Process optimization method based on time-varying honing force model and honing tooth vibration characteristic analysis

Abstract

The invention belongs to the technical field of gear machining, and particularly relates to a process optimization method based on a time-varying honing force model and honing vibration characteristic analysis. Reversing staying duration parameters of a workpiece gear in axial reciprocating motion are introduced, the reversing staying duration delta t is mapped into the axial feeding amount fz through a displacement function, the influence of the servo motor starting and stopping dynamic process on honing force is accurately simulated, a gear honing time-varying honing force model and a gear honing vibration dynamics model are built through a concentrated mass method, and honing force is obtained. The two models are used for simulation calculation, and vibration displacement sequences under different reversing staying durations can be systematically analyzed, so that reversing staying duration parameters can be optimized according to the vibration displacement degree, the reversing impact vibration amplitude is reduced, the blank of systematic research on the influence of the reversing staying duration parameters on the process stability is filled, and the method is suitable for large-scale popularization and application. And the reliability and the surface quality consistency of the gear honing process in high-precision gear machining are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of gear processing, and in particular relates to a process optimization method based on a time-varying honing force model and honing vibration characteristic analysis. Background Art

[0002] Honing, a process for finishing hardened gears, effectively improves tooth surface texture and is a common method for achieving high-speed, low-noise transmission gears. During the honing process, the honing wheel and the workpiece gear mesh and roll at a preset axial angle. The abrasive grains on the honing wheel apply pressure to the workpiece tooth surface while sliding relative to it, removing excess material from the workpiece tooth surface.

[0003] The contact state and honing thickness between the honing wheel and the workpiece gear constantly change from engagement to engagement, and the magnitude and direction of the honing force also change accordingly. This is commonly referred to as a time-varying honing force. This time-varying honing force not only affects machining accuracy but can also stimulate self-excited vibrations in the machine tool, thereby reducing the stability of the honing process and affecting machining quality. Furthermore, during oscillatory honing, the workpiece's axial reciprocating motion generates additional vibration shocks during its reversing process, further exacerbating the instability of the machining system. However, there is currently a lack of systematic research on the concept, optimization methods, and impact of the reversing dwell parameters of honing machine tools on vibration characteristics. This, to a certain extent, limits the application of this process in high-precision gear manufacturing. Summary of the Invention

[0004] In order to solve at least one of the technical problems mentioned in the background technology, the purpose of this application is to provide a process optimization method based on a time-varying honing force model and honing vibration characteristic analysis.

[0005] The technical solution provided by the present invention is:

[0006] A process optimization method based on a time-varying honing force model and honing vibration characteristic analysis is applicable to a honing system including a honing wheel, a workpiece gear, and a workpiece shaft support, comprising:

[0007] S1: Combining the time-varying meshing stiffness and damping parameters between the honing wheel and the workpiece gear during the honing process, as well as the time-varying honing force generated by the change in honing thickness, a time-varying honing force model is constructed to simulate the influence of different honing thicknesses on the honing force.

[0008] S2: Based on the vibration characteristics of each processing component under the excitation of time-varying honing force during the gear honing process, a gear honing vibration dynamics model is constructed to simulate the vibration response of each processing component under different time-varying honing forces.

[0009] S3: Collect experimental data from the actual gear honing process and theoretical data simulated using the gear honing time-varying honing force model and gear honing vibration dynamics model. By comparing and analyzing the experimental data and theoretical data, verify the accuracy of the two models and retain the gear honing time-varying honing force model and gear honing vibration dynamics model that have been verified to be accurate and meet the requirements.

[0010] S4: Preset different commutation dwell times, use the gear honing time-varying honing force model and gear honing vibration dynamics model to simulate different commutation dwell times, and obtain corresponding simulation data. The process is as follows:

[0011] S41: Initialize a discrete value set of the commutation dwell time Δt.

[0012] S42: Select the first value in the discrete numerical set, and use the displacement function z(t) to obtain the corresponding displacement time series. The displacement time series is used to characterize the change process of the position of the workpiece gear in the z-axis direction over time. The z-axis direction is the axial feed direction of the workpiece gear.

[0013] S43: Dynamically adjust the feed rate f of the workpiece gear in the z-axis direction according to the displacement time series z , and then change the honing thickness, and use the honing time-varying honing force model to simulate and obtain the corresponding time-varying honing force.

[0014] S44: Using the gear honing vibration dynamics model, the vibration response caused by the time-varying honing force is simulated to obtain the corresponding vibration displacement sequence.

[0015] S45: Repeat steps S42-S44 to simulate other Δt values ​​in the discrete numerical value set to obtain corresponding vibration displacement sequences, and retain the mapping relationship between the commutation dwell time and the vibration displacement sequence.

[0016] S5: Based on the mapping relationship, a corresponding time history diagram and / or Poincare mapping diagram reflecting the dynamic behavior is drawn, and a vibration characteristic analysis is performed on the diagram. The commutation dwell time is optimized based on the vibration characteristic analysis results.

[0017] As a further improvement of the present invention, the formula of the displacement function z(t) is as follows:

[0018]

[0019] Where t is the time variable, t0 and t1 are the start time of movement and the time before stopping respectively, z0 and z1 are the position of the workpiece before movement and the position before stopping on the z axis respectively, v z is the feed speed of the workpiece gear along the z-axis.

