CN114595536A - Multivariable multi-target optimization method for dynamic performance of slewing bearing - Google Patents
Multivariable multi-target optimization method for dynamic performance of slewing bearing Download PDFInfo
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Abstract
The invention discloses a multivariable multi-target optimization method for dynamic performance of a slewing bearing, and belongs to the technical field of slewing bearings. The invention establishes a fully parameterized dynamic model of the slewing bearing by using ADAMS, performs full-factor experimental design on key design parameters such as the channel curvature radius of the slewing bearing, the bore diameter of a cage pocket, an initial contact angle, the gear tooth displacement coefficient and the like by adopting an experimental Design (DOE) method, and calculates and analyzes the change trend of the dynamic characteristics of the slewing bearing under the single-factor influence of the key design parameters. Based on a linear weighting method, a new objective function is constructed and designed by using different unified dimension methods and weight coefficient methods, a multivariable multi-objective optimization design method for the dynamic performance of the slewing bearing product is provided, and optimal design parameters are generated. The invention saves a large amount of product development time and manpower, has low cost and high precision, and has important practical value for researching and developing high-performance slewing bearing products.
Description
Technical Field
The invention belongs to the technical field of slewing bearings, and particularly relates to a multivariable multi-target optimization method for dynamic performance of a slewing bearing.
Background
1. The slewing bearing is a novel mechanical device, mainly comprises parts such as a driving gear, a bearing outer ring with a gear ring, a rolling body and a retainer, can simultaneously bear the effects of axial load, radial load and overturning moment, has the outstanding advantages of compact structure, stable transmission, simple and convenient installation, easy maintenance, long service life and the like, and is widely applied to the fields of industrial robots, wind generating sets, military equipment, medical instruments and the like.
2. The existing analysis technology of the slewing bearing mainly focuses on the design analysis of the static and dynamic characteristics of the rolling body and the raceway, key influence factors such as the static and dynamic contact action of the rolling body and the inner and outer rings of the bearing and the pocket of the retainer, the meshing action of the driving gear and the gear ring and the like are not considered, and the comprehensive performance of the slewing bearing product is not accurately known and mastered, so that repeated design, trial production, debugging and improvement are needed, the product development cycle is long, a large amount of manpower, material resources and financial resources are consumed, and the dynamic performance of the slewing bearing in practical application cannot be estimated.
3. The existing design technology of the slewing bearing is designed according to the statics principle by adopting the traditional experience design method, and the key design parameters such as the curvature radius of a channel of the slewing bearing, the bore diameter of a pocket of a retainer, an initial contact angle, the gear tooth displacement coefficient and the like and the dynamic performance of the slewing bearing are not subjected to multi-factor and multi-target associated optimization design, so that the problems of tooth breakage, abrasion, large vibration noise, poor dynamic precision, low fatigue life and the like of a developed slewing bearing product frequently occur under the actual working condition, even serious faults occur from the problems, and the economic benefit and the production safety of an enterprise are influenced.
Disclosure of Invention
The invention overcomes the defects of the prior art method, and provides a multivariable multi-target optimization method for the dynamic performance of a slewing bearing. Compared with an empirical design method and an experimental method, the method has the advantages of short development period, low cost and convenience in operation, and can be suitable for design research and development of different engineering application requirements and different types of slewing bearing products. The method has important guiding significance for understanding and mastering various performance indexes of the slewing bearing product under the actual working condition and improving the dynamic characteristics of the slewing bearing.
The technical scheme adopted by the invention is as follows: a multivariable multi-target optimization method for dynamic performance of a slewing bearing comprises the following implementation steps:
step 1: and establishing a fully-parameterized slewing bearing dynamic model in ADAMS software.
Step 2: and (3) correspondingly constraining and contacting each part of the slewing bearing according to the actual working condition, and calculating the dynamic contact force by using an Impact function method (Impact).
And step 3: and calculating the change trend of the dynamic performance of the contact force between the rolling body and the raceway, the gear meshing force, the mass center of the inner gear ring, the radial vibration displacement and the axial vibration displacement under the single factors of the curvature radius of the channel, the aperture of the cage pocket, the initial contact angle, the gear tooth displacement coefficient and the like.
