example, it can be set to a positive integer between 5 and 20. This capacity configuration aims to maintain sufficient sample points to smooth out random fluctuations while avoiding the introduction of excessive computational phase delay. To avoid computational errors during system startup, when the number of spatial sequence point sets is insufficient... In the initial stage, the system temporarily suspends the polynomial approximation solution and maintains the current base rate pressing action until the data volume meets the window capacity requirements. During the forming process, whenever the spatial domain adaptive resampling algorithm outputs a new pair of spatial displacement and spatial pressure data, the industrial computer appends the new data pair to the front of the sliding window and simultaneously discards the oldest data pair with the oldest timestamp within the window. Through this data update logic, the sliding window can cover the working area where the press slider is located in real time.

[0047] S302, the industrial computer retains memory in the current sliding window. A local polynomial approximation algorithm is applied to a spatial sequence data pair. The system uses spatial displacement as the independent variable and spatial pressure as the dependent variable to establish a second-order continuous polynomial model within a local interval. The mathematical expression of this approximation model is as follows: ; In the formula, This represents the smoothed spatial pressure value output after model fitting. This represents the input spatial displacement variable. , and These represent the quadratic, linear, and constant terms in the second-order polynomial fitting coefficients, respectively. This model maps the originally discrete physical measurement points into continuously differentiable analytic functions, thus reducing the amplification effect of tiny noise spikes being transmitted to higher-order derivatives from a mathematical structure perspective.

[0048] S303, to solve for the unknown coefficients in the above polynomial model, the processing kernel inside the industrial computer performs matrix calculations based on the least squares method within one control cycle. Due to the large number of data points contained in the sliding window... If the number of coefficients to be determined exceeds the number of variables to be determined, the system constructs an overdetermined system of equations to find the optimal fit. This solution process follows the principle of minimizing the sum of squared residuals between all actual space pressure observations and model-predicted values ​​within the window, thereby calculating the fitting coefficients corresponding to the current moment. , and The unique solution. For matrix construction and inversion of overdetermined equations based on the least squares method, those skilled in the art can use conventional linear algebra numerical calculation programs to implement it. The specific matrix operation process is a well-known technique in this field and will not be described in detail here.

[0049] Through continuous iteration and polynomial coefficient solving within the aforementioned sliding window, the industrial computer helps to obtain a smooth function curve characterizing the stress deformation state of a local region with each spatial step update. This continuous function allows the system to directly extract the required rigid contact characteristic parameters using mathematical analytical methods, reducing the risk of misjudgment due to abnormal jumps in local data.

[0050] In this embodiment, after acquiring the local polynomial approximation model, the industrial computer extracts mechanical characteristic parameters representing the material's deformation state through analytical mathematical operations, and determines the evolution of the physical state during the forming process accordingly. The specific operations of this stage include the following sub-steps: S304, the industrial computer's processing kernel, performs first and second-order analytical differentiation on the continuous polynomial model fitted within the current sliding window. As a preferred method, the system directly differentiates the model function instead of using discrete difference calculations to obtain the transient tangent stiffness of the current region. The transient tangential stiffness reflects the real-time incremental rate of change of forming resistance with displacement, and its mathematical expression is: ; In the formula, This represents the smoothed spatial pressure value output after model fitting; This represents the input spatial displacement variable. To ensure real-time feature extraction and reduce phase delay, this input spatial displacement variable... Here, we specifically substitute the latest pushed spatial displacement data point within the current sliding window for calculation. and These represent the quadratic and linear coefficients in the aforementioned second-order polynomial fitting coefficients, respectively.

[0051] Based on this, the system continues to calculate the second derivative of the polynomial model to obtain the stiffness second derivative, which characterizes the curvature variation of the force curve. The second derivative of stiffness reflects the rate of change of transient tangential stiffness and is used to characterize the degree of nonlinear abrupt change in the internal resistance of a material. Its analytical expression is: ; Through the aforementioned mathematical analysis process, the industrial computer transforms physical feature extraction into a direct call to the underlying fitting coefficients, which to some extent helps improve the real-time performance of the computation and maintain the smoothness of the numerical values.

[0052] S305, Industrial Computer Real-Time Monitoring of Stiffness Second Derivative The numerical evolution of the curve is compared with a preset curvature mutation trigger threshold. Dynamic comparison was performed. During the free plastic rheological stage before the outer ring blank of the spherical bearing comes into contact with the inner ring, the deformation resistance of the material increases relatively slowly, and the second derivative of stiffness remains at a low level. As the press slide continues to feed, when the material of the outer ring blank completes spatial contraction and comes into physical contact with the outer surface of the inner ring, the overall forming stiffness of the system undergoes a structural jump. This macroscopic mechanical contact behavior is mathematically manifested as a significant inflection point in the force curve, causing the second derivative of stiffness to show a significant upward trend.

[0053] For curvature change trigger threshold For specific settings, those skilled in the art can extract the peak value of the second derivative at the instant of rigid contact based on the force-displacement curves of historical processing samples, and set it in conjunction with a certain safety factor. For example, 3 to 5 times the upper limit of the average second derivative in the normal free rheological stage can be taken as the trigger threshold. Such methods of threshold statistics and empirical coefficient selection based on historical data are well-known techniques in the field and will not be elaborated here.

