CN113312726A - GCr15 bearing surface layer performance optimization method based on particle swarm optimization and ultrasonic rolling - Google Patents
GCr15 bearing surface layer performance optimization method based on particle swarm optimization and ultrasonic rolling Download PDFInfo
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Abstract
The invention relates to a GCr15 bearing surface layer performance optimization method based on a particle swarm algorithm and ultrasonic rolling, which comprises the following steps of: (1) determining factors, levels and indexes according to the technological parameters of the ultrasonic rolling equipment and the GCr15 bearing surface layer performance indexes, and performing an orthogonal test; (2) constructing a surface performance mathematical model by using a stepwise regression method; (3) carrying out variance analysis on the mathematical model; (4) performing multi-objective optimization of the surface layer performance; (5) and solving the optimal surface performance index parameter domain and the corresponding processing process parameter domain. The invention combines the stepwise regression method and the particle swarm optimization, carries out multi-objective optimization on the surface performance of the ultrasonic rolling GCr15 bearing, has simple calculation process and strong practicability, realizes the comprehensiveness of the optimization algorithm, and can improve the surface quality of the workpiece and the fatigue performance of the workpiece by using the optimal surface performance index parameter domain and the processing parameter domain obtained by the optimization method.
Description
Technical Field
The invention relates to the technical field of surface precision machining, in particular to a GCr15 bearing surface layer performance optimization method based on a particle swarm algorithm and ultrasonic rolling.
Background
The bearing is widely applied to various mechanical equipment, is called by the name of a mechanical joint, and the design quality of the bearing directly influences the performance of the bearing and even a main machine. With the continuous improvement of the automation level, more strict requirements are put on the performance of the bearing, so that the surface performance of the bearing needs to be optimally designed. The optimization design targets may be surface roughness, hardening strength, residual stress, etc., and some of these optimization targets are as large as possible and some are as small as possible. How to give consideration to all indexes and all factors, making a decision from a plurality of design schemes, and selecting a scheme which can meet all requirements is a problem frequently encountered in the optimization design of the bearing.
In recent years, scholars at home and abroad respectively use theoretical analysis, machining tests, finite element simulation, numerical calculation and other methods to optimize the machining process of the bearing. In the aspect of multi-objective optimization, systematic deep research on the surface performance of the bearing is less, and the optimization design by combining a particle swarm algorithm and an ultrasonic rolling bearing surface mode is rarely mentioned. Currently, it is the key to realize the control of the surface performance to explore the relationship and influence rule between the surface performance parameters and the processing parameters. The establishment of the optimal matching criterion of the machining parameters and the surface performance parameters and the realization of the accurate control of the machining parameters are closely concerned in the bearing production field. Therefore, in order to improve the surface properties of the bearing, improve the surface quality and prolong the service life of the bearing, the control of the surface properties is urgently required to be deeply researched.
Disclosure of Invention
The invention aims to provide a GCr15 bearing surface layer performance optimization method based on a particle swarm algorithm and ultrasonic rolling, which is clear in optimization direction, high in speed and remarkable in optimization effect, and can accurately determine a globally optimal surface layer performance index parameter domain and a corresponding processing process parameter domain, so that the bearing surface layer performance is improved, and the surface quality is improved.
In order to achieve the purpose, the invention adopts the technical scheme that: a GCr15 bearing surface layer performance optimization method based on particle swarm optimization and ultrasonic rolling comprises the following steps:
s1, determining factors, levels and indexes according to the technological parameters of the ultrasonic rolling equipment and the GCr15 bearing surface layer performance indexes, and performing an orthogonal test;
s2, constructing a GCr15 bearing surface performance mathematical model by using a stepwise regression method based on the orthogonal test analysis result;
s3, carrying out variance analysis on the mathematical model to ensure the mathematical model to be accurate and reliable;
s4, performing multi-objective optimization on the surface performance of the GCr15 bearing by using a particle swarm optimization;
and S5, solving to obtain a globally optimal GCr15 bearing surface performance index parameter domain and a corresponding processing process parameter domain.
