CN106525418A - Joint rigidity analyzing method for bi-side locking handle-main shaft under high rotating speed conditions - Google Patents

Abstract

The invention discloses a joint rigidity analyzing method for a bi-side locking handle-main shaft under high rotating speed conditions, specifically to a joint portion rigidity modeling method taking non-uniform distribution of bi-joint-side pressure, and the system joint rigidity under high rotating speed conditions is analyzed based on the method. The method includes the steps of establishing a three-dimensional fractal normal and tangential rigidity model, analyzing to obtain pressure values of each node on a bi-joint side based on static force, calculating the equivalent rigidity value corresponding to the nodes, and obtaining the torsion and radial rigidity value through a confirmation model, and finally revealing the influence trend of broaching tool force, disk spring rigidity and disc spring pretightening force on the rigidity of the joint portion under different rotation speed and high rotation speed. The method is characterized in that the influence of elasto-plastic deformation and domain expansion factor are taken into consideration in the fractal theory, and nonuniformity of the pressure distribution on the joint surface is considered in the finite element analysis, thereby conducting accurate modeling and analyzing the joint rigidity of T40 handle-main shaft under high rotating speed conditions.

Description

A kind of joint portion rigidity for sided locking knife handle-main shaft under high speed conditions Analysis method

Technical field

The invention belongs to handle of a knife-axis system dynamic analysis field, is related to a kind of for sided locking knife handle-main shaft Joint portion stiffness analysis method under high speed conditions, more specifically a kind of double combination surface pressure uneven distribution that considers Bound fraction shape rigidity modeling method, and system joint portion rigidity under high speed conditions is analyzed based on the method.

Background technology

Handle of a knife is the vitals of connecting machine tool main shaft and cutter, and its main shaft-cutter handle combining part is the weak ring of the system One of section, joint portion stiffness characteristics directly affect system machining accuracy.BT40 types handle of a knife-axis system is a kind of traditional list Face contacts handle of a knife, can produce local detachment in high speed conditions inferior pyramidal faying face, have a strong impact on its overall performance, sided locking Handle of a knife-axis system effectively raises the joint portion rigidity under high speed conditions, improves system machining accuracy.Sided locking Handle of a knife is made up of handle of a knife body, disc spring, three part of tapered sleeve, by applying broach force together with main shaft close-coupled, in height Under speed conditions, disc spring can promote tapered sleeve to adjust between its male cone (strobilus masculinus) and main shaft inner conical surface automatically, and handle of a knife end face and main shaft end face Between night distribution, remain being brought into close contact for double combination face, so as to improve overall dynamics performance.But turning higher than certain During the fast upper limit, taper faying face still can occur to hold greatly local detachment, so as to reduce joint portion rigidity, affect dynamic performance. Due to it is traditional be that the interference effect of the external environment such as noise in Experimental Identification method affects larger to rigidity estimation results, and the party Method is only limitted to analysis without handle of a knife under speed conditions-axis system joint portion rigidity Research.In order to handle of a knife main shaft joint portion rigidity It is analyzed, the mode that fractal theory is combined with emulation provides a kind of effective way for the joint portion rigidity modeling.Divide shape Theory is a kind of effective modeling method of analysis faying face, and in the method, faying face characterization parameter has Scaling, do not receive The advantage such as instrumental resolution and sample length impact, is widely used in and estimates the exposure parameters such as joint surface contact stiffness damping. The three-dimensional fractal model considered in the present invention expands the impact of factor pair point shape rigidity with domain while considering elastic-plastic deformation, and Three-Dimensional contact normal direction and shear stiffness model are established based on this.By carrying out three-dimensional modeling and finite element to sided locking knife handle Static analysis obtains the uneven node pressure distribution situation in double combination face, and three-dimensional fractal model is combined with finite element analysis Mode can effectively improve the estimate accuracy of joint portion rigidity.The method can be used to solve current sided locking knife handle structure again It is miscellaneous, it is difficult to analyze the bottleneck of joint portion stiffness analysis, realize the sided locking knife handle-axis system joint portion under high speed conditions Rigidity modeling is analyzed.