[0020] As a further improvement of the present invention, the process of establishing the time-varying honing force model for gear honing includes:

[0021] The two components of the feed amount of the workpiece gear along the z-axis direction of the workpiece radial feed axis and the normal feed amount of the end section are synthesized into the honing thickness;

[0022] The deformation of the workpiece gear is obtained according to the honing thickness and the speed ratio between the workpiece gear and the honing wheel at the meshing point;

[0023] A spring-damper system is used at the meshing point between the honing wheel and the workpiece gear to replace the tooth surface meshing process. The honing normal force is obtained according to the workpiece gear deformation, time-varying meshing stiffness and meshing damping.

[0024] The honing friction force is obtained according to the honing normal force and the tooth surface friction coefficient;

[0025] The two components of honing normal force and honing friction force are combined into the time-varying honing force F, which is expressed as follows:

[0026]

[0027] Where, F n is the honing normal force, μ is the tooth surface friction coefficient, k m is the time-varying meshing stiffness, c m is the meshing damping, v1 and v2 are the speeds of the honing wheel and workpiece gear at the meshing point, f x is the feed amount of the workpiece gear along the workpiece radial feed axis x-axis direction, f z is the feed amount of the workpiece gear along the workpiece axial feed axis z-axis direction, α k ,θ k , δ0 are the involute pressure angle, involute spread angle and involute starting angle of the workpiece gear respectively.

[0028] As a further improvement of the present invention, the time-varying meshing stiffness k m The contact ratio of helical gear meshing ε α , the maximum stiffness k' in the normal section and the meshing period T are determined by the following formula:

[0029]

[0030] In the above formula, ε max is ε α The rounded-up value of ε min is ε α The floor value of .

[0031] As a further improvement of the present invention, the meshing damping c m is based on the time-varying mesh stiffness k m The average value k ave, base circle radius r of honing wheel and workpiece gear b1 、r b2 The formula is as follows:

[0032]

[0033] As a further improvement of the present invention, the gear honing vibration dynamics model includes:

[0034] The honing wheel, workpiece gear and workpiece shaft tailstock are respectively taken as research objects, and the lumped mass method is used to establish the motion differential equations.

[0035] For honing wheels there are:

[0036]

[0037] For workpiece gears there are:

[0038]

[0039] For the workpiece spindle tailstock there are:

[0040]

[0041] Where m1, m2, and m3 are the masses of the honing wheel, workpiece gear, and workpiece shaft tailstock, respectively. 1x 、k 1y 、k 1z k is the stiffness of the honing wheel in the X, Y, and Z directions, respectively. 2x 、k 2y 、k 2z k is the stiffness of the workpiece gear in the X, Y, and Z directions, respectively. 3x 、k 3y 、k 3z is the stiffness of the workpiece shaft tailstock in the X, Y, and Z directions, x1, y1, z1, and θ1 are the displacements of the honing wheel in the X, Y, Z, and rotation directions, x2, y2, z2, and θ2 are the displacements of the workpiece gear in the X, Y, Z, and rotation directions, x3, y3, and z3 are the displacements of the workpiece shaft tailstock in the X, Y, and Z directions, c 1x 、c 1y 、c 1z is the damping of the honing wheel in the X, Y and Z directions respectively, c 2x 、c 2y 、c 2z is the damping of the workpiece gear in the X, Y, and Z directions, c 3x 、c 3y 、c 3zis the damping of the workpiece shaft tailstock in the X, Y, and Z directions, J1 and J2 are the moments of inertia of the honing wheel and the workpiece gear, M1 and M2 are the driving torques of the honing wheel and the workpiece gear, R1 and R2 are the radii of the honing wheel and the workpiece gear, and F x 、F y 、F z are the components of the time-varying honing force F in the X, Y, and Z directions, respectively.

[0042] As a further improvement of the present invention, in step S44, an adaptive numerical integration algorithm combining fourth-order and fifth-order accuracy is used to calculate the corresponding vibration displacement sequence.

[0043] The present invention also includes a computer program product, which includes a computer program. When the computer program is executed by a processor, it implements the steps of the process optimization method based on the time-varying honing force model and the honing vibration characteristic analysis as described above, and then obtains the optimal commutation dwell time according to the vibration characteristic analysis results.

[0044] The present invention also includes a storage medium storing a computer program. When the computer program is executed by a processor, the steps of the process optimization method based on the time-varying honing force model and the honing vibration characteristic analysis are implemented, and the optimal commutation dwell time is obtained according to the vibration characteristic analysis results.

[0045] The present invention also includes a computer device, which includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the computer program is executed by the processor, the steps of the process optimization method based on the time-varying honing force model and the honing vibration characteristic analysis are implemented as described above, and then the optimal commutation dwell time is obtained according to the vibration characteristic analysis results.

[0046] The technical solution provided by the present invention has the following beneficial effects:

[0047] The present invention provides a process optimization method based on the time-varying honing force model and honing vibration characteristic analysis, introduces the reversing dwell time parameter of the workpiece gear in the axial reciprocating motion, and maps the reversing dwell time Δt to the axial feed amount f through the displacement function. z , accurately simulate the influence of the servo motor start-stop dynamic process on the honing force, use the concentrated mass method to construct the honing time-varying honing force model and the honing vibration dynamics model, and use these two models for simulation calculations. It can systematically analyze the vibration displacement sequence under different commutation dwell times, so that the commutation dwell time parameters can be optimized according to the degree of vibration displacement to reduce the commutation impact vibration amplitude, filling the gap in systematic research on the influence of commutation dwell time parameters on process stability, and improving the reliability of the honing process and surface quality consistency in high-precision gear processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a flow chart of a process optimization method based on a time-varying honing force model and honing vibration characteristic analysis provided in Example 1 of the present invention.

