CN116305633A - Tooth surface modification optimization method of secondary reduction gear system based on NSGA-II algorithm - Google Patents
Tooth surface modification optimization method of secondary reduction gear system based on NSGA-II algorithm Download PDFInfo
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Abstract
The invention discloses a tooth surface modification optimization method of a secondary reduction gear system based on an NSGA-II algorithm, which comprises the following steps: establishing a gear system model of the secondary speed reducer according to the actual structure; determining a plurality of typical operating conditions of the two-stage reduction gear system; determining a shape modification method; establishing a multi-objective optimized mathematical model taking the minimum of peak and peak values of the load transfer errors under multiple working conditions as an objective function; based on NSGA-II algorithm, optimizing tooth surface modification parameters of a first-stage reduction gear pair and a second-stage reduction gear pair by using a secondary development interface of professional gear analysis software and Python language programming optimization program to obtain respective Pareto optimal solution sets; and selecting a tooth surface modification optimization scheme in the Pareto optimal solution set to finish the tooth surface modification optimization work. The invention combines NSGA-II multi-objective genetic algorithm with professional gear analysis software, and provides an optimization method with stronger optimizing capability and quicker and more accurate optimizing for the tooth surface shape modification optimization work of multiple working conditions.
Description
Technical Field
The invention belongs to the technical field of tooth surface modification optimization of a secondary speed reducer gear system, and particularly relates to a tooth surface modification optimization method of a secondary speed reducer gear system based on an NSGA-II multi-target genetic algorithm.
Background
The electric automobile is powered by the motor, and the motor can realize stepless speed regulation, forward rotation and reverse rotation, so that a complex multi-gear transmission in the fuel oil automobile is not needed, but the electric automobile is still necessary to be provided with a speed reducer from the aspects of power performance, economy and the like. The two-stage speed reducer is the most common speed reducing mechanism on the current electric automobile and mainly comprises a first-stage gear pair, a second-stage gear pair, an input shaft, an intermediate shaft, an output shaft, a bearing, a shell and other parts. The power from the motor is transmitted to the intermediate shaft after being decelerated by the first-stage gear pair, and then transmitted to the output shaft after being decelerated by the second-stage gear pair, so that the power transmission is realized.
In the transmission process of the gear system, transmission errors, namely the difference between the actual rotation angle and the theoretical rotation angle of the driven wheel when the driving wheel rotates by a certain angle, are inevitably generated due to load deformation, manufacturing errors and assembly errors of gears, shafts, bearings, a shell and the like. The research result shows that the corresponding relation exists between the gear noise and the transmission error. Through the mode of tooth surface shaping, the peak value of the transmission error can be effectively reduced, so that vibration noise generated in the gear meshing process is reduced. At present, a manual shape correction or orthogonal table method is often adopted in engineering to determine the tooth surface shape correction parameters, and the traditional method for determining the tooth surface shape correction parameters is low in efficiency and easy to obtain a local optimal result because the motor torque range is wider, the working conditions are more, and the tooth surface shape correction parameters are more. Therefore, how to quickly and accurately determine a tooth surface modification scheme aiming at multiple working conditions is a problem to be solved urgently.
The invention in China publication No. CN114880813A provides a three-shunt speed reducer noise reduction method based on gradual modification and gradual optimization, and the scheme establishes a three-shunt speed reducer helical gear model in the ROMAX, optimizes tooth surface microscopic modification parameters by adopting a genetic algorithm, and has a good effect after the optimized tooth surface microscopic modification parameters. However, the optimization algorithm used in the scheme is a common genetic algorithm, so that local optimization is easy to fall into when multi-objective optimization is carried out, and the optimization model adopted in the scheme is used for reducing the situation that the tooth surface contact spots are unbalanced in order to reduce transmission errors as much as possible in the optimization process.
Disclosure of Invention
The invention provides a tooth surface modification optimization method of a secondary reduction gear system based on an NSGA-II (Nondominated Sorting Genetic Algorithm-II) multi-target genetic algorithm, which can quickly and accurately reduce transmission errors under multiple working conditions under the condition of ensuring good tooth surface contact state and effectively improve NVH (Noise, vibration, harshness) performance of the secondary reduction gear system.
