A method for calculating static and dynamic characteristics of a nonlinear rubber isolator

Abstract

The application discloses a kind of nonlinear rubber vibration isolator static and dynamic characteristics calculation method, comprising the following steps: S1: Yeoh third-order model is used as the hyperelastic constitutive model of vibration isolator rubber material;S2: determine the material parameter C ij In Yeoh model;S3: the physical model of rubber vibration isolator is constructed, and the rubber part of physical model is the Yeoh model of material parameter C ij Determined in S2;S4: the static deformation of rubber vibration isolator is analyzed to the model of rubber vibration isolator constructed in S3;S5: the vertical natural frequency of rubber vibration isolator is output to the dynamic analysis of the model of rubber vibration isolator constructed in S3.In the application, the proposed nonlinear rubber vibration isolator static and dynamic characteristics calculation method can effectively calculate the dynamic and static characteristics of strong nonlinear large deformation rubber vibration isolator, and has high calculation precision, which can be effectively used for the design of large deformation low-frequency rubber vibration isolator.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of isolator design, in particular to a method for calculating static and dynamic characteristics of a nonlinear rubber isolator. BACKGROUND

[0002] Rubber isolators (as shown in Figure 1 ) are important components for vibration reduction in engineering, and their stiffness and damping can effectively reduce the propagation of external excitation in the system, thus having good vibration reduction effect. Therefore, they are widely used in various mechanical, aviation, precision instruments and transportation fields to reduce external forces such as vibration and impact.

[0003] Modern isolation theory is increasingly mature, and there are mainly two methods for designing rubber isolators, one is test and experience combination, and the other is traditional modeling simulation method. Both of them can obtain the required technical requirements through a large number of tests and repeated finite element calculations, so these two methods are widely recognized and used in engineering practice. Test and experience combination is the most traditional and commonly used method in the design of isolators at present. According to the performance requirements of the isolator, the design task can be completed by experience and test. However, with the emergence of new isolation requirements, various new structures or special size isolators appear, and the traditional design method cannot meet the design requirements of new isolators. For example, most of the rubber isolators on the market have high natural frequency in the small deformation range when they are statically loaded. For some high-power low-speed rotating motors on ships, the low-frequency vibration reduction effect is not obvious, and large deformation and low-frequency rubber isolators need to be developed. However, the current design method of rubber isolators suitable for traditional small deformation is not suitable for the design of large deformation and strong nonlinear rubber isolators. SUMMARY

[0004] To solve the technical problems in the background art, the present application provides a method for calculating static and dynamic characteristics of a nonlinear rubber isolator, which can be effectively used for the design of large deformation and low frequency rubber isolators.

[0005] The method for calculating static and dynamic characteristics of a nonlinear rubber isolator provided by the present application comprises the following steps:

[0006] S1: Yeoh three-order model is used as the hyperelastic constitutive model of the rubber material of the isolator;

[0007] S2: determine the material parameters C ij in the Yeoh model;

[0008] S3: Construct a physical model of the rubber vibration isolator, the physical model has a large diameter end and a small diameter end, the physical model comprises a metal inner ring sleeved in a metal outer ring and a rubber part arranged between the metal inner ring and the metal outer ring, and a constitutive model of the rubber part is a Yeoh model with material parameters C determined in S2; ij

[0009] S4: Analyzing the static deformation of the rubber vibration isolator by the model constructed in S3;

[0010] S5: Dynamically analyzing the model constructed in S3 to output the vertical natural frequency of the rubber vibration isolator.

[0011] It should be noted that the strain energy density function is a function for describing the elastic energy density stored by the material during deformation. The physical properties (stress-strain relationship) of the rubber material can be represented by the strain energy density function. The original strain energy general expression is proposed by Rivlin in 1951:

[0012]

[0013] where W is the strain energy density function, C ij is a material constant, and the larger the parameter N is, the more accurate the model is in describing the mechanical behavior of the rubber material, but at the same time, there are problems of difficulty in solving and large amount of calculation. Although this model is suitable for most hyperelastic materials, it has the disadvantage of complex calculation, so it is often simplified on this basis. Common simplified models include Mooney-Rivlin, Neo-Hookean model and Yeoh model.

