Asymmetric gear worm grinding wheel gear grinding heat equivalent simulation analysis and process parameter optimization method

Abstract

The invention provides an asymmetric gear worm grinding wheel gear grinding heat equivalent simulation analysis and process parameter optimization method. The method comprises the steps of establishing a transient equivalent simulation analysis model of asymmetric gear worm grinding wheel gear grinding, determining the grinding heat influence degree of different process parameters on tooth surfaces on the two sides, obtaining an optimal process parameter solution set and the like. According to the method, the difference of grinding heat of tooth surfaces on the two sides in the asymmetric worm grinding wheel tooth grinding machining process is considered, technological parameter optimization is carried out, and a theoretical model and a guidance basis are provided for guaranteeing the asymmetric gear tooth grinding machining performance. The method is high in universality and wide in applicability, and can be subsequently popularized and applied to the manufacturing process of other asymmetric gears or other types of gears.

Description

Technical Field

[0001] The present invention relates to the field of mechanical manufacturing, and in particular to a method for thermal equivalent simulation analysis and process parameter optimization of asymmetric gear worm grinding wheel gear grinding. Background Art

[0002] With the continuous increase in power density and input speed of electric drive systems, as well as the growing demand for regenerative braking, dual-pressure-angle asymmetric gears are gaining popularity. Dual-pressure-angle asymmetric gears feature different pressure angles on the drive and non-drive sides, adapting to the varying service performance requirements of the tooth flanks. Through appropriate pressure angle design, dual-pressure-angle asymmetric gears can effectively increase tooth root thickness, improving gear load capacity and strength.

[0003] The worm wheel gear grinding process is one of the main processes for achieving efficient and precise machining of gears. However, almost all the energy in the grinding process is converted into heat energy and concentrated in the grinding zone, of which about 60% to 95% of the heat is transferred to the workpiece, and the remaining less than 10% of the heat is carried away by the grinding chips. Therefore, the heat generated by grinding has very adverse effects on the surface properties of the gears, such as burns, metallographic transformations, cracks, and reduced fatigue strength. For asymmetric gears, the grinding heat of the tooth surfaces on both sides during the grinding process is different due to the different pressure angles. How to control the grinding temperature consistency of the tooth surfaces on both sides of the asymmetric gear by adjusting the grinding parameters such as grinding allowance, feed speed, and grinding wheel linear speed is of great significance to ensure its machining accuracy. However, the current asymmetric gear worm wheel gear grinding process still has the following technical gaps in grinding heat control and process parameter optimization:

[0004] A. The asymmetric tooth shape leads to differences in the grinding contact angle, chip thickness, and heat flux distribution between the drive and non-drive sides. Existing studies have not considered the differences in heat sources and analytical models under different pressure angles.

[0005] B. Traditional process parameters do not consider the impact of the difference in pressure angles on the grinding force-thermal coupling, lack a process parameter optimization method for asymmetric gear worm grinding wheels, and are difficult to achieve consistent control of grinding temperature on both sides.

[0006] Therefore, it is of great significance to develop a research method for thermal analysis and parameter optimization of asymmetric gear worm grinding wheel. Summary of the Invention

[0007] The purpose of the present invention is to provide a method for thermal equivalent simulation analysis and process parameter optimization of asymmetric gear worm grinding wheel gear grinding to solve the problems existing in the prior art.

[0008] The technical solution employed to achieve the objectives of the present invention is a method for thermal equivalence simulation analysis and process parameter optimization of asymmetric gear worm grinding wheel grinding. The method utilizes spatially staggered meshing of the worm grinding wheel and the workpiece gear to achieve dual-pressure-angle asymmetric gear grinding. The method comprises the following steps:

[0009] 1) Establish a transient equivalent simulation analysis model for asymmetric worm wheel gear grinding. Worm wheel gear grinding is equated to the meshing transmission between a rack tool and a workpiece gear. A transient equivalent simulation analysis model is constructed using two adjacent teeth of an asymmetric gear as the research object and a single rack tooth as the grinding tool. The axial feed motion of the grinding wheel and its rotational motion are combined to form the movement of the grinding tool along the axis of the research object.

[0010] 2) Based on the transient equivalent simulation analysis model, an orthogonal experiment was designed and simulated to determine the influence of different process parameters on the grinding heat of the tooth flanks on both sides. The relationship between the grinding heat of the tooth flanks on both sides of the asymmetric gear and the process parameters was analyzed and established.