Further, the process parameters of the ultrasonic rolling equipment in the step S1 are rotating speed, feeding speed, amplitude and static pressure, and the GCr15 surface layer performance indexes are surface roughness, work hardening degree and residual stress.
Further, the orthogonal test in step S1 employs a four-factor five-level orthogonal test.
Further, the mathematical model in step S2 is:
wherein Ra is surface roughness; NH is the work hardening degree; σ is the residual stress; b0Is a constant; n is the rotation speed; f is the feed speed; a is the amplitude; g is static pressure; b is a regression coefficient.
Further, the process of introducing the variables using the stepwise regression method in step S2 includes the following steps:
s21, removing insignificant variables in the mathematical model;
s22, introducing a new variable into the mathematical model;
wherein, the variable means: rotational speed, feed rate, amplitude and static pressure.
Further, in step S3, the multi-factor analysis of variance is performed by using minitab software, and when F >0.05, the mathematical model is significant at the confidence level, i.e. the model can be used for optimization.
Further, the multi-objective optimization model expression in step S4 is as follows:
wherein:
in the formula, n is the rotating speed; f is the feed speed; a is the amplitude; g is the static pressure.
Further, in the particle swarm algorithm of step S4, the population size M is set to 30, the inertia weight ω adopts a linear decreasing weight strategy, and the inertia weight ω updates the formula as follows:
in the formula, TmaxIs the maximum iteration number; i is the current iteration number; omegamin＝0.4,ωmax＝0.9。
The invention has the following beneficial effects:
1. the method optimizes the performance of the bearing surface layer through the particle swarm optimization and the ultrasonic rolling technology, has the advantages of convenience in implementation and high convergence speed while ensuring high precision compared with other optimization algorithms, can avoid local optimization and realize global optimization by combining individual experience and population experience through the multi-target particle swarm optimization, and enables multi-target optimization results to be more accurate and reliable.
2. The invention combines the stepwise regression method and the particle swarm optimization, carries out multi-objective optimization on the surface performance of the ultrasonic rolling GCr15 bearing, has simple calculation process and strong practicability, comprehensively considers various performance indexes in the optimization process, realizes the comprehensiveness of the optimization algorithm, and greatly improves the surface quality and the fatigue resistance of the bearing processed by the optimization method.
3. The method combines the orthogonal test and the particle swarm optimization algorithm, and guides the optimization range and direction of the particles in the particle swarm through the result of the orthogonal test analysis, thereby accelerating the optimization speed of the particle swarm.
4. The particle swarm optimization does not need to convert multiple targets into single-target optimization and data standardization processing, and the efficiency of the multiple-target optimization is improved.
5. The globally optimal surface performance index parameter domain and the corresponding processing process parameter domain obtained by the method can control more processing process parameters at the same time, so that the optimal surface performance of the bearing is realized.
Drawings
FIG. 1 is a flow chart of stepwise regression method in the example;
FIG. 2 is a flow chart of the multi-objective PSO algorithm;
FIG. 3 is a schematic diagram of the distribution of randomly generated particle populations in a feasible solution space in an embodiment;
FIG. 4 is a diagram illustrating the optimization results of the multi-objective particle swarm optimization algorithm performed 50 iterations in the embodiment;
FIG. 5 is a diagram illustrating the optimization results of the multi-objective PSO algorithm performed 100 iterations in the embodiment;
FIG. 6 is a diagram illustrating the optimization results of the multi-objective PSO algorithm in the embodiment when the multi-objective PSO algorithm is iterated 200 times;
FIG. 7 is a diagram illustrating the optimization results of the multi-objective particle swarm optimization algorithm performed 250 iterations in the embodiment;
FIG. 8 is a diagram showing the optimization results of 0.5 for both the self-learning factor and the social learning factor in the example;
FIG. 9 is a diagram showing the optimization results of the embodiment in which both the self-learning factor and the social learning factor are 1.5;
FIG. 10 is a diagram showing the optimization results of the embodiment in which both the self-learning factor and the social learning factor are 2;
FIG. 11 is a parallel coordinate diagram of a multi-target particle swarm algorithm computation process in the embodiment.