[0014] The determination of the stress-strain relationship is mainly determined by the partial derivative form of the first and second strain invariants. For the Yeoh model of the rubber hyperelastic constitutive model, the high-order term of the first strain invariant I1 is represented, and the strain energy density function is usually represented as a polynomial expansion. The form of this polynomial expansion allows the consideration of polynomial terms of different orders. Each term represents the energy stored by the material under different degrees of strain. In hyperelastic materials, this energy density function can more accurately describe the behavior of the material under large deformation conditions, because the Yeoh model considers high-order strain invariants, thus more comprehensively reflecting the nonlinear behavior of the material, so the Yeoh model is selected in the present application.

[0015] Preferably, the strain energy density function W of the Yeoh third-order model as the hyperelastic constitutive model of the rubber material of the vibration isolator in step S1 is simplified as:

[0016] W=C 10 (I1-3)+C 20 (I1-3) 2 +C​30 (I1-3) 3

[0017] wherein C 10 , C 20 , C 30 are material coefficients of Yeoh third order model, and I1 is the first strain invariant.

[0018] Preferably, the tensile stress-strain test data of the rubber material obtained in step S2 according to the national standard GB / T 528-2009 "Test Method for Tensile Stress-Strain Properties of Vulcanized or Thermoplastic Rubber" is fitted by using the least square method to obtain the material parameters C ij .

[0019] Preferably, the dynamic-static ratio of the rubber isolator is used to approximate the dynamic-static ratio of the rubber material, that is, step S5 further includes inputting the dynamic modulus parameter Ed of the rubber material.

[0020]

[0021] wherein: Δ- the dynamic-static ratio of the rubber isolator; K d - dynamic stiffness; K s - static stiffness, Es- static elastic modulus.

[0022] Preferably, the formula for determining the dynamic stiffness is:

[0023]

[0024] f- natural frequency, m- rated load mass;

[0025] The formula for determining the static stiffness is:

[0026]

[0027] wherein: P- rated load, X 1.1 is the deformation of the isolator at 1.1 times the rated load; X 0.9 is the deformation of the isolator at 0.9 times the rated load.

[0028] Preferably, the determination of the static elastic modulus of the rubber is:

[0029] The tensile stress and strain relationship curve of the rubber material is obtained by stretching the rubber material of the isolator, the tensile stress and strain relationship curve in the elastic range of the rubber material is intercepted, and the slope of the curve is calculated. The slope is the static elastic modulus.

[0030] Specifically, step S4 further includes applying boundary constraint conditions to the model of S3, as in the existing finite element analysis.

[0031] As with the existing finite element analysis, specifically, step S5 further comprises imposing boundary constraint conditions on the model of S3.

[0032] In the present application, the proposed nonlinear rubber isolator static and dynamic characteristics calculation method can effectively improve the calculation accuracy of the static and dynamic characteristics of the strong nonlinear large deformation rubber isolator, and can effectively calculate the static and dynamic characteristics of the strong nonlinear large deformation rubber isolator, with high calculation accuracy.

[0033] The present application can effectively guide the design of rubber isolators with low-frequency isolation effect and carrying capacity for improving the low-frequency isolation problem of low-speed and high-power machinery.

[0034] The present application can effectively reduce the design cost of large deformation low-frequency rubber isolators.

[0035] Additional aspects and advantages of the present application will be partially given in the following description, partially will become apparent from the following description, or will be understood by the practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 It is a schematic diagram of the rubber isolator structure in the prior art;

[0037] Figure 2 It is a schematic diagram of imposing boundary constraint conditions on the model in step S4;

[0038] Figure 3 It is a tensile stress-strain curve of the rubber material in the embodiment;

[0039] Figure 4 It is a tensile stress-strain curve of the rubber material in the elastic range in the embodiment;

[0040] Figure 5 It is a schematic diagram of imposing boundary constraint conditions on the model in step S5. DETAILED DESCRIPTION

[0041] The embodiments of the present application will be described in detail below, and examples of the embodiments are shown in the drawings, wherein the same or similar symbols represent the same or similar elements or elements with the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and are only used to explain the present application, and cannot be understood as a limitation on the present application.