[0011] 3) Construct a process parameter optimization model for asymmetric gear worm grinding wheel, and use intelligent optimization algorithm to obtain the optimal process parameter solution set to obtain the optimal process parameters.

[0012] Furthermore, step 1) specifically includes the following sub-steps:

[0013] 1.1) Determine the relevant parameters of the asymmetric gear and rack tools, generate point cloud data of the rack tool using Matlab, and use UG software to build a three-dimensional model of two adjacent teeth of the asymmetric gear and one tooth of the equivalent rack.

[0014] 1.2) Use HyperMesh software to mesh the 3D model and import it into Abaqus software to complete the setting of gear material properties and tool material properties.

[0015] Furthermore, in step 2), a relationship between the grinding heat of the tooth surfaces on both sides of the asymmetric gear and the process parameters is established based on multiple regression analysis.

[0016] After regression analysis, the relationship between the left tooth surface grinding heat and process parameters is obtained:

[0017]

[0018] After regression analysis, the relationship between the right tooth surface grinding heat and process parameters is obtained:

[0019]

[0020] Where B is the grinding allowance, V X is the feed speed, V Y is the rack linear speed.

[0021] Furthermore, step 3) specifically includes the following sub-steps:

[0022] 3.1) A multi-objective optimization model for the asymmetric worm wheel grinding process is established, with the tooth surface temperature difference T and grinding efficiency y as the targets. The tooth surface temperature difference calculation formula is shown in Equation (3). The grinding efficiency calculation formula is shown in Equation (4). The constraints are shown in Equation (5).

[0023] T=x2-x1 (3)

[0024]

[0025] Where x1 is the grinding heat of the left tooth surface, and x2 is the grinding heat of the right tooth surface.

[0026] 3.2) Solve the multi-objective optimization model to obtain the process parameter solution set.

[0027] 3.3) Based on relevant processing parameters and processing experience, determine the optimal feed rate, optimal rack tool linear speed and optimal grinding allowance.

[0028] Furthermore, MOSFOA is used to solve the multi-objective optimization model to obtain the process parameter solution set.

[0029] Further, step 3.2) specifically includes the following sub-steps:

[0030] 3.2.1) Initialize the process parameter optimization population: The process parameter population is represented as (a1, a2, ..., a m ), where m is a positive integer, a i For the i-th process parameter in the population, input a i The upper and lower limits are denoted as a max and a min .

[0031] Set r to a random number between [0, 1], and randomly initialize the process parameter population within the value range [0, 1] according to the process optimization model.

[0032] Set the maximum number of iterations it, the number of iterations nu = 0, and the maximum capacity of the archive M.

[0033] Randomly select a process parameter and assign it to the optimal process parameter E, and select a target value and assign it to the archived optimal target value.

[0034] Among them, the i-th process parameter a in the population i As shown below:

[0035] a i =a min +r×(amax -a min ) (6)

[0036] 3.2.2) Determine whether the current iteration number nu < it holds. If so, proceed to step 3.2.3); otherwise, proceed to step 3.2.8).

[0037] 3.2.3) Calculate the target values of the tooth surface temperature difference T and grinding efficiency y of the objective function, find the non-dominated solutions and store them in the archive.

[0038] 3.2.4) Judge the storage capacity of the archive: If the number of archived solutions reaches the maximum archive capacity, go to step 3.2.5); otherwise, go to step 3.2.6).

[0039] 3.2.5) Use the greedy strategy to save the current optimal solutions. Set a predefined distance for each solution, and calculate the number of solutions within this distance to measure the corresponding crowding degree. Then, use the roulette wheel method to eliminate one or more solutions according to the crowding degree.

[0040] 3.2.6) Judge the behavior of the superb fairy-wren during population update, and update the population according to the calculation formulas in different behavior stages.

[0041] 3.2.7) Update the optimal collaborative process parameters: Update the process parameter population, nu = nu + 1, and then go to step 3.2.2).

[0042] 3.2.8) Output the values of the process parameter population stored in the archive and the target values of the objective function. Further, step 3.2.6) specifically includes the following sub-steps:

[0043] 3.2.6.1) Define the environmental hazard factor s and the proportion b of young birds in the population. The proportion b of young birds in the population is a random number in the interval [0, 1], and the environmental hazard factor s = r1 * 20 + r2 * 20

[0044] In the formula, r1 and r2 are both random numbers in the interval [-1, 1] or random numbers satisfying a certain distribution to simulate the fluctuation of risks.