In order to achieve the purpose of the invention, the tooth surface modification optimization method of the secondary reduction gear system based on the NSGA-II algorithm comprises the following steps:
s1, establishing a secondary speed reducer gear system model in professional gear analysis software according to an actual structure;
s2, determining various typical working conditions of the two-stage speed reducer gear system;
s3, determining a shape modifying method;
s4, determining an optimization variable, an optimization target and constraint conditions, and establishing a multi-target optimization mathematical model taking the minimum load transfer error peak-to-peak value under multiple working conditions as an objective function;
s5, based on an NSGA-II (Nondominated Sorting Genematic Algorithm-II) algorithm, utilizing a secondary development interface of professional gear analysis software, and compiling an automatic optimization program by using Python language, and respectively optimizing tooth surface modification parameters of a first-stage reduction gear pair and a second-stage reduction gear pair to obtain respective Pareto optimal solution sets;
s6, selecting a tooth surface modification optimization scheme in the Pareto optimal solution set, and completing tooth surface modification optimization work;
further, in step S1, the gear comprises an input shaft, an intermediate shaft, an output shaft, a first-stage reduction gear pair, a second-stage reduction gear pair, a bearing, a reducer housing and the like; the speed reducer shell is imported through an external entity grid file;
further, in step S2, according to the characteristics of the motor, the working torque range of the motor is discretized, so as to obtain various typical working conditions;
further, in step S3, the tooth surface modification method includes pressure angle modification, tooth form drum modification, helix angle modification, and tooth form drum modification;
further, the optimization variable in the step S4 is the pinion pressure angle modification amount x of the meshing gear pair 1 Tooth drum shape correction amount x 2 Helix angle modification x 3 And tooth drum repair amount x 4 ；
Further, in step S4, since the torque range of the motor is relatively wide, in order to make the optimization result effective for multiple working conditions, the minimum load transmission error peak-to-peak value under three different load working conditions is selected as three objective functions, and the expression is as follows:
wherein T is ej Indicating the load-bearing transmission error of the gear pair in one engagement period under the working condition j.
Further, in step S4, the constraint range of the optimization variable is determined according to the actual processing capability, wherein:
further, the constraint in step S4 includes, in addition to the constraint for the optimization variable in claim 4, an integer constraint for the optimization variable in consideration of the accuracy constraint of gear processing:
x i ∈integers,i＝1,2,3,4 (3)
further, in order to effectively ensure that the unbalanced load phenomenon does not occur in the tooth surface load distribution situation, the constraint conditions in step S4 further include:
P edgemaxj /P maxj <k (4)
wherein k is a number less than 1, P edgemaxj For maximum contact stress of tooth surface edge under working condition j, P maxj The maximum contact stress of the tooth surface under the working condition j.
Further, the step S5 includes the following steps:
s501, setting population scale, maximum evolution algebra, crossover probability and mutation probability;
s502, initializing a population;
s503, calculating an objective function, and grading the population by Pareto;
s504, respectively calculating the crowdedness of the individual under each Pareto grade;
s505, selecting, crossing and mutating;
s506, generating a new population by utilizing an elite selection strategy;
s507, setting a maximum evolution algebra Gen as a termination condition, if the maximum evolution algebra is not met, adding 1 to the evolution times count and returning to the step S503 to continue operation; if the maximum evolution times are met, the optimization is finished, and a final Pareto solution set is obtained.
Further, in step S5, the secondary development interface of the professional gear analysis software functions in the following two points: 1) Using a secondary development interface to make each individual in the population generated by NSGA-II algorithm contain the pressure angle modification quantity x 1 Tooth drum shape correction amount x 2 Helix angle modification x 3 And tooth drum repair amount x 4 Transmitting the data to professional gear analysis software and carrying out bearing contact analysis calculation; 2) Using a secondary development interface to analyze the bearing contact to obtain a result, namely a bearing transfer error T under working conditions ej Maximum contact stress P of tooth surface edge edgemaxj Maximum contact stress P with tooth surface maxj And passed back to the NSGA-ii algorithm for fast non-dominant ranking and congestion calculation.