The content of the invention

The present invention is intended to provide a kind of joint portion stiffness analysis for sided locking knife handle-main shaft under high speed conditions Method.Being mainly characterized by for the method is theoretical and Finite Element Static Analysis using three-dimensional fractal microscopic contact rigidity modeling is combined Method, reverses to the sided locking knife handle under high speed conditions-axis system joint portion and radial rigidity modeling, and is divided Analysis, becomes so as to disclose the impact of (rotating speed, broach force, disc spring rigidity and disc spring pretightning force) to joint portion rigidity different technical parameters Gesture.

The present invention is realized using following technological means：

S1, while considering that the impact of the factor is expanded in elastic-plastic deformation and domain, obtained accurate three-dimensional fractal theory, and base Contact normal direction and shear stiffness model are established in the theory.

S2, to sided locking knife handle-axis system 3-D geometric model, and add osculating element, carry out finite element static(al) Analysis, extracts each node pressure values in double combination face, the faying face of each node place regional area is obtained by being multiplied by grid area Pressure value.

It is S3, theoretical based on three-dimensional fractal, each node correspondence is calculated as input using node regional area faying face pressure value Faying face contact normal direction and shear stiffness value.

S4, set up each node correspondence normal stiffness, shear stiffness and double combination face torsional rigidity, the modulus of conversion of radial rigidity Type, calculates joint portion and reverses and radial rigidity value.

S5, by asking for different rotating speeds and high speed conditions under different broach forces, disc spring pretightning force, disc spring rigidity it is corresponding Joint portion rigidity value, discloses the effect tendency of rotating speed, broach force, disc spring rigidity and disc spring pretightning force to joint portion rigidity.

The characteristics of of the invention with reference to the theoretical method with Finite Element Static Analysis of three-dimensional fractal microscopic contact rigidity modeling, Sided locking knife handle under high speed conditions-axis system joint portion is reversed and radial rigidity modeling, so as to disclose different works Effect tendency of the skill parameter (rotating speed, broach force, disc spring rigidity and disc spring pretightning force) to joint portion rigidity.

Description of the drawings

Reverse and radial rigidity schematic diagram Fig. 1 joint portions；

Effect tendency of Fig. 2 different rotating speeds to joint portion rigidity；

Effect tendency of the broach force to joint portion rigidity under the high speed conditions of Fig. 3 25000r/min；

Effect tendency of the disc spring rigidity to joint portion rigidity under the high speed conditions of Fig. 4 25000r/min；

Effect tendency of the disc spring pretightning force to joint portion rigidity under the high speed conditions of Fig. 5 25000r/min；

Specific embodiment

The present invention is described in further detail below in conjunction with accompanying drawing 1-5.

Step (1) sets up three-dimensional normal direction and shear stiffness model；

Based on M-B fractal theories, with reference to Hertz theory, while consider that factor ψ is expanded in elastic-plastic deformation and domain, by place Single micro-bulge normal load in different distortion region is integrated and proof resilience normal load, elastoplasticity normal load is obtained And total plastic property normal load difference is as follows：

Wherein H_G1,H_G2The coefficient related to material properties and faying face fractal parameter is,

Hardness of the H for softer material, H=2.8Y (Y is yield strength value)；K is the parameter related to Poisson's ratio, k=0.454+0.41 ν；a′_1c,a′_2cRespectively elasticity, elastoplasticity and plastic deformation between critical cross-section product.

Then the total normal load of faying face is represented by F=F_e+F_ep+F_p。

In normal stiffness modeling, it is respectively with elastic-plastic deformation region normal contact stiffness in elastic deformation：

In shear stiffness modeling, it is respectively with the tangential contact stiffness in elastic-plastic deformation region in elastic deformation：

In formula G' be joint portion equivalent shear modulus, 1/G'=(2- ν₁)/G₁+(2-ν₂)/G₂；H₁,H₂By formulaObtain.

To sum up, faying face normal direction is respectively with tangential total contact stiffness：K_n=K_ne+K_nep, K_t=K_te+K_tep。

Step (2) Finite Element Static Analysis；

3-D geometric model is set up to sided locking BTF40 handle of a knifes-axis system, by using TARGE object elements with CONTAC osculating elements are set up double combination face and contact right, using mapping mode to two-sided handle of a knife grid division, main shaft are entered Row axial restraint is constrained, and applies broach force in handle of a knife small end, is integrally applied rotating speed constraint to system, is carried out static analysis.Dividing Extract the node pressure values on conical surface faying face and end face faying face in analysis result respectively, and calculate in each node place grid institute In regional area faying face pressure value.