[0045] 3.2.6.2) Judge the behavior stage of the superb fairy-wren according to the values of the environmental hazard factor s and the proportion b of young birds in the population.

[0046] When the proportion r of young birds in the population > 0.5, the superb fairy-wren population is in the growth stage of young birds. At this time, each individual is updated using the following formula:

[0047]

[0048] where a t i，jrepresents the coordinates of individual i at iteration (or evaluation) time t, and r(0,1) is a random noise term used to enhance search diversity. If this update leads to a better value for the objective function, the new position is added to the population. This stage tends to involve extensive movement in the solution space, achieving extensive exploration.

[0049] When the proportion of young birds in the population r≤0.5 and the environmental risk factor s<20, the magnificent fairy-wren population is in the breeding and nursing stage, and the individuals are updated using the following formula:

[0050]

[0051] where a b is the current global optimal position, C is a constant (usually 0.8), and p is used to describe the process of the gradual expansion of the activity range of the adult bird during "take-turn teaching". It can be calculated using the ratio of the sine function to the current number of evaluations, for example:

[0052]

[0053] Where FEs is the number of evaluations performed so far, and MaxFEs is the maximum number of evaluations. In this way, as the breeding and incubation cycle progresses, the activity range of individuals in the local area gradually increases, which is conducive to the deep development of the population near the known optimal solution.

[0054] When the proportion of young birds in the population r≤0.5 and the environmental risk factor s>20, the magnificent fairy-wren population is in the natural enemy avoidance stage, and individuals are updated using the following formula:

[0055]

[0056] Where ab represents the global optimal solution location, l is the random step size generated by Levy flight, used for large-scale jumps, and k gradually changes with the number of evaluations to coordinate the escape distance. When a natural enemy attacks, the escape of an individual and the coordinated interference of other individuals can significantly improve the search's jumpiness, thus breaking free from the constraints of local optimality. Finally, to unify the update mechanisms of these three stages into the same search, it can be written as:

[0057]

[0058] Where r is the threshold for determining the proportion of juveniles within the population. If r > 0.5, it indicates a large number of juveniles, stimulating wide-area exploration during the juvenile growth phase. If r ≤ 0.5, it indicates a large number of adults, requiring further assessment of the risk factor s. If s < 20, the population enters the breeding and nursing phase, conducting localized, intensive search. If s ≥ 20, the population enters the predator avoidance phase, employing random hopping.

[0059] The technical benefits of this invention are undeniable: it addresses the problem of insufficient gear precision caused by inconsistent grinding temperatures on both sides of the tooth surface during asymmetric worm wheel grinding. It also provides a theoretical model and guidance for ensuring the performance of asymmetric gear grinding. The invention is highly versatile and widely applicable, and can be subsequently applied to the manufacturing of other asymmetric and other types of gears. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a flow chart of the thermal equivalent simulation analysis and process parameter optimization method for asymmetric gear worm grinding wheel;

[0061] Figure 2 Schematic diagram of worm grinding wheel transformation;

[0062] Figure 3 Schematic diagram of the equivalent meshing in and out of the rack;

[0063] Figure 4 Mesh diagram for asymmetric gear and rack tool;

[0064] Figure 5 Flowchart of algorithm optimization for multi-objective Magnificent Fairywren;

[0065] Figure 6 This is a partial simulation temperature cloud map. DETAILED DESCRIPTION

[0066] The present invention will be further described below with reference to the following examples, but it should not be understood that the scope of the present invention is limited to the following examples. Without departing from the above technical ideas of the present invention, various substitutions and modifications can be made according to common technical knowledge and customary means in the art, and all should be included in the scope of protection of the present invention.

[0067] Example 1:

[0068] This embodiment provides a method for thermal equivalent simulation analysis and process parameter optimization of asymmetric gear worm grinding wheel grinding, in which the worm grinding wheel and the workpiece gear are engaged with each other in a spatial staggered axis to realize the grinding of asymmetric gears with double pressure angles. Figure 1 , the method comprises the following steps:

[0069] 1) Establish a transient equivalent simulation analysis model for asymmetric gear worm grinding wheel grinding. Worm grinding wheel grinding is equivalent to the meshing transmission between a rack tool and a workpiece gear. Two adjacent teeth of an asymmetric gear are used as the research object, and a single tooth of the rack is used as the grinding tool to construct a transient equivalent simulation analysis model. The axial feed motion of the grinding wheel and the rotational motion of the grinding wheel are combined into the movement of the grinding tool along the axial direction of the research object. Step 1) specifically includes the following sub-steps:

[0070] 1.1) Determine the relevant parameters of the asymmetric gear and rack tools, generate point cloud data of the rack tool using Matlab, and use UG software to build a three-dimensional model of two adjacent teeth of the asymmetric gear and one tooth of the equivalent rack.