And 4, step 4: the method comprises the steps of carrying out full-factor experimental design on key design parameters such as the curvature radius of a slewing bearing channel, the aperture of a cage pocket, an initial contact angle, gear tooth displacement coefficients and the like by adopting an experimental Design (DOE) method, constructing and designing a new objective function by utilizing different unified dimension methods and weight coefficient methods based on a linear weighting method, carrying out multivariable multi-objective optimization on the dynamic performance of the slewing bearing, and obtaining an optimized combined design parameter result.
Specifically, the specific operation steps according to step 1 are:
the method comprises the steps of carrying out parametric definition and three-dimensional modeling on structural parameters such as tooth number, modulus, pitch circle, addendum height and displacement coefficient of a driving gear and an inner gear ring by using an ADAMS (automatic dynamic analysis system) self-provided gear module, sequentially defining and three-dimensional modeling the structural parameters such as channel curvature radius of the diameters of four virtual raceways of an inner ring and an outer ring, the diameters and the number of rolling elements, the inner diameter and the outer diameter of a retainer, the diameter and the number of pockets and the like by combining the structural parameters of a slewing bearing, carrying out parametric definition on contact parameters of all the rolling elements and the four raceways of the inner ring and the outer ring according to the structural parameters and the material parameters of the slewing bearing, and finally assembling the gear, the inner gear ring, the outer gear ring, the retainer and the rolling elements to complete full-parametric dynamic modeling of the slewing bearing.
Specifically, the specific operation steps according to step 2 are:
2.1) a connecting rod is used for approximately replacing a motor, a synchronous belt transmission mechanism and a speed reducer; adding corresponding constraints to each part in the slewing bearing, connecting the outer ring with the earth and the four virtual raceways in a fixed pair manner, connecting the connecting rod with the earth in a fixed pair manner, connecting the connecting rod with the retainer and the pinion in a revolute pair manner, and connecting the inner gear ring with the gear ring and the virtual raceways in a fixed pair manner; and then carrying out corresponding contact setting on the slewing bearing, wherein the specific contact is that all rolling bodies are in contact with the virtual raceway and the retainer, and a pair of internal gear wheels are in contact.
2.2) calculating the contact force by adopting an Impact function method (Impact): applying the formula: fn＝Kδe+ CV, formula FnNormal contact force; k is a stiffness coefficient; delta is the normal penetrating force of the contact point; e is a stiffness force index; c is a damping coefficient; v is the contact point normal relative velocity.
Specifically, the specific operation steps according to step 3 are:
and 3.1) selecting the curvature radius of a channel, the aperture of a cage pocket, the initial contact angle and the gear tooth displacement coefficient as key design parameters, respectively recording the parameters as DV _1, DV _2, DV _3 and DV _4, and respectively and uniformly taking four discrete quantities.
3.2) calculation of the meshing force (f) between the gears by means of ADAMS1(x) Rolling element and raceway contact force (f)2(x) Inner gear ring centroid axial vibration displacement (f)3(x) Inner gear ring centroid radial displacement (f)4(x) And obtaining the variation trend of the single-factor key design parameter influencing the dynamic of the lower slewing bearing.
Specifically, the specific operation steps according to step 4 are:
4.1) establishing a multi-objective optimization mathematical model, wherein the formula is as follows:
in the formula: t (x) ═ f1(x)，f2(x)…，fi(x)]TReferred to as a vector objective function; f. ofi(x) Is a sub-targeting function; s is a design variable discrete set; and creates an objective function:
in the formula: f. ofi' (x) is the function f of each sub-targeti(x) A dimensionless sub-target function after unified dimension processing; w is aiFor each dimensionless sub-target function fi' (x).
4.2) carrying out unified dimension treatment: equalization processing method:
in the formula
As a sub-targeting function fi(x) Average value of (d); minimum value processing method:
in the formula, min is a sub-target function fi(x) The minimum value in the value domain.
