CN105653775A - Mechanical fixing combining part modeling method - Google Patents

Abstract

The invention relates to a mechanical fixing combining part modeling method, and belongs to the field of mechanical structure dynamic feature analysis. The mechanical fixing combining part modeling method is characterized in that 1, two parts for forming a fixing combining part are set to be a first part and a second part; the fixing combining part of the first part and the second part is equivalent to a transversely isotropy virtual material; and five independent elastic constants and densities of the transversely isotropy virtual material are obtained; and 2, the elastic constants and the densities of the transversely isotropy virtual material are input into finite element software to obtain a finite element model of a mechanical structure with the fixing combining part. The invention provides a novel, effective, convenient and fast method for the fixing combining part dynamic modeling; the seamless connection integration of the fixing combining part dynamic modeling and limited element analysis software is realized; and the complexity of the conventional fixing combining part spring-damper modeling and the inconvenience of the limited element analysis software integration and practical operation are avoided.

Description

Mechanical fixation joint modeling method

Technical Field

The invention belongs to the technical field of mechanical structure dynamic characteristic analysis, and particularly relates to a mechanical fixation joint modeling method.

Background

In the initial stage of mechanical structure design, a dynamic model of the mechanical structure needs to be established to evaluate the dynamic characteristics of the mechanical structure. By applying finite element method, modal analysis and comprehensive technology, the dynamic characteristics of the complex structural part can be accurately pre-cut in the design stage. However, the major cause of the large errors in the overall dynamic behavior analysis of the mechanical structure is the difficulty in accurately modeling the joint dynamics at the joint of the parts. At present, the mechanical fixed joint is generally modeled by a method of equivalent the fixed joint to a viscoelastic element, which is simple and practical and has been adopted by many researchers and engineers, but the method neglects the coupling effect among the units and the unit degrees of freedom of the joint, so that the modeling precision is not high, and the method is difficult to be connected with finite element software and is not easy to operate.

Disclosure of Invention

The invention aims to overcome the defects of the prior art, improve the modeling precision, be easy to connect and integrate with finite element software and be simple and convenient to operate, and provides the modeling method for the mechanical fixed joint.

The invention is realized by the following technical scheme.

A method of modeling a mechanically fixed joint, the method comprising the steps of:

i, setting two parts forming a fixed joint part as a first part and a second part respectively, enabling the fixed joint part of the first part and the fixed joint part of the second part to be equivalent to a virtual material with transverse isotropy, and obtaining five independent elastic constants and densities of the virtual material with transverse isotropy:

1) determining the elastic modulus E of the transverse isotropic virtual material in the direction of the symmetry axis z_z：

$E_z=K_n^{*}{E}^{\′}\frac{h}{\sqrt{A_a}}$ ①

Wherein,for dimensionless normal contact stiffness of the joint, E' is the equivalent elastic modulus andE₁、E₂、υ₁、υ₂respectively representing the modulus of elasticity and Poisson's ratio, A, of part one and part two_aThe name of the bonding part defines the contact area, and h is the thickness of the bonding part;

the dimensionless normal contact stiffness of the joint is:

$\begin{array}{c}{K}_n^{*}=\frac{4(3-D)D{\left(\frac{2-D}{D}\right)}^{D/2}{A}_r^{*D/2}}{3\sqrt{2\mathrm{\π}}(2-D)(1-D)}\×\[{\left(\frac{2-D}{D}\right)}^{(1-D)/2}{A}_r^{*(1-D)/2}-a_c^{*(1-D)/2}\]\\ +\frac{1.03\×2^{0.825+0.15D}{\left(2.8K\mathrm{\φ}\right)}^{0.15}D{\left(\frac{2-D}{D}\right)}^{D/2}}{3{\mathrm{\π}}^{0.075D+0.275}{G}^{*0.15(D-1)}{\left(\ln \mathrm{\α}\right)}^{0.075}}\×\frac{A_r^{*D/2}{a}_c^{*0.425(1-D)}\[1-{\left(\frac{1}{6}\right)}^{-0.425}\]}{(1.425-0.425D)(2-D)\×0.425(1-D)}\\ +\frac{1.40\×2^{0.474D-1.633}{\left(2.8K\mathrm{\φ}\right)}^{0.474}{E}^{\′0.526}{\left(\frac{2-D}{D}\right)}^{D/2}}{3{\mathrm{\π}}^{0.237D-0.211}{G}^{*0.474(D-1)}{\left(\ln \mathrm{\α}\right)}^{0.237}}\×\frac{{\mathrm{DA}}_r^{*D/2}{a}_c^{*0.263(1-D)}\[{\left(\frac{1}{6}\right)}^{0.263}-{\left(\frac{1}{110}\right)}^{-0.263}\]}{(1.263-0.263D)(2-D)\×0.263(1-D)}\end{array}$ ②

