CN117390789B - Disc spring rigidity prediction method based on friction coefficient research - Google Patents
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- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
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Abstract
The invention discloses a disc spring rigidity prediction method based on friction coefficient research, which belongs to the technical field of disc spring rigidity prediction and comprises the following steps: performing numerical simulation on the disc spring under the action of different friction coefficients; 2. determining the influence relation of friction coefficient on the rigidity of the disc spring, and obtaining the maximum main stress and friction stress of all units of the contact surface of the superimposed disc spring under one period; 3. obtaining the maximum stress S of the surface of the disc spring without friction by an A-L method; 4. determining tangential stress caused by friction according to friction stress, and determining surface maximum stress S under the influence of friction factors through maximum stress S of disc spring surface 1 The method comprises the steps of carrying out a first treatment on the surface of the 5. And solving the load of the disc spring under different friction coefficients according to the disc spring A-L method and the fractal theory, and solving the rigidity of the disc spring. According to the method for predicting the rigidity of the disc spring based on the friction coefficient research, the influence of the friction coefficient on the rigidity of the disc spring in the combined disc spring is researched, and the problem that the rigidity prediction accuracy of the combined disc spring is lower under the condition that the number of sheets is increased is solved.
Description
Technical Field
The invention relates to the technical field of disc spring rigidity prediction, in particular to a disc spring rigidity prediction method based on friction coefficient research.
Background
The belleville spring is a spring with a conical section and a washer form, and has the remarkable characteristics of strong bearing capacity, short stroke, small installation space requirement, suitability for high-temperature working environments and the like. During the stress process of the disc spring, contact friction phenomena usually occur, including contact between the superposed conical surfaces, contact between bearing end plates and contact at the position of the disc spring guide tube, so that the disc spring shows a delay effect during the reciprocating loading process, and the loading curve and the unloading curve of the disc spring are different. The Almen-Laszlo (a-L) theory or a method based on the plate and shell theory. In these methods, the belleville springs are reduced to a circular planar plate of small thickness and take into account the deformation effects of the inner forces of the membrane and the inner forces of the bending, which are generated when the load is perpendicular to the mid-plane. However, friction is generated when the disc spring is in contact with the support surface, and this effect was neglected in previous studies.
At present, the research on the disc springs generally considers the influence factors of friction of the disc springs, but most of the research is focused on the characteristics and static mechanical properties of single disc springs, and the research on the combined disc springs is limited. Furthermore, the disc springs themselves have geometrical nonlinearities, whereas the combination disc springs also involve contact nonlinearities. When the disc springs are subjected to external load, the friction effect among the disc springs, which is increased in number, is gradually accumulated and enhanced.
Disclosure of Invention
The invention aims to provide a disc spring rigidity prediction method based on friction coefficient research, which is used for researching the influence of friction coefficient on the rigidity of a disc spring in a combined disc spring and solving the problem of lower rigidity prediction accuracy of the combined disc spring under the condition of increasing the number of sheets.
In order to achieve the above purpose, the invention provides a disc spring rigidity prediction method based on friction coefficient research, which comprises the following steps:
1. performing numerical simulation on the disc spring under the action of different friction coefficients;
2. determining the influence relation of friction coefficient on the rigidity of the disc spring, and obtaining the maximum main stress and friction stress of all units of the contact surface of the laminated disc spring in one period through ANSYS Workbench finite element software;
3. obtaining the maximum stress S of the surface of the disc spring without friction by an A-L method;
the maximum stress of the edge of the disc spring in the relation of the load and the deformation obtained by the A-L method is the sum of tangential stress caused by radial displacement and tangential stress caused by bending, namely the expression of the maximum stress S of the surface of the disc spring is as follows:
wherein,
wherein E is elastic modulus, v is Poisson's ratio, M is shear modulus, f is deformation of the disc spring, h is maximum deformation of the disc spring, t is thickness of the disc spring, and C 1 、C 2 Is the disc spring parameter, H is the disc spring height, t' is the reduced thickness of the disc spring with the bearing surface, and alpha is the ratio of the outer diameter to the inner diameter of the disc spring;
α＝D/d；
wherein D is the outer diameter of the disc spring, and D is the inner diameter of the disc spring;
4. according to the friction stress obtained in the second step, obtaining tangential stress caused by friction, and determining the surface maximum stress S under the influence of friction factors through the maximum stress S of the surface of the disc spring obtained in the third step 1 ；
Maximum stress S of surface under influence of friction factor 1 The expression of (2) is:
S 1 ＝S+σ (4)
wherein sigma is tangential stress on the contact surface;
5. and (3) solving the load of the disc spring under different friction coefficients according to the disc spring A-L method and the fractal theory, and further solving the rigidity of the disc spring.