[0049] Figure 2 This is a schematic diagram of an involute helical surface of a workpiece gear provided in Example 1 of the present invention.

[0050] Figure 3 This is a schematic diagram of a normal force model for honing in gear honing provided in Example 1 of the present invention.

[0051] Figure 4 This is a schematic diagram of a gear honing vibration dynamics model provided in Example 1 of the present invention.

[0052] Figure 5 This is a frequency domain response comparison diagram of experimental data and theoretical data of a workpiece in the z-axis direction at different feed speeds when the reversing dwell time is 0.2s provided in Example 1 of the present invention.

[0053] Figure 6 This is a frequency domain response comparison diagram of experimental data and theoretical data of a workpiece in the z-axis direction at different feed speeds when the reversing dwell time is 0.6s provided in Example 1 of the present invention.

[0054] Figure 7 This is a frequency domain response comparison diagram of experimental data and theoretical data of a workpiece in the z-axis direction at different feed speeds when the reversing dwell time is 1 s provided in Example 1 of the present invention.

[0055] Figure 8 This is a comparison curve of the RMS values ​​of experimental data and theoretical data under different working conditions provided in Example 1 of the present invention.

[0056] Figure 9 This is a time history comparison diagram under different reversing dwell times provided in Example 1 of the present invention.

[0057] Figure 10 A comparison diagram of Poincare mapping under different switching dwell times provided in Example 1 of the present invention. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0059] Example 1

[0060] like Figure 1 As shown, Figure 1 A flow chart of a process optimization method based on a time-varying honing force model and honing vibration characteristic analysis provided in Example 1 of the present invention. The method is applicable to a honing processing system composed of a honing wheel, a workpiece gear and a workpiece shaft frame. In this system, the workpiece gear realizes three-dimensional motion control through the workpiece shaft frame: axial feed motion (z-axis), radial feed motion (x-axis) and rotational motion around its own axis. The workpiece shaft frame accurately drives the workpiece gear to form an interlaced axis meshing with the honing wheel at a preset axis angle, and at the same time, through axial high-frequency reciprocating motion, the honing wheel abrasive and the workpiece tooth surface produce controllable relative sliding, thereby realizing a precision processing process of micro-material removal. Computer simulation is used to simulate the honing process of a workpiece gear to be processed by a honing machine tool, and the vibration displacement simulated by the honing process is output.

[0061] The method specifically comprises the following steps:

[0062] S1: Based on the time-varying meshing stiffness and damping parameters between the honing wheel and the workpiece gear during the honing process, as well as the time-varying honing force generated by the change in honing thickness, a time-varying honing force model is constructed to simulate the influence of different honing thicknesses on the honing force. The specific establishment process is as follows:

[0063] The feed amount f of the workpiece gear along the workpiece radial feed axis z-axis direction z The two components of the honing thickness a are synthesized into the normal feed of the end section f1. p .like Figure 2 As shown, Figure 2 Schematic diagram of an involute helical surface of a workpiece gear provided in Example 1 of the present invention. f1 and the feed rate f in the x-axis direction of the workpiece gear x The angle between them is α1, and the formula for f1 is as follows:

[0064]

[0065] In the above formula, α k ,θ k , δ0 are the involute pressure angle, involute expansion angle and involute starting angle of the workpiece gear respectively, α1 is α k ,θ k , δ0 is the complementary angle of the sum of the triangles.

[0066] The experimental object of this study is that the honing wheel does not move and the workpiece is fed in the positive direction along the x-axis and z-axis. Therefore, the honing thickness a p for:

[0067]

[0068] According to the honing thickness a p And the speed ratio of the workpiece gear and the honing wheel at the meshing point, the equivalent honing thickness a is obtainedeq The honing process removes excess material by sliding the abrasive grains bonded to the honing wheel base against the workpiece surface. eq As the deformation amount δ caused by the honing wheel on the workpiece gear during honing, the formula is as follows:

[0069]

[0070] like Figure 3 As shown, Figure 3 This is a schematic diagram of a honing normal force model for honing provided in Example 1 of the present invention. The involute helical gear transmission system is a typical vibration system. When studying the normal honing force, the lumped mass method can be used at the meshing point to construct the normal honing force model. A spring-damper system is used at the meshing point between the honing wheel and the workpiece gear to replace the tooth surface meshing process, while the meshing force direction is maintained on the meshing line. According to the workpiece gear deformation δ, the time-varying meshing stiffness k m and meshing damping c m , and the honing normal force F is obtained n , the formula is as follows:

[0071]

[0072] Right now

[0073] In the above formula, is the first derivative of the workpiece gear δ.

[0074] Time-varying mesh stiffness k m It is calculated based on the definition of gear tooth stiffness in the national standard of gear stiffness, which is calculated by the overlap of the helical gear meshing ε α , the maximum stiffness k' in the normal section and the meshing period T are determined by the following formula:

[0075]

[0076] In the above formula, ε max is ε α The rounded-up value of ε min is ε α The floor value of .

[0077] Meshing damping c m It is calculated based on the definition of gear tooth stiffness in the national standard. Specifically, it is calculated based on the time-varying meshing stiffness k m The average value k ave , base circle radius r of honing wheel and workpiece gear b1 、r b2 The formula is as follows:

[0078]

[0079] During the internal meshing power honing process, the honing wheel and the workpiece are equivalent to the meshing motion of a pair of staggered helical gears. The time-varying honing force F can be regarded as the resultant force of the honing normal force and the honing friction force. The honing friction force is the product of the honing normal force and the tooth surface friction coefficient. The formula for the time-varying honing force F is as follows:

[0080]

[0081] Through the above process, a time-varying honing force model for gear honing was established, which can simulate the influence of different honing thicknesses on the honing force.