dimensionless normal contact total load P of joint^*Comprises the following steps:

when D ≠ 1.5,

③

when the D is equal to 1.5,

④

wherein, P^*For the joint to contact the total load dimensionless normal andrepresents a dimensionless actual contact area of the joint anda_c ^*represents the dimensionless critical contact area of the microprotrusions andG^*is dimensionless fractal roughness andd is a profile fractal dimension; k is a hardness coefficient and is 0.454+0.41 upsilon, and upsilon is the Poisson ratio of a softer material in the contact material;α is a constant greater than 1, typically α ═ 1.5 for random surfaces subject to a positive-too distribution;

2) obtaining the elastic modulus E of the equivalent transverse isotropy virtual material in the direction of the isotropic axis x (or y)_x：

$E_x=\frac{{\mathrm{D\ψ}}^{\frac{2-D}{2}}{a}_l}{A_a(2-D)}{E}^{\′}$ ⑤

Wherein, a_lThe maximum contact area of the micro-convex body is psi, and the fractal domain expansion factor is psi;

3) determining the shear modulus G of the equivalent transverse isotropy virtual material in the x-z plane by using the formulas ③, ④, ⑥, ⑦ and ⑧_xz：

$G_{xz}=K_t^{*}*G^{\′}*\frac{h}{\sqrt{A_a}}$ ⑥

Wherein, K_t ^*For dimensionless tangential contact stiffness of the joint, G' is the equivalent shear modulus andG₁、G₂、υ₁、υ₂respectively representing the shear modulus and Poisson ratio of the first part and the second part;

the dimensionless tangential contact stiffness of the joint is:

$K_t^{*}=\frac{8{\mathrm{D\&psi;}}^{1+0.25D^2-D}}{\sqrt{\mathrm{\&pi;}}(1-D)}{\left(\frac{2-D}{D}{A_r}^{*}\right)}^{0.5D}\&lsqb;{\left(\frac{2-D}{D}{\mathrm{\&psi;}}^{0.5D-1}{A_r}^{*}\right)}^{0.5-0.5D}-{a_c}^{*0.5-0.5D}\&rsqb;,(1<D\&le;2$ ⑦

${K_t}^{*}=\frac{2+2\sqrt{5}}{\sqrt{\mathrm{\&pi;}}}\sqrt{\frac{\sqrt{5}-1}{2}{A_r}^{*}}ln\frac{(\sqrt{5}-1){A_r}^{*}}{2{a_c}^{*}},(D=1)$ ⑧

4) determining Poisson ratio upsilon of equivalent transverse isotropy virtual material_zx: poisson ratio upsilon of equivalent transverse isotropy virtual material_zxTaking an approximate value of 0;

5) determining Poisson ratio upsilon of equivalent transverse isotropy virtual material_xy: poisson ratio upsilon of equivalent transverse isotropy virtual material_xyTaking an approximate value of 0;

6) determining the density rho of the equivalent transverse isotropic virtual material as follows:

$\mathrm{\&rho;}=\frac{{\mathrm{D\&psi;}}^{\frac{2-D}{2}}{a}_l({\mathrm{\&rho;}}_1+{\mathrm{\&rho;}}_2)}{2(2-D)A_a}$ ⑨

where ρ is₁、ρ₂The material densities of the part one and the part two respectively;

and II, inputting the elastic constant and the density of the equivalent transverse isotropic virtual material into finite element software to obtain a finite element model of the mechanical structure with the fixed joint part.

