Method for predicting torsional rigidity of highly strengthened diesel engine plate spring damper

Abstract

The invention provides a method for predicting torsional rigidity of a plate spring damper of a highly strengthened diesel engine. The method comprises the following steps: S1, acquiring key structure and material parameters of the damper; s2, deducing a leaf spring reed deflection equation through a Bernoulli-Euler beam theory according to the key structure and material parameters of the shock absorber, calculating the torsional rigidity of the shock absorber, and establishing a torsional rigidity calculation mechanical model of the leaf spring shock absorber; s3, adopting an orthogonal test method to perform sampling design on structural parameters of the shock absorber, and calculating the torsional rigidity of the plate spring shock absorbers of different structures based on the torsional rigidity calculation mechanical model of the plate spring shock absorber established in the step S2; and S4, constructing a regression model of structural parameters (input) and torsional rigidity (output) of the shock absorber. The method has the beneficial effects that the torsional rigidity of the shock absorber can be quickly and accurately predicted by constructing the plate spring shock absorber proxy model, and technical support is provided for efficient development of the plate spring shock absorber.

Description

Technical Field

[0001] The invention belongs to the technical field of diesel engine vibration control, and in particular relates to a method for predicting torsional stiffness of a high-strength diesel engine leaf spring damper. Background Art

[0002] The performance of diesel engines is greatly affected by torsional vibration. Severe torsional vibration may even cause fatigue damage to the diesel engine shaft system. Torsional vibration dampers are a major suppression measure to reduce the torsional vibration of the shaft system. Reasonable damper matching is of great significance to reducing the vibration of the diesel engine shaft system and improving vehicle comfort. At present, the commonly used torsional vibration dampers on diesel engines include three types: rubber dampers, silicone oil dampers and leaf spring dampers. Among them, rubber dampers are mainly used in small and medium-power diesel engines. When the torsional vibration of the diesel engine shaft system is large, the rubber may fail. Silicone oil dampers have the advantages of simple structure and low price. They are widely used in high-power diesel engines. However, silicone oil dampers are difficult to frequency-modulate the torsional vibration of the shaft system and cannot meet the needs of high-power diesel engine shaft system vibration control. Leaf spring dampers are widely used in the field of high-strength high-power diesel engines due to their high reliability, excellent vibration reduction performance, and not easily affected by corrosive media.

[0003] The torsional stiffness of the shock absorber directly affects the matching characteristics of the diesel engine shaft system and the shock absorber. The current research is based on the Bernoulli-Euler beam theory, and the mechanical analysis model of the leaf spring reed is derived. The calculation model of the reed deflection of the diesel engine leaf spring shock absorber and the torsional stiffness of the shock absorber are constructed. However, the numerical model of the leaf spring shock absorber stiffness established by the leaf spring mechanical analysis method has a large amount of calculation and low calculation efficiency. It is of great significance to carry out research on the rapid stiffness prediction method of the high-strength diesel engine leaf spring shock absorber for the development and design of the shock absorber. Summary of the invention

[0004] In view of this, the present invention aims to propose a method for predicting the torsional stiffness of a highly reinforced diesel engine leaf spring damper to solve at least one technical problem in the background technology.

[0005] To achieve the above object, the technical solution of the present invention is achieved as follows:

[0006] A method for predicting torsional stiffness of a high-strength diesel engine leaf spring damper comprises the following steps:

[0007] S1: Obtain key structural and material parameters of the shock absorber;

[0008] S2: According to the key structure and material parameters of the shock absorber, the leaf spring deflection equation is derived through the Bernoulli-Euler beam theory, the shock absorber torsional stiffness is calculated, and the torsional stiffness computational mechanics model of the leaf spring shock absorber is established;

[0009] S3: using an orthogonal test method to perform a sampling design of shock absorber structural parameters, and based on the leaf spring shock absorber torsional stiffness calculation mechanics model established in step S2, calculating the torsional stiffness of leaf spring shock absorbers with different structures;

[0010] S4: Taking the structural parameters of the leaf spring shock absorber in step S3 as input and the shock absorber torsional stiffness theoretical value K obtained in step S3 as output, a regression model of the shock absorber structural parameters (input) and torsional stiffness (output) is constructed.