[0054] S306, when the industrial computer determines the currently calculated second derivative of stiffness Greater than or equal to the set curvature change trigger threshold At this point, the system identifies that the outer ring blank of the spherical bearing and the inner ring of the spherical bearing have reached the critical point of rigid contact. To improve the robustness of the judgment, the system can be set to only confirm the contact state when the second derivative of stiffness on multiple consecutive spatial steps exceeds this threshold. To prevent internal micro-cracks or surface scratches from occurring on the inner ring of the spherical bearing due to overload, the control logic deployed in the industrial computer subsequently initiates a state machine switching mechanism. The industrial computer sends a braking command to the direct-drive servo motor, controlling the press slider to terminate the current flow rate and maintain a constant-speed pressing action. At this time, the system transitions from the continuous large-displacement forming stage to the subsequent alternating pulsating stage. This state machine switching helps establish corresponding operational boundaries to ensure the structural integrity of the bearing assembly.

[0055] After completing the identification of the rigid contact critical point and triggering the state machine switch, the industrial computer controls the press slide to transition from the basic constant-speed pressing mode to the variable-parameter alternating pulsating forming stage. This stage aims to gradually release the residual stress inside the material during the forming process through reciprocating micro-feeding and retracting movements. In this embodiment, its specific kinematic definition includes the following sub-steps: The S401 industrial computer's trajectory planning module establishes a discrete pulsating period sequence in memory. The period index number of the alternating pulsating process is defined as... ,in It is a positive integer and its initial value is 1. In a complete [number]th [year]... Within each pulse cycle, the mechanical motion of the press slide is decomposed into a downward forward feed phase and a subsequent upward reverse retraction phase. To provide a baseline for trajectory calculation, the system records the spatial displacement coordinates of the press slide at the instant the rigid contact critical point is identified as the initial top dead center position, denoted as . .

[0056] S402, in the During the forward feed phase of each pulse cycle, the industrial computer outputs a forward position displacement command to the direct-drive servo motor. This command drives the press slide downwards, guiding the outer ring blank of the spherical bearing further towards the inner ring of the spherical bearing. The specific target position of this action (i.e., the bottom dead center position of the current cycle) is... The positive feed step size set by the system for the current cycle. With the The position of the upper dead point at the end of each pulsation cycle It is obtained by summing the results. This is the initial positive feed step size for the pulsating start-up phase. The values ​​can be preset by those skilled in the art in combination with the yield characteristics of the metal material and the transmission accuracy of the underlying hardware. The empirical method of assigning the initial parameters is a well-known technology in the field and will not be elaborated here.

[0057] S403, when the press slide reaches the current bottom dead center position Subsequently, the industrial computer outputs a reverse position tracking command to the direct-drive servo motor, initiating the reverse retraction phase. During this phase, the press slide moves upward a specified distance, causing the forming die to disengage from the heavy-load compression state with the spherical bearing outer ring blank, thus releasing the elastic strain accumulated in the local deformation zone of the metal lattice. The endpoint coordinates of this retraction action (i.e., the new top dead center position formed in the current cycle) are... By determining the lower dead center position of the current cycle Subtract the system to get the first The reverse yield amplitude is dynamically set for each pulse cycle. The calculation shows that the initial reverse backoff amplitude serves as the activation condition for the pulsating logic. It can be initialized based on conventional material elastic recovery experimental data, and the values ​​of subsequent cycles are also controlled by dynamic variable parameter logic.

[0058] During the reciprocating alternating motion described above, the industrial computer's underlying position control loop employs an S-shaped acceleration / deceleration curve for trajectory planning and transition. The application of this nonlinear acceleration / deceleration curve helps smooth the electromagnetic torque impact of the direct-drive servo motor during forward / reverse switching, reducing mechanical chatter generated by sudden changes in direction in the ball screw drive assembly. The variable-parameter kinematic model constructed through the above steps helps the system provide corresponding spatial displacement references within each pulse cycle, thus establishing the foundational execution logic for subsequent synchronous extraction of physical features in a specific phase at the bottom dead center.

[0059] During the execution of the aforementioned alternating pulsating trajectory, when the press slide reaches the end of the forward feed phase, directly extracting the dynamic mechanical feedback at this point often results in interference from the slide's mechanical inertia and the dynamic friction between the molds. This can cause the measured data to deviate from the true material deformation resistance. To eliminate these dynamic interference factors, the industrial computer deploys a motion domain phase-locking and quasi-static data extraction mechanism in the bottom dead center region of each pulsation cycle. The specific execution steps include: S404, In this embodiment, the industrial computer reads the actual spatial position of the press slide in real time using a high-frequency optical grating ruler, and performs time-differential calculations on it to obtain the real-time feed speed of the slide. To prevent the slider from abnormally stopping before reaching the target depth due to excessive local resistance and erroneously triggering the phase-locking logic, the system presets a position tolerance zone in memory. and the minimum velocity threshold approaching zero When the actual position of the press slide enters the tolerance zone of the bottom dead center position of the current cycle (i.e., the absolute difference from the bottom dead center position is less than or equal to...), Furthermore, the absolute value of its real-time feed rate decreases to less than or equal to the minimum speed threshold. Only then will the real-time kernel of the industrial computer trigger the motion domain lock state. For extremely small speed thresholds... and position tolerance zone The specific value can be determined by those skilled in the art through conventional electrical calibration, taking into account the steady-state fluctuation characteristics of the direct-drive servo motor and the clearance of the mechanical transmission link. For example, the minimum speed threshold can be set between 0.1 mm / s and 0.5 mm / s. The specific calibration method is well-known in the art and will not be elaborated here.