The invention has the beneficial effects that: the method provides a new effective and convenient method for dynamic modeling of the fixed joint part, realizes seamless connection and integration of the dynamic modeling of the fixed joint part and finite element analysis software, and avoids the complexity of traditional fixed joint part spring-damper modeling and the inconvenience of integration and actual operation of the traditional fixed joint part spring-damper modeling and the finite element analysis software.

Drawings

The invention is further illustrated with reference to the following figures and examples.

Fig. 1 is a schematic view of a fixed joint.

FIG. 2 is a schematic diagram of an equivalent virtual material model of a fixed joint.

Fig. 3 is a schematic view of the fixed joint separated from the overall structure.

FIG. 4 is a schematic view of a dumbbell test coupon.

In the figure, 1, a first part, 2, a second part, 3, a joint, 4, an equivalent transverse isotropic virtual material, 5, a transverse isotropic layer, 6, a first hexagon socket bolt, 7, a second hexagon socket bolt.

Detailed Description

Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements, unless otherwise indicated.

The invention provides a modeling method of a mechanical fixed joint, wherein the fixed joint is generally a bolt joint, and the number of connected parts is generally 2. The part comprising a fixed joint is shown in figure 1 with relative displacement between the parts 1, 2. The fixed joint 3 is equivalent to a cross-section isotropic virtual material 4, the contact between the first part 1 and the second part 2 is actually the contact between the micro-convex bodies on the two contact surfaces on the microcosmic scale, the contact part has thickness, and the thickness of the contact part is generally considered to be 1mm in the industry, so the invention is equivalent to the cross-section isotropic virtual material. The equivalent virtual material is fixedly connected with the parts on both sides, as shown in figure 2. The fixed joint may be considered to have isotropic properties in the x-y plane, with the z-axis being the axis of symmetry, as shown in fig. 3.

The invention provides a mechanical fixed joint modeling method, which comprises the following steps:

i, setting two parts forming a fixed joint part as a first part 1 and a second part 2 respectively, enabling the fixed joint part of the first part 1 and the fixed joint part of the second part 2 to be equivalent to a transverse isotropic virtual material, and obtaining five independent elastic constants and densities of the transverse isotropic virtual material:

1) determining the elastic modulus E of the transverse isotropic virtual material in the direction of the symmetry axis z_z：

$E_z=K_n^{*}{E}^{\&prime;}\frac{h}{\sqrt{A_a}}$ ①

Wherein,for dimensionless normal contact stiffness of the joint, E' is the equivalent elastic modulus andE₁、E₂、υ₁、υ₂the modulus of elasticity and Poisson's ratio, A, of part one 1 and part two 2, respectively_aThe name of the bonding part defines the contact area, and h is the thickness of the bonding part;

the dimensionless normal contact stiffness of the joint is:

$\begin{array}{c}{K}_n^{*}=\frac{4(3-D)D{\left(\frac{2-D}{D}\right)}^{D/2}{A}_r^{*D/2}}{3\sqrt{2\mathrm{\&pi;}}(2-D)(1-D)}\&times;\&lsqb;{\left(\frac{2-D}{D}\right)}^{(1-D)/2}{A}_r^{*(1-D)/2}-a_c^{*(1-D)/2}\&rsqb;\\ +\frac{1.03\&times;2^{0.825+0.15D}{\left(2.8K\mathrm{\&phi;}\right)}^{0.15}D{\left(\frac{2-D}{D}\right)}^{D/2}}{3{\mathrm{\&pi;}}^{0.075D+0.275}{G}^{*0.15(D-1)}{\left(\ln \mathrm{\&alpha;}\right)}^{0.075}}\&times;\frac{A_r^{*D/2}{a}_c^{*0.425(1-D)}\&lsqb;1-{\left(\frac{1}{6}\right)}^{-0.425}\&rsqb;}{(1.425-0.425D)(2-D)\&times;0.425(1-D)}\\ +\frac{1.40\&times;2^{0.474D-1.633}{\left(2.8K\mathrm{\&phi;}\right)}^{0.474}{E}^{\&prime;0.526}{\left(\frac{2-D}{D}\right)}^{D/2}}{3{\mathrm{\&pi;}}^{0.237D-0.211}{G}^{*0.474(D-1)}{\left(\ln \mathrm{\&alpha;}\right)}^{0.237}}\&times;\frac{{\mathrm{DA}}_r^{*D/2}{a}_c^{*0.263(1-D)}\&lsqb;{\left(\frac{1}{6}\right)}^{0.263}-{\left(\frac{1}{110}\right)}^{-0.263}\&rsqb;}{(1.263-0.263D)(2-D)\&times;0.263(1-D)}\end{array}$ ②