[0071] 1.2) Use HyperMesh software to mesh the 3D model and import it into Abaqus software to complete the setting of gear material properties and tool material properties.

[0072] 2) Design orthogonal experiments based on the transient equivalent simulation analysis model, and conduct simulation experiments to determine the extent to which different process parameters affect the grinding heat of the tooth surfaces on both sides. Analyze and establish a relationship between the grinding heat of the tooth surfaces on both sides of the asymmetric gear and the process parameters. In this embodiment, a relationship between the grinding heat of the tooth surfaces on both sides of the asymmetric gear and the process parameters is established based on multivariate regression analysis.

[0073] After regression analysis, the relationship between the left tooth surface grinding heat and process parameters is obtained:

[0074]

[0075] After regression analysis, the relationship between the right tooth surface grinding heat and process parameters is obtained:

[0076]

[0077] Where B is the grinding allowance, V X is the feed speed, V Y is the rack linear speed.

[0078] 3) Construct a process parameter optimization model for asymmetric gear worm grinding wheel, and use intelligent optimization algorithm to obtain the optimal process parameter solution set to obtain the optimal process parameters. Step 3) specifically includes the following sub-steps:

[0079] 3.1) A multi-objective optimization model for the asymmetric worm wheel grinding process is established, with the tooth surface temperature difference T and grinding efficiency y as the targets. The grinding temperature calculation formula is shown in Equation (3). The grinding efficiency calculation formula is shown in Equation (4). The constraints are shown in Equation (5).

[0080] T=x2-x1 (3)

[0081]

[0082] Where x1 is the grinding heat of the left tooth surface, and x2 is the grinding heat of the right tooth surface.

[0083] When determining the constraints, first consider the grinding wheel linear speed constraint. To ensure the performance of the grinding wheel, ensure that the grinding wheel linear speed does not exceed the upper limit specified by the grinding wheel manufacturer, nor is it too low to affect the processing efficiency, thus setting V Yminm / s≤V Y ≤V Ymax m / s. Secondly, the grinding wheel feed speed constraint. If the grinding wheel feed speed is too high, the machine tool rigidity is insufficient, which is easy to produce tooth surface chatter marks. If it is too low, the processing time will be prolonged. Set V Xmin mm / min≤V X ≤V Xmax mm / min. Finally, the grinding thickness constraint. Too large a grinding thickness will increase the tooth surface roughness value and seriously cause gear burns. Too small a grinding thickness will increase the number of processing times and extend the processing time, so set B min mm≤B≤B max mm.

[0084] 3.2) Solve the multi-objective optimization model to obtain the process parameter solution set. The multi-objective optimization model ensures that the grinding temperature difference on both sides of the tooth surface is almost the same, ensuring the processing quality.

[0085] 3.3) Based on relevant processing parameters and processing experience, determine the optimal feed rate, optimal rack tool linear speed and optimal grinding allowance.

[0086] Example 2:

[0087] The main contents of this embodiment are the same as those of embodiment 1, wherein MOSFOA (Multi-Objective SuperbFairy-wren Optimization Algorithm) is used to solve the multi-objective optimization model to obtain the process parameter solution set. Figure 5 , step 3.2) specifically includes the following sub-steps:

[0088] 3.2.1) Initialize the process parameter optimization population: The process parameter population is represented as (a1, a2, ..., a m ), where m is a positive integer, a i For the i-th process parameter in the population, input a i The upper and lower limits are denoted as a max and a min .

[0089] Set r to a random number between [0, 1], and randomly initialize the process parameter population within the value range [0, 1] according to the process optimization model.

[0090] Set the maximum number of iterations it, the number of iterations nu = 0, and the maximum capacity of the archive M.

[0091] Randomly select a process parameter and assign it to the optimal process parameter E, and select a target value and assign it to the archived optimal target value.