Further, a load-bearing tooth surface contact analysis method based on a mixing method is adopted, the method is quite close to the result of contact analysis by adopting full finite elements, and has great advantages in efficiency, and the basic theory is as follows:
firstly, generating a finite element grid of a gear according to macroscopic parameters of the gear, and obtaining a flexibility matrix of tooth surface grid nodes through a Guyan reduction method:
wherein f bij(1) Representing the bending-shear compliance coefficient, f, of the driving gear contact point j to the contact point i bij(2) The bending-shearing compliance coefficient of the driven gear contact point j to the contact point i is shown, and n is the number of contact points at the engagement position.
Secondly, according to the Hertz contact theory, local contact deformation vectors u of each sectional contact line are obtained:
u＝[u 1 u 2 u 3 … u n ] T (6)
wherein u is i Representing the local contact deformation of the ith contact point;
listing an n-order bearing tooth surface contact equation set according to the deformation coordination condition of the contact point:
wherein P is the load distribution vector of the meshing position, x is the load transmission error of the meshing position, d is the residual clearance column vector at the contact point, w is the initial tooth flank clearance column vector formed by factors including gear manufacturing error, assembly error, meshing dislocation quantity, gear shaping quantity and the like, e is the unit row vector, and P is the total normal load of gear transmission.
Finally, the load transmission error and the tooth surface load distribution at the meshing position can be finally obtained by iteratively solving the nonlinear equation set. Finally, the above analysis is carried out on different meshing positions in one meshing period, so that the bearing transmission error of the gear pair in one meshing period and the contact stress distribution of the whole tooth surface can be obtained.
Further, in step S6, the relationships between the optimization schemes in the Pareto solution set obtained are all non-dominant, that is, there is no clear good-bad relationship between the optimization results, and the optimization results can be selected according to requirements.
Compared with the related art, the invention has at least the following advantages:
1) The NSGA-II algorithm is a multi-target genetic algorithm, and introduces a rapid non-dominant sorting technology, a crowding degree sorting technology, an elite selection strategy and the like, so that the time complexity of the algorithm is reduced; meanwhile, the distribution space of the optimal solution set is expanded. The excellent individuals are saved by adopting a non-dominant sorting method, the diversity of the population is guaranteed by using elite selection strategies, and the method has the characteristics of good robustness, strong optimizing capability and the like.
2) The invention is based on NSGA-II multi-objective genetic algorithm, utilizes professional gear analysis software secondary development interface, and adopts Python language to compile automatic optimization program. The method has strong universality, can be suitable for two-stage speed reducers of different types, and can quickly and accurately obtain corresponding tooth surface modification schemes.
3) In the optimization model, the constraint condition for avoiding the offset load of the tooth surface contact spots is added, the constraint can effectively ensure that the phenomenon of the offset load of the tooth surface contact spots caused by the reduction of the load transmission error can not occur in the optimization process, and the NSGA-II genetic algorithm has strong capability in the aspect of multi-objective optimization, so that the transmission error under multiple working conditions can be rapidly and accurately reduced under the condition of ensuring the good contact state of the tooth surface.
4) The NSGA-II multi-objective genetic algorithm is combined with the professional gear analysis software, so that an optimization method with stronger optimizing capability and quicker and more accurate optimizing is provided for the tooth surface modification optimization work aiming at multiple working conditions, and the time cost of enterprises in the tooth surface modification optimization work process is reduced.
Drawings
FIG. 1 is a flowchart of a method for optimizing tooth surface modification of a secondary reducer gear system based on NSGA-II algorithm, which is provided by an embodiment of the invention.
Fig. 2 is a schematic diagram of a two-stage reduction gear system in accordance with an embodiment of the present invention.
Fig. 3 is a schematic diagram of the pressure angle modification in an embodiment of the present invention.
Fig. 4 is a schematic diagram of a toothed drum shape modification in an embodiment of the present invention.
Fig. 5 is a schematic diagram of helix angle modification in an embodiment of the present invention.