Detailed Description
The technical solutions of the present invention are clearly and completely described below with reference to the accompanying drawings and the specific embodiments, but it should be understood that the scope of the present invention is not limited by the specific embodiments.
The invention provides a GCr15 bearing surface layer performance optimization method based on a particle swarm algorithm and ultrasonic rolling, which comprises the following steps of:
and S1, determining factors, levels and indexes according to the technological parameters of the ultrasonic rolling equipment and the GCr15 bearing surface layer performance indexes, and performing an orthogonal test.
In the embodiment, the process parameters of the ultrasonic rolling equipment refer to rotating speed, feeding speed, amplitude and static pressure, the surface performance indexes of the GCr15 bearing are surface roughness, work hardening degree and residual stress, and four-factor five-level orthogonal test is performed based on the surface roughness, the work hardening degree and the residual stress.
S2, constructing a GCr15 bearing surface performance mathematical model by using a stepwise regression method based on the orthogonal test analysis result;
s3, carrying out variance analysis on the mathematical model to ensure the mathematical model to be accurate and reliable;
s4, performing multi-objective optimization on the surface performance of the GCr15 bearing by using a particle swarm optimization;
and S5, solving to obtain a globally optimal GCr15 bearing surface performance index parameter domain and a corresponding processing process parameter domain.
And carrying out four-factor five-level orthogonal test on the surface layer of the ultrasonic rolling bearing. In the orthogonal test, the settings of the processing parameters at different levels are shown in table 1, and the orthogonal test results are shown in table 2.
Table 1 setting of process parameters in orthogonal experiments
TABLE 2 results of orthogonal experiments
Results of orthogonal assay analysis:
when the feeding speed is the same, the rotating speed is smaller, the surface roughness of the bearing is smaller, and the surface roughness is continuously increased along with the increase of the rotating speed; the influence of the feeding speed on the surface roughness is similar to that of the rotating speed, and when the rotating speed is the same, the bearing surface roughness is continuously increased along with the increase of the feeding speed; when the static pressure and the feeding speed are constant, the influence of the amplitude on the surface roughness shows a trend of firstly reducing and then increasing; at constant feed rate and amplitude, the static pressure effect on the surface roughness tends to decrease and then increase.
With the increase of the rotating speed, the work hardening degree is increased firstly and then reduced; when the rotating speed and the amplitude are constant, the work hardening degree of the bearing surface is slowly reduced along with the increase of the feeding speed; when the rotation speed and the feeding speed are the same, the degree of work hardening of the bearing surface is obviously improved along with the increase of the amplitude, and when the rotation speed and the amplitude are the same, the degree of work hardening of the bearing surface is also continuously improved along with the increase of the static pressure.
When the static pressure and the amplitude are unchanged, the residual compressive stress is gradually reduced along with the increase of the rotating speed; the residual compressive stress is gradually increased with the increase of the amplitude when the static pressure and the rotation speed are the same, and the residual compressive stress is significantly increased with the increase of the static pressure when the amplitude and the rotation speed are the same.
Based on the orthogonal test analysis result, a mathematical model equation of the GCr15 bearing surface layer performance is constructed by a stepwise regression method:
wherein Ra is surface roughness; NH is the work hardening degree; σ is the residual stress; b0Is a constant; n is the rotation speed; f is the feed speed; a is the amplitude; g is static pressure; b is a regression coefficient.
Therefore, the nonlinear function relation between the targets such as surface roughness, residual stress, work hardening degree and the like and the ultrasonic rolling strengthening process parameters such as rotating speed, feeding speed, static pressure, amplitude and the like is established.
The process of introducing variable rotation speed n, feed speed f, amplitude A and static pressure G by using a stepwise regression method comprises the following steps: s21, removing insignificant variables in the mathematical model; s22, introducing new variables into the mathematical model.