[0060] S405, when the motion domain interlock state is triggered, the industrial computer sends a position holding command to the underlying position control loop, causing the press slide to maintain a brief dwell time window at the current bottom dead center position. As a preferred approach, the duration of this dwell time window is typically set in conjunction with the dynamic response characteristics of the mechanical system, for example, it can be set to the tens to hundreds of milliseconds. During this period, the press slide is in a macroscopically stationary state, and the inertial force generated by the mechanical transmission system and the dynamic friction force on the contact surface between the forming die and the outer ring blank of the spherical bearing are gradually attenuated. With the elimination of the aforementioned dynamic disturbance factors, the underlying force state of the system changes from dynamic to quasi-static. During this period, the industrial computer continuously reads the high-frequency feedback signal from the dynamic force sensor and adjusts the dwell time window accordingly. The continuously discrete pressure data collected within the window are fed into a feature analysis queue for a specific period. Assume that a total of [number missing] data are collected within this window. 1 valid pressure data point, denoted as follows: , where positive integer index Increasing from 1 to .

[0061] S406, to further reduce the impact of the sensor's underlying electrical white noise on the value of a single sampling point, the industrial computer processes the data stored in the feature analysis queue. The arithmetic mean of the pressure data points is calculated to extract the representative value for the current pressure data point. Quasi-static forming force of the physical state at the dead point under one pulsation cycle The specific solution logic is as follows: the system will collect data within the dwell time window. Discrete pressure transient acquisition value Perform cumulative summation, and then divide the sum by the total number of valid data points. Thus, the quasi-static forming force of that period can be calculated. .

[0062] Through the aforementioned motion domain phase-locking and average value calculation operations, the system obtains quasi-static mechanical characteristics that exclude interference from system inertia, dynamic friction, and high-frequency electrical noise. This characteristic data can largely reflect the actual compressive resistance of the outer ring material of the spherical bearing at a specific displacement depth under the current pulsation cycle, and helps to provide a basic static physical reference for the subsequent control algorithm to dynamically adjust the pulsation parameters of the next cycle.

[0063] In this embodiment, as the alternating pulsating forming stage continues, the industrial computer successively extracts the corresponding quasi-static forming forces at the bottom dead center of each pulsation cycle. To macroscopically reflect the evolution trend of the material's resistance to deformation throughout the entire pulsating forming stage, the system needs to reconstruct these discrete single-point features into a continuous quasi-static envelope and extract key physical parameters from it. The specific operations of this reconstruction and analytical extraction include the following sub-steps: The S501 industrial computer establishes a quasi-static feature sequence in its global data area of ​​memory. Whenever the... After the motion domain phase-locking and quasi-static data extraction logic for each pulse cycle is completed, the system will determine the lower dead center position of the current cycle. The quasi-static forming force extracted during this period The data are combined to form two-dimensional feature data pairs that include the mapping relationship between position and mechanics, and then pressed into the aforementioned quasi-static feature sequence. On a macroscopic scale, this series of data pairs composed of bottom dead center features forms a forming envelope curve in the two-dimensional coordinate system that is stripped of dynamic inertia and high-frequency friction interference. This envelope curve can largely reflect the material deformation resistance response of the spherical bearing outer ring blank under pure physical extrusion conditions as the feed depth increases.

[0064] S502, in order to evaluate the transient rate of change of material deformation resistance in subsequent control, the system needs to process the discrete envelope point set into a continuous form. As a preferred approach, the industrial computer is configured with a capacity of [missing information - likely a capacity value]. The macroscopic sliding window. Regarding the capacity of the macroscopic sliding window. The specific settings can be configured by those skilled in the art, taking into account the size of the pulse step size and the desired smoothness. Typically, it can be set to a positive integer covering 3 to 10 pulse cycles. The system retrieves the latest pushed sequence from the stack in real time. Using a set of characteristic data pairs, with the position of the dead center at the bottom of the cycle as the independent variable and the quasi-static forming force as the dependent variable, a quasi-static envelope model is established using a local polynomial approximation algorithm. Its second-order polynomial mathematical expression is: ; In the formula, This represents the continuous envelope forming force output after approximation fitting; This represents the input spatial location variable; , and These represent the quadratic coefficient, linear coefficient, and constant term in the quasi-static envelope fitting coefficients, respectively. The least-squares matrix solution process for the fitting coefficients within this sliding window can be implemented using conventional numerical calculation programs by those skilled in the art; its underlying algebraic operation logic is well-known in the field and will not be elaborated upon here.

[0065] To avoid algorithmic logic dead zones during the initial stage of alternating pulse startup, and considering that the cumulative number of sample points in the first few pulse cycles may be less than the set window capacity... Industrial computers are equipped with initial protection mechanisms. (This is in contrast to situations where data volume is insufficient.) During this phase, the system temporarily suspends the high-order polynomial fitting and instead uses the discrete difference quotient of two adjacent pulsating cycles (i.e., the difference between the quasi-static forming force of the current cycle and the previous cycle divided by the corresponding difference in the bottom dead center position) to temporarily replace the calculation of the curve change rate until the amount of sequence data meets the capacity requirement of the sliding window.

[0066] S503, in obtaining the current number After establishing a quasi-static envelope model for a given period, an industrial computer performs first-order analytical differentiation on the continuous polynomial to extract the quasi-static envelope stiffness, which characterizes the system's macroscopic deformation resistance. This parameter reflects the actual rate of increase in forming resistance with feed depth under conditions excluding dynamic disturbances, and is an important indicator for evaluating whether the material has reached its plastic flow limit. Its analytical derivative formula is: ; In the formula, For the system in the first The quasi-static envelope stiffness is obtained through analytical calculation of the current pulsation cycle; this calculation process will use the current pulsation cycle as the basis for the calculation. The lower dead point position of each pulsation cycle Substitute it into the differentiated expression as a positional variable; and These are the coefficients of the quadratic term and the coefficients of the linear term obtained from the aforementioned window fitting solution, respectively.