Fig. 6 is a schematic diagram of a tooth drum modification in accordance with an embodiment of the present invention.
FIG. 7 is a graph showing the peak-to-peak ratio of the load transmission errors under different conditions before and after optimizing the first stage reduction gear pair according to the embodiment of the present invention.
FIG. 8 is a graph showing the peak-to-peak ratio of the load transmission errors under different conditions before and after optimizing the second stage reduction gear pair according to the embodiment of the present invention.
FIG. 9 is a graph of the contact patch of the tooth surface of the primary reduction gear set of the embodiment of the present invention with the drive wheel unmodified under condition 3.
FIG. 10 is a graph of tooth surface contact patch of a first stage reduction gear pair after a driver is shaped under condition 3 in accordance with an embodiment of the present invention.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
As shown in fig. 1, the tooth surface modification optimization method of the secondary reduction gear system based on NSGA-ii (Nondominated Sorting Genematic Algorithm-ii) algorithm provided by the invention comprises the following steps:
and S1, establishing a secondary speed reducer gear system model in professional gear analysis software according to the actual structure.
In some embodiments of the invention, the professional gear analysis software employs MASTA.
The two-stage speed reducer gear system model comprises an input shaft, an intermediate shaft, an output shaft, a first-stage speed reduction gear pair, a second-stage speed reduction gear pair, a bearing, a speed reducer shell and the like, wherein other parts except the speed reducer shell are all completed through parametric modeling, and the speed reducer shell is imported through an external physical grid file. In some embodiments of the invention, the two-stage reduction gear system model is established as shown in FIG. 2. The spiral angle of the primary reduction gear pair is 26.5 degrees, the normal modulus is 2mm, the normal pressure angle is 17 degrees, the number of teeth of the pinion is 26, the tooth width is 18mm, the number of teeth of the bull gear is 59, the tooth width is 18mm, the spiral angle of the secondary reduction gear pair is 26.5 degrees, the normal modulus is 2.29mm, the normal pressure angle is 17 degrees, the number of teeth of the pinion is 25, the tooth width is 30mm, the number of teeth of the bull gear is 72, the tooth width is 26mm, and the gear materials are 20CrMnTi.
And S2, determining various typical working conditions of the two-stage speed reducer gear system.
According to the characteristics of the motor, the working torque range of the motor is discretized to obtain various typical working conditions, and in some embodiments of the invention, the two-stage speed reducer gear system comprises working conditions 1, 2, 3, 4, 5 and 6, and specific parameters are shown in table 1:
TABLE 1
S3, determining a shape modifying method.
The tooth surface modification methods selected include four types of pressure angle modification, tooth form drum modification, helix angle modification, and tooth form drum modification, as shown in fig. 3 to 6.
S4, determining an optimization variable, an optimization target and constraint conditions, and establishing a multi-target optimization mathematical model taking the minimum load transfer error peak-to-peak value under multiple working conditions as an objective function in order to enable the optimization result to be effective to multiple working conditions due to the wider torque range of the motor.
In some embodiments of the present invention, a multi-objective optimized mathematical model is built that targets the minimum of the load transfer error peaks under conditions 1, 3, and 5 (in other embodiments, other conditions may be selected, or other numbers of conditions are not limited to 3):
optimizing variables: x is x 1 、x 2 、x 3 、x 4 ；
Optimization target:
constraint conditions:
x i ∈integers,i＝1,2,3,4
wherein x is 1min Is the minimum value of the pressure angle shaping quantity, x 1max For maximum pressure angle trim, x 2min Is the minimum value of the tooth drum shape modification quantity, x 2max Is the minimum value of the tooth drum shape modification quantity, x 3min Is the minimum value of the spiral angle modification quantity, x 3max Is the minimum value of the spiral angle modification quantity, x 4min Is the minimum value of the tooth drum-shaped trimming quantity, x 4max Is the minimum value of the tooth-to-drum repair quantity, k is a number less than 1, P edgemaxj For maximum contact stress of tooth surface edge under working condition j, P maxj The maximum contact stress of the tooth surface under the working condition j.