Referring to fig. 1, firstly, according to the significance of the F test, whether a new variable is introduced or deleted is judged, if no new variable is introduced, the program is ended, if a new variable is introduced, the significance of the introduced variable is analyzed, and if F is less than 0.05, the variable is deleted, and the next round of operation is performed again.
In the equation (1), the surface roughness, the work hardening degree and the residual stress of the surface layer performance indexes are subjected to multivariate nonlinear analysis, the factor item with strong significance is introduced, and the factor item with weak significance is eliminated, so that an optimal data model equation is obtained. The operation of the stepwise regression method is shown in FIG. 1.
In order to ensure that the constructed mathematical model has reliability and stability, variance analysis, namely F test, needs to be carried out on the mathematical model. The value of F represents the confidence level of the model in the analysis of variance, and when F >0.05, the mathematical model is considered significant at the confidence level, i.e. it can be optimized using this model. The larger the F value is, the larger the complex correlation coefficient is, and the higher the reliability of the established mathematical model is.
In this embodiment, a multi-factor analysis of variance is performed using minitab software. The F value can be obtained by inputting the test parameter values, and the precision of the model is explained by the F value, the correlation coefficient and the adjustment correlation coefficient. At R2>And in 95%, the larger the correlation coefficient and the adjusted correlation coefficient are, the more accurate the model is built. Obtaining the correlation coefficient R of the surface roughness equation by minitab software1 298.68%, adjusting the related coefficient R2 297.74%, F104.80; coefficient of correlation R of the work hardening equation3 297.26%, adjusting the correlation coefficient R4 296.35%, F106.64; correlation coefficient R of residual stress equation5 298.17%, adjusting the correlation coefficient R6 296.63% and F63.47, the model has high correlation and the fitting effect on the data is good.
The GCr15 bearing surface performance indexes mainly comprise surface roughness, residual stress and work hardening degree, different process parameters have different influences on the surface performance in the ultrasonic extrusion process, and in order to improve the ultrasonic rolling reinforced surface quality and improve the reinforcing efficiency, the surface performance needs to be subjected to multi-target optimization, so that an optimal performance index parameter domain and a corresponding processing process parameter domain are obtained.
And taking the minimized surface roughness, the maximized work hardening degree and the residual stress as the objective functions of the multi-objective optimization model. Because the residual stress of the surface layer is compressive stress and the result obtained by the model is a negative value, when the multi-objective optimization model is established, the minimum value of the residual stress is obtained, and the expression of the multi-objective optimization model is as follows:
on the premise of meeting the safety requirement in the machining process, the ultrasonic rolling machining process parameter range is set as follows by combining the condition limitations of a numerical control machine tool and ultrasonic rolling equipment:
in the embodiment, referring to fig. 2, an operation flow of a multi-target particle swarm algorithm is that firstly, a population is initialized, then, a non-inferior solution is added to an external archive, then, an individual optimal pbest and a population optimal gbest are updated, the speed and the position of a particle are updated, then, an external archive set is updated and maintained, then, whether a termination condition is met is judged, if the termination condition is met, an external archive set is output, and a program is ended; and if the termination condition is not met, continuously returning to update the individual optimal pbest and the population optimal gbest, and updating the speed and the position of the particle again until the termination condition is met.
In the optimization process, the particles continuously adjust and update the positions according to the current position of the particles, the information of the individual optimum and the population optimum. The multi-target particle swarm algorithm can avoid local optimization and realize global optimization.
In the particle swarm optimization, the value of the population size M ranges from 20 to 60, and for a certain specific problem or some more complex problems, the value of M can reach 100-200. In the embodiment, the increase of the population scale M is not obvious for improving the optimization effect of the algorithm, but can greatly increase the operation complexity of the algorithm and prolong the operation time, so the value of the population scale M is set to be 30 in the particle algorithm; the inertia weight omega adopts a linear decreasing weight strategy, and the updating formula is as follows:
in the formula, TmaxIs the maximum iteration number; i is the current iteration number; omegamin＝0.4,ωmax＝0.9。
In particle swarm optimization, learning is also generally introducedFactors, i.e. self-learning factors c1Social learning factor c2. When c is going to1When the value is 0, the particle only has global searching capability, the algorithm convergence is fast at the moment, but the phenomenon of 'premature early' is easy to occur, and the local optimum is easy to fall into; when c is going to2When the value is 0, the particle only has self-learning ability, which results in slow convergence of the algorithm and failure to find a global optimal solution. Therefore, c is usually1And c2Two constants which are not 0 are set to ensure that the particles have self-learning ability and social learning ability.