[0067] Based on this, the system continues to perform second-order analytical differentiation on the quasi-static envelope model to extract the second-order derivative of the quasi-static stiffness, which characterizes the degree of nonlinear abrupt change in forming resistance. Its analytical derivative formula is: ; Through the aforementioned data processing path—from discrete feature points to fitted envelopes and then to analytical differentiation—the industrial computer obtains smooth stiffness and curvature characteristics with clear physical meaning. This analytical characteristic based on quasi-static data helps reduce computational abrupt changes caused by mechanical vibrations during conventional press-fitting processes, thus establishing a corresponding state feedback benchmark for subsequent adaptive adjustment of feed and retraction bidirectional pulsation parameters and prediction of forming endpoints.

[0068] After obtaining the quasi-static envelope stiffness characterizing the material's macroscopic deformation resistance, the industrial computer incorporates this physical characteristic into a closed-loop control loop to dynamically update the subsequent alternating pulsating trajectory parameters. The specific control logic for this stage includes the following sub-steps: S504, In this embodiment, the control program inside the industrial computer controls the current... Quasi-static envelope stiffness per period Real-time evaluation is performed. During the shrinkage process of the outer ring blank of the spherical bearing to cover the inner ring, the macroscopic deformation resistance of the material typically exhibits a non-linear increasing trend as the internal assembly clearance gradually disappears. If a constant positive feed step size is continuously used throughout the pulsating forming stage, when the local material stiffness increases significantly, the system is prone to generating transient overload extrusion stress in the bottom dead center region, which may increase the risk of microcracks or surface damage inside the spherical bearing. The system introduces a reverse modulation mechanism: when an increase in quasi-static envelope stiffness is detected, the positive feed step size of the next cycle is correspondingly reduced; when the stiffness is at a low level, a larger feed step size is maintained, thereby maintaining appropriate processing efficiency while ensuring structural safety.

[0069] To avoid algorithm divergence in the extreme region caused by simple linear proportional control, the industrial computer uses a nonlinear exponential decay function to construct the aforementioned inverse modulation control law. Considering that transient stiffness negative values ​​may be calculated during the actual polynomial fitting and differentiation process due to local data fluctuations or noise interference, the system aligns the static envelope stiffness before substituting it into the exponential equation. Perform a non-negativity check. If a negative value is detected, the control logic will force it to zero or take a valid positive value from the previous cycle to prevent a control disaster caused by a surge in feed step size due to an explosion of negative powers in exponential operations. The system then calculates the next execution cycle (i.e., the [number]th cycle) accordingly. Positive feed step size (per cycle) Its mathematical expression is: ; In the formula, Indicates the system is the first The target value of the positive feed step size is calculated from each pulse cycle; and These represent the system's preset maximum allowable feed step size and minimum safe feed step size, respectively. The stiffness modulation sensitivity coefficient set in the control logic is used to adjust the rate at which the feed step size decreases as stiffness increases. The first one obtained from the aforementioned analytical calculation Quasi-static envelope stiffness per cycle; is the base of the natural logarithm.

[0070] For the boundary parameters in the aforementioned control law, those skilled in the art can calibrate them by combining the specific equipment displacement resolution and the conventional forming process window of the material. For example, It can usually be set between 0.5 mm and 2.0 mm to ensure initial propulsion efficiency; The base value can be set between 0.01 mm and 0.05 mm. This base value setting helps the system maintain a small amount of physical propulsion even in high-stiffness regions, reducing the risk of control program deadlock due to the calculation step size returning to zero. For The specific value can be normalized and adapted by extracting the order of magnitude of stiffness changes in historical processing data. Such conventional control parameter tuning methods are well-known technologies in this field and will not be elaborated here.

[0071] S506, after completing the solution of the above nonlinear equations, to prevent the calculated values ​​from exceeding the limits due to transient jumps in sensor data under extreme operating conditions, the industrial computer performs a process check on the calculated values ​​in its underlying software. Implement hard-limiting safety protection. The system determines whether the target value is within... Within the set range; if a value exceeds the limit, it is forcibly constrained to the corresponding upper and lower boundary values. The feed step size data after boundary verification is then pushed into the execution queue of the underlying position control loop. When the first... During the forward feed phase of each pulse cycle, the direct-drive servo motor drives the press slide according to the updated step size command. Through the parametric modulation based on real-time physical feature feedback, the system can adaptively adjust the amount of mechanical displacement applied each time during the variable local plastic forming process, which helps to provide a relatively smooth mechanical transition boundary for the subsequent approach to the forming endpoint.

[0072] In the S507 industrial computer, after calculating the forward feed step size for the next cycle, it simultaneously executes reverse yield step size modulation logic based on the second derivative of quasi-static stiffness. In alternating pulsating forming, a significant increase in the second derivative of stiffness often indicates rapid work hardening or stress concentration in localized materials. To fully release the internal distortion stress in this region and prevent damage to the inner ring of the spherical bearing, the system sets a threshold when the second derivative of quasi-static stiffness... When the value increases, the reverse retraction step size of the next cycle increases accordingly; conversely, if the forming process is smooth, a smaller retraction amplitude is maintained to ensure processing efficiency. The mathematical expression for its reverse modulation control law is: ; In the formula, Indicates the system is the first The target value of the reverse yield step size is calculated from each pulse cycle; and These represent the preset maximum safety clearance and minimum basic clearance, respectively; The yield gain coefficient is used to calibrate the system and adjust the sensitivity of the yield step size to changes in curvature. This is the second derivative of the quasi-static stiffness extracted for the current period.