4.3) selecting the weight coefficient w by a sorting method, an entropy method and a variation coefficient methodi(ii) a The sorting method comprises the following steps: introducing dispersion and average deviation according to minimum points of the i dimensionless sub-target functions, and determining the weight of each dimensionless sub-target through the dispersion and average deviation; entropy method: the weighting to the sub-objective function is realized by extracting the information entropy of each sub-objective function; coefficient of variation method: and judging the contribution degree of the sub-targeting functions by utilizing the discrete degree, calculating the absolute and relative variation degrees of each sub-targeting function, and then solving the variation coefficient of each sub-targeting function and normalizing to obtain the variation coefficient weight.
4.4) carrying out full factor test design on the model by using the function of design of experiments (DOE) in ADANS/View, uniformly taking four values from DV _1 to DV _4 to obtain the dynamic performance of the slewing bearing under different combination parameters of a series, and based on the result, adopting linear weightingSolving multiple targets and optimizing by the method, wherein the formula is as follows:
in the formula: f. ofi(x) (i ═ 1,2, … n) for each sub-targeting function; w is aiAre weight coefficients. And finally, obtaining the optimal parameter combination of the dynamic performance of the slewing bearing.
The invention has the beneficial effects that:
(1) the multivariable multi-target optimization method for the dynamic performance of the slewing bearing comprehensively considers the variation trend of the dynamic characteristics of the slewing bearing under single factors and multiple factors of key design parameters, can realize the optimal performance of the slewing bearing product, and has important practical significance in practical application.
(2) The method adopts the design of experiments (DOE) to carry out full-factor experimental analysis, compared with the empirical design and experimental method, the method has the advantages of short development period, low cost, convenient operation, suitability for different engineering requirements, important guiding significance for understanding and mastering various performance indexes of the slewing bearing product and improving the dynamic characteristic of the slewing bearing, and important practical value for researching and developing the high-performance slewing bearing product.
Drawings
FIG. 1 is a diagram of a parameterized dynamic model of a slewing bearing.
Fig. 2 is a view showing an internal structure of a virtual raceway.
Fig. 3 is a rolling element numbering diagram.
FIG. 4 is a graph of slewing bearing dynamics at different channel radii of curvature.
FIG. 5 is a graph of slewing bearing dynamics at different pocket diameters.
FIG. 6 is a graph of slewing bearing dynamic characteristics at different initial contact angles.
FIG. 7 is a dynamic graph of a slewing bearing under different tooth index.
FIG. 8 is a chart of slewing bearing dynamic characteristics before and after multi-objective optimization.
Detailed Description
The invention will be described in detail with reference to the following figures and specific embodiments:
example 1: a multivariable multi-target optimization method for dynamic performance of a slewing bearing comprises the following implementation steps:
step 1: and establishing a fully-parameterized slewing bearing dynamic model in ADAMS software. The method comprises the steps of carrying out parametric definition and three-dimensional modeling on structural parameters such as tooth number, modulus, pitch circle, addendum height and displacement coefficient of a driving gear and an inner gear ring by using an ADAMS (automatic dynamic analysis system) self-provided gear module, sequentially defining and three-dimensional modeling the structural parameters such as channel curvature radius of the diameters of four virtual raceways of an inner ring and an outer ring, the diameters and the number of rolling elements, the inner diameter and the outer diameter of a retainer, the diameter and the number of pockets and the like by combining the structural parameters of a slewing bearing, carrying out parametric definition on contact parameters of all the rolling elements and the four raceways of the inner ring and the outer ring according to the structural parameters and the material parameters of the slewing bearing, and finally assembling the gear, the inner gear ring, the outer gear ring, the retainer and the rolling elements to complete full-parametric dynamic modeling of the slewing bearing (figure 1).
Step 2: and (3) correspondingly constraining and contacting each part of the slewing bearing according to the actual working condition, and calculating the dynamic contact force by using an Impact function method (Impact).