[0092] Among them, the i-th process parameter a in the populationi As shown below:

[0093] a i = a min + r×(a max - a min ) (6)

[0094] 3.2.2) Determine whether the current iteration number nu < it holds. If so, go to step 3.2.3); otherwise, go to step 3.2.8).

[0095] 3.2.3) Calculate the target values of the tooth surface temperature difference T and the grinding efficiency y of the objective function, find the non-dominated solutions and store them in the archive.

[0096] 3.2.4) Judge the storage capacity of the archive: If the number of archived solutions reaches the maximum archive capacity, go to step 3.2.5); otherwise, go to step 3.2.6).

[0097] 3.2.5) Use the greedy strategy to save the current optimal solutions. Set a predefined distance for each solution, and calculate the number of solutions within this distance to measure the corresponding crowding degree. Then, according to the crowding degree, eliminate one or more solutions by the roulette method.

[0098] 3.2.6) Judge the behavior of the superb fairy-wrens during population update, and update the population according to the calculation formulas in different behavior stages. Step 3.2.6) specifically includes the following sub-steps:

[0099] 3.2.6.1) Define the environmental hazard factor s and the proportion b of juvenile birds in the population. The proportion b of juvenile birds in the population is a random number in the interval [0, 1], and the environmental hazard factor s = r1 * 20 + r2 * 20

[0100] In the formula, r1 and r2 are both random numbers in the interval [-1, 1] or random numbers satisfying a certain distribution to simulate the fluctuation of risks.

[0101] 3.2.6.2) Judge the behavior stage of the superb fairy-wrens according to the values of the environmental hazard factor s and the proportion b of juvenile birds in the population.

[0102] When the proportion r of juvenile birds in the population > 0.5, the superb fairy-wren population is in the juvenile growth stage. At this time, the individuals are updated using the following formula:

[0103]

[0104] where a t i,jrepresents the coordinates of individual i at iteration (or evaluation) time t, and r(0,1) is a random noise term used to enhance search diversity. If this update leads to a better value for the objective function, the new position is added to the population. This stage tends to involve extensive movement in the solution space, achieving extensive exploration.

[0105] When the proportion of young birds in the population r≤0.5 and the environmental risk factor s<20, the magnificent fairy-wren population is in the breeding and nursing stage, and the individuals are updated using the following formula:

[0106]

[0107] where a b is the current global optimal position, C is a constant (usually 0.8), and p is used to describe the process of the gradual expansion of the activity range of the adult bird during "take-turn teaching". It can be calculated using the ratio of the sine function to the current number of evaluations, for example:

[0108]

[0109] Where FEs is the number of evaluations performed so far, and MaxFEs is the maximum number of evaluations. In this way, as the breeding and incubation cycle progresses, the activity range of individuals in the local area gradually increases, which is conducive to the deep development of the population near the known optimal solution.

[0110] When the proportion of young birds in the population r≤0.5 and the environmental risk factor s>20, the magnificent fairy-wren population is in the natural enemy avoidance stage, and individuals are updated using the following formula:

[0111]

[0112] Where ab represents the global optimal solution location, l is the random step size generated by Levy flight, used for large-scale jumps, and k gradually changes with the number of evaluations to coordinate the escape distance. When a natural enemy attacks, the escape of an individual and the coordinated interference of other individuals can significantly improve the search's jumpiness, thus breaking free from the constraints of local optimality. Finally, to unify the update mechanisms of these three stages into the same search, it can be written as:

[0113]

[0114] Where r is the threshold for determining the proportion of juveniles within the population. If r > 0.5, it indicates a large number of juveniles, stimulating wide-area exploration during the juvenile growth phase. If r ≤ 0.5, it indicates a large number of adults, requiring further assessment of the risk factor s. If s < 20, the population enters the breeding and nursing phase, conducting localized, intensive search. If s ≥ 20, the population enters the predator avoidance phase, employing random hopping.

[0115] 3.2.7) Update the optimal collaborative process parameters: update the process parameter population, nu = nu + 1, and then go to step 3.2.2).

[0116] 3.2.8) Output the process parameter population values stored in the archive and the target value of the objective function.