[0073] The industrial computer calculates the reverse backoff step size. Similar to the aforementioned positive feed step size They are pushed together into the execution queue of the underlying position control loop, forming the first... A complete variable-parameter pulsation command for each cycle. Through independent adaptive decoupling control of bidirectional step sizes, the system can effectively balance structural safety and press-fitting efficiency as it approaches the forming endpoint.

[0074] In the manufacturing process of spherical plain bearings, the internal clearance of the product is an important quality parameter for measuring the forming quality. However, under the condition of plastic extrusion with the mold closed, this clearance parameter is an implicit physical quantity that is difficult to measure directly online due to the obstruction of the metal blank. Therefore, in this embodiment, the industrial computer converts the geometric clearance control target into mechanical state monitoring, and determines the forming endpoint by dynamically comparing the structural stiffness obtained from the aforementioned analysis. The specific execution logic of this control process includes the following sub-steps: S601, the control kernel of the industrial computer, retrieves a preset forming process formula file during the initialization phase. This file stores the critical physical reference values ​​characterizing the finished product's clearance compliance, i.e., the target structural stiffness. During the alternating pulsating forming stage, as the material of the outer ring blank of the spherical bearing gradually shrinks inward and fits against the internal components, the macroscopic deformation resistance of the entire assembly gradually increases. By setting a target structural stiffness, the system can assess whether the internal structure has reached the expected compact state when it reaches a specific resistance level.

[0075] S602, regarding the target structural stiffness The specific methods for obtaining and setting these parameters can be comprehensively calibrated by combining offline data from finished product clearance measurements, feature point extraction from force-displacement curves, and finite element mechanical simulation analysis. This empirical calibration and numerical derivation method, which uses offline test samples to infer online stress parameters, is a well-known technique in the field and will not be elaborated upon here.

[0076] S603, as the variable parameter alternating pulsating execution sequence continues to advance, each time the industrial computer calculates the current number of iterations through analytical differentiation... Quasi-static envelope stiffness per period Subsequently, the system incorporates this real-time characteristic parameter into the forming termination determination loop. The control program then uses the preset target structural stiffness... Subtract the current quasi-static envelope stiffness The stiffness approximation deviation for the current period is calculated in real time. This is used to quantify the physical gap between the current state and the ideal final shape.

[0077] The S604 industrial computer monitors stiffness approximation deviation in real time during each pulse cycle's data processing tick. The numerical evolution of the spherical bearing. In the early and middle stages of pulsating forming, due to the existence of a certain clearance between the outer ring blank of the spherical bearing and the internal components, the system as a whole exhibits relatively low resistance to deformation. At this time, the stiffness approximation deviation is usually a large positive value. As the extrusion depth increases, the material density increases, the quasi-static envelope stiffness gradually approaches the target value, and the deviation value continuously decreases.

[0078] S605, when the industrial computer determines the stiffness approximation deviation for the current cycle. When the quasi-static envelope stiffness is less than or equal to zero, the control logic initially identifies that the current quasi-static envelope stiffness has reached or exceeded the set target structural stiffness. To prevent false shutdowns caused by sudden increases in stiffness due to localized material hard spots or high-frequency noise from sensors, the system introduces a state debouncing confirmation mechanism. Industrial computers require continuous... Within one pulse cycle (here) The sampling frequency of the device can be set to, for example, a positive integer from 3 to 5, to determine the stiffness approximation deviation. Only when all clearances remain less than or equal to zero is the final forming endpoint confirmed. This physical state transition indicates that the plastic rheological changes in the outer ring blank of the spherical bearing have reduced the internal assembly clearance to within the design tolerance range. Based on this determination, the industrial computer's underlying state machine immediately outputs an internal trigger signal indicating that the forming endpoint has been reached. This trigger signal serves as a stop command for the entire press-fitting control process, helping the system to promptly terminate the subsequent forward feed action of the direct-drive servo motor. This provides the corresponding logical criteria for cutting off the extrusion power applied to the forming die and transitioning to the holding or unloading stage.

[0079] After determining that the forming endpoint has been reached and outputting a trigger signal, the system needs to perform a series of finishing control operations to solidify the geometry and prepare for the next processing cycle. The specific execution logic of this control process includes the following sub-steps: S606, in this embodiment, after the industrial computer receives the internal trigger signal indicating that the forming endpoint has been reached, it controls the bottom position control ring to freeze the current displacement command, so that the press slide remains relatively stationary at the final determined forming depth, thereby transitioning from the alternating pulsation stage to the holding pressure process. As a preferred method, the industrial computer then starts its built-in high-precision timer to accumulate the holding pressure time. After a metal material undergoes deep plastic deformation, its crystal lattice usually retains a certain elastic recovery tendency. By setting a reasonable process holding pressure time parameter (for example, it can be set between 1 and 3 seconds based on material characteristics), it helps to better release and redistribute the local residual stress in the outer ring of the spherical bearing, thereby reducing the amount of workpiece springback after the mold opens. During this period, the industrial computer continuously monitors the feedback values ​​of the dynamic force sensor. To prevent dead zones in algorithm control, the system introduces a pressure holding abnormal drop monitoring mechanism. If a transient drop in pressure value that exceeds the normal stress relaxation range is detected (for example, the pressure drop exceeds a specific percentage threshold of the set peak value within tens of milliseconds, which can usually be set in combination with the attenuation limit of the material's normal stress relaxation curve, for example, set to 10% to 20%), the system determines that there may be hidden cracking of the material or failure of the mold structure, and will immediately trigger an abnormal shutdown interruption and illuminate the hardware alarm signal.