2.1) a connecting rod is used for approximately replacing a motor, a synchronous belt transmission mechanism and a speed reducer; and respectively establishes four virtual raceways which are respectively N1、N2、W1、W2(FIG. 2); adding corresponding restraint to each part in the slewing bearing, and connecting the outer ring with the earth and the virtual raceway W1、W2The connecting rod is connected with the ground in a fixed pair mode, the connecting rod is connected with the retainer and the pinion in a rotating pair mode, and the inner gear ring is connected with the gear ring and the virtual roller path N1、N2The connection is realized in a fixed pair mode; and then the slewing bearings are correspondingly arranged in a contact mode, No. 1-28 rolling bodies (shown in figure 3) are respectively in contact with the four virtual raceways and the retainer, and a pair of internal gears are in contact.
2.2) calculating the contact force by adopting an Impact function method (Impact): applying a formula: fn＝Kδe+ CV, formula FnNormal contact force; k is a stiffness coefficient; delta is the normal direction of contact pointPenetration force; e is a stiffness force index; c is a damping coefficient; v is the contact point normal relative velocity.
And step 3: and calculating the change trend of the dynamic performance of the contact force between the rolling body and the raceway, the gear meshing force, the mass center of the inner gear ring, the radial vibration displacement and the axial vibration displacement under the single factors of the curvature radius of the channel, the aperture of the cage pocket, the initial contact angle, the gear tooth displacement coefficient and the like.
3.1) selecting a channel curvature radius (DV _1), a retainer pocket aperture (DV _2), an initial contact angle (DV _3) and a gear tooth displacement coefficient (DV _4) as key design parameters, and uniformly taking four discrete quantities respectively; the values of DV _1 are 12.875mm, 13.000mm, 13.125mm and 13.250mm, the values of DV _2 are 25.2mm, 25.4mm, 25.6mm and 25.8mm, the values of DV _3 are 40 degrees, 45 degrees, 50 degrees and 55 degrees, and the values of DV _4 are 0, 0.2, 0.4 and 0.6.
3.2) calculating the meshing force (f) between the gears by using ADAMS1(x) Rolling element and raceway contact force (f)2(x) Inner gear ring centroid axial vibration displacement (f)3(x) Inner gear ring centroid radial displacement (f)4(x) ). The outer ring of the slewing bearing is fixed, the inner gear ring applies axial load 6000N and overturning moment is 1 multiplied by 106N.mm, adding a drive rotating speed STEP (time,0,0d,0.1,310d), wherein the initial contact angle is 45 degrees, the aperture of a cage pocket is 25.2mm, the tooth displacement coefficient is 0, and the curvature radius of a channel is 12.875mm, 13.000mm, 13.125mm and 13.250mm respectively to obtain a dynamic characteristic curve of the slewing bearing under different curvature radii of the channel (figure 4); the initial contact angle is 45 degrees, the curvature radius of the inner and outer ring channels is 13.0mm, the tooth displacement coefficient is 0, the aperture of the cage pocket is 25.2mm, 25.4mm, 25.6mm and 25.8mm respectively, and the dynamic characteristic curve of the slewing bearing under different pocket apertures is obtained (figure 5); the curvature radius of the inner and outer ring channels is 13.0mm, the bore diameter of the cage pocket is 25.2mm, the tooth displacement coefficient is 0, and the initial contact angles are respectively 40 degrees, 45 degrees, 50 degrees and 55 degrees to obtain a dynamic characteristic curve of the slewing bearing under the same initial contact angle (figure 6); the curvature radius of the inner and outer ring channels is 13.0mm, the initial contact angle is 45 degrees, the aperture of the cage pocket is 25.2mm, and the tooth displacement coefficients are respectively 0, 0.2, 0.4 and 0.6, so as to obtain the dynamic characteristic curve of the slewing bearing under different tooth displacement coefficients (figure 7).
And 4, step 4: the method comprises the steps of carrying out full-factor experimental design on key design parameters such as the curvature radius of a slewing bearing channel, the aperture of a cage pocket, an initial contact angle, gear tooth displacement coefficients and the like by adopting an experimental Design (DOE) method, constructing and designing a new objective function by utilizing different unified dimension methods and weight coefficient methods based on a linear weighting method, carrying out multivariable multi-objective optimization on the dynamic performance of the slewing bearing, and obtaining an optimized combined design parameter result.