In order to save the operation time when selecting the learning factor, the number of iterations is uniformly set to 50. In general c1And c2Is defaulted to 2, but from the particle convergence point of view, c1＝c2The conventional value of 2 is not suitable for optimizing the processing parameters of the ultrasonic rolling GCr15 bearing. FIG. 8, FIG. 9, FIG. 10 show c1And c2The convergence of the particles was taken at 0.5, 1.5 and 2, respectively. Through the pair c1And c2Different values are taken to find c1＝c2The convergence effect is more preferable when the value is 0.5. Optimizing the result by comparative analysis, the learning factor is taken as c1＝c20.5, the number of iterations N is taken to be 250. Three evaluation index parameters of the ultrasonic rolling GCr15 bearing surface layer performance are optimized by adopting a multi-target particle swarm algorithm, and randomly generated particle swarm is randomly distributed in a feasible solution space as shown in figure 3; the optimization results for an iteration number of 50 are shown in fig. 4; the optimization results when the number of iterations is 100 are shown in fig. 5; the optimization results when the number of iterations is 200 are shown in fig. 6; the optimization results for a number of iterations of 250 are shown in fig. 7.
Based on a mathematical model of each target of the GCr15 bearing surface performance, and in combination with a multi-target particle swarm optimization, optimization is carried out within the ultrasonic rolling process parameter range to obtain a forming surface performance optimal performance index parameter domain and a corresponding processing process parameter domain.
As can be seen from fig. 3-7, the randomly generated particle populations are randomly distributed in the feasible solution space, and the particle distribution is disordered; iterating the optimization result for 50 times, wherein the particles begin to converge to a smaller feasible solution space, but the number of optimal solutions is smaller; compared with the optimization result of iteration for 50 times, the optimization result of iteration for 100 times shows an obvious convergence trend, the number of optimal solutions is greatly increased, and the optimal solutions are distributed more uniformly; iterating the optimization result for 200 times, wherein more particles are concentrated in the optimal solution, the convergence trend is good, the obtained optimal front edge is smoother, and the optimal solution is uniformly distributed; in the optimization result obtained by the iteration of 250 times, the particle convergence effect is good, but the convergence effect is not significantly improved compared with the result obtained by the iteration of 200 times, and the iteration number is set to 200 in order to save the calculation time.
Fig. 11 is a parallel coordinate diagram of a calculation process of the multi-target particle swarm algorithm in the embodiment. The parallel coordinate graph can display all selected processing technological parameters and surface layer performance evaluation index parameters as vertical strips, each solution in the calculation process is represented by a continuous broken line formed by taking a proper value from each vertical strip, and the parallel coordinate graph in the whole calculation process can visually display results under different parameter combinations. Wherein the black lines represent the whole solution calculation process, the middle brighter silver line represents the calculation process of the optimal solution, and it can be seen from the figure that in the optimization process, when the surface roughness is reduced, the work hardening degree is reduced, and the residual stress is reduced; when the residual stress is increased, the surface roughness becomes large and the work hardening degree is reduced; when the work hardening degree is increased, the surface roughness becomes large and the residual stress becomes small. Therefore, the surface roughness, the work hardening degree and the residual stress are mutually restricted and influenced, the improvement of one performance can cause the reduction of the other performance, and the three can not reach the optimal simultaneously, so that only one group is relatively optimal. It is therefore easier to obtain an optimal solution when the rotation speed and the feed speed take smaller values and the amplitude and the static pressure take larger values.
And according to the result obtained by the optimization of the multi-target particle swarm algorithm, obtaining the optimal parameter domain of the processing process parameters and the surface performance index parameters from the optimal solution set, as shown in Table 3.
