CN111597659A - Finite element evaluation method for strength of disc spring - Google Patents
Finite element evaluation method for strength of disc spring Download PDFInfo
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- CN111597659A CN111597659A CN202010451854.7A CN202010451854A CN111597659A CN 111597659 A CN111597659 A CN 111597659A CN 202010451854 A CN202010451854 A CN 202010451854A CN 111597659 A CN111597659 A CN 111597659A
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Abstract
The invention discloses a finite element evaluation method for the strength of a disc spring, which uses a linear elastic finite element model for calculation, records the discrete relation between the Mises stress on a calculation path from the upper surface to the lower surface at the inner diameter of the disc spring and the relative length of the path, establishes a continuous function through interpolation, calculates the length of an elastic interval based on the continuous function, then calculates the ratio of the length of a plastic zone to the total length, namely the yield ratio, and finally judges the strength of the disc spring based on the yield ratio; through the mode, the method is suitable for preliminary strength evaluation of the disc spring with the structure similar to that of the GB/T disc spring, the test times of the novel disc spring can be effectively reduced, the research and development efficiency of the novel disc spring is improved, and the research and development cost is effectively reduced.
Description
Technical Field
The invention belongs to the technical field of spring finite element analysis, and particularly relates to a finite element evaluation method for strength of a disc spring.
Background
The disc spring has large bearing capacity under the condition of small deformation, has better space utilization rate, can have the mechanical characteristics of normal rigidity, variable rigidity, zero rigidity and negative rigidity, can be combined in different modes, and is widely applied to the fields of machine tool industry, petroleum industry, automobile industry, aerospace industry and the like.
The bus of the GB/T1972 disc spring is a line segment, and the design and calculation of the line segment can be referred to by a theoretical formula; other complex and varied disc springs may have their generatrices formed from multiple segments, each of which may be line segments or other curves, and whose design calculations rely on finite element analysis.
In some specific scenes, the GB/T1972 disc spring is difficult to apply, and a novel disc spring needs to be designed. In the design process of the novel disc spring, the cost for evaluating the strength of the disc spring through a test means is high, the period is long, and the requirement for preliminarily evaluating the strength of the disc spring by a numerical simulation method is strong.
In order to solve the above problems, the inventor developed a finite element evaluation method for the strength of the disc spring.
Disclosure of Invention
The present invention is directed to a finite element evaluation method for disc spring strength to solve the above problems.
The invention realizes the purpose through the following technical scheme:
a finite element evaluation method for the strength of a disc spring comprises the following steps:
s1, establishing a linear elastic finite element model of the disc spring;
s2, calculating the Mises stress of the disc spring;
s3, extracting Mises stress of each point on the calculation path from the upper surface to the lower surface at the inner diameter, and obtaining the discrete relation between the stress and the relative length of the path;
s4, generating a continuous interpolation function of the stress and the path relative length through interpolation;
s5, searching an interval with the stress lower than the yield strength of the spring material from the midpoint of the path to two sides on the continuous stress interpolation function, and calculating the length of the elastic interval;
s6, calculating the proportion of the plastic yield area in the calculation path;
s7, judging whether the proportion of the plastic yield area to the calculation path when the working stroke of the disc spring is equal to 0.75 time of the free stroke is less than 0.18, if so, entering a step S8, otherwise, designing the spring again if the strength is unqualified;
s8, judging whether the proportion of the plastic yield area to the calculation path when the working stroke of the disc spring is equal to the free stroke is less than 0.38; if the strength of the disc spring is qualified, otherwise, the strength of the disc spring is unqualified, and the spring needs to be redesigned.
Specifically, the finite element model comprises a disc spring, an upper pressure plate and a lower pressure plate which are processed according to a contact relation, and a friction coefficient is set; the upper pressure plate and the lower pressure plate are modeled by rigid surfaces or deformable bodies, the disc spring is modeled by the deformable bodies, the lower pressure plate restrains all degrees of freedom, the upper pressure plate restrains other degrees of freedom except the loading direction, and the upper pressure plate is loaded in the loading direction according to displacement.
Specifically, the linear elastic finite element model of the disc spring may be an axisymmetric model or a three-dimensional model.
Specifically, the point on the calculated path in step S3 is taken as each node on the calculated path; the relative length of the path is calculated as the length before deformation.
Preferably, the points on the calculated path of step S3 are taken as the respective nodes on the calculated path, and the remaining further sample points.
Further preferably, the points on the calculated path of step S3 are taken to be 2 times the number of nodes on the calculated path and are uniformly set.