[0042] A nonlinear rubber isolator static and dynamic characteristics calculation method comprises the following steps:

[0043] S1: The Yeoh third-order model is used as the hyperelastic constitutive model of the vibration isolator rubber material. In step S1, the strain energy density function W of the Yeoh third-order model as the hyperelastic constitutive model of the vibration isolator rubber material is simplified to:

[0044] W=C 10 (I1-3)+C 20 (I1-3) 2 +C 30 (I1-3) 3

[0045] Among them, C 10 C 20 C 30 All are material coefficients of the Yeoh third-order model, with I1 being the first strain invariant;

[0046] S2: Determine the material parameters C in the Yeoh model i j; i and j are integers, and in this embodiment C i j includes C 10 C 20 C 30 ;

[0047] Based on the tensile stress-strain test data of rubber materials obtained according to the national standard GB / T528-2009 "Test Procedure for Determination of Tensile Stress-Strain Properties of Vulcanized Rubber or Thermoplastic Rubber", the material parameter C was obtained by fitting using the least squares method. 10 C 20 C 30 ;

[0048] The material parameters determined by the above method in this embodiment are shown in Table 1 below:

[0049] Table 1 Material parameters of Yeoh constitutive model

[0050]

[0051] S3: Constructing the physical model of the rubber vibration isolator (e.g.) Figure 1 As shown), the physical model has a large-diameter end and a small-diameter end. The physical model includes a metal inner ring fitted inside a metal outer ring, and a rubber part disposed between the metal inner ring and the metal outer ring. The rubber part is made of material with parameter C determined by S2. ij The Yeoh model;

[0052] S4: Static deformation analysis of the rubber isolator model built in S3: Specifically, boundary constraint conditions are applied to the model of S3, the connection between the metal outer ring of the rubber isolator and the ground is simulated by fixed support, and the binding form is used to simulate the adhesive state between the rubber and the metal ring between the metal inner and outer rings of the rubber isolator. The model applies a vertical load of 600N vertically downward on the metal inner ring to simulate the 60kg load (equivalent static load of the engine unit device acting on the rubber isolator) borne by the rubber isolator, specifically as shown in Figure 5 , and then static analysis is performed to output the static deformation of the rubber isolator as 7.35mm;

[0053] S5: Dynamic analysis of the rubber isolator model built in S3 to output the vertical natural frequency of the rubber isolator;

[0054] Specifically, when performing dynamic analysis on the rubber isolator, the key is to determine the dynamic modulus of the rubber material of the isolator;

[0055] The dynamic modulus parameter Ed of the rubber material is determined by using the dynamic-static ratio of the rubber isolator to approximate the dynamic-static ratio of the rubber material;

[0056]

[0057] wherein: Δ - dynamic-static ratio of the rubber isolator; K d - dynamic stiffness; K s - static stiffness, Es - static elastic modulus;

[0058] The formula for determining the dynamic stiffness is:

[0059]

[0060] f - natural frequency, m - rated load mass;

[0061] The formula for determining the static stiffness is:

[0062]

[0063] wherein: P - rated load, X 1.1 is the deformation of the isolator at 1.1 times the rated load; X 0.9 is the deformation of the isolator at 0.9 times the rated load;

[0064] After calculation, Δ = 1.62;

[0065] The determination method of the static elastic modulus of the rubber is:

[0066] The material is in the elastic deformation stage, the stress and strain are in proportional relationship, that is, in accordance with Hooke's law, and the proportional coefficient is called the elastic modulus of the material. The rubber material of the vibration isolator is stretched, and the tensile stress and strain relationship curve is obtained as shown in Figure 3 The tensile stress and strain relationship curve in the elastic range of the rubber material is intercepted (as shown in Figure 4 The slope of the curve is the static elastic modulus, and the static elastic modulus in the embodiment is 1.78 MPa, so the dynamic modulus of the rubber material of the vibration isolator is 2.8836 MPa.

[0067] Step S5 further comprises applying boundary constraint conditions to the model of S3. Due to the nonlinearity of the rubber material, pre-stress analysis is not used in modal analysis, but a mass of 60 kg is added to simulate the initial stress state, and the remaining constraint boundary conditions remain consistent with the static deformation constraint conditions. The natural frequency analysis calculation model of the vibration isolator is as shown in Figure 5

[0068] The finally output vertical natural frequency of the rubber vibration isolator is 7.44 Hz; the rubber vibration isolator of the above embodiment is tested, and the static deformation of the rubber vibration isolator is 7.71 mm, and the vertical natural frequency is 7.6 Hz. Through data comparison, it can be known that the vertical natural frequency and the static deformation of the rubber vibration isolator obtained by the method are relatively accurate.

