CN107358011B - Bearing parameter optimization method based on cylindrical roller bearing load distribution calculation - Google Patents
Bearing parameter optimization method based on cylindrical roller bearing load distribution calculation Download PDFInfo
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Abstract
The invention discloses a bearing parameter optimization method based on cylindrical roller bearing load distribution calculation, which comprises the following steps: s1: preliminarily calculating the sizes of the inner ring and the outer ring of the hollow cylindrical roller bearing, the number of the rolling bodies, the hollowness of the rolling bodies and the design parameters of the radial play of the bearing according to the working condition requirement; s2: calculating the load distribution of the hollow cylindrical roller bearing: s3: and comparing the calculation result of the load distribution of the hollow cylindrical roller bearing calculated by the steps S1 and S2 with the allowable value of the load of the rolling element, and carrying out parameter optimization on the bearing which does not meet the regulation. The method further optimizes parameters which do not meet the regulations by calculating and measuring various parameters of the bearing, thereby ensuring that the production and design of the bearing meet the national standards.
Description
Technical Field
The invention relates to the technical field of fatigue life analysis of cylindrical roller bearings, in particular to a bearing parameter optimization method based on load distribution calculation of the cylindrical roller bearings.
Background
As a novel bearing, the hollow cylindrical roller bearing has the advantages of high rotation precision, high rigidity, high limit rotation speed, high bearing capacity and the like, and is particularly suitable for high-speed heavy-load occasions because the preload installation process is simple, and the rollers can be fully loaded and the hollow rollers are always preloaded. To date, although scholars at home and abroad have made a lot of work on theoretical studies of hollow cylindrical roller bearings, they have achieved many meaningful results. However, there are many places where it is necessary to be perfected that the elastic approach of the hollow cylindrical roller is the sum of the contact deformation amount and the bending deformation amount of the hollow cylindrical roller. At present, the contact deformation calculation formula of the solid cylindrical roller is mostly directly adopted for solving the contact deformation of the hollow cylindrical roller. However, the influence of the hollowness on the contact deformation amount is not considered in the contact deformation amount calculation formula, so that the calculation result error is large. At present, the bending deformation of the hollow cylindrical roller is mostly calculated by adopting an elastic curved beam method, and a large error is also generated. Therefore, a large error exists in the calculation of the load distribution of the hollow cylindrical roller bearing based on the traditional calculation method of the elastic approach quantity of the hollow cylindrical roller.
Disclosure of Invention
According to the problems in the prior art, the invention discloses a bearing parameter optimization method based on cylindrical roller bearing load distribution calculation, which comprises the following steps:
s1: preliminarily calculating the sizes of the inner ring and the outer ring of the hollow cylindrical roller bearing, the number of the rolling bodies, the hollowness of the rolling bodies and the design parameters of the radial play of the bearing according to the working condition requirement;
s2: calculating the load distribution of the hollow cylindrical roller bearing:
s21: analyzing the contact deformation of the hollowness and the hollow cylindrical roller according to the contact deformation theory of the rollercThe relationship of (1);
s22: establishing a finite element model of the contact deformation of the hollow cylindrical roller, carrying out physical simulation on the contact deformation of the hollow cylindrical roller by adopting finite element analysis software, and verifying the hollowness h of the rollerrWhether the relation with the contact deformation amount of the hollow cylindrical roller is correct or not;
s23: contact combined with rollerThe deformation theory is to calculate the contact deformation of the hollow cylindrical rollerc；
S24: calculating the bending deformation of the hollow cylindrical rollerb；
S25: according to the contact deformation of the hollow cylindrical rollercAnd the amount of bending deformation of the hollow cylindrical rollerbCalculating elastic approach of hollow cylindrical rollerhr；
S26: according to the elastic approach of the hollow cylindrical roller calculated in S25hrAnd calculating a load deformation relational expression of the hollow cylindrical roller and the inner ring and the outer ring of the bearing, and further completing the solution of the load distribution of the hollow cylindrical roller bearing according to the deformation coordination condition.
S3: and comparing the calculation result of the load distribution of the hollow cylindrical roller bearing calculated by the steps S1 and S2 with the allowable value of the load of the rolling element, and carrying out parameter optimization on the bearing which does not meet the regulation.