TABLE 3 optimal GCr15 bearing surface performance index parameter domain and corresponding processing technique parameter domain
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. The GCr15 bearing surface layer performance optimization method based on the particle swarm optimization and ultrasonic rolling is characterized by comprising the following steps of:
s1, determining factors, levels and indexes according to the technological parameters of the ultrasonic rolling equipment and the GCr15 bearing surface layer performance indexes, and performing an orthogonal test;
s2, constructing a GCr15 bearing surface performance mathematical model by using a stepwise regression method based on the orthogonal test analysis result;
s3, carrying out variance analysis on the mathematical model to ensure the mathematical model to be accurate and reliable;
s4, performing multi-objective optimization on the surface performance of the GCr15 bearing by using a particle swarm optimization;
and S5, solving to obtain a globally optimal GCr15 bearing surface performance index parameter domain and a corresponding processing process parameter domain.
2. The particle swarm optimization and ultrasonic rolling based GCr15 bearing surface performance optimization method according to claim 1, wherein the process parameters of the ultrasonic rolling equipment in step S1 are rotation speed, feed speed, amplitude and static pressure, and the GCr15 bearing surface performance indexes are surface roughness, work hardening degree and residual stress.
3. The GCr15 bearing surface layer performance optimization method based on particle swarm optimization and ultrasonic rolling according to claim 2, wherein the orthogonal test in the step S1 is a four-factor five-level orthogonal test.
4. The GCr15 bearing surface layer performance optimization method based on particle swarm optimization and ultrasonic rolling according to claim 3, wherein the mathematical model in the step S2 is as follows:
wherein Ra is surface roughness; NH is the work hardening degree; σ is the residual stress; b0Is a constant; n is the rotation speed; f is the feed speed; a is the amplitude; g is static pressure; b is a regression coefficient.
5. The GCr15 bearing surface layer performance optimization method based on particle swarm optimization and ultrasonic rolling according to claim 4, wherein the step S2 of introducing the variables by using a stepwise regression method comprises the following steps:
s21, removing insignificant variables in the mathematical model;
s22, introducing a new variable into the mathematical model;
wherein, the variable means: rotational speed, feed rate, amplitude and static pressure.
6. The particle swarm optimization and ultrasonic rolling based GCr15 bearing surface layer performance optimization method according to claim 5, wherein in step S3, a multi-factor variance analysis is performed by using minitab software, and when F >0.05, the mathematical model is significant at the confidence level, i.e. the model can be used for optimization.
7. The GCr15 bearing surface layer performance optimization method based on particle swarm optimization and ultrasonic rolling according to claim 6, wherein the multi-objective optimization model expression in the step S4 is as follows:
wherein:
in the formula, n is the rotating speed; f is the feed speed; a is the amplitude; g is the static pressure.
8. The GCr15 bearing surface layer performance optimization method based on particle swarm optimization and ultrasonic rolling according to claim 7, wherein in the particle swarm optimization of step S4, the M value of the population size is set to be 30, the inertia weight ω adopts a linear decreasing weight strategy, and the update formula of the inertia weight ω is as follows:
in the formula, TmaxIs the maximum iteration number; i is the current iteration number; omegamin＝0.4,ωmax＝0.9。
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Cited By (3)
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| CN114549690A (en) * | 2022-02-22 | 2022-05-27 | 清华大学 | Automatic generation method and device of bearing drawing, electronic equipment and storage medium |
| CN114836615A (en) * | 2022-03-17 | 2022-08-02 | 大连交通大学 | Multi-frequency ultrasonic residual stress removal time distribution optimization method |
| CN116227181A (en) * | 2023-02-17 | 2023-06-06 | 郑州轻工业大学 | Optimization method for flash groove parameters and forging process parameters of hinge Liang Duanzao die |
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| CN116227181A (en) * | 2023-02-17 | 2023-06-06 | 郑州轻工业大学 | Optimization method for flash groove parameters and forging process parameters of hinge Liang Duanzao die |
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