dimensionless normal contact total load P of joint^*Comprises the following steps:

when D ≠ 1.5,

③

when the D is equal to 1.5,

④

wherein, P^*For the joint to contact the total load dimensionless normal andA_r ^*represents a dimensionless actual contact area of the joint anda_c ^*represents the dimensionless critical contact area of the microprotrusions andG^*is dimensionless fractal roughness andd is a profile fractal dimension; k is a hardness coefficient and is 0.454+0.41 upsilon, and upsilon is the Poisson ratio of a softer material in the contact material;α is a constant greater than 1, typically α ═ 1.5 for random surfaces subject to a positive-too distribution;

2) obtaining the elastic modulus E of the equivalent transverse isotropy virtual material in the direction of the isotropic axis x or y_x：

$E_x=\frac{{\mathrm{D\&psi;}}^{\frac{2-D}{2}}{a}_l}{A_a(2-D)}{E}^{\&prime;}$ ⑤

Wherein, a_lThe maximum contact area of the micro-convex body is psi, and the fractal domain expansion factor is psi;

3) determining the shear modulus G of the equivalent transverse isotropy virtual material in the x-z plane by using the formulas ③, ④, ⑥, ⑦ and ⑧_xz：

$G_{xz}={K_t}^{*}*G^{\&prime;}*\frac{h}{\sqrt{A_a}}$ ⑥

Wherein, K_t ^*For dimensionless tangential contact stiffness of the joint, G' is the equivalent shear modulus andG₁、G₂、υ₁、υ₂respectively representing the shear modulus and Poisson ratio of the part I1 and the part II 2;

the dimensionless tangential contact stiffness of the joint is:

${K_t}^{*}=\frac{8{\mathrm{D\&psi;}}^{1+0.25D^2-D}}{\sqrt{\mathrm{\&pi;}}(1-D)}{\left(\frac{2-D}{D}{A_r}^{*}\right)}^{0.5D}\&lsqb;{\left(\frac{2-D}{D}{\mathrm{\&psi;}}^{0.5D-1}{A_r}^{*}\right)}^{0.5-0.5D}-{a_c}^{*0.5-0.5D}\&rsqb;,(1<D\&le;2$ ⑦

${K_t}^{*}=\frac{2+2\sqrt{5}}{\sqrt{\mathrm{\&pi;}}}\sqrt{\frac{\sqrt{5}-1}{2}{A_r}^{*}}\ln \frac{(\sqrt{5}-1){A_r}^{*}}{2{a_c}^{*}},(D=1)$ ⑧

4) determining Poisson ratio upsilon of equivalent transverse isotropy virtual material_zx: poisson ratio upsilon of equivalent transverse isotropy virtual material_zxTaking an approximate value of 0;

5) determining Poisson ratio upsilon of equivalent transverse isotropy virtual material_xy: poisson ratio upsilon of equivalent transverse isotropy virtual material_xyTaking an approximate value of 0;

6) determining the density rho of the equivalent transverse isotropic virtual material as follows:

$\mathrm{\&rho;}=\frac{{\mathrm{D\&psi;}}^{\frac{2-D}{2}}{a}_l({\mathrm{\&rho;}}_1+{\mathrm{\&rho;}}_2)}{2(2-D)A_a}$ ⑨

where ρ is₁、ρ₂The material densities of the part I1 and the part II 2 respectively;

and II, inputting the elastic constant and the density of the equivalent transverse isotropic virtual material into finite element software to obtain a finite element model of the mechanical structure with the fixed joint part.