Preferably, in the first step, the disc spring is subjected to numerical simulation under the action of different friction coefficients, and the method comprises the following steps: creating a three-dimensional model of the disc spring, setting material properties, meshing, applying load, setting boundary conditions, and submitting analysis.
Preferably, in the second step, one period is-0.55 h to +0.55h.
Preferably, in the second step, the specific operation is as follows: and (3) processing the surfaces of the plurality of disc springs to obtain disc spring components with friction coefficients of 0 and other different friction coefficients, testing to obtain the change condition of rigidity under different friction influences, and taking two disc springs as objects to extract the maximum main stress and friction stress of the surfaces of the disc springs by setting different friction coefficients.
Preferably, in the fifth step, the load of the disc spring under different friction coefficients is calculated according to the disc spring A-L method and the fractal theory, and further the rigidity of the disc spring is calculated, wherein the expression of the disc spring load under different friction coefficients is as follows:
wherein H is the height of the disc spring, P is the normal load, and mu is the friction coefficient;
the normal load expression is as follows:
the disc spring rigidity is:
wherein K is the disc spring stiffness.
Therefore, the disc spring rigidity prediction method based on friction coefficient research has the following technical effects:
(1) The tangential stress caused by friction is introduced on the basis of the A-L method, and the load-deformation formula of the disc spring calculated by the A-L method considering friction is obtained by correcting the maximum stress formula of the surface of the disc spring.
(2) The fractal theory can be used for developing a fractal friction model and simulating and predicting the friction behavior of a complex surface, and the stiffness model of the disc spring can be used for predicting the stiffness change condition of the disc spring under the friction condition well.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a flow chart of a method for predicting disc spring stiffness based on friction coefficient study according to the present invention;
FIG. 2 is a schematic diagram of parameters of a disc spring structure based on a method for predicting stiffness of the disc spring under friction coefficient study;
FIG. 3 is a test device of a disc spring assembly based on a method for predicting stiffness of a disc spring under friction coefficient study according to the present invention; wherein (a) in fig. 3 is an extrusion experiment loading device; fig. 3 (b) shows a disc spring assembly core;
FIG. 4 is a graph showing the load-displacement characteristics of a disc spring based on a method for predicting stiffness of the disc spring under friction coefficient study according to the present invention;
FIG. 5 is a finite element disc spring model of a disc spring stiffness prediction method based on friction coefficient research of the invention;
FIG. 6 is a graph showing the load versus coefficient of friction for a method for predicting disc spring stiffness based on coefficient of friction studies in accordance with the present invention;
FIG. 7 is a simplified model of a disc spring based on a method for predicting stiffness of the disc spring under friction coefficient study of the present invention;
FIG. 8 is a graph showing the comparison of the rigidity of two disc springs according to different calculation methods of the method for predicting the rigidity of the disc springs based on the friction coefficient research of the present invention.
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs.
Example 1
As shown in FIG. 1, the invention provides a disc spring rigidity prediction method based on friction coefficient research, which comprises the following steps:
s1, modeling and numerical simulation are carried out on the disc spring through finite element software;
numerical simulation is carried out on the disc spring under the action of different friction coefficients by adopting ANSYS finite element software, and the numerical simulation method mainly comprises the steps of modeling the disc spring, setting material properties, meshing, applying load and boundary conditions, submitting analysis and the like. After creating a three-dimensional model according to the disc spring structural parameters of FIG. 2, material parameters are first set, the disc spring material is 60Si 2 Mn spring steel. And then, grid independence verification is carried out when grids are divided, and proper grid size is selected to ensure calculation accuracy and speed. And then applying load and boundary conditions to the disc spring according to actual working conditions, and finally submitting analysis to perform finite element simulation.
S2, determining the influence relation of friction coefficient on the rigidity of the disc spring, comparing with an experiment to verify the accuracy of the model, and further obtaining stress data of all units of the contact surface of the superimposed disc spring in a period of +/-0.55 h through finite elements;
three kinds of disc springs with different surface treatments are manufactured as samples for tests, namely galvanization, graphite smearing and lubricating oil adding (no friction) are respectively carried out, so that disc spring assemblies with friction coefficients of 0.16, 0.1 and 0 are obtained, and rigidity tests are respectively carried out on the three disc spring assemblies. The tension and compression experiment of the disc spring is carried out on a universal experiment machine (the measuring range of the experiment machine is 100 kN). The disc spring structure parameters are shown in table 1. The purpose of the experiment is to measure the force-displacement curve of the disc spring assembly during compression. According to the actual use working condition of the disc spring, the loading device of the disc spring assembly is designed, the disc springs are connected together through the guide rod, and the disc springs are placed into the sleeve to play a role in guiding and preventing the disc springs from sideslip. The lower end is fixed to the testing machine through the base, and the upper end is connected with the sensor through the double-headed nut, and then the sensor is connected to the testing machine, and the testing loading device is shown in fig. 3. In the disc spring rigidity test, the lower end of the tester is fixed, the upper end is loaded, displacement control is adopted, and static load is applied. The test loading displacement is +/-10 mm, and the test machine acquires input displacement and output force data in real time to obtain a relation curve of compression force and displacement borne by the disc spring assembly.