Adds the constraint condition (P) of avoiding the offset load of the tooth surface contact spots edgemaxj /P maxj <k) The constraint can effectively ensure that the phenomenon of unbalanced load of the tooth surface contact spots caused by reducing the load transmission error does not occur in the optimization process.
In some embodiments of the present invention, specific values of the parameters in the constraint condition are obtained:
wherein x is 1 ～x 4 The pressure angle modification amount, the tooth form drum modification amount, the helix angle modification amount and the tooth form drum modification amount (mu m) of the right tooth surface of the pinion gear of the meshing gear pair are respectively, T ej For the bearing transmission error (μm) in the process of the engagement of the crankshaft gear ring and the scissor pair teeth under the working condition j in Table 1, P maxj And P edgemaxj The maximum contact stress of the tooth surface and the maximum contact stress of the edge of the tooth surface in the process of meshing the crankshaft gear ring and the scissor pair teeth under the working condition j in the table 1 are respectivelyLarge contact stress (MPa). f (f) 1 (x 1 ,x 2 ,x 3 ,x 4 ) The transmission error peak value, f, is the gear bearing under the working condition 1 2 (x 1 ,x 2 ,x 3 ,x 4 ) The transmission error peak value, f, is the gear bearing under the working condition 3 3 (x 1 ,x 2 ,x 3 ,x 4 ) The transmission error peak to peak for the gear carrier under condition 5, integers.
Wherein, in some embodiments of the invention, the load transfer error T under the working condition j ej Maximum contact stress P of tooth surface edge edgemaxj Maximum contact stress P with tooth surface maxj All are calculated by running a load-bearing tooth surface contact analysis program in professional gear analysis software, and the load-bearing tooth surface contact analysis is calculated by adopting a classical gear slice model.
S5, based on an NSGA-II algorithm, utilizing a secondary development interface of professional gear analysis software, compiling an automatic optimization program by using Python language, and respectively optimizing tooth surface modification parameters of a first-stage reduction gear pair and a second-stage reduction gear pair, wherein the method comprises the following specific steps of:
s501, setting the population scale as 25, the maximum evolution algebra as 100, the crossover probability as 0.9 and the mutation probability as 0.2;
s502, initializing a population;
s503, calculating an objective function, and grading the population by Pareto;
s504, respectively calculating the crowdedness of the individual under each Pareto grade;
s505, selecting, crossing and mutating;
s506, generating a new population by utilizing an elite selection strategy;
s507, setting a maximum evolution algebra Gen as a termination condition, if the maximum evolution algebra is not met, adding 1 to the evolution times count and returning to the step S503 to continue operation; if the maximum evolution times are met, the optimization is finished, and a final Pareto solution set is obtained.
In some of the embodiments of the present invention, table 2 shows the Pareto solution set for the resulting first stage reduction gear pair and table 3 shows the Pareto solution set for the resulting second stage reduction gear pair.
TABLE 2
TABLE 3 Table 3
Finally, scheme 5 in table 2 was selected as the profile modification of the first stage reduction gear pair, and scheme 3 in table 3 was selected as the profile modification of the second stage reduction gear pair. (the relationship between the solutions in the table is non-dominant, each solution has its own advantages, here chosen because the performance is relatively more average under three conditions.)
After the shape is modified and optimized by the method, the peak value of the load-bearing transmission error of the first-stage reduction gear pair is reduced under all working conditions, and the average reduction amplitude reaches 40 percent, as shown in a figure 7; the peak value of the load-bearing transmission error of the second-stage reduction gear pair is reduced under all working conditions, and the average reduction amplitude reaches 38%, as shown in fig. 8. The result shows that the optimization method can effectively reduce the peak value of the load-bearing transmission error of each reduction gear pair in the whole torque range, and further effectively improve the NVH (Noise, vibration and Harshness) performance of the secondary reduction gear system.
After the shape is modified and optimized by the method, the tooth surface contact state under each working condition is improved, and the tooth surface contact spots are all in central contact. Taking the first stage reduction gear pair as an example under the working condition 3, the tooth surface contact spots before and after optimization are shown in fig. 9 and 10.