[0117] Example 3:

[0118] Worm grinding wheel can be regarded as the meshing transmission between the rack tool and the gear. The two adjacent teeth of the asymmetric gear (G) are the research object, and a single rack tooth (W) is used as the grinding tool to replace the worm grinding wheel. The meshing of the two is regarded as an equivalent three-dimensional model. UG is used for three-dimensional modeling, and HyperMesh is used for meshing. Worm grinding wheel includes grinding wheel rotation motion, grinding wheel radial feed, grinding wheel axial feed, and workpiece rotation motion. Due to the low axial feed speed of the grinding wheel, in the transient grinding simulation model, the grinding wheel axial feed motion and the grinding wheel rotation motion are combined into the equivalent model. The movement of W along the G axis is as follows: Figure 2 The state of the rack tool engaging and disengaging is shown in Figure 3 As shown, 3a and 3b are the states when the rack and pinion are engaged, and 3c and 3d are the states when the rack and pinion are disengaged.

[0119] The main contents of this embodiment are the same as those of embodiment 1 or 2, wherein, in step 1.2), first, the finite element mesh model divided by the HyperMesh software is imported into the Abaqus software; then, the Property module of the simulation software is used to complete the setting of the gear material properties and the tool material properties, and the Johnson-Cook constitutive model is used to describe the relationship between the material properties and stress and temperature; secondly, through the meshing relationship of the gear rack, an assembly is established in the Assembly module, and an explicit dynamic thermal coupling analysis step is defined in the Step module; thirdly, through the Interaction module, the rigid body properties of the tool, the coupling relationship between the gear and the center of the circle, and the contact relationship between the gear and the tool are established; then, the Load module sets the boundary conditions, the initial temperature field, and the gear and tool speeds; finally, a task is created under the job module for finite element simulation analysis. Figure 4 The mesh division and temperature field diagram of some simulations are shown. 4a is the mesh division diagram, 4b is the temperature field diagram Figure I , 4c is the temperature field diagram Figure II .

[0120] Example 4:

[0121] The main contents of this embodiment are the same as any one of embodiments 1 to 3, wherein, in step 2), the main process parameters affecting the grinding process of the tooth surfaces on both sides are determined, mainly including the grinding allowance, feed speed, and rack linear speed as shown in Table 1:

[0122] Table 1 Grinding factor design table

[0123]

[0124] In order to study the influence of different parameters on the grinding temperature of asymmetric gears, each parameter contains three levels. The orthogonal experimental design method is adopted to design a three-factor three-level simulation scheme as shown in Table 2.

[0125] Table 2 Three-factor three-level orthogonal experimental design table

[0126]

[0127]

[0128] The equivalent simulation test of asymmetric gear worm grinding wheel was carried out, and the transient temperature of the tooth surface grinding on both sides under different conditions and the corresponding process parameters were obtained as shown in Table 3. Figure 6 , Figure 6 6a, 6b, 6c, and 6d show schematic diagrams of the maximum temperatures on the left and right tooth surfaces under simulation experiments with different machining parameters, respectively.

[0129] Table 3 Simulation results of three-factor three-level orthogonal experiment

[0130]

[0131]

[0132] Example 5:

[0133] The main contents of this embodiment are the same as any one of Embodiments 1 to 4. In particular, this embodiment is implemented on a certain type of asymmetric gear for an electric drive transmission, with a normal module of 1.5 mm, pressure angles of 20° and 25° on both sides of the gear teeth, and 100 teeth. The gear material is 20CrMnTi, and the rack tool material properties are shown in Table 3.

[0134] Table 3 Rack tool material properties

[0135]

[0136] A three-factor three-level design scheme was formulated and simulated. The grinding temperature of 27 groups of schemes was simulated using finite element simulation software to obtain the left and right tooth surface grinding temperatures of each group of schemes; the rack tool linear speed was set to three levels of 30, 35, and 40 m / s, the grinding wheel feed speed was set to three levels of 80, 90, and 100 mm / min, and the grinding thickness was set to three levels of 0.03, 0.04, and 0.05.

[0137] Table 4 Three-factor three-level orthogonal experiment table

[0138]

[0139]

[0140] A comprehensive optimization model considering the temperature difference on the tooth surface and grinding efficiency is constructed, with the control variables being the grinding allowance, feed rate, and rack tool linear speed. This is shown below:

[0141]

[0142] Combining the magnificent fairywren optimization algorithm and the multi-objective optimization solution mechanism, a multi-objective magnificent fairywren optimization algorithm is proposed. The algorithm is used to solve the optimal solution of the optimization model in step 4, and the optimal process parameter solution set is obtained as shown in Table 5 to ensure the processing quality.