In order to fully reflect the characteristics of the joint and simplify the structure as much as possible, a dumbbell-shaped test piece designed in article "metal material joint method tangential stiffness correction and experimental verification" of article No. 6, volume 43, journal of agricultural machinery, is used, as shown in fig. 4. The fixed joint shown in fig. 4 is also referred to as a bolted joint, which is a general form of a mechanical joint. In this embodiment, the first part 1 and the second part 2 which are sequentially arranged from top to bottom are fixedly combined together by the vertically arranged first socket head cap 6 and the vertically arranged second socket head cap 7, and the method of the present invention is verified by taking this structure as an example.

The mating surface materials of the dumbbell model joint are HT250 steel and No. 45 steel, and the parameters of the mating surface are shown in Table 1.

TABLE 1 physical parameters of the contact surfaces of part 1 and part 2

According to the data in table 1, the parameters of the equivalent transverse isotropic virtual material of the joint part are shown in table 2 under the working conditions that the first hexagon socket head cap screw 6 and the second hexagon socket head cap screw 7 bear three tightening torques of 30N · m, 60N · m and 90N · m.

TABLE 23 parameters of the transverse isotropy virtual materials obtained under the working conditions

The comparison between the calculated natural frequency obtained by the equivalent transverse isotropic virtual material model and the experimental identification natural frequency is shown in table 3 under the working conditions that the first hexagon socket head cap screw 6 and the second hexagon socket head cap screw 7 are respectively subjected to 30 N.m, 60 N.m and 90 N.m.

TABLE 3 comparison of calculated and Experimental Natural frequencies

The absolute value of the relative error of each order of theoretical modal frequency is within 10 percent, and the actual engineering requirements are met.

The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (1)

1. A method for modeling a mechanical fixation joint, comprising: the modeling method comprises the following steps:

i, setting two parts forming a fixed joint part as a first part (1) and a second part (2), and enabling the fixed joint part of the first part (1) and the second part (2) to be equivalent to a virtual material with transverse isotropy to obtain five independent elastic constants and densities of the virtual material with transverse isotropy:

1) determining the elastic modulus E of the transverse isotropic virtual material in the direction of the symmetry axis z_z：

$E_z=K_n^{*}{E}^{\&prime;}\frac{h}{\sqrt{A_a}}$ ①

Wherein,for dimensionless normal contact stiffness of the joint, E' is the equivalent elastic modulus andE₁、E₂、υ₁、υ₂respectively representing the modulus of elasticity and Poisson's ratio, A, of part one (1) and part two (2)_aThe name of the bonding part defines the contact area, and h is the thickness of the bonding part;

the dimensionless normal contact stiffness of the joint is:

$\begin{array}{c}{K}_n^{*}=\frac{4(3-D)D{\left(\frac{2-D}{D}\right)}^{D/2}{A}_r^{*D/2}}{3\sqrt{2\mathrm{\&pi;}}(2-D)(1-D)}\&times;\&lsqb;{\left(\frac{2-D}{D}\right)}^{(1-D)/2}{A}_r^{*(1-D)/2}-a_c^{*(1-D)/2}\&rsqb;\\ +\frac{1.03\&times;2^{0.825+0.15D}{\left(2.8K\mathrm{\&phi;}\right)}^{0.15}D{\left(\frac{2-D}{D}\right)}^{D/2}}{3{\mathrm{\&pi;}}^{0.075D+0.275}{G}^{*0.15(D-1)}{\left(\ln \mathrm{\&alpha;}\right)}^{0.075}}\&times;\frac{A_r^{*D/2}{a}_c^{*0.425(1-D)}\&lsqb;1-{\left(\frac{1}{6}\right)}^{0.425}\&rsqb;}{(1.425-0.425D)(2-D)\&times;0.425(1-D)}\\ +\frac{1.40\&times;2^{0.474D-1.633}{\left(2.8K\mathrm{\&phi;}\right)}^{0.474}{E}^{\&prime;0.526}{\left(\frac{2-D}{D}\right)}^{D/2}}{3{\mathrm{\&pi;}}^{0.237D-0.211}{G}^{*0.474(D-1)}{\left(\ln \mathrm{\&alpha;}\right)}^{0.237}}\&times;\frac{{\mathrm{DA}}_r^{*D/2}{a}_c^{*0.263(1-D)}\&lsqb;{\left(\frac{1}{6}\right)}^{-0.263}-{\left(\frac{1}{110}\right)}^{-0.263}\&rsqb;}{(1.263-0.263D)(2-D)\&times;0.263(1-D)}\end{array}$ ②