[0069] Therefore, the method has high calculation precision, can effectively improve the calculation precision of the dynamic and static characteristics of the strong nonlinear large deformation rubber vibration isolator, and can effectively calculate the dynamic and static characteristics of the strong nonlinear large deformation rubber vibration isolator;

[0070] The application can effectively guide the design of the rubber vibration isolator with low-frequency vibration isolation effect and bearing capacity for improving the low-speed, high-power mechanical low-frequency vibration isolation problem;

[0071] The patent can effectively reduce the design cost of the large deformation low-frequency rubber vibration isolator.

[0072] The above is only a preferred specific embodiment of the application, but the protection scope of the application is not limited thereto, and any person skilled in the art can make equivalent replacement or change according to the technical solution and the inventive concept of the application within the technical range disclosed by the application, which should be covered within the protection scope of the application.

[0073] ​In the present application, unless specifically stipulated and limited otherwise, the terms "mounting", "connection", "linking", "fixing" and the like should be understood in a broad sense. For example, it can be fixed connection, or detachable connection, or integral; it can be mechanical connection, or electrical connection, or communication with each other; it can be direct connection, or indirect connection through intermediate medium; it can be internal communication of two elements, or interaction relationship between two elements, unless specifically limited otherwise. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0074] In the present application, unless specifically stipulated and limited otherwise, the first feature is "on" or "under" the second feature. The first and second features can be in direct contact, or the first and second features can be in indirect contact through an intermediate medium. Moreover, the first feature "above", "over" and "on" the second feature can be that the first feature is directly above or obliquely above the second feature, or only indicates that the horizontal height of the first feature is higher than that of the second feature. The first feature "below", "under" and "under" the second feature can be that the first feature is directly below or obliquely below the second feature, or only indicates that the horizontal height of the first feature is less than that of the second feature.

Claims

1. A method of calculating static and dynamic characteristics of a nonlinear rubber isolator, characterized by, Comprising the following steps: S1: Yeoh three-order model as the hyperelastic constitutive model of the rubber material of the vibration isolator; S2: Determining material parameters in Yeoh model C ij ; S3: constructing a physical model of the rubber vibration isolator, the physical model having a large-diameter end and a small-diameter end, the physical model comprising a metal inner ring sleeved in a metal outer ring and a rubber part arranged between the metal inner ring and the metal outer ring, the rubber part being of the material parameters determined in S2 C ij Yeoh model; S4: analyzing the static deformation of the rubber vibration isolator by the model constructed in S3; S5: outputting the vertical natural frequency of the rubber vibration isolator by dynamic analysis of the model constructed in S3; In step S5, the dynamic modulus parameter of the rubber material is also input Ed ; ； In the formulae: - dynamic-static ratio of the rubber isolator; - dynamic stiffness; - static stiffness, Es- static modulus of elasticity; The formula for determining the dynamic stiffness is: ； - natural frequency, m - rated load mass; The formula for determining the static stiffness is: ； where P = rated load, X 1.1 is the deflection of the isolator at 1.1 times the rated load; X 0.9 is the deflection of the isolator at 0.9 times the rated load; The determination method of the static elastic modulus of the rubber is: The rubber material of the vibration isolator is stretched to obtain the tensile stress and strain relationship curve, the tensile stress and strain relationship curve in the elastic range of the rubber material is intercepted, and the slope of the curve is calculated, which is the static elastic modulus.

2. The method of claim 1, wherein, The strain energy density function W of the Yeoh three-order model as the hyperelastic constitutive model of the rubber material of the vibration isolator in step S1 is: ； where, C 10 , C 20 , C 30 are material coefficients of the Yeoh third-order model, I 1 is the first strain invariant.

3. The method of claim 1, wherein, Step S4 further comprises applying boundary constraint conditions to the model of S3.

4. The method of claim 1, wherein, Step S5 further comprises applying boundary constraint conditions to the model of S3.

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