The above embodiments are merely illustrative of the calculation process of the present invention, and are not limiting thereof. Although the invention has been described in detail with reference to the foregoing examples, it will be understood by those skilled in the art that modifications may be made to the computing process described in the foregoing embodiments, or equivalents may be substituted for elements thereof, without departing from the spirit and scope of the computing method of the invention in its corresponding aspects.
Claims (10)
1. The tooth surface modification optimization method of the secondary reduction gear system based on the NSGA-II algorithm is characterized by comprising the following steps of:
s1, establishing a secondary speed reducer gear system model in professional gear analysis software according to an actual structure;
s2, determining various working conditions of the gear system of the secondary speed reducer;
s3, determining a shape modifying method;
s4, determining an optimization variable, an optimization target and constraint conditions, and establishing a multi-target optimization mathematical model taking the minimum load transfer error peak-to-peak value under multiple working conditions as an objective function, wherein the multi-target optimization mathematical model is added with a constraint condition for avoiding the contact spot unbalanced load of a tooth surface;
s5, optimizing tooth surface modification parameters of the first-stage reduction gear pair and the second-stage reduction gear pair respectively by using a secondary development interface of professional gear analysis software and using a Python language programming optimization program based on an NSGA-II algorithm to obtain respective Pareto optimal solution sets;
s6, selecting a tooth surface modification optimization scheme in the Pareto optimal solution set, and completing tooth surface modification optimization work.
2. The method for optimizing the tooth surface modification of the secondary reduction gear system based on the NSGA-II algorithm according to claim 1, wherein the secondary reduction gear system model comprises an input shaft, an intermediate shaft, an output shaft, a first-stage reduction gear pair, a second-stage reduction gear pair, a bearing and a reduction gear shell, and other parts except the reduction gear shell are all completed through parametric modeling, and the reduction gear shell is imported through an external physical grid file.
3. The method for optimizing the tooth surface modification of a secondary reduction gear system based on the NSGA-ii algorithm according to claim 1, wherein in step S2, the working torque range of the motor is discretized according to the characteristics of the motor used, so as to obtain a plurality of different working conditions.
4. The method for optimizing the tooth surface modification of a secondary reduction gear system based on the NSGA-ii algorithm according to claim 1, wherein in step S3, the tooth surface modification method used is determined to include four kinds of pressure angle modification, tooth form drum modification, helix angle modification and tooth direction drum modification.
5. The method for optimizing the tooth surface modification of a secondary reduction gear system based on the NSGA-ii algorithm according to claim 1, wherein the optimization variable in step S4 is the pinion pressure angle modification x of the meshing gear pair 1 Tooth drum shape correction amount x 2 Helix angle modification x 3 And tooth drum repair amount x 4 。
6. The method for optimizing tooth surface modification of a secondary reduction gear system based on NSGA-ii algorithm according to claim 1, wherein in step S4, the minimum of peak-to-peak values of load transmission errors under a plurality of different load conditions is selected as an objective function, and the minimum of peak-to-peak values of transmission errors under three different load conditions is taken as an objective function as an example, and the expression of the objective function is as follows:
wherein T is ej Representing the bearing transmission error of the gear pair in one engagement period under the working condition j, f 1 (x 1 ,x 2 ,x 3 ,x 4 )、f 2 (x 1 ,x 2 ,x 3 ,x 4 )、f 3 (x 1 ,x 2 ,x 3 ,x 4 ) Representing gear bearings under 3 different working conditionsLoad transfer error peak-to-peak;
the constraint range of the optimization variable is determined according to the actual processing capacity, wherein:
wherein x is 1min Is the minimum value of the pressure angle shaping quantity, x 1max For maximum pressure angle trim, x 2min Is the minimum value of the tooth drum shape modification quantity, x 2max Is the minimum value of the tooth drum shape modification quantity, x 3min Is the minimum value of the spiral angle modification quantity, x 3max Is the minimum value of the spiral angle modification quantity, x 4min Is the minimum value of the tooth drum-shaped trimming quantity, x 4max Is the minimum value of the tooth-to-drum trimming quantity;
the expression for avoiding the partial load of the tooth surface contact spots as the constraint condition
P edgemaxj /P maxj <k (4)
Wherein k is a number less than 1, P edgemaxj For maximum contact stress of tooth surface edge under working condition j, P maxj The maximum contact stress of the tooth surface under the working condition j.