dimensionless normal contact total load P of joint^*Comprises the following steps:

when D ≠ 1.5,

③

when the D is equal to 1.5,

④

wherein, P^*For the joint to contact the total load dimensionless normal andA_r ^*represents a dimensionless actual contact area of the joint anda_c ^*represents the dimensionless critical contact area of the microprotrusions andG^*is dimensionless fractal roughness andd is a profile fractal dimension; k is a hardness coefficient and is 0.454+0.41 upsilon, and upsilon is the Poisson ratio of a softer material in the contact material;α is a constant greater than 1, typically α ═ 1.5 for random surfaces subject to a positive-too distribution;

2) obtaining the elastic modulus E of the equivalent transverse isotropy virtual material in the direction of the isotropic axis x or y_x：

$E_x=\frac{{\mathrm{D\&psi;}}^{\frac{2-D}{2}}{a}_l}{A_a(2-D)}{E}^{\&prime;}$ ⑤

Wherein, a_lThe maximum contact area of the micro-convex body is psi, and the fractal domain expansion factor is psi;

3) determining the shear modulus G of the equivalent transverse isotropy virtual material in the x-z plane by using the formulas ③, ④, ⑥, ⑦ and ⑧_xz：

$G_{xz}={K_t}^{*}*G^{\&prime;}*\frac{h}{\sqrt{A_a}}$ ⑥

Wherein, K_t ^*For dimensionless tangential contact stiffness of the joint, G' is the equivalent shear modulus andG₁、G₂、υ₁、υ₂respectively representing the shear modulus and Poisson ratio of the part I (1) and the part II (2);

the dimensionless tangential contact stiffness of the joint is:

${K_t}^{*}=\frac{8{\mathrm{D\&psi;}}^{1+0.25D^2-D}}{\sqrt{\mathrm{\&pi;}}(1-D)}{\left(\frac{2-D}{D}{A_r}^{*}\right)}^{0.5D}\&lsqb;{\left(\frac{2-D}{D}{\mathrm{\&psi;}}^{0.5D-1}{A_r}^{*}\right)}^{0.5-0.5D}-{a_c}^{*0.5-0.5D}\&rsqb;,(1<D\&le;2$ ⑦

${K_t}^{*}=\frac{2+2\sqrt{5}}{\sqrt{\mathrm{\&pi;}}}\sqrt{\frac{\sqrt{5}-1}{2}{A_r}^{*}}ln\frac{(\sqrt{5}-1){A_r}^{*}}{2{a_c}^{*}},(D=1)$ ⑧

4) determining Poisson ratio upsilon of equivalent transverse isotropy virtual material_zx: poisson ratio upsilon of equivalent transverse isotropy virtual material_zxTaking an approximate value of 0;

5) determining Poisson ratio upsilon of equivalent transverse isotropy virtual material_xy: poisson ratio upsilon of equivalent transverse isotropy virtual material_xyTaking an approximate value of 0;

6) determining the density rho of the equivalent transverse isotropic virtual material as follows:

$\mathrm{\&rho;}=\frac{{\mathrm{D\&psi;}}^{\frac{2-D}{2}}{a}_l({\mathrm{\&rho;}}_1+{\mathrm{\&rho;}}_2)}{2(2-D)A_a}$ ⑨

where ρ is₁、ρ₂The material densities of the part I (1) and the part II (2) are respectively;

and II, inputting the elastic constant and the density of the equivalent transverse isotropic virtual material into finite element software to obtain a finite element model of the mechanical structure with the fixed joint part.