[0082] S2: Based on the vibration characteristics of each processing component under the excitation of the time-varying honing force during the gear honing process, a gear honing vibration dynamics model is constructed to simulate the vibration response of each processing component under different time-varying honing forces. The specific establishment process is as follows:

[0083] Since the servo motor drives the workpiece axis to realize feed honing in gear honing, the influence of the vibration of the workpiece axis tailstock on the honing process needs to be considered during modeling. Figure 4 As shown, Figure 4 This is a schematic diagram of a gear honing vibration dynamics model provided in Example 1 of the present invention. Figure 4 In this paper, a three-dimensional rectangular coordinate system is established with the horizontal feed direction as the X direction, the vertical feed direction as the Y direction, and the workpiece gear axis as the Z direction, as shown in the upper left corner of the figure. The honing wheel, workpiece gear, and workpiece shaft tailstock are respectively studied, and the lumped mass method is used to establish the differential equations of motion.

[0084] For honing wheels there are:

[0085]

[0086] For workpiece gears there are:

[0087]

[0088] For the workpiece spindle tailstock there are:

[0089]

[0090] In the above formula, m1, m2, and m3 are the masses of the honing wheel, workpiece gear, and workpiece shaft tailstock, respectively. 1x 、k 1y 、k 1z k is the stiffness of the honing wheel in the X, Y, and Z directions, respectively. 2x 、k 2y 、k 2zk is the stiffness of the workpiece gear in the X, Y, and Z directions, respectively. 3x 、k 3y 、k 3z is the stiffness of the workpiece shaft tailstock in the X, Y, and Z directions, x1, y1, z1, and θ1 are the displacements of the honing wheel in the X, Y, Z, and rotation directions, x2, y2, z2, and θ2 are the displacements of the workpiece gear in the X, Y, Z, and rotation directions, x3, y3, and z3 are the displacements of the workpiece shaft tailstock in the X, Y, and Z directions, c 1x 、c 1y 、c 1z is the damping of the honing wheel in the X, Y and Z directions respectively, c 2x 、c 2y 、c 2z is the damping of the workpiece gear in the X, Y, and Z directions, c 3x 、c 3y 、c 3z is the damping of the workpiece shaft tailstock in the X, Y, and Z directions, J1 and J2 are the moments of inertia of the honing wheel and the workpiece gear, M1 and M2 are the driving torques of the honing wheel and the workpiece gear, R1 and R2 are the radii of the honing wheel and the workpiece gear, and F x 、F y 、F z are the components of the time-varying honing force F in the X, Y, and Z directions, respectively.

[0091] S3: Collect experimental data from the actual gear honing process and theoretical data simulated using the gear honing time-varying honing force model and gear honing vibration dynamics model. By comparing and analyzing the experimental data and theoretical data, verify the accuracy of the two models and retain the gear honing time-varying honing force model and gear honing vibration dynamics model that have been verified to be accurate and meet the requirements.

[0092] After verifying the accuracy of the gear honing vibration dynamics model established based on the mathematical model of the time-varying honing force, the gear honing process can be simulated using the time-varying honing force model and the gear honing vibration dynamics model to simulate the influence of different honing thicknesses on the honing force, and then simulate the vibration response of each processing component under different time-varying honing forces.

[0093] S4: Preset different commutation dwell times, use the gear honing time-varying honing force model and gear honing vibration dynamics model to simulate different commutation dwell times, and obtain corresponding simulation data. The specific steps can be broken down into the following:

[0094] S41: Initialize a discrete value set of the commutation dwell time Δt. In this embodiment, the commutation dwell time Δt is set to be 1s, 0.6s, and 0.2s respectively. The element values ​​of the discrete value set can be preset according to actual conditions, and the embodiment of the present invention does not limit this.

[0095] S42: Select a value from the discrete numerical set, for example, Δt=1s, and use the displacement function z(t) to obtain the corresponding displacement time series. The formula of the displacement function z(t) is as follows:

[0096]

[0097] Where t is the time variable, t0 and t1 are the start time of movement and the time before stopping respectively, z0 and z1 are the position of the workpiece before movement and the position before stopping on the z axis respectively, v z is the feed speed of the workpiece gear along the workpiece axial feed axis z-axis direction.

[0098] The principle of setting different reversing dwell times in the simulation is: by changing the z-axis feed speed v z Thus changing the feed rate f z To achieve the purpose of defining the time function, when the system time t enters the preset dwell interval [t1, t1+Δt), the z-axis feed speed v is forced to be set z =0, and maintain the displacement z(t)=z1 until the end of the stay.

[0099] S43: According to the above principle, the feed amount f of the workpiece gear in the z-axis direction is dynamically adjusted according to the displacement time sequence. z , and then change the honing thickness, and use the honing time-varying honing force model simulation to obtain the corresponding time-varying honing force, which can accurately simulate the dynamic transition process of the servo motor start-stop control in actual processing.

[0100] S44: Using the gear honing vibration dynamics model, simulate the vibration response caused by the time-varying honing force and obtain the corresponding vibration displacement sequence. Because the nonlinear differential equations in the gear honing vibration dynamics model have no analytical solution, this embodiment uses an adaptive numerical integration algorithm that combines fourth-order and fifth-order accuracy—the Runge-Kutta method—to solve them. Computational stability is ensured through adaptive time step control, significantly improving the efficiency and robustness of solving complex differential equations while maintaining accuracy.