[0011] Furthermore, the structural parameters in step S1 include the effective bending length of the leaf spring of the leaf spring shock absorber, the length of the bent portion where the gasket of the leaf spring shock absorber is located, the wide side height of the effective length of the leaf spring shock absorber, the narrow side height of the effective length of the leaf spring shock absorber, the reed width of the leaf spring shock absorber, the minimum radius of the bent portion of the leaf spring of the leaf spring shock absorber, and the number of groups of circumferential leaf springs of the leaf spring shock absorber.

[0012] Furthermore, the material parameters in step S1 include the elastic modulus and Poisson's ratio of the leaf spring.

[0013] Furthermore, step S2 includes establishing the bending moment equations of the two springs of the leaf spring shock absorber, and establishing a leaf spring bending mechanics model based on the Kirchhoff hypothesis of the Bernoulli-Euler beam theory:

[0014] Integrate the deflection equation to calculate the deflection equation of the two springs of the leaf spring shock absorber and the torsional stiffness of the shock absorber:

[0015] The total moment Mz around the center of rotation of the shock absorber in step S2 is:

[0016] Mz=nFR

[0017] Mz is the total moment around the center of rotation of the shock absorber, in N / M;

[0018] n represents the number of shock absorber reed groups;

[0019] F is the concentrated load on the reed, in Newtons;

[0020] R represents the minimum radius of the bending part of the leaf spring, in mm;

[0021] Establish the computational mechanics model of torsional stiffness of leaf spring shock absorber:

[0022]

[0023] K is the theoretical calculated value of the torsional stiffness of the shock absorber, in N·m / rad;

[0024] n represents the number of shock absorber reed groups;

[0025] F is the concentrated load borne by the reed, in N;

[0026] R represents the minimum radius of the bending part of the leaf spring, in mm;

[0027] Mz is the total moment around the center of rotation of the shock absorber, in N / M;

[0028] v L is the deflection of the reed end, in mm.

[0029] Furthermore, step S4 includes taking the effective bending length of the leaf spring, the length of the bending part where the gasket is located, the wide side height of the effective length of the spring leaf, the narrow side height of the effective length of the spring leaf, the width of the spring leaf, the minimum radius of the bending part of the leaf spring, and the number of groups of circumferential leaf springs as input, and taking the calculated value of the torsional stiffness of the leaf spring damper in step S3 as output, and predicting the torsional stiffness of the leaf spring damper based on the proxy model established in step S4.

[0030] Furthermore, step S4 also includes testing by SVM kernel function;

[0031] The SVM kernel function uses the Gaussian RBF kernel function, and finally the minimum mean square error (MSE) and complex correlation coefficient R of the prediction results are used. 2 , average prediction accuracy Predict_Accuracy three dimensions for accuracy testing.

[0032] Compared with the prior art, the method for predicting torsional stiffness of a highly reinforced diesel engine leaf spring damper described in the present invention has the following advantages:

[0033] In response to the problems of difficulty in calculating the torsional stiffness of the traditional leaf spring shock absorber mechanical model, deep theoretical foundation and low evaluation efficiency, this patent proposes a new leaf spring shock absorber stiffness prediction method. By constructing a leaf spring shock absorber proxy model, the torsional stiffness of the shock absorber can be quickly and accurately predicted, providing technical support for the efficient development of leaf spring shock absorbers. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The accompanying drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings:

[0035] Figure 1 It is a schematic diagram of a method for predicting stiffness of a highly reinforced diesel engine leaf spring damper according to Embodiment 1 of the present invention;

[0036] Figure 2 This is a schematic diagram of the mechanical model of the leaf spring shock absorber according to Example 1 of the present invention;

[0037] Figure 3The deflection result of the leaf spring described in Example 1 of the present invention is

[0038] Figure 4 This is the prediction result of the torsional stiffness of the leaf spring damper described in Example 1 of the present invention. DETAILED DESCRIPTION

[0039] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0040] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0041] Aiming at the problem that the torsional stiffness calculation of the traditional leaf spring shock absorber mechanical model is difficult, the theoretical basis is deep, and the evaluation efficiency is low, this patent proposes a new leaf spring shock absorber stiffness prediction method. The technical route is as follows Figure 1 As shown in the figure, this method can provide guidance for the parametric design and matching of leaf spring shock absorbers. The specific steps are as follows:

[0042] (1) Leaf spring damper parameter extraction

[0043] According to the structure and material properties of the leaf spring shock absorber, the structure and material parameters of the leaf spring shock absorber are obtained. The structural parameters include the effective bending length of the leaf spring X1, the length of the bending part where the gasket is located X2, the effective length of the spring wide side height X3, the effective length of the spring narrow side height X4, the spring width X5, the minimum radius of the bending part of the leaf spring X6, and the number of circumferential leaf spring groups X7. The material parameters include the elastic modulus and Poisson's ratio of the leaf spring.

[0044] (2) Establishment of computational mechanics model for torsional stiffness of leaf spring shock absorber

[0045] 1) Establish the bending moment equation of leaf spring leaf 1 and leaf 2: The parameter model of leaf spring damper leaf group is as follows: Figure 2 As shown, the bending moment M1(x) of the spring leaf 1 is as shown in formula (1).

[0046]

[0047] S is the fixed length of the leaf spring 1 of the leaf spring shock absorber;

[0048] L is the total length of the leaf spring 1 of the leaf spring shock absorber;

[0049] x is the length of the leaf spring 1 in the horizontal direction;

[0050] F is the moment of the leaf spring 1 in the vertical direction.

[0051] The bending moment M2(x) of spring 2 is:

[0052]

[0053] S is the fixed length of the leaf spring 2 of the leaf spring shock absorber;

[0054] L is the total length of the leaf spring 2 of the leaf spring shock absorber;

[0055] x is the length of the leaf spring 2 in the horizontal direction;

[0056] F is the moment of the leaf spring 2 in the vertical direction.

[0057] 2) Based on the Kirchhoff hypothesis of Bernoulli-Euler beam theory, a leaf spring bending mechanics model is established:

[0058]

[0059] E is the elastic modulus of the reed material, in MPa;

[0060] I is the moment of inertia of the section, in mm 4 ;

[0061] v1 is the deflection of reed 1, in mm;

[0062] v2 is the deflection of reed 2, in mm;

[0063]

[0064] E is the elastic modulus of the reed material, in MPa;

[0065] I is the moment of inertia of the section, in mm 4 ;

[0066] v1 is the deflection of reed 1, in mm;

[0067] v2 is the deflection of reed 2, in mm:

[0068]

[0069] b represents the width of the leaf spring, in mm;

[0070] a1 represents the effective length and width height of the reed, in mm;

[0071] a2 represents the height of the narrow side of the effective length of the reed, in mm;

[0072] In the formula, h(x) = a1 + kx, where k = (a2 - a1) / L. Substituting the section inertia formula (7) into formula (5) and formula (6) yields:

[0073]

[0074] In the formula, integrating formula (8) and formula (9) once gives:

[0075]

[0076] 3) Calculation of reed deflection: Integrate the deflection equation to calculate the deflection equations of reed 1 and reed 2;

[0077] 4) Calculation of torsional stiffness of shock absorber: The total moment Mz around the center of rotation of the shock absorber is:

[0078] Mz=nFR (12)

[0079]

[0080] Where n is the number of spring groups of the shock absorber, F is the concentrated load borne by the spring, R is the minimum radius of the bending part of the leaf spring, and v is the L is the reed end deflection;

[0081] (3) Leaf spring shock absorber structural parameter sampling design and torsional stiffness calculation

[0082] Orthogonal test design is a method for multi-factor test sampling. It selects some representative points from the comprehensive test for testing. These points have the characteristics of "uniformity" and "orderliness". This patent intends to use the orthogonal test method to perform the sampling design of shock absorber structural parameters. Based on the leaf spring shock absorber stiffness calculation mechanics model established in step (2), the shock absorber structural parameter sampling scheme is input into the numerical evaluation model established in step (2), and the torsional stiffness of the leaf spring shock absorber with different structural parameter schemes is calculated based on the Bernoulli-Euler beam theory, providing a data basis for the leaf spring shock absorber stiffness prediction agent model.