The contact deformation of the hollowness and the hollow cylindrical rollercIn a relationship of
c＝f(λ,q,r,hr)
Wherein λ ═ 2 (1-. mu.),2) [ pi ] E, mu ] and E are respectively Poisson's ratio and elastic modulus of the roller material, q is a linear load acting on the hollow cylindrical roller, r is an outer circle radius of the hollow cylindrical roller, and h isrHollowness of a hollow cylindrical roller, hr＝ri/r，riIs the inner hole radius of the hollow cylindrical roller.
Contact deformation of hollow cylindrical rollercThe following calculation is adopted:
in the formula, the size of the coefficient k is determined according to the finite element calculation result.
Amount of bending deformation of the hollow cylindrical rollerbThe following calculation is adopted:
wherein q is a linear load, E is an elastic modulus of the hollow cylindrical roller material, and hrHollowness of a hollow cylindrical roller, hr＝riR, r is the outer circle radius of the hollow cylindrical rolleriIs the inner bore radius of the hollow cylindrical roller, and the undetermined coefficient k1、k2、k3And m and n are determined according to the finite element calculation result.
Elastic approach of the hollow cylindrical rollerhrThe following method is adopted:
by adopting the technical scheme, the bearing parameter optimization method based on cylindrical roller bearing load distribution calculation provided by the invention can further optimize parameters which do not meet the regulation by calculating and measuring various parameters of the bearing such as the number of rolling elements, the hollowness of the rolling elements and the load distribution, thereby ensuring that the production and design of the bearing meet the national standard. The method is characterized in that the elastic approach quantity of the hollow cylindrical roller is calculated according to the elasticity of the hollow cylindrical roller, the elastic approach quantity of the hollow cylindrical roller is calculated through physical simulation by adopting finite element analysis software, the change rule of the contact deformation quantity and the bending deformation quantity of the hollow cylindrical roller along with relevant parameters is found through analysis and research on a large number of finite element calculation results, and the elastic approach quantity formula of the hollow cylindrical roller is finally established. The invention perfects the contact deformation theory of the hollow cylindrical roller, provides a theoretical basis for load distribution calculation and fatigue life calculation of the hollow cylindrical roller bearing, and provides theoretical guidance for design and development and application of the hollow cylindrical roller bearing.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a finite element mesh model of a hollow cylindrical roller of a certain radius.
FIG. 2 shows the contact deformation of a hollow cylindrical roller with a certain radius varying with the load at different hollowness.
FIG. 3 is a comparison of the contact deformation test results of a hollow cylindrical roller with a certain radius and the calculation results of the method of the present invention.
FIG. 4 is a comparison of the bending deformation test results of a hollow cylindrical roller with a certain radius and the calculation results of the method of the present invention.
FIG. 5 is a comparison of the elastic approach of a compression test of a hollow cylindrical roller of a certain radius and the calculation results of the method of the present invention.
Detailed Description
In order to make the technical solutions and advantages of the present invention clearer, the following describes the technical solutions in the embodiments of the present invention clearly and completely with reference to the drawings in the embodiments of the present invention:
a bearing parameter optimization method based on cylindrical roller bearing load distribution calculation specifically comprises the following steps:
s1: preliminarily calculating the sizes of the inner ring and the outer ring of the hollow cylindrical roller bearing, the number of the rolling bodies, the hollowness of the rolling bodies and the design parameters of the radial play of the bearing according to the working condition requirement;
s2: calculating the load distribution of the hollow cylindrical roller bearing:
s21: according to the contact deformation theory of the roller, the contact deformation between the hollowness and the hollow cylindrical roller is providedcIs as follows
c＝f(λ,q,r,hr)
Wherein λ ═ 2 (1-. mu.),2) [ pi ] E, mu ] and E are respectively Poisson's ratio and elastic modulus of the roller material, q is a linear load acting on the hollow cylindrical roller, r is an outer circle radius of the hollow cylindrical roller, and h isrHollowness of a hollow cylindrical roller, hr＝ri/r，riIs a hollow cylinderThe inner bore radius of the roller.
S22: establishing a finite element model of the contact deformation of the hollow cylindrical roller, carrying out physical simulation on the contact deformation of the hollow cylindrical roller by adopting finite element analysis software, and verifying the hollowness h of the rollerrThe relation with the contact deformation of the hollow cylindrical roller;
s23: calculating the contact deformation of the hollow cylindrical roller by combining the contact deformation theory of the rollerc；
Contact deformation of hollow cylindrical rollercThe following calculation is adopted:
in the formula, the size of the coefficient k is determined according to the finite element calculation result.