Table 1 disc spring parameters
| Parameters (parameters) | Numerical value |
| Outer diameter D/mm | 71 |
| Inner diameter d/mm | 36 |
| Thickness t/mm | 4 |
| Free height H/mm | 5.6 |
| Deformation h/mm | 1.6 |
As can be seen from the graph values and trends of fig. 4, as the friction coefficient (forward and reverse) increases, the load of the disc spring increases, indicating that the friction of the disc spring always acts as a hindrance during loading-unloading, because the friction force is a force generated by mutual friction between two contact surfaces, and when the disc spring is compressed or stretched, the contact area between the discs increases, resulting in more friction force.
According to the test, a disc spring combination model was constructed using 56 discs, see fig. 5. And (5) importing the constructed disc spring three-dimensional model into a Workbench for analysis. The finite element model is divided by adopting Solid 186 grid units (the running cost is lower, the calculation time is shorter), the grid density is set to be 2mm, and under the size, the finite element analysis of the disc spring model is relatively stable, so that the analysis efficiency can be improved, and the calculation precision can be ensured.
The load-displacement curve of the disc spring under consideration of friction is shown in fig. 6. The numerical simulation results and test results are shown in fig. 6. When the friction coefficient is 0, the test result is similar to the numerical simulation result, the absolute load error is less than 1%, the accuracy of the numerical model is shown, and the stress extraction is performed based on two numerical models.
And positioning the two superimposed disc springs with friction coefficients of 0, 0.1 and 0.16 to a unit with the maximum equivalent stress and extracting the stress value corresponding to the unit to obtain the maximum main stress and friction stress, wherein the stress data extraction is shown in Table 2.
Table 2 different friction disc spring surface stress extraction
The change in coefficient of friction that can be obtained from table 2 causes a change in the maximum stress on the surface of the disc spring, which is related to the disc spring size data and material, to be exerted by an axial load on the disc spring in a single disc spring. In the combination disc springs, the stress of the disc springs is complicated because the two disc springs are slightly slipped when loaded or due to the influence of surface friction.
S3, obtaining the maximum stress S on the surface of the disc spring through an A-L method.
Since the disk spring has a central symmetry, the deformation of its surroundings is identical when subjected to axial loading. Therefore, the disc spring can be simplified into a single thin plate, and can be subjected to micro-element analysis at any angle. The geometric median plane of the sheet is selected in the (r, θ, z) cylindrical coordinate system as shown as the plane of the coordinate (r, θ) plane perpendicular to the z axis. And the axial load is expressed as a function q (r, θ); the displacement of the thin plate is u, v and w along the r, theta and z directions respectively; the elastic modulus and Poisson's ratio are E, v respectively. Based on the above assumptions and parameters, the following models were built, as shown in fig. 7.
As can be seen from the thin shell theory, the bending moment has the following relation with its corresponding curvature variation:
wherein M is r Is a radial bending moment M t Is tangential bending moment, K r Is the radial curvature, K t Is tangential curvature and W is flexural rigidity. Radial and tangential stresses generated by bending moments:
wherein sigma r Is radial stress, sigma t Is tangential stress, A-L assumes radial strain ε 'due to film forces' r =0 and the amount of change K in radial curvature due to bending force r =0. Substituting the formula (1) into the formula (2) to obtain:
σ r ＝νσ t (3)
from hooke's law:
wherein ε r Is radial strain.
Substituting formula (3) into formula (4) to obtain epsilon r ＝0。
Therefore, the total radial strain of the disc spring is 0 according to the assumption of the A-L method in the derivation process. Under this condition, the maximum stress of the upper edge in the relation of the load and the deformation obtained by the A-L method is the sum of the tangential stress caused by radial displacement and the tangential stress caused by bending, namely the maximum stress of the surface of the disc spring:
wherein,
wherein E is elastic modulus, v is Poisson's ratio, M is shear modulus, f is deformation of the disc spring, h is maximum deformation of the disc spring, t is thickness of the disc spring, and C 1 、C 2 Is the disc spring parameter, H is the disc spring height, t' is the reduced thickness of the disc spring with bearing surface, α is the ratio of the outer diameter to the inner diameter of the disc spring, α=d/D.