[0080] S607: When the accumulated holding time of the timer reaches the preset time parameter and no abnormal pressure drop occurs, the holding phase ends normally. The industrial computer then sends a reverse zero-return motion command to the direct-drive servo motor. This command controls the press slide to rapidly rise upwards along a preset unloading speed curve until it returns to the safe avoidance position calibrated at the beginning of the processing cycle (usually the mechanical origin of the equipment). During unloading, the forming mold completely disengages from the press-formed spherical bearing product, completing the demolding operation. For the speed and acceleration control strategy in the return phase, those skilled in the art can use conventional trapezoidal or S-shaped speed planning algorithms in conjunction with production cycle requirements. The underlying servo kinematic planning logic is well-known in the field and will not be elaborated here.

[0081] In step S608, after the press slide safely returns to the target avoidance position, the industrial computer performs a process reset and production data persistence operation for the control state. To prevent data loss due to network fluctuations in the industrial field, the system prioritizes structurally packaging the key physical parameters extracted during the complete pressing process (including the final achieved quasi-static envelope stiffness, the cumulative total positive feed displacement, and the pressure decay curve during the holding phase) and attempts to upload them to the data server of the enterprise manufacturing execution system. Only after confirming receipt of a successful handshake signal from the server, or after securely writing the data to local non-volatile storage media in case of network anomalies, can the industrial computer reset the global data area allocated in its memory. This reset operation includes clearing the aforementioned pulsation cycle sequence, feature analysis queue, and historical feature data in the sliding window, and fully restoring the state machine parameters to standby mode. This operation helps eliminate the interference of residual cached data on the next calculation cycle, providing an initial data environment for the pressing cycle of the next workpiece. Through the reliable recording of the above data and the safe switching of states, this structured process state data provides a corresponding data foundation for subsequent product quality traceability and offline optimization of process parameters.

[0082] Specific application examples: 1. Implementation Background and Processing Targets: The object being processed is a certain type of aerospace self-lubricating radial spherical plain bearing (outer diameter 120mm). The outer ring blank is made of 304 stainless steel (good plasticity), and the inner ring is made of GCr15 bearing steel (high hardness but prone to brittleness).

[0083] Technological challenges: After shaping, the outer ring must tightly wrap around the inner ring, and the spherical sliding clearance between the inner and outer rings must be strictly controlled between 0.02mm and 0.05mm. Excessive clearance results in a loose bearing, while insufficient clearance (or interference fit) can lead to micro-cracks in the inner ring or substandard friction torque.

[0084] 2. Implementation process (in conjunction with the explanation of the steps and accompanying drawings of this invention): Initial parameter settings and data resampling smoothing (S100-S200): Industrial computer initialization, setting the servo press base pressing rate mm / s, sampling frequency kHz. Spatial adaptive resampling step size Set to 0.01mm.

[0085] Reference Figure 3(Spatial Domain Adaptive Resampling and Smoothing Denoising Effect Diagram) During the free plastic rheological stage of the press being pressed at a constant speed of 5 mm / s, the original pressure and displacement data collected by the sensor over time at high frequency are shown as the light gray jagged line (representing the original high-frequency time domain data) in the figure. Due to mechanical chatter and electrical noise, this line exhibits strong spikes and overlaps, which can easily produce computational singularities when directly used for derivative calculations. Therefore, the system extracts the original data according to a minimum effective step size of 0.01 mm to construct a spatial domain feature analysis queue.

[0086] Free plastic rheological stage and stiffness abrupt change identification (S300): The press continues to press down at a constant speed, causing the outer ring blank to undergo free deformation. An industrial computer uses a local polynomial approximation (sliding window) to approximate this. Establish a second-order continuous polynomial model The fit generated Figure 3 The thick black solid line in the image (representing the spatial resampling plus polynomial approximation curve) completely filters out the light gray noise and truly reflects the macroscopic compressive resistance law of the blank.

[0087] Subsequently, the system performs second-order analytical differentiation on the model in real time to calculate the second derivative of the stiffness. . Reference Figure 4 (Evolution of the second derivative of stiffness and the triggering diagram of state machine switching). Figure 4 The thick black solid line represents the second derivative of the analytical stiffness, reflecting the severity of the bending (curvature) of the force curve. Before contact, this value is extremely low and stable; when the displacement reaches... Figure 3 The rigid contact critical point represented by the vertical black dashed line (i.e., the displacement coordinate at the instant when the inner wall of the outer ring blank just contacts the inner bearing ring, approximately 8.5mm) is... Figure 4 The thick black solid line in the middle rises sharply, instantly surging to 120kN / mm. 2 .

[0088] Figure 4 The horizontal black dashed line in the image represents the pre-set curvature change trigger threshold within the industrial computer. (Set as 80kN / mm) 2 When the thick black solid line breaks through this safety red line upwards, the system immediately determines that the inner and outer rings have made physical contact and instantly triggers a braking command to stop the constant speed downward pressure, preventing the high-hardness inner bearing ring from being crushed.

[0089] Variable parameter alternating pulsation stage and feature extraction (S400-S500): The system has switched to pulse mode. (Refer to...) Figure 5(Variable parameter alternating pulsating spatial displacement trajectory diagram), the black sawtooth broken lines in the diagram represent the mechanical motion trajectory of the press slide after entering the pulsating forming stage. Each downward broken line segment represents the slide's forward feed to continue extruding the blank; each upward broken line segment represents the slide's reverse retraction to release local stress concentration.