[0101] S45: Repeat the above steps S42-S44 to simulate Δt=0.6s and Δt=0.2s in the discrete value set to obtain the corresponding vibration displacement sequence, and retain the mapping relationship between the commutation dwell time and the vibration displacement sequence.

[0102] S5: Based on the above mapping relationship, a corresponding time history diagram and / or Poincare mapping diagram reflecting the dynamic behavior is drawn, and a vibration characteristic analysis is performed on the diagram. The commutation dwell time is optimized according to the vibration characteristic analysis result.

[0103] Time history graphs can be used to determine the dynamic behavior of a workpiece gear during machining based on the temporal variation of the vibration displacement. Significant jitter (irregular fluctuations) in the displacement-time curve indicates system instability. This instability can lead to a decrease in the gear's dynamic performance (such as smoothness of motion and machining accuracy). The greater the jitter amplitude, the greater the system instability and the worse the gear's dynamic performance.

[0104] The Poincare map effectively reveals the dynamic characteristics of the honing system by recording the discrete sampling points of the system state in phase space. The smaller the distribution density of the mapping points, the more unstable the system state and the worse the dynamic performance.

[0105] By analyzing the time history diagram or Poincare map, the corresponding characteristics of the system's vibration displacement can be obtained, thereby providing an optimization basis for the commutation dwell time parameters, suppressing self-excited vibration, improving processing stability, and thus improving the processing accuracy and surface quality of gear processing.

[0106] Example 2

[0107] Based on the process optimization method based on the time-varying honing force model and the analysis of the honing vibration characteristics provided in Example 1, this embodiment further provides a computer program product, which includes a computer program. When the computer program is executed by the processor, it implements the process optimization method based on the time-varying honing force model and the analysis of the honing vibration characteristics as described above, and then obtains the optimal commutation dwell time according to the vibration characteristic analysis results.

[0108] This embodiment also provides a storage medium storing a computer program. When the computer program is executed by a processor, the process optimization method based on the time-varying honing force model and honing vibration characteristic analysis as described above is implemented, and the optimal commutation dwell time is obtained according to the vibration characteristic analysis results.

[0109] This embodiment also provides a computer device, which can be a smartphone, tablet computer, laptop computer, desktop computer, rack server, blade server, tower server, or cabinet server (including a standalone server or a server cluster consisting of multiple servers) capable of executing programs.

[0110] The computer device of this embodiment includes at least, but is not limited to, a memory and a processor that can be interconnected via a system bus. In this embodiment, the memory (i.e., a readable storage medium) includes flash memory, a hard disk, a multimedia card, a card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, a magnetic disk, an optical disk, etc. In some embodiments, the memory can be an internal storage unit of the computer device, such as the hard disk or internal memory of the computer device. In other embodiments, the memory can also be an external storage device of the computer device, such as a plug-in hard disk equipped with the computer device, a smart media card (SMC), a secure digital (SD) card, a flash memory card, etc. Of course, the memory can also include both the internal storage unit of the computer device and its external storage device. In this embodiment, the memory is generally used to store the operating system and various application software installed on the computer device. In addition, the memory can also be used to temporarily store various types of data that have been output or are about to be output.

[0111] In some embodiments, the processor may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip. The processor is generally used to control the overall operation of a computer device.

[0112] Model accuracy verification experiment

[0113] In order to verify the effectiveness of the time-varying honing force model and the honing vibration dynamics model provided by the present invention, technicians developed the following comparative experiment to test the above two models and evaluate the model's ability to predict the vibration characteristics of the actual honing process.

[0114] 1. Experimental Content

[0115] 1.1. Collect vibration signals. Install a vibration acceleration sensor on the gear honing machine, fix the probe along the z-axis of the workpiece, set different working conditions (workpiece z-axis feed speed, reversing dwell time), and collect vibration acceleration signals during the machining process.

[0116] 1.2 Simulation of theoretical data: Based on the time-varying honing force model and the honing vibration dynamics model, the corresponding working condition parameters (workpiece z-axis feed speed, reversal dwell time) are input, and the frequency domain response of the workpiece z-axis vibration displacement and the RMS value in the time domain are simulated.

[0117] 1.3 Data Comparative Analysis

[0118] Frequency domain analysis: Perform FFT transformation on the experimental acceleration signal to extract the main vibration frequency and compare it with the simulated frequency domain response curve.

[0119] Time domain analysis: The displacement signal is obtained by quadratically integrating the experimental acceleration signal. The RMS value of the experimental data is calculated and compared with the RMS value of the displacement predicted by the model.

[0120] 2. Experimental Results and Analysis

[0121] 2.1. Honing vibration frequency characteristics under fixed commutation dwell time

[0122] When the dwell time of reversing is 0.2s, Figure 5 As shown, Figure 5 This is a frequency domain response comparison diagram of experimental data and theoretical data of a workpiece in the z-axis direction at different feed speeds when the reversing dwell time is 0.2s provided in Example 1 of the present invention. Figure 5 (a) is a comparison of the frequency domain responses of the experimental data and the theoretical data when the commutation dwell time is 0.2s and the z-axis feed speed is 130mm / min; Figure 5 (b) is a frequency domain response comparison diagram of experimental data and theoretical data when the commutation dwell time is 0.2s and the z-axis feed speed is 115mm / min; Figure 5 (c) is a frequency domain response comparison diagram of experimental data and theoretical data when the reversing dwell time is 0.2s and the z-axis feed speed is 100mm / min. Figure 5 As can be seen from the simulation results, the theoretical data obtained using the time-varying honing force model and the honing vibration dynamics model are highly consistent with the experimental data. At three feed rates (100, 115, and 130 mm / min), the main frequency in both the experimental and simulation experiments remained stable at around 65 Hz, indicating that the effect of the workpiece z-axis feed rate on the honing vibration frequency is negligible.