4.1) establishing a multi-objective optimization mathematical model, wherein the formula is as follows:
in the formula: t (x) ═ f1(x)，f2(x)…，fi(x)]TReferred to as a vector objective function; f. ofi(x) Is a sub-targeting function; s is a design variable discrete set; and creates an objective function:
in the formula: f. ofi' (x) is a function f of each sub-objectivei(x) A dimensionless sub-target function after unified dimension processing; w is aiFor each dimensionless sub-target function fi' (x).
4.2) carrying out unified dimension treatment: equalization processing method:
in the formula
As a sub-targeting function fi(x) Average value of (d); minimum value processing method:
in the formula, min is a sub-target function fi(x) The minimum value in the value domain.
4.3) selecting the weight coefficient w by a sorting method, an entropy method and a variation coefficient methodi(ii) a The sorting method comprises the following steps: introducing dispersion and average deviation according to minimum points of the i dimensionless sub-target functions, and determining the weight of each dimensionless sub-target through the dispersion and average deviation; comprises the following specific stepsFirstly, setting a single-target optimization model: minfi' (x), (i ═ 1,2,3,4), and the optimal solution set was determined as:
obtaining dispersion:
in the formula
Meaning dimensionless sub-target function fi'(x) is f'l(x) Of (2) an optimal solution xlFunction value of (d), mean square error:
post-solving weight coefficient wi：
And construct a new objective function f (x) w1f4′(x)+w2f3′(x)+w3f2′(x)+w4f1' (x); entropy method: the weighting to the sub-objective function is realized by extracting the information entropy of each sub-objective function; the specific steps are that firstly, the values of each sub-target function are respectively assumed as follows: f. ofi(xj) (i ═ 1,2,3, 4; j is 1,2,3 … 256), and the proportion of the jth scheme under the ith sub-objective function is obtained as follows:
the entropy value of the ith sub-objective function is:
where k is a constant, and the difference coefficient of the ith sub-objective function is: gi＝1-eiThen to giCarrying out normalization processing to obtain a weight coefficient:
and construct a new objective function: f (x) w1f4′(x)+w2f3′(x)+w3f2′(x)+w4f1' (x); coefficient of variation method: the method comprises the following steps of judging the contribution degree of the sub-targeting functions by utilizing the discrete degree, calculating the absolute and relative variation degrees of each sub-targeting function, then obtaining the variation coefficient of each sub-targeting function and normalizing the variation coefficient to obtain the variation coefficient weight, and specifically comprises the following steps: firstly, assume that the value of each sub-target function is fi(xj) (i ═ 1,2,3, 4; j equals 1,2,3 … 256), the ith sub-objective function f is obtainedi(x) The mean value of (a) is:
the standard deviation of the ith sub-objective function is:
the ith sub-target coefficient of variation is:
then, the variation coefficient of each sub-target is normalized to obtain the weight coefficient:
and create a new objective function: f (x) w1f4′(x)+w2f3′(x)+w3f2′(x)+w4f1′(x)。
4.4) performing full factor test design on the model by using the function of design of experiments (DOE) in ADAS/View, uniformly taking four values from DV _1 to DV _4 to obtain the dynamic performance of the slewing bearing under different combination parameters of a series, and solving and optimizing multiple targets by using a linear weighting method based on the result, wherein the formula is as follows:
in the formula: f. ofi(x) (i is 1,2, … n) is a function of each sub-target, n is a positive integer, and w is selected according to actual conditionsiAre weight coefficients. And finally, obtaining the optimal parameter combination of the dynamic performance of the slewing bearing.