S24: calculating the bending deformation of the hollow cylindrical rollerb；
Wherein q is a linear load, E is an elastic modulus of the hollow cylindrical roller material, and hrHollowness of a hollow cylindrical roller, hr＝riR, r is the outer circle radius of the hollow cylindrical rolleriIs the inner bore radius of the hollow cylindrical roller, and the undetermined coefficient k1、k2、k3And m and n are determined according to the finite element calculation result.
S25: according to the contact deformation of the hollow cylindrical rollercAnd the amount of bending deformation of the hollow cylindrical rollerbCalculating elastic approach of hollow cylindrical rollerhr；
S26: according to the elastic approach of the hollow cylindrical roller calculated in S25hrCalculating the inside and outside of hollow cylindrical roller and bearingAnd (3) solving the load distribution of the hollow cylindrical roller bearing according to the load deformation relational expression of the ring and the deformation coordination condition.
S3: and comparing the calculation result of the load distribution of the hollow cylindrical roller bearing calculated by the steps S1 and S2 with the allowable value of the load of the rolling element, and carrying out parameter optimization on the bearing which does not meet the regulation.
Example (b):
the bearing is a standard part, and the optimization design of the bearing is more meaningful only for a certain type of bearing. Therefore, according to the working conditions, the basic parameters of the bearing of a certain type adopted in the embodiment are as follows: radius R of inner ring racewayi27.5mm, outer ring raceway radius Ro37.5mm, 14 rolling element number Z, 5mm rolling element radius r and 9.6mm rolling element effective length l.
According to Harris bearing theory, the rated dynamic load of the rolling bodies of the bearing with the model number can be calculated
The allowable load of the rolling body of the bearing can be determined according to specific working conditions, and in the embodiment, the allowable rolling body load is calculated by 10 percent of the rated dynamic load of the rolling body, namely the allowable rolling body load Qrc0＝Qrc*10％＝1281N。
FIG. 1 is a loaded finite element mesh model of a hollow cylindrical roller. The contact deformation of the hollow cylindrical roller is the sum of 4-point displacement minus 3-point displacement and 2-point displacement minus 1-point displacement, however, due to the symmetrical structure, it is obvious that the two quantities of the difference between 4-point displacement and 3-point displacement and the difference between 2-point displacement and 1-point displacement are equal and equal toc2; but the amount of bending deformationbEqual to the difference between the 3-point displacement and the 2-point displacement; thus, the elastic approach of the hollow cylindrical roller is obtainedhr＝c+b。
FIG. 2 shows the contact deformation with load (in the figure, q is the relationship between the contact deformation and the load at different hollowness of a hollow cylindrical roller with a radius r of 5mm01280N/mm in each case). In FIG. 2, r5-0 represents the result of finite element calculation of contact deformation of the solid cylindrical roller, and r5-40 representsThe contact deformation finite element calculation result of the hollow cylindrical roller with the hollowness of 40 percent, and other symbols represent the meanings and the like. From the calculation results in fig. 2, it is apparent that the hollowness greatly affects the contact deformation amount of the hollow cylindrical roller when the load is the same. Therefore, the correctness of the calculation method provided by the invention is verified. On the basis of analyzing and researching the contact deformation finite element calculation results of a large number of hollow cylindrical rollers, when r is 5mm and the hollowness is 60%, the coefficient k in the contact deformation calculation formula of the hollow cylindrical rollers is 6.4.
FIG. 3 is a comparison of the results of the contact deformation test of the hollow cylindrical roller with the results of the calculation of the formula of the present invention. In fig. 3, the discrete points are the results of the contact deformation amount in the compression test of the hollow cylindrical roller, and the continuous curve is the calculation result of the formula of the present invention. As is apparent from the data in fig. 3, it is reliable to calculate the contact deformation amount of the hollow cylindrical roller by using the present invention.
FIG. 4 is a comparison of the results of the bending deflection compression test of the hollow cylindrical roller and the results of the formula calculation of the present invention. In fig. 4, the discrete points are the test results, and the continuous curve is the calculation results of the formula. As is apparent from the data in fig. 4, the fitting degree of the bending deformation test result of the hollow cylindrical roller and the calculation result of the invention formula is extremely high. Therefore, the method is reliable in calculating the bending deformation of the hollow cylindrical roller by adopting the formula.