7. The NSGA-ii algorithm-based two-stage reduction gear system tooth flank shape optimization method according to claim 6, wherein the constraints in step S4 further include integer constraints for optimization variables, taking into account the accuracy constraints of gear machining:
x i ∈integers,i＝1,2,3,4 (3)
wherein integers represent integers.
8. The method for optimizing the tooth surface modification of a secondary reduction gear system based on the NSGA-ii algorithm according to any one of claims 1 to 7, characterized in that step S5 comprises the steps of:
s501, setting population scale, maximum evolution algebra, crossover probability and mutation probability;
s502, initializing a population;
s503, calculating an objective function, and grading the population by Pareto;
s504, respectively calculating the crowdedness of the individual under each Pareto grade;
s505, selecting, crossing and mutating;
s506, generating a new population by utilizing an elite selection strategy;
s507, setting a maximum evolution algebra Gen as a termination condition, if the maximum evolution algebra is not met, adding 1 to the evolution times count and returning to the step S503 to continue operation; if the maximum evolution times are met, the optimization is finished, and a final Pareto solution set is obtained.
9. The method for optimizing the tooth surface modification of the secondary reduction gear system based on the NSGA-ii algorithm according to claim 8, wherein in the step S5, the secondary development interface of the professional gear analysis software functions in the following two points:
1) Using a secondary development interface to make each individual in the population generated by NSGA-II algorithm contain the pressure angle modification quantity x 1 Tooth drum shape correction amount x 2 Helix angle modification x 3 And tooth drum repair amount x 4 Transmitting the tooth surface contact analysis calculation to professional gear analysis software;
2) Using a secondary development interface to analyze the bearing contact to obtain a result, namely a bearing transfer error T under working conditions ei Maximum contact stress P of tooth surface edge edgemaxi Maximum contact stress P with tooth surface maxi And passed back to the NSGA-ii algorithm for fast non-dominant ranking and congestion calculation.
10. The method for optimizing the tooth surface modification of the secondary reduction gear system based on the NSGA-II algorithm according to claim 9, wherein a load-bearing tooth surface contact analysis method based on a mixing method is adopted, and the basic theory is as follows:
firstly, generating a finite element grid of a gear according to macroscopic parameters of the gear, and obtaining a flexibility matrix of tooth surface grid nodes through a Guyan reduction method:
wherein f bij(1) Representing the bending-shear compliance coefficient, f, of the driving gear contact point j to the contact point i bij(2) A bending-shearing flexibility coefficient of the contact point j of the driven gear to the contact point i is shown, and n is the number of the contact points of the meshing position;
secondly, according to the Hertz contact theory, local contact deformation vectors u of each sectional contact line are obtained:
u＝[u 1 u 2 u 3 … u n ] T (6)
wherein u is i Representing the local contact deformation of the ith contact point;
listing an n-order bearing tooth surface contact equation set according to the deformation coordination condition of the contact point:
wherein P is the load distribution vector of the meshing position, x is the load transmission error of the meshing position, d is the residual clearance column vector at the contact point, w is the initial tooth flank clearance column vector formed by factors including gear manufacturing error, assembly error, meshing dislocation quantity, gear shaping quantity and the like, e is the unit row vector, and P is the total normal load of gear transmission.
Finally, the load transmission error and the tooth surface load distribution at the meshing position are finally obtained by iteratively solving the nonlinear equation set, and finally, the load transmission error and the contact stress distribution of the whole tooth surface of the gear pair in one meshing period can be obtained by carrying out the analysis on different meshing positions in one meshing period once.
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| CN116663156B (en) * | 2023-07-10 | 2023-11-07 | 陕西法士特齿轮有限责任公司 | Microcosmic modification method and microcosmic modification system for tooth surface of cylindrical gear of transmission |
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