4.4) carrying out unified dimensional processing on the subtargets, solving by using different weight coefficients to obtain a plurality of groups of weight coefficients, constructing a plurality of groups of new objective functions, and carrying out corresponding calculation on the new objective functions constructed by the different weight coefficients and the dimensionless subobjective functions to obtain the optimum design variable combination of the slewing bearing, as shown in table 1:
TABLE 1 optimal reference combinations found under different objective optimization functions
4.4) carrying out full factor test design on the model by using the function of experiment Design (DOE) in ADANS/View, uniformly taking four values from DV _1 to DV _4 to obtain the dynamic performance of the slewing bearing under different combination parameters of a series, and solving multiple targets and optimizing by using a linear weighting method based on results, wherein the formula is as follows:
in the formula: f. ofi(x) (i ═ 1,2, … n) for each sub-targeting function; w is aiAre weight coefficients. The optimal parameters for obtaining the slewing bearing are that the curvature radius of a channel, the bore diameter of a cage pocket, the initial contact angle and the tooth displacement coefficient are 12.875mm, 25.2mm, 55 degrees and 0.6 respectively. The values of the design variables of the parameterized dynamic model of the slewing bearing are set as optimized values and compared with the initial values, and the performance parameters of the optimized slewing bearing are improved to different degrees before optimization (figure 8).
Aiming at the defect problems existing in the empirical design method, the invention provides a multivariable multi-objective optimization method for the dynamic performance of a slewing bearing based on a parameterized dynamic model, a fully parameterized dynamic model of the slewing bearing is established by using dynamic simulation software, an optimized design result of the slewing bearing is generated by using a design of experiments (DOE) method and the multivariable multi-objective optimization design method, the dynamic performance of the slewing bearing under the combined action of key design parameters is pre-estimated, and a new design method is provided for researching and developing high-performance slewing bearing products.
The invention provides a parameterized dynamic model method and a multivariable multi-objective optimization design method of a slewing bearing product, saves a large amount of product development time and labor, has low cost and high precision, and has important practical value for researching and developing high-performance slewing bearing products.
While the present invention has been described in detail with reference to the embodiments, the present invention is not limited to the embodiments and various changes can be made without departing from the spirit and scope of the present invention by those skilled in the art.
Claims (5)
1. A multivariable multi-target optimization method for dynamic performance of a slewing bearing is characterized by comprising the following steps: the method comprises the following specific steps:
step 1: establishing a fully-parameterized slewing bearing dynamic model in ADAMS software;
step 2: corresponding constraint and contact arrangement are carried out on all parts of the slewing bearing by combining with actual working conditions, and dynamic contact force is calculated by an Impact function method;
and step 3: calculating the change trends of the dynamic performance of the contact force between the rolling body and the raceway, the gear meshing force, the mass center of the inner gear ring, the radial direction and the axial vibration displacement under the single factors of the curvature radius of the channel, the aperture of the pocket hole of the retainer, the initial contact angle and the gear tooth displacement coefficient;
and 4, step 4: the method comprises the steps of carrying out full-factor experimental design on key design parameters of the curvature radius of a slewing bearing channel, the aperture of a cage pocket, an initial contact angle and a gear tooth displacement coefficient by adopting an experimental design DOE method, constructing and designing a new objective function by utilizing different unified dimension methods and weight coefficient methods based on a linear weighting method, carrying out multivariable multi-objective optimization on the dynamic performance of the slewing bearing, and obtaining an optimized combined design parameter result.
2. The multivariate multiobjective optimization method of dynamic performance of a slewing bearing of claim 1, wherein:
the specific steps of the step 1 are as follows: the method comprises the steps of carrying out parametric definition and three-dimensional modeling on structural parameters of tooth number, modulus, pitch circle, addendum height and tooth displacement coefficient of a driving gear and an inner gear ring by using an ADAMS (automatic dynamic analysis system) self-provided gear module, defining and three-dimensional modeling structural parameters of channel curvature radius, rolling body diameter and number, inner diameter and outer diameter of a retainer, pocket diameter and number of four virtual raceways of an inner ring and an outer ring in sequence by combining the structural parameters of a slewing bearing, carrying out parametric definition on contact parameters of all rolling bodies and four raceways of an inner ring and an outer ring according to the structural parameters and material parameters of the slewing bearing, and finally assembling the gear, the inner gear ring, the outer gear ring, the retainer and the rolling bodies to complete full-parametric dynamic modeling of the slewing bearing.