FIG. 5 is a graph showing the results of the test of the elastic approach of the hollow cylindrical roller when r is 5mm and the hollowness is 60% in comparison with the results of the calculation of the formula of the present invention. It can be clearly found from the data in fig. 5 that the elasticity approach amount test result of the hollow cylindrical roller and the calculation result of the invention formula have extremely high goodness of fit. Therefore, the elastic approach of the hollow cylindrical roller is reliably calculated by adopting the formula of the invention.
And on the basis of the calculation result of the elastic approach quantity of the hollow cylindrical roller, adding the deformation of the ferrule, and further completing the solution of the load distribution of the hollow cylindrical roller bearing according to the deformation coordination condition. In the radial play u of the bearingrThe results of the load distribution calculations at different hollowness values obtained at 0 are given in the following table:
obviously, as can be seen from the calculation results in the table above, when the hollowness is 0%, 40% and 50%, the maximum rolling element load of the bearing is larger than the allowable value, and the maximum rolling element load of the bearing can be gradually reduced by increasing the hollowness of the rollers so as to meet the requirement. In addition, the design requirements can be met by changing the design parameters of the bearing such as the play and the like.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.
Claims (1)
1. The bearing parameter optimization method based on cylindrical roller bearing load distribution calculation is characterized by comprising the following steps of:
s1: preliminarily calculating the sizes of the inner ring and the outer ring of the hollow cylindrical roller bearing, the number of the rolling bodies, the hollowness of the rolling bodies and the design parameters of the radial play of the bearing according to the working condition requirement;
s2: calculating the load distribution of the hollow cylindrical roller bearing:
s21: analyzing the contact deformation of the hollowness and the hollow cylindrical roller according to the contact deformation theory of the rollercThe amount of deformation of the hollowness in contact with the hollow cylindrical rollercIn a relationship of
c＝f(λ,q,r,hr)
Wherein λ ═ 2 (1-. mu.),2) [ pi ] E, mu ] and E are respectively Poisson's ratio and elastic modulus of the roller material, q is a linear load acting on the hollow cylindrical roller, r is an outer circle radius of the hollow cylindrical roller, and h isrHollowness of a hollow cylindrical roller, hr＝ri/r，riThe radius of an inner hole circle of the hollow cylindrical roller;
s22: building (2)Establishing a finite element model of the contact deformation of the hollow cylindrical roller, performing physical simulation on the contact deformation of the hollow cylindrical roller by adopting finite element analysis software, and verifying the hollowness h of the rollerrWhether the relation with the contact deformation amount of the hollow cylindrical roller is correct or not;
s23: calculating the contact deformation of the hollow cylindrical roller by combining the contact deformation theory of the rollercAmount of contact deformation of hollow cylindrical rollercThe following calculation is adopted:
in the formula, the size of the coefficient k is determined according to the finite element calculation result;
s24: calculating the bending deformation of the hollow cylindrical rollerbAmount of bending deformation of the hollow cylindrical rollerbThe following calculation is adopted:
wherein q is a linear load, E is an elastic modulus of the hollow cylindrical roller material, and hrHollowness of a hollow cylindrical roller, hr＝riR, r is the outer circle radius of the hollow cylindrical rolleriIs the inner bore radius of the hollow cylindrical roller, and the undetermined coefficient k1、k2、k3Determining the sizes of m and n according to the finite element calculation result;
s25: according to the contact deformation of the hollow cylindrical rollercAnd the amount of bending deformation of the hollow cylindrical rollerbCalculating elastic approach of hollow cylindrical rollerhrElastic approach of the hollow cylindrical rollerhrThe following calculation is adopted:
s26: according to the elastic approach of the hollow cylindrical roller calculated in S25hrCalculating a load deformation relational expression of the hollow cylindrical roller and the inner ring and the outer ring of the bearing, and further completing the solution of the load distribution of the hollow cylindrical roller bearing according to a deformation coordination condition;
s3: and comparing the calculation result of the load distribution of the hollow cylindrical roller bearing calculated by the steps S1 and S2 with the allowable value of the load of the rolling element, and carrying out parameter optimization on the bearing which does not meet the regulation.
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