[0083] (4) Construction of leaf spring shock absorber stiffness prediction proxy model

[0084] Taking the effective bending length X1 of the leaf spring of different design schemes in step (3), the length of the bending part where the gasket is located X2, the wide side height of the effective length of the spring leaf X3, the narrow side height of the effective length of the spring leaf X4, the width of the spring leaf X5, the minimum radius of the bending part of the leaf spring X6, and the number of groups of circumferential leaf springs X7 as input, and the theoretical calculated value K of the torsional stiffness of the shock absorber obtained in step (3) as output, a regression model of the shock absorber structural parameters (input) and torsional stiffness (output) is constructed based on the support vector machine (SVM). The SVM model is calculated as follows:

[0085] f(x)=wΦ(x)+b (14)

[0086] Among them, w is the hyperplane weight coefficient vector, which is equal to the dimension of the high-dimensional feature space, Φ(x) is the mapping relationship from low-dimensional to high-dimensional feature space, and b is the offset.

[0087] Considering the allowable fitting error, the penalty factor c and relaxation factor ξ are introduced i ,ξ i * , the support vector regression machine solution can be transformed into an optimization problem, as shown in formula (15):

[0088]

[0089] By introducing the Lagrange multiplier, equation (15) can be transformed into equation (16):

[0090]

[0091] The Lagrange multiplier α i , α i * , β i , β i * (i=1,2,3...N), according to the extreme value condition:

[0092]

[0093] Substituting formula (17) into formula (16), we can get the dual form of formula (15):

[0094]

[0095] Introduce the kernel function K(x,x i )=Φ(x)·Φ(x i ), the inner product calculation of high-dimensional space is transformed into the solution of low-dimensional space function, and the support vector machine regression model is obtained:

[0096]

[0097] At present, there are four main kernel functions commonly used by SVM for mapping analysis. The results show that the Gaussian RBF kernel function has the highest fitting accuracy. This study uses the Gaussian RBF kernel function for regression analysis. Finally, the minimum mean square error (MSE) and complex correlation coefficient R of the prediction results are used to 2 , average prediction accuracy Predict_Accuracy three dimensions for accuracy testing, the specific theory is shown in formulas (20)-(22).

[0098]

[0099] Where N represents the number of solutions, y i represents the theoretical value of torsional stiffness of leaf spring shock absorber calculated based on Bernoulli-Euler mechanical model, Represents the average torsional stiffness of the leaf spring shock absorber calculated based on the mechanical model theory, represents the prediction result of the torsional stiffness of the leaf spring shock absorber. The closer the MSE is to 0, the higher the R 2 The closer it is to 1, the closer the average prediction accuracy Predict_Accuracy is to 100%, and the higher the accuracy of the prediction model.

[0100] (5) Leaf spring shock absorber torsional stiffness prediction accuracy test

[0101] In order to verify the accuracy of the shock absorber stiffness prediction method proposed in this patent, a leaf spring shock absorber is taken as the research object. Based on step (1), the shock absorber structural parameters are extracted, and the deflection of the leaf spring spring is calculated using the Bernoulli-Euler beam theory in step (2). Figure 3 As shown, Figure 3 It can be seen that the deflection of the spring 1 is 0.35212mm. According to formula (13), the calculated value of the torsional stiffness of the shock absorber is 248.4KNm / rad. The test value of the torsional stiffness of the shock absorber is 250KNm / rad. The deviation between the simulation and the test is 1%. Therefore, the mechanical model of the leaf spring shock absorber based on the Bernoulli-Euler beam theory has high accuracy. The effective bending length of the leaf spring, the length of the bending part where the gasket is located, the height of the wide side of the effective length of the spring, the height of the narrow side of the effective length of the spring, the width of the spring, the minimum radius of the bending part of the leaf spring, and the number of groups of circumferential leaf springs are used as inputs, and the calculated value of the torsional stiffness of the leaf spring shock absorber in step (3) is used as output. The torsional stiffness of the leaf spring shock absorber is predicted based on the proxy model established in step (4), as shown in FIG. Figure 4 shown. Figure 4 It can be seen that the prediction results of the modeling group samples are MSE = 0.0010748, R 2 =0.99557, the prediction result of the prediction group sample is MSE=0.00089146, R 2 =0.99431, the average prediction accuracy of all sample prediction groups is 98%. The leaf spring damper torsional stiffness prediction method proposed in this patent has a high prediction accuracy, and this method provides technical guidance for the efficient development and design of leaf spring dampers.