3. The multivariate multiobjective optimization method of dynamic performance of a slewing bearing of claim 1, wherein: the specific operation steps of the step 2 are as follows:
2.1) a connecting rod is used for approximately replacing a motor, a synchronous belt transmission mechanism and a speed reducer, corresponding constraints are added on each part in the slewing bearing, an outer ring is connected with the ground and four virtual raceways in a fixed pair mode, the connecting rod is connected with the ground in a fixed pair mode, the connecting rod is connected with a retainer and a pinion in a revolute pair mode, and an inner gear ring is connected with a gear ring and the virtual raceways in a fixed pair mode; then carrying out corresponding contact setting on the slewing bearing, wherein the specific contact is that all rolling bodies are in contact with the virtual roller path and the retainer, and a pair of internal gear wheels are in contact;
2.2) calculating the contact force by adopting an Impact function method Impact: applying a formula: fn＝Kδe+ CV, formula FnNormal contact force; k is a stiffness coefficient; delta is the normal penetrating force of the contact point; e is a stiffness force index; c is a damping coefficient; v is the contact point normal relative velocity.
4. The multivariate multiobjective optimization method of dynamic performance of a slewing bearing of claim 1, wherein: the specific operation steps of step 3 are as follows:
3.1) selecting a channel curvature radius, a retainer pocket aperture, an initial contact angle and a gear tooth displacement coefficient as key design parameters, respectively recording the parameters as DV _1, DV _2, DV _3 and DV _4, and respectively and uniformly taking four discrete quantities;
3.2) calculating the meshing force f between the gears by using ADAMS1(x) Contact force f between rolling element and raceway2(x) Inner gear ring centroid axial vibration displacement f3(x) Inner gear ring centroid radial displacement f4(x) And then obtaining the variation trend of the single-factor key design parameter influencing the dynamic of the lower slewing bearing.
5. The multivariate multi-objective optimization method for dynamic performance of slewing bearings according to claim 1, characterized in that:
the specific operation steps of step 4 are as follows:
4.1) establishing a multi-objective optimization mathematical model, wherein the formula is as follows:
in the formula: t (x) ═ f1(x)，f2(x)…，fi(x)]TReferred to as a vector objective function; f. ofi(x) Is a sub-targeting function; s is a design variable discrete set, and an objective function is created:
in the formula: f. ofi' (x) is the function f of each sub-targeti(x) A dimensionless sub-target function after unified dimension processing; w is aiFor each dimensionless sub-target function fi' (X) weight coefficient;
4.2) carrying out unified dimension treatment: equalization processing method:
in the formula
As a sub-objective function fi(x) Average value of (d); minimum value processing method:
in the formula, min is a sub-target function fi(x) A minimum value in the value domain;
4.3) selecting the weight coefficient w by a sorting method, an entropy method and a variation coefficient methodi(ii) a The sorting method comprises the following steps: introducing dispersion and average deviation according to minimum points of the i dimensionless sub-target functions, and determining the weight of each dimensionless sub-target through the dispersion and average deviation; entropy method: the weighting to the sub-objective function is realized by extracting the information entropy of each sub-objective function; coefficient of variation method: judging the contribution degree of the sub-objective functions by using the dispersion degree, calculating the absolute and relative variation degrees of each sub-objective function, then solving the variation coefficient of each sub-objective function and normalizing to obtain the variation coefficient weight;
4.4) carrying out full factor test design on the model by using the DOE function in ADANS/View, uniformly taking four values from DV _1 to DV _4 to obtain the dynamic performance of the slewing bearing under different combination parameters of a series, and solving multi-objective optimization and formula by using a linear weighting method based on the result:
in the formula: f. ofi(x) (i ═ 1,2, … n) for each sub-targeting function; and finally, obtaining the optimal parameter combination of the dynamic performance of the slewing bearing.
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