[0143] Table 5: Table of some optimal process parameter solutions

[0144]

[0145]

[0146] According to the optimization results, under the premise of ensuring the performance of the grinding wheel, ensure that the grinding wheel linear speed neither exceeds the upper limit specified by the grinding wheel manufacturer nor is too low to affect the processing efficiency. Consider the influence of the grinding wheel feed speed on the rigidity of the machine tool, ensure the processing quality of the gear, and ensure that problems such as excessive tooth surface roughness and gear burn will not occur. Combined with relevant processing parameters and processing experience, the parameters feed speed are finalized as 38.4909m / s, rack tool linear speed is 80.0066mm / min, and grinding allowance is 0.03375mm.

Claims

1. A method for thermal equivalent simulation analysis and process parameter optimization of asymmetric gear worm grinding wheel grinding, wherein the worm grinding wheel and the workpiece gear are spatially staggered in meshing to achieve dual-pressure angle asymmetric gear grinding; characterized in that: The method includes the following steps: 1) Establish a transient equivalent simulation analysis model for gear grinding with an asymmetric gear hob worm wheel; wherein, the gear grinding with the worm wheel is equivalent to the meshing transmission of a rack cutter and a workpiece gear; taking two adjacent teeth of the asymmetric gear as the research object, and using a single tooth of the rack as the grinding tool to construct a transient equivalent simulation analysis model; synthesize the axial feed motion of the grinding wheel and the rotational motion of the grinding wheel into the movement of the grinding tool along the axis of the research object; 2) Design an orthogonal experiment based on the transient equivalent simulation analysis model, and conduct a simulation experiment to determine the influence degree of different process parameters on the grinding heat of both side tooth surfaces; analyze and establish the relationship between the grinding heat of both side tooth surfaces of the asymmetric gear and the process parameters; 3) Construct a process parameter optimization model for gear grinding with an asymmetric gear hob worm wheel, and use an intelligent optimization algorithm to obtain the optimal process parameter solution set and get the optimal process parameters.

2. The method for thermal equivalent simulation analysis and process parameter optimization of asymmetric gear worm grinding wheel according to claim 1, characterized in that: Step 1) specifically includes the following sub-steps: 1.1) Determine the relevant parameters of the asymmetric gear and the rack cutter, use Matlab to generate the point cloud data of the rack cutter, and combine with UG software to establish a three-dimensional model of two adjacent teeth of the asymmetric gear and one tooth of the equivalent rack; 1.2) Use HyperMesh software to mesh the three-dimensional model, import it into Abaqus software, and complete the setting of the gear material properties and the tool material properties.

3. The method for thermal equivalent simulation analysis and process parameter optimization of asymmetric gear worm grinding wheel according to claim 1, characterized in that: In step 2), establish the relationship between the grinding heat of both side tooth surfaces of the asymmetric gear and the process parameters based on multiple regression analysis; After regression analysis, the relationship between the grinding heat of the left tooth surface and the process parameters is obtained: After regression analysis, the relationship between the grinding heat of the right tooth surface and the process parameters is obtained: Where B is the grinding allowance, V X is the feed speed, V Y is the rack linear speed.

4. The method for thermal equivalent simulation analysis and process parameter optimization of asymmetric gear worm grinding wheel according to claim 3, characterized in that: Step 3) specifically includes the following sub-steps: 3.1) Establish a multi-objective optimization model for gear grinding with an asymmetric gear hob worm wheel with the tooth surface temperature difference T and the grinding efficiency y as the objectives; wherein, the calculation formula of the tooth surface temperature difference is shown in formula (3); the calculation formula of the grinding efficiency is shown in formula (4); the constraint conditions are shown in formula (5); T = x2 - x1 (3) In the formula, x1 is the grinding heat of the left tooth surface; x2 is the grinding heat of the right tooth surface; 3.2) Solve the multi-objective optimization model to obtain the process parameter solution set; 3.3) Combine the relevant processing parameters and processing experience to determine the optimal feed speed, the optimal linear speed of the rack cutter, and the optimal grinding allowance.

5. The method for thermal equivalent simulation analysis and process parameter optimization of asymmetric gear worm grinding wheel according to claim 4, characterized in that: Use MOSFOA to solve the multi-objective optimization model to obtain the process parameter solution set.