[0123] When the dwell time of reversing is 0.6s, Figure 6 As shown, Figure 6 This is a frequency domain response comparison diagram of experimental data and theoretical data of a workpiece in the z-axis direction at different feed speeds when the reversing dwell time is 0.6s provided in Example 1 of the present invention. Figure 6 (a) is a comparison of the frequency domain responses of the experimental data and the theoretical data when the commutation dwell time is 0.6 s and the z-axis feed speed is 130 mm / min; Figure 6 (b) is a comparison of the frequency domain responses of the experimental data and the theoretical data when the commutation dwell time is 0.6s and the z-axis feed speed is 115mm / min; Figure 6 (c) is a frequency domain response comparison diagram of experimental data and theoretical data when the reversing dwell time is 0.6s and the z-axis feed speed is 100mm / min. Figure 6 It can be seen that the theoretical data obtained by simulating the time-varying honing force model and the honing vibration dynamics model are highly consistent with the experimental data. The main frequencies of the experiment and simulation are both stable at around 55 Hz, indicating that the z-axis feed speed has little effect on the honing vibration frequency.

[0124] When the reversing dwell time is 1.0s, Figure 7 As shown, Figure 7 This is a frequency domain response comparison diagram of experimental data and theoretical data of a workpiece in the Z direction at different feed speeds when the reversing dwell time is 1 s provided in Example 1 of the present invention. Figure 7 (a) is a comparison of the frequency domain responses of the experimental data and the theoretical data when the commutation dwell time is 1.0 s and the z-axis feed speed is 130 mm / min; Figure 7 (b) is a frequency domain response comparison diagram of experimental data and theoretical data when the commutation dwell time is 1.0s and the z-axis feed speed is 115mm / min; Figure 7 (c) is a frequency domain response comparison diagram of experimental data and theoretical data when the reversing dwell time is 1.0s and the z-axis feed speed is 100mm / min. Figure 7 It can be seen that the theoretical data obtained by simulating the time-varying honing force model and the honing vibration dynamics model are highly consistent with the experimental data. The main frequencies of the experiment and simulation are both stable at around 50 Hz, indicating that the change of the z-axis feed speed has little effect on the honing vibration frequency.

[0125] Horizontal comparison Figures 5 to 7 , the commutation dwell time was extended from 0.2s to 1.0s, and the main frequency was reduced from 65Hz to 50Hz, indicating that extending the commutation dwell time can significantly reduce the honing vibration frequency (by 30%).

[0126] Therefore, the theoretical frequency domain response is highly consistent with the experimental data in terms of the main frequency position and amplitude trend, which verifies the model's ability to accurately predict dynamic vibration characteristics.

[0127] 2.2. Influence of reversing dwell time on vibration characteristics at the same feed speed

[0128] like Figure 8 As shown, Figure 8 This is a comparison curve of the RMS values ​​of experimental data and theoretical data under different working conditions provided in Example 1 of the present invention.

[0129] When the z-axis feed speed is 130 mm / min, see Figure 8 (a), Figure 8(a) is a comparison curve of the RMS value of the workpiece vibration displacement in the z-axis direction under different reversing dwell times when the feed speed is 130 mm / min. When the reversing dwell time is extended from 0.2 s to 1.0 s, the experimental RMS value decreases from 0.9 μm to 0.68 μm, and the simulation value decreases from 1.2 μm to 0.98 μm, showing the same trend.

[0130] When the z-axis feed speed is 115 mm / min, see Figure 8 (b) Figure 8 (b) is a comparison curve of the RMS value of the workpiece vibration displacement in the z-axis direction under different reversing dwell times when the feed speed is 115 mm / min. When the reversing dwell time is extended from 0.2 s to 1.0 s, the experimental RMS value decreases from 0.9 μm to 0.68 μm, and the simulation value decreases from 1.15 μm to 0.98 μm, showing the same trend.

[0131] When the z-axis feed speed is 100 mm / min, see Figure 8 (c) Figure 8 (c) is a comparison curve of the RMS value of the workpiece vibration displacement in the z-axis direction under different reversing dwell times when the feed speed is 100 mm / min. When the reversing dwell time is extended from 0.2 s to 1.0 s, the experimental RMS value decreases from 0.9 μm to 0.68 μm, and the simulation value decreases from 1.15 μm to 0.85 μm, showing the same trend.

[0132] from Figure 8 It can be seen from the figure that increasing the commutation dwell time can reduce the vibration energy, and the model successfully captures this trend.

[0133] 2.3 Comprehensive Verification Conclusion

[0134] The accuracy of the time-varying honing force model and the honing vibration dynamics model was verified through frequency domain main frequency matching and time domain RMS trend consistency analysis. The model can be further used to simulate the influence of different honing thicknesses on the honing force, as well as to predict the vibration response of the machined parts under complex working conditions, providing theoretical support for process optimization.