[0102] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting torsional stiffness of a highly reinforced diesel engine leaf spring damper, characterized in that: The steps include: S1: Obtain key structural and material parameters of the shock absorber; S2: According to the key structure and material parameters of the shock absorber, the leaf spring deflection equation is derived through the Bernoulli-Euler beam theory, the shock absorber torsional stiffness is calculated, and the torsional stiffness computational mechanics model of the leaf spring shock absorber is established; S3: using an orthogonal test method to perform a sampling design of shock absorber structural parameters, and based on the leaf spring shock absorber torsional stiffness calculation mechanics model established in step S2, calculating the torsional stiffness of leaf spring shock absorbers with different structures; S4: Taking the structural parameters of the leaf spring shock absorber in step S3 as input and the shock absorber torsional stiffness theoretical value K obtained in step S3 as output, a regression model of the shock absorber structural parameters (input) and torsional stiffness (output) is constructed.

2. The method for predicting torsional stiffness of a high-strength diesel engine leaf spring damper according to claim 1, characterized in that: The structural parameters in step S1 include the effective bending length of the leaf spring of the leaf spring shock absorber, the length of the bent portion where the gasket of the leaf spring shock absorber is located, the wide side height of the effective length of the leaf spring shock absorber, the narrow side height of the effective length of the leaf spring shock absorber, the width of the leaf spring of the leaf spring shock absorber, the minimum radius of the bent portion of the leaf spring of the leaf spring shock absorber, and the number of groups of circumferential leaf springs of the leaf spring shock absorber.

3. The method for predicting torsional stiffness of a high-strength diesel engine leaf spring damper according to claim 1, characterized in that: The material parameters in step S1 include the elastic modulus and Poisson's ratio of the leaf spring.

4. The method for predicting torsional stiffness of a highly reinforced diesel engine leaf spring damper according to claim 1, characterized in that: Step S2 includes establishing the bending moment equations of the two springs of the leaf spring shock absorber, and establishing a leaf spring bending mechanics model based on the Kirchhoff hypothesis of the Bernoulli-Euler beam theory: Integrate the deflection equation to calculate the deflection equation of the two springs of the leaf spring shock absorber and the torsional stiffness of the shock absorber: The total moment Mz around the center of rotation of the shock absorber in step S2 is: Mz=nFR; Mz is the total moment around the center of rotation of the shock absorber, in N / M; n represents the number of shock absorber reed groups; F is the concentrated load on the reed, in Newtons; R represents the minimum radius of the bending part of the leaf spring, in mm; Establish the computational mechanics model of torsional stiffness of leaf spring shock absorber: K is the theoretical calculated value of the torsional stiffness of the shock absorber, in N·m / rad; n represents the number of shock absorber reed groups; F is the concentrated load borne by the reed, in N; R represents the minimum radius of the bending part of the leaf spring, in mm; Mz is the total moment around the center of rotation of the shock absorber, in N / M; v L is the deflection of the reed end, in mm.

5. The method for predicting torsional stiffness of a highly reinforced diesel engine leaf spring damper according to claim 1, characterized in that: Step S4 includes taking the effective bending length of the leaf spring, the length of the bending part where the gasket is located, the wide side height of the effective length of the spring leaf, the narrow side height of the effective length of the spring leaf, the width of the spring leaf, the minimum radius of the bending part of the leaf spring, and the number of groups of circumferential leaf springs as input, and taking the calculated value of the torsional stiffness of the leaf spring damper in step S3 as output, and predicting the torsional stiffness of the leaf spring damper based on the proxy model established in step S4.

6. The method for predicting torsional stiffness of a highly reinforced diesel engine leaf spring damper according to claim 1, characterized in that: Step S4 also includes testing by SVM kernel function; The SVM kernel function uses the Gaussian RBF kernel function, and finally the minimum mean square error and complex correlation coefficient R of the prediction results are used. 2 , average prediction accuracy Predict_Accuracy three dimensions for accuracy testing.

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