6. The method for thermal equivalent simulation analysis and process parameter optimization of asymmetric gear worm grinding wheel gear grinding according to claim 5, characterized in that: Step 3.2) specifically includes the following sub-steps: 3.2.1) Initialize the process parameter optimization population: The process parameter population is represented as (a1, a2, ..., a m ), where m is a positive integer, a i For the i-th process parameter in the population, input a i The upper and lower limits are denoted as a max and a min ; Set r as a random number between [0, 1], and randomly initialize the process parameter population within the numerical range [0, 1] according to the process optimization model; Set the maximum number of iterations it, the number of iterations nu = 0, and the maximum capacity M of the archive; Randomly select a process parameter and assign it to the optimal process parameter E, and select a target value and assign it to the optimal target value archived; in, The i-th process parameter a in the population i As shown below: a i =a min +r×(a max -a min ) (6) 3.2.2) Judge whether the current number of iterations nu < it holds. If so, enter step 3.2.3); otherwise, enter step 3.2.8); 3.2.3) Calculate the target values of the objective functions of the tooth surface temperature T and the machining efficiency y, find the non-dominated solutions and store them in the archive; 3.2.4) Determine the storage capacity of the archive library: if the number of archives reaches the maximum archive capacity, go to step 3.2.5); otherwise, go to step 3.2.6); 3.2.5) Use a greedy strategy to save the current optimal solution. For each solution, set a predefined distance. Count the number of solutions within this distance to measure the corresponding congestion level. Then, use a roulette wheel method to eliminate one or more solutions based on the congestion level. 3.2.6) Determine the behavior of the Magnificent Fairywren during population renewal and update the population based on calculation formulas for different behavioral stages; 3.2.7) Update the optimal collaborative process parameters: update the process parameter population, nu = nu + 1, and then go to step 3.2.2); 3.2.8) Output the process parameter population values stored in the archive and the target value of the objective function.

7. The method for thermal equivalent simulation analysis and process parameter optimization of asymmetric gear worm grinding wheel according to claim 6, characterized in that: Step 3.2.6) specifically includes the following sub-steps: 3.2.6.1) Define the environmental risk factor s and the proportion of young birds in the population b, where the proportion of young birds in the population b is a random number in the interval [0,1], and the environmental risk factor s = r1*20+r2*20 Where r1 and r2 are both random numbers in the interval [-1, 1] or random numbers that satisfy a certain distribution to simulate risk fluctuations; 3.2.6.2) Determine the behavioral stage of the magnificent fairy-wren based on the environmental risk factor s and the proportion of juvenile birds in the population b; When the proportion of young birds in the population r>0.5, the magnificent fairy-wren population is in the juvenile growth stage, and the individuals are updated using the following formula: in represents the coordinates of the i-th individual at iteration time t, and r(0,1) is a random noise term used to enhance the diversity of the search. If this update can achieve a better value for the objective function, the new position is replaced into the population. This stage tends to move around a large area in the solution space to achieve extensive exploration. When the proportion of young birds in the population r≤0.5 and the environmental risk factor s<20, the magnificent fairy-wren population is in the breeding and nursing stage, and the individuals are updated using the following formula: where a b is the current global optimal position, C is a constant (usually 0.8), and p is used to describe the process of the gradual expansion of the activity range of the adult bird during "take-turn teaching". It can be calculated using the ratio of the sine function to the current number of evaluations, for example: Where FEs is the number of evaluations currently performed, and MaxFEs is the maximum number of evaluations. In this way, as the breeding and incubation cycle progresses, the activity range of individuals in the local area gradually increases, which is conducive to the in-depth development of the population near the known optimal solution. When the proportion of young birds in the population r≤0.5 and the environmental risk factor s>20, the magnificent fairy-wren population is in the natural enemy avoidance stage, and individuals are updated using the following formula: Where ab represents the global optimal solution location, l is the random step size generated by Levy flight, which is used for large-scale jumps, and k gradually changes with the number of evaluations to coordinate the escape distance. When a natural enemy attacks, the escape of an individual and the coordinated interference of other individuals can greatly improve the jumpability of the search, thus breaking free from the constraints of local optimality. Finally, to unify the update mechanisms of these three stages into the same search, it can be written as: Among them, r is the judgment threshold of the proportion of young birds within the population. If r>0.5, it means that there are many young birds, and it is necessary to stimulate wide-area exploration during the growth stage of young birds; if r≤0.5, it means that there are many adult birds, and the size of the risk factor s needs to be further judged; if s<20, it enters the breeding and feeding stage to conduct local fine search; if s≥20, it enters the natural enemy avoidance stage and randomly jumps.

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