Specifically, step S4 employs a variety of interpolation algorithms to generate the continuous interpolation function.
The invention has the beneficial effects that:
the finite element evaluation method for the strength of the disc spring is suitable for preliminary strength evaluation of the disc spring with a structure similar to that of the disc spring of GB/T1972, can effectively reduce the test times of the novel disc spring, improves the research and development efficiency of the novel disc spring, and effectively reduces the research and development cost.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic diagram of the relationship between a disc spring and a pressure plate;
FIG. 3 is a schematic diagram of a finite element mesh of a disc spring;
FIG. 4 is a contour plot of Mises stress for a Belleville spring;
FIG. 5 is a schematic diagram of a computation path;
FIG. 6 is a graph of Mises relative stress versus calculated path relative length.
In the figure: 1-a disc spring; 2-an upper pressing plate; 3, pressing a plate; 4-an elastic region; 5-a plastic region; 6-plastic zone boundary.
Detailed Description
The invention will be further described with reference to the accompanying drawings in which:
as shown in FIG. 1, a finite element evaluation method for disc spring strength comprises the following steps:
s1, establishing a linear elastic finite element model of the disc spring;
s2, calculating the Mises stress of the disc spring;
s3, extracting Mises stress of each point on the calculation path from the upper surface to the lower surface at the inner diameter, and obtaining the discrete relation between the stress and the relative length of the path;
s4, generating a continuous interpolation function of the stress and the path relative length through interpolation;
s5, searching an interval with the stress lower than the yield strength of the spring material from the midpoint of the path to two sides on the continuous stress interpolation function, and calculating the length of the elastic interval;
s6, calculating the proportion of the plastic yield area in the calculation path;
s7, judging whether the proportion of the plastic yield area to the calculation path when the working stroke of the disc spring is equal to 0.75 time of the free stroke is less than 0.18, if so, entering a step S8, otherwise, designing the spring again if the strength is unqualified;
s8, judging whether the proportion of the plastic yield area to the calculation path when the working stroke of the disc spring is equal to the free stroke is less than 0.38; if the strength of the disc spring is qualified, otherwise, the strength of the disc spring is unqualified, and the spring needs to be redesigned.
In some embodiments, the yield ratio criterion of the disc spring is: when the working stroke is equal to 0.75 times of the free stroke, the yield ratio is recommended to be not more than 0.14 and not more than 0.18 at most; when the working stroke is a free stroke, the yield ratio is recommended to be not more than 0.25 and not more than 0.38 at the highest. If the two conditions are met, the strength of the disc spring is qualified, otherwise, the strength of the disc spring is unqualified, and the disc spring is redesigned.
Specifically, the linear elastic finite element model of the disc spring may be an axisymmetric model or a three-dimensional model.
Specifically, the point on the calculated path in step S3 is taken as each node on the calculated path; the relative length of the path is calculated as the length before deformation.
Preferably, the points on the calculated path of step S3 are taken as the respective nodes on the calculated path, and the remaining further sample points.
Further preferably, the points on the calculated path of step S3 are taken to be 2 times the number of nodes on the calculated path and are uniformly set.
Specifically, step S4 employs a variety of interpolation algorithms to generate the continuous interpolation function.
In step 1, as shown in fig. 2, in the self-research dedicated finite element calculation, a linear elastic axisymmetric finite element model of the disc spring 1 is established, in which i is an upper surface at an inner diameter position of the disc spring 1, ii is a lower surface at the inner diameter position, iii is a lower surface at an outer diameter position, and iv is an upper surface at the outer diameter position. The finite element model comprises a disc spring 1, an upper pressure plate 2 and a lower pressure plate 3 which are processed according to a contact relation, and friction coefficients can be set. The upper pressing plate 2 and the lower pressing plate 3 are modeled by rigid surfaces, the lower pressing plate 3 restrains all degrees of freedom, the upper pressing plate 2 restrains other degrees of freedom except the loading direction, and the upper pressing plate 2 is loaded in the loading direction according to displacement. The disc spring 1 is modeled as a deformable body with a finite element mesh as shown in figure 3, this embodiment being calculated using second order axisymmetric elements.
And 2, calculating the Mises stress of the disc spring 1. FIG. 4 shows the contour of Mises stress for Belleville spring 1, with Belleville spring 1 having a yield strength of 1400 MPa.
And 4, generating a continuous interpolation function of the relative stress and the relative path length by quadratic polynomial interpolation, as shown in fig. 6.