[0135] Process parameter optimization experiment

[0136] To investigate the effects of varying commutation dwell times on the vibration characteristics of a gear honing system, researchers analyzed the vibration characteristics revealed by time history plots and Poincare maps to determine the optimal commutation dwell time parameters to improve surface quality and process stability in gear machining. The following comparative experiments were conducted, focusing on verifying the system's vibration displacement response characteristics for three commutation dwell times: 1.0s, 0.6s, and 0.2s. This provides a basis for parameter optimization in high-precision gear machining.

[0137] 1. Experimental Content

[0138] Set the basic parameters of the workpiece to be processed as follows: module m n =2.211, number of teeth z=27, helix angle β=32°, pressure angle α k =17°.

[0139] The experiment used three comparison schemes, setting commutation dwell times of 1.0s, 0.6s, and 0.2s, respectively. Simulations were performed using the aforementioned time-varying honing force model and honing vibration dynamics model to obtain the corresponding vibration displacement sequence. The mapping relationship between the commutation dwell time and the vibration displacement sequence was retained. Based on this mapping relationship, a time history graph and a Poincare map were plotted as a basis for optimization. The time history graph was used to observe the rate of change of displacement amplitude and the smoothness of the curve; the Poincare map was used to quantify the distribution density of the phase space point set (sampling frequency 10kHz).

[0140] 2. Experimental Results and Analysis

[0141] like Figure 9 As shown, Figure 9 This is a time history comparison diagram under different reversing dwell times provided in Example 1 of the present invention. Figure 9 (a) is the time history diagram when the reversing dwell time is 1s. Figure 9 (b) is the time history diagram when the reversing dwell time is 0.6s. Figure 9 (c) is the time history diagram when the switching dwell time is 0.2s. Figure 9 It can be seen that as the reversing dwell time of the workpiece axis before reverse motion decreases from 1.0s to 0.2s, the amplitude of the time history diagram gradually increases from 0.6835, 0.8305 to 0.9616, and the irregularity of the curve gradually increases, indicating that the longer the reversing dwell time, the stronger the system instability and the worse the dynamic performance of the gear.

[0142] like Figure 10 As shown, Figure 10 A comparison diagram of Poincare mapping under different switching dwell times provided in Example 1 of the present invention. Figure 10 (a) is the Poincare map when the switching dwell time is 1s. Figure 10 (b) is the Poincare map when the switching dwell time is 0.6s. Figure 10(c) is the Poincare map for a commutation dwell time of 0.2 seconds. When the commutation dwell time is set to 1 second, the mapped points are tightly clustered, indicating stable system operation. When the dwell time is shortened to 0.6 seconds, the mapped points begin to spread outward, indicating a decrease in system stability. When the dwell time is further reduced to 0.2 seconds, the mapped points exhibit a clear chaotic diffusion distribution, indicating that the system has entered an unstable state and its dynamic performance has significantly deteriorated.

[0143] In summary, as the commutation dwell time decreases, the vibration trajectory of the workpiece gear gradually intensifies from a nearly smooth state, and the stability of the system gradually deteriorates.

[0144] Therefore, according to the above vibration characteristics analysis results, the commutation dwell time parameter is optimized to 1 s, which can reduce the commutation impact vibration amplitude, thereby improving the reliability and surface quality consistency of the honing process in high-precision gear machining.

[0145] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present invention can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present invention can be achieved. This is not limited herein.

[0146] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of such features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0147] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A process optimization method based on a time-varying honing force model and honing vibration characteristics analysis, characterized in that: Suitable for honing systems comprising a honing wheel, a workpiece gear and a workpiece quill, comprising: S1: Based on the time-varying meshing stiffness and damping parameters between the honing wheel and the workpiece gear during the honing process, as well as the time-varying honing force generated by the change in honing thickness, a time-varying honing force model is constructed to simulate the influence of different honing thicknesses on the honing force. S2: Based on the vibration characteristics of each machining component under the excitation of time-varying honing force during the gear honing process, a gear honing vibration dynamics model is constructed to simulate the vibration response of each machining component under different time-varying honing forces; S3: Collect experimental data from the actual gear honing process and theoretical data simulated using the gear honing time-varying honing force model and gear honing vibration dynamics model. By comparing and analyzing the experimental data and theoretical data, verify the accuracy of the two models. Keep the gear honing time-varying honing force model and gear honing vibration dynamics model that have been verified to be accurate and meet the requirements. S4: Preset different commutation dwell times, use the gear honing time-varying honing force model and the gear honing vibration dynamics model to simulate different commutation dwell times, and obtain corresponding simulation data; the process is as follows: S41: Initialize a discrete value set of the commutation dwell time Δt; S42: selecting the first value in the discrete numerical value set, and obtaining a corresponding displacement time series using the displacement function z(t), wherein the displacement time series is used to characterize a change in the position of the workpiece gear in the z-axis direction over time, wherein the z-axis direction is the axial feed direction of the workpiece gear; S43: Dynamically adjust the feed rate f of the workpiece gear in the z-axis direction according to the displacement time sequence z , and then change the honing thickness, and use the honing time-varying honing force model to simulate and obtain the corresponding time-varying honing force; S44: using a gear honing vibration dynamics model, simulating a vibration response caused by the time-varying honing force to obtain a corresponding vibration displacement sequence; S45: Repeat steps S42-S44 to simulate other Δt values ​​in the discrete numerical value set to obtain corresponding vibration displacement sequences, and retain the mapping relationship between the commutation dwell time and the vibration displacement sequence; S5: According to the mapping relationship, a corresponding time history diagram and / or Poincare mapping diagram reflecting the dynamic behavior is drawn, and a vibration characteristic analysis is performed on the diagram, and the commutation dwell time is optimized according to the vibration characteristic analysis result.