[0090] In the initial stage, the forward feed step size mm, reverse yield step size mm. The press will deliberately pause for 100ms each time it presses down to the deepest point (bottom dead center). Figure 5 The gray-filled circles in the diagram represent bottom dead center latch-up data extraction, which means that data extraction latching is triggered within this relatively static time window. This completely eliminates the interference of mechanical motion inertia and dynamic sliding friction on the pressure sensor, extracting the pure quasi-static forming force. .

[0091] As the pulsation cycle progresses, the material undergoes work hardening, and the system executes a reverse modulation control law based on stiffness characteristics: the target value of the forward feed step size... Target value of reverse retreat step .like Figure 5 As shown in the broken line trajectory, based on the increase in internal stiffness, the system adaptively reduces the downward feed step size (the downward extension of the broken line becomes smaller and smaller, for example, the positive step size is reduced to 0.08 mm) and increases the yield step size to 0.01 mm to fully release residual stress.

[0092] Target equivalence, pressure holding unloading and endpoint determination (S600): Reference Figure 6 (Quasi-static envelope reconstruction and target equivalent control chart), the gray-filled circular scatter points in the figure represent discrete quasi-static feature points for each period, corresponding to... Figure 5 The clean mechanical data extracted during the dwell period at the bottom dead center are shown. The horizontal axis represents the ultimate compression depth of the current cycle, and the vertical axis represents the actual compressive resistance of the material after excluding dynamic disturbances.

[0093] Industrial computers approximate these discrete gray dots using a quadratic polynomial algorithm. These connect to form a smooth and continuous macroscopic force curve, i.e. Figure 6 The thick black solid line in the middle (represents the quasi-static force envelope curve).

[0094] The system calculates the slope of this thick solid line in real time by differentiating it, and obtains the quasi-static envelope stiffness. And calculate the stiffness approximation deviation. The system will calculate the envelope stiffness in real time. Offline calibration of target structural stiffness Dynamic comparison was performed at 250 kN / mm. At the 14th pulsation cycle, the system determined the stiffness approximation deviation. This means that the stiffness approaches and reaches the target value, and after three consecutive cycles of anti-shake confirmation, the system determines that the internal clearance has shrunk to the perfect standard of 0.03mm.

[0095] The system immediately terminated the processing pulse command, held the pressure at the current depth for 2.5 seconds, unloaded, and returned to the origin. Random inspection of the finished products showed that the clearance was perfectly within 0.03mm, with no microcracks.

[0096] Experimental verification and effect comparison: To verify the effectiveness of the present invention, a comparative experiment was conducted on the same hardware platform (100-ton precision servo press). 200 sets of spherical plain bearing blanks from the same batch were randomly divided into two groups of 100 sets each.

[0097] Control group (traditional process): The traditional displacement force dual-threshold constant speed continuous pressing method is adopted. Pressing is carried out at a constant speed of 2mm / s until the set peak pressure (e.g., 800kN) or fixed displacement is reached, and then the pressure is maintained and unloaded directly.

[0098] Experimental group (process of this invention): adopts the method of "spatial domain resampling + stiffness mutation identification + variable parameter micro-pulsation + quasi-static envelope control".

[0099] Experimental Results Statistical Table: Conclusion: The present invention completely solves the industry pain points of easy crushing of the inner ring and poor implicit control accuracy of clearance in traditional processes by transforming the complex nonlinear physical contact process into rigorous mathematical analytical features (first and second derivative extraction) and introducing real-time feature feedback of variable parameter alternating pulsation.

Claims

1. A method for progressive shaping of spherical bearing rings, characterized in that, Includes the following steps: During the continuous pressing of the outer ring blank of the spherical bearing, the transient pressure sequence and the transient displacement sequence in the time domain are collected simultaneously. Spatial domain adaptive resampling is performed on the time-domain transient pressure sequence and the time-domain transient displacement sequence to obtain a discrete spatial sequence point set; The second derivative of stiffness is calculated based on the discrete spatial sequence point set. When the second derivative of stiffness reaches the preset curvature change trigger threshold, it is determined that the outer ring blank of the spherical bearing and the inner ring of the spherical bearing have reached the rigid contact critical point, and the continuous pressing is terminated. Enter the alternating pulsating forming stage, which includes forward feed and reverse retraction, and extract quasi-static displacement data and quasi-static forming force at the bottom dead center of the current pulsation cycle; Based on the quasi-static displacement data and the quasi-static forming force, the quasi-static envelope model is reconstructed and analytically differentiated to obtain the quasi-static envelope stiffness and the second derivative of the quasi-static stiffness. The forward feed step size of the next cycle is modulated according to the quasi-static envelope stiffness, and the reverse yield step size of the next cycle is modulated according to the second derivative of the quasi-static stiffness. When the quasi-static envelope stiffness is not less than the preset target structural stiffness, it is determined that the clearance forming between the outer ring blank of the spherical bearing and the inner ring of the spherical bearing has met the standard and the alternating pulsating forming stage is terminated.

2. The progressive shaping method for spherical bearing rings according to claim 1, characterized in that, The step of performing spatial domain adaptive resampling on the time-domain transient pressure sequence and the time-domain transient displacement sequence to obtain a discrete spatial sequence point set specifically includes: Set a minimum effective spatial step size, and use the time-domain transient displacement corresponding to the initial moment in the time-domain transient displacement sequence as the initial spatial anchor point; When the absolute value of the difference between the current transient displacement in the time domain and the spatial anchor point is not less than the minimum effective spatial step, and the sign of the difference is consistent with the positive direction set for downward feed, the current transient pressure in the time domain and the transient displacement in the time domain are extracted into the discrete spatial sequence point set. The temporal transient displacement triggered by the extraction at the current moment is updated to a new spatial anchor point.