And 5, searching an interval with the stress lower than the yield strength of the spring material from the midpoint of the path to two sides on a continuous stress interpolation function, and calculating the length L2 between the elastic areas 4. As shown in FIG. 6, the range of the elastic region 4 obtained by linear elasticity analysis and elastoplasticity analysis of the material of the disc spring 1 is substantially equal, and for the sake of calculation, the results of the linear elasticity analysis are used as the standard.
Step 6, as shown in fig. 6, the total length of the path is calculated and the length L2 between the elastic zones 4 is subtracted to obtain the length L1+ L3 of the plastic zone 5, and the ratio of the plastic yielding zone to the total length of the calculated path is calculated, wherein (L1+ L3)/(L1+ L2+ L3) is the yield ratio. The yield ratio is related to the load of the disc spring 1 and increases with increasing displacement load.
Step 7, judging the yield ratio of the disc spring 1 according to the following criteria: when the working stroke is equal to 0.75 times of the free stroke, the yield ratio is recommended to be not more than 0.14 and not more than 0.18 at most; when the working stroke is a free stroke, the yield ratio is recommended to be not more than 0.25 and not more than 0.38 at the highest. If the two conditions are met, the strength of the disc spring 1 is qualified, otherwise, the strength of the disc spring 1 is unqualified, and the disc spring is redesigned.
The recommended value and the limiting value of the yield ratio criterion of the disc spring 1 are obtained by calculating the yield ratio statistics of A, B, C three types of disc springs 1 in the GB/T1972 disc spring 1, the strength criterion of the GB/T1972 disc spring 1 is comprehensively considered, and the method can be used for preliminary strength evaluation of the disc spring 1 with a structure similar to that of the GB/T1972 disc spring 1. It is noted that this strength criterion can be used when designing the new disc spring 1 using the finite element method, but it cannot be used as the only criterion. The novel disc spring 1 with qualified strength determined by the method still needs to carry out a certain amount of physical tests to test the strength of the disc spring 1.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (7)
1. A finite element evaluation method for the strength of a disc spring is characterized by comprising the following steps:
s1, establishing a linear elastic finite element model of the disc spring;
s2, calculating the Mises stress of the disc spring;
s3, extracting Mises stress of each point on the calculation path from the upper surface to the lower surface at the inner diameter, and obtaining the discrete relation between the stress and the relative length of the path;
s4, generating a continuous interpolation function of the stress and the path relative length through interpolation;
s5, searching an interval with the stress lower than the yield strength of the spring material from the midpoint of the path to two sides on the continuous stress interpolation function, and calculating the length of the elastic interval;
s6, calculating the proportion of the plastic yield area in the calculation path;
s7, judging whether the proportion of the plastic yield area to the calculation path when the working stroke of the disc spring is equal to 0.75 time of the free stroke is less than 0.18, if so, entering a step S8, otherwise, designing the spring again if the strength is unqualified;
s8, judging whether the proportion of the plastic yield area to the calculation path when the working stroke of the disc spring is equal to the free stroke is less than 0.38; if the strength of the disc spring is qualified, otherwise, the strength of the disc spring is unqualified, and the spring needs to be redesigned.
2. The finite element evaluation method of the strength of the disc spring according to claim 1, wherein the finite element model comprises three parts of the disc spring, the upper pressure plate and the lower pressure plate which are processed according to a contact relationship and are provided with friction coefficients; the upper pressure plate and the lower pressure plate are modeled by rigid surfaces or deformable bodies, the disc spring is modeled by the deformable bodies, the lower pressure plate restrains all degrees of freedom, the upper pressure plate restrains other degrees of freedom except the loading direction, and the upper pressure plate is loaded in the loading direction according to displacement.
3. A finite element evaluation method of disc spring strength according to claim 2, wherein the finite element model of linear elasticity of disc spring may be an axisymmetric model or a three-dimensional model.
4. A finite element evaluation method of disc spring strength according to claim 1, wherein the points on the calculated path of step S3 are taken as respective nodes on the calculated path; the relative length of the path is calculated as the length before deformation.
5. A finite element method of disk spring strength according to claim 4, wherein the points on the calculated path of step S3 are taken as nodes on the calculated path, and the remaining more sampled points.
6. A finite element evaluation method of disc spring strength according to claim 5, wherein the points on the calculated path of step S3 are taken to be 2 times the number of nodes on the calculated path and are uniformly arranged.
7. A finite element method for evaluating a strength of a disc spring as claimed in claim 1, wherein step S4 uses a plurality of interpolation algorithms to generate a continuous interpolation function.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113821886A (en) * | 2021-09-22 | 2021-12-21 | 中国人民解放军陆军装甲兵学院 | Design method, system and device of disc spring buffer |
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