2. The process optimization method based on the time-varying honing force model and honing vibration characteristic analysis according to claim 1 is characterized in that: The formula of the displacement function z(t) is as follows: Where t is the time variable, t0 and t1 are the start time of movement and the time before stopping respectively, z0 and z1 are the position of the workpiece before movement and the position before stopping on the z axis respectively, v z is the feed speed of the workpiece gear along the z-axis.

3. The process optimization method based on the time-varying honing force model and honing vibration characteristic analysis according to claim 1 is characterized in that: The process of establishing the time-varying honing force model for gear honing includes: The two components of the feed amount of the workpiece gear along the z-axis direction of the workpiece radial feed axis and the normal feed amount of the end section are synthesized into the honing thickness; Obtaining a deformation amount of the workpiece gear according to the honing thickness and a speed ratio between the workpiece gear and the honing wheel at an engagement point; A spring-damper system is used at the meshing point between the honing wheel and the workpiece gear to replace the tooth surface meshing process, and the honing normal force is obtained according to the workpiece gear deformation, time-varying meshing stiffness and meshing damping; The honing friction force is obtained according to the honing normal force and the tooth surface friction coefficient; The honing normal force and the honing friction force are combined into the time-varying honing force F, which is expressed as follows: Where, F n is the honing normal force, μ is the tooth surface friction coefficient, k m is the time-varying meshing stiffness, c m is the meshing damping, v1 and v2 are the speeds of the honing wheel and workpiece gear at the meshing point, f x is the feed amount of the workpiece gear along the workpiece radial feed axis x-axis direction, f z is the feed amount of the workpiece gear along the workpiece axial feed axis z-axis direction, α k ,θ k , δ0 are the involute pressure angle, involute spread angle and involute starting angle of the workpiece gear respectively.

4. The process optimization method based on the time-varying honing force model and honing vibration characteristic analysis according to claim 3 is characterized in that: The time-varying meshing stiffness k m The contact ratio of helical gear meshing ε α , the maximum stiffness k in the normal section ′ and the meshing period T, the formula is as follows: In the above formula, ε max is ε α The rounded-up value of ε min is ε α The floor value of .

5. The process optimization method based on the time-varying honing force model and honing vibration characteristic analysis according to claim 4 is characterized in that: The meshing damping c m is based on the time-varying meshing stiffness k m The average value k ave , base circle radius r of honing wheel and workpiece gear b1 、r b2 The formula is as follows:

6. The process optimization method based on time-varying honing force model and honing vibration characteristic analysis according to claim 1 is characterized in that: The gear honing vibration dynamics model includes: The honing wheel, workpiece gear and workpiece shaft tailstock are respectively taken as research objects, and the lumped mass method is used to establish the motion differential equations. For honing wheels there are: For workpiece gears there are: For the workpiece spindle tailstock there are: Where m1, m2, and m3 are the masses of the honing wheel, workpiece gear, and workpiece shaft tailstock, respectively. 1x 、k 1y 、k 1z k is the stiffness of the honing wheel in the X, Y, and Z directions, 2x 、k 2y 、k 2z k is the stiffness of the workpiece gear in the X, Y, and Z directions, respectively. 3x 、k 3y 、k 3z is the stiffness of the workpiece shaft tailstock in the X, Y, and Z directions, x1, y1, z1, and θ1 are the displacements of the honing wheel in the X, Y, Z, and rotation directions, x2, y2, z2, and θ2 are the displacements of the workpiece gear in the X, Y, Z, and rotation directions, x3, y3, and z3 are the displacements of the workpiece shaft tailstock in the X, Y, and Z directions, c 1x 、c 1y 、c 1z is the damping of the honing wheel in the X, Y and Z directions respectively, c 2x 、c 2y 、c 2z is the damping of the workpiece gear in the X, Y, and Z directions, c 3x 、c 3y 、c 3z is the damping of the workpiece shaft tailstock in the X, Y, and Z directions, J1 and J2 are the moments of inertia of the honing wheel and the workpiece gear, M1 and M2 are the driving torques of the honing wheel and the workpiece gear, R1 and R2 are the radii of the honing wheel and the workpiece gear, and F x 、F y 、F z are the components of the time-varying honing force F in the X, Y, and Z directions, respectively.

7. The process optimization method based on time-varying honing force model and honing vibration characteristic analysis according to claim 1 is characterized in that: In step S44, an adaptive numerical integration algorithm combining fourth-order and fifth-order accuracy is used to calculate the corresponding vibration displacement sequence.

8. A computer program product comprising a computer program, characterized in that: When the computer program is executed by the processor, the steps of the process optimization method based on the time-varying honing force model and the gear honing vibration characteristic analysis as described in any one of claims 1 to 7 are implemented, and the optimal commutation dwell time is analyzed according to the vibration displacement sequence corresponding to different commutation dwell times.

9. A storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the process optimization method based on the time-varying honing force model and honing vibration characteristic analysis as described in any one of claims 1 to 7 are implemented, and the optimal commutation dwell time is obtained according to the vibration characteristic analysis results.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the computer program is executed by a processor, the steps of the process optimization method based on the time-varying honing force model and honing vibration characteristic analysis as described in any one of claims 1 to 7 are implemented, and the optimal commutation dwell time is obtained according to the vibration characteristic analysis results.

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