3. The progressive shaping method for spherical bearing rings according to claim 1, characterized in that, The calculation of the second derivative of stiffness based on the discrete spatial sequence point set specifically includes: Establish a computational sliding window, and retrieve the latest preset number of discrete spatial sequence points and incorporate them into the computational sliding window; The displacement of the discrete spatial sequence point set within the calculation sliding window is taken as the independent variable, and the pressure of the discrete spatial sequence point set within the calculation sliding window is taken as the dependent variable. A second-order continuous polynomial model is established within the calculation sliding window using a local polynomial approximation algorithm. The second-order analytical derivative of the stiffness is obtained by performing second-order analytical differentiation on the second-order continuous polynomial model.

4. The progressive shaping method for spherical bearing rings according to claim 1, characterized in that, The extraction of quasi-static displacement data and quasi-static forming force at the bottom dead center of the pulsation cycle specifically includes: The displacement data collected in real time during the alternating pulsating forming stage is used as the actual spatial position, and the real-time feed speed is calculated based on the time change rate of the actual spatial position for real-time monitoring. When the actual spatial position enters the position tolerance zone of the lower dead center position, and the absolute value of the real-time feed speed drops to no more than the preset minimum speed threshold, the motion domain lock state is triggered. In the motion domain lock state, maintain a preset dwell time window at the current bottom dead center position; Collect continuous discrete pressure data within the dwell time window and perform arithmetic mean calculation to extract the quasi-static forming force, and use the current bottom dead center position as the quasi-static displacement data.

5. The progressive shaping method for spherical bearing rings according to claim 1, characterized in that, The process of reconstructing the quasi-static envelope model based on the quasi-static displacement data and the quasi-static forming force, and performing analytical differentiation to obtain the quasi-static envelope stiffness and the second derivative of the quasi-static stiffness, specifically includes: The extracted quasi-static displacement data and the quasi-static forming force are combined into a feature data pair and pressed into a quasi-static feature sequence; Establish a macroscopic sliding window, retrieve a preset number of feature data pairs that are latest pushed onto the stack in the quasi-static feature sequence, and establish a quasi-static envelope model; The quasi-static envelope stiffness is obtained by performing a first-order analytical derivative on the quasi-static envelope model, and the second-order derivative of the quasi-static stiffness is obtained by performing a second-order analytical derivative on the quasi-static envelope model.

6. The progressive shaping method for spherical bearing rings according to claim 1, characterized in that, The step of modulating the positive feed step size of the next cycle according to the quasi-static envelope stiffness specifically includes: A non-negativity check is performed on the quasi-static envelope stiffness. When the quasi-static envelope stiffness is non-negative, the target value of the positive feed step size for the next cycle is calculated using a nonlinear exponential decay function. Furthermore, the greater the quasi-static envelope stiffness, the smaller the calculated target value of the positive feed step size; Hard limiting safety protection is implemented on the calculated forward feed step size target value, constraining the value of the forward feed step size target value between the preset maximum allowable feed step size and minimum safe feed step size.

7. The method for progressive shaping of spherical bearing rings according to claim 1, characterized in that, The step of modulating the reverse backoff step size of the next cycle according to the second derivative of the quasi-static stiffness specifically includes: The target value of the reverse backoff step size for the next cycle is calculated using a reverse modulation control law that is positively correlated with the second derivative of the quasi-static stiffness. Furthermore, as the second derivative of the quasi-static stiffness increases, the calculated target value of the reverse yield step size is increased. The calculated target value of the reverse yield step size is constrained between the preset maximum safe yield amplitude and the minimum basic yield amplitude.

8. The progressive shaping method for spherical bearing rings according to claim 1, characterized in that, The determination that the clearance forming between the outer ring blank of the spherical bearing and the inner ring of the spherical bearing meets the standard specifically includes: The difference between the target structure stiffness and the quasi-static envelope stiffness of the current period is calculated to obtain the stiffness approximation deviation; When the stiffness approximation deviation remains no greater than zero within a consecutive preset number of pulsation cycles, it is confirmed that the quasi-static envelope stiffness has reached the target structural stiffness, and an internal trigger signal indicating the arrival of the forming endpoint is output, determining that the clearance forming between the outer ring blank of the spherical bearing and the inner ring of the spherical bearing has met the standard.

9. The progressive shaping method for spherical bearing rings according to claim 1, characterized in that, After determining that the clearance forming between the outer ring blank and the inner ring of the spherical bearing meets the standard and terminating the alternating pulsating forming stage, the process further includes: At the final determined forming depth, the pressure holding stage begins and the pressure holding time is accumulated. During the pressure holding phase, the pressure value is continuously monitored. If the pressure value drops by more than the set pressure drop percentage threshold, it is determined that an abnormal pressure drop has occurred and an abnormal shutdown is triggered. If the pressure holding time reaches the preset time parameter of the process and no abnormal pressure drop occurs, then reverse zeroing is performed to return to the safe avoidance position.

10. The method for progressive shaping of spherical bearing rings according to claim 9, characterized in that, After performing the reverse zero-return to the safe avoidance position, the quasi-static envelope stiffness finally reached in the current forming process, the total accumulated positive feed displacement, and the pressure decay curve of the holding stage are packaged and uploaded to a non-volatile storage medium, and the historical feature data is cleared and the state machine parameters are reset.

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