S4, determining the surface maximum stress S under the influence of friction factors through the input data and the maximum stress S of the surface of the disc spring 1 。
From Coulomb's law of friction, the shear stress is proportional to the normal compressive stress on the contact surface, i.e
τ μ ＝μσ (8)
Wherein τ μ μ is the coefficient of friction and σ is the tangential stress on the contact surface.
Carrying out data fitting on the friction tangential stress obtained by finite element simulation and the maximum principal stress to obtain the new maximum stress of the surface of the disc spring:
S 1 ＝S+σ (9)
s5, obtaining the rigidity of the disc spring under different friction coefficients according to the disc spring A-L method.
The a-L method assumes a radial strain of 0 for the disc spring during the derivation. Under the above conditions, the relation between the normal load P and the displacement f of the disc spring is deduced as follows:
wherein D is the outer diameter of the disc spring, and D is the inner diameter of the disc spring;
according to the change condition of tangential stress under different friction coefficients of finite element simulation, after correcting a disc spring surface maximum stress formula, adopting the derivation of an A-L method, and after correcting a formula (10), a load-deformation calculation formula about friction can be obtained as follows:
the calculation method of the disc spring rigidity K is the ratio of load to displacement, namely:
FIG. 8 shows the comparison of the stiffness of two disc springs according to different calculation methods.
Therefore, the method for predicting the rigidity of the disc spring based on the friction coefficient research is adopted to research the influence of the friction coefficient on the rigidity of the disc spring in the combined disc spring, and solves the problem that the rigidity prediction accuracy of the combined disc spring is lower under the condition that the number of sheets is increased.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (4)
1. The disc spring rigidity prediction method based on friction coefficient research is characterized by comprising the following steps of:
1. performing numerical simulation on the disc spring under the action of different friction coefficients;
2. determining the influence relation of friction coefficient on the rigidity of the disc spring, and obtaining the maximum main stress and friction stress of all units of the contact surface of the laminated disc spring in one period through ANSYS Workbench finite element software;
3. obtaining the maximum stress S of the surface of the disc spring without friction by an A-L method;
the maximum stress of the edge of the disc spring in the relation of the load and the deformation obtained by the A-L method is the sum of tangential stress caused by radial displacement and tangential stress caused by bending, namely the expression of the maximum stress S of the surface of the disc spring is as follows:
wherein,
wherein E is elastic modulus, v is Poisson's ratio, M is shear modulus, f is deformation of the disc spring, h is maximum deformation of the disc spring, t is thickness of the disc spring, and C 1 、C 2 Is the disc spring parameter, H is the disc spring height, t' is the reduced thickness of the disc spring with the bearing surface, and alpha is the ratio of the outer diameter to the inner diameter of the disc spring;
α＝D/d；
wherein D is the outer diameter of the disc spring, and D is the inner diameter of the disc spring;
4. obtaining tangential stress caused by friction according to the friction stress obtained in the second stepDetermining the maximum stress S of the surface under the influence of friction factors through the maximum stress S of the surface of the disc spring obtained in the step three 1 ；
Maximum stress S of surface under influence of friction factor 1 The expression of (2) is:
S 1 ＝S+σ (4)
wherein sigma is tangential stress on the contact surface;
5. according to the disc spring A-L method and the fractal theory, the load of the disc spring under different friction coefficients is obtained, and then the rigidity of the disc spring is obtained;
and fifthly, solving the load of the disc spring under different friction coefficients according to a disc spring A-L method and a fractal theory, and further solving the rigidity of the disc spring, wherein the expression of the disc spring load under different friction coefficients is as follows:
wherein H is the height of the disc spring, P is the normal load, and mu is the friction coefficient;
the normal load expression is as follows:
the disc spring rigidity is:
wherein K is the disc spring stiffness.
2. The method for predicting the stiffness of a disc spring based on friction coefficient research of claim 1, wherein in the first step, numerical simulation is performed on the disc spring under the action of different friction coefficients, and the method comprises the following steps: creating a three-dimensional model of the disc spring, setting material properties, meshing, applying load, setting boundary conditions, and submitting analysis.
3. The method for predicting the rigidity of a disc spring under friction coefficient research according to claim 1, wherein in the second step, one period is-0.55 h to +0.55h.
4. The method for predicting disc spring stiffness under friction coefficient study of claim 1, wherein in the second step, the specific operation is as follows: and (3) processing the surfaces of the plurality of disc springs to obtain disc spring components with friction coefficients of 0 and other different friction coefficients, testing to obtain the change condition of rigidity under different friction influences, and taking two disc springs as objects to extract the maximum main stress and friction stress of the surfaces of the disc springs by setting different friction coefficients.
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