Step (3) calculates the corresponding equivalent normal direction of each node on double combination face and shear stiffness；

By the conical surface and end face faying face node place partial pressure value substitute into faying face fractal method to shear stiffness model In, calculate equivalent normal direction and shear stiffness value corresponding to each node on double combination face.

Step (4) calculations incorporated portion radial direction and torsional rigidity；

As taper faying face and end face faying face are rotationally symmetrical surf, therefore the radial direction set up respectively in the y-direction is firm Spend and as follows around the torsional rigidity model of y-axis：

N in formula_T, n_ERespectively taper-face contact face and end contact face interstitial content；Respectively conical surface faying face Node normal stiffness and shear stiffness；Respectively end face faying face normal stiffness and shear stiffness；θ is contact surface section Point position angle；Respectively conical surface faying face and the distance between end face faying face node and x-axis.

Step (5) discloses rotating speed and impact of the broach force to joint portion rigidity；

Under the conditions of calculating different rotating speeds, joint portion is reversed and radial rigidity value, discloses impact of the rotating speed to joint portion rigidity and becomes Gesture；Different broach forces under the high speed conditions of 25000r/min, different disc spring rigidity and different disc spring pretightning forces are calculated to joint portion The impact with radial rigidity is reversed, and makes tendency chart.

Claims (2)

1. a kind of joint portion stiffness analysis method for sided locking knife handle-main shaft under high speed conditions, the method are adopted With reference to the theoretical method with Finite Element Static Analysis of three-dimensional fractal microscopic contact rigidity modeling, to the double-sided lock under high speed conditions Tight handle of a knife-axis system joint portion is reversed and radial rigidity modeling, and is analyzed, so as to disclose different rotating speeds, broach force, dish The effect tendency of spring rigidity and disc spring pretightning force technological parameter to joint portion rigidity；

It is characterized in that：

S1, while consider that the impact of the factor is expanded in elastic-plastic deformation and domain, it is theoretical to have obtained accurate three-dimensional fractal, and based on being somebody's turn to do Theory establishes contact normal direction and shear stiffness model；

S2, to sided locking knife handle-axis system 3-D geometric model, and add osculating element, carry out Finite Element Static Analysis, The each node pressure values in double combination face are extracted, the combination surface pressure of each node place regional area is obtained by being multiplied by grid area Value；

It is S3, theoretical based on three-dimensional fractal, the corresponding knot of each node is calculated as input using node regional area faying face pressure value Conjunction face contacts normal direction and shear stiffness value；

S4, each node correspondence normal stiffness, shear stiffness and double combination face torsional rigidity, the transformation model of radial rigidity are set up, Calculate joint portion to reverse and radial rigidity value；

S5, by asking for different rotating speeds and high speed conditions under different broach forces, disc spring pretightning force, the corresponding combination of disc spring rigidity Portion's rigidity value, discloses the effect tendency of rotating speed, broach force, disc spring rigidity and disc spring pretightning force to joint portion rigidity.

2. a kind of joint portion rigidity for sided locking knife handle-main shaft under high speed conditions according to claim 1 Analysis method, it is characterised in that：

Step (1) sets up three-dimensional normal direction and shear stiffness model；

Based on M-B fractal theories, with reference to Hertz theory, while consider that factor ψ is expanded in elastic-plastic deformation and domain, by not It is integrated with the single micro-bulge normal load of deformed region and proof resilience normal load, elastoplasticity normal load and total is obtained Plasticity normal load difference is as follows：

$F_e=\left\{\begin{array}{cc}\frac{2^{(11-2D)/2}}{3{\mathrm{\π}}^{(4-D)/2}}\·\frac{D-1}{5-2D}{\left(ln\mathrm{\γ}\right)}^{1/2}{G}^{(D-2)}{\mathrm{E\ψ}}^{(3-D)/2}{a}_l^{(D-1)/2}(a_l^{(5-2D)/2}-a_{1c}^{(5-2D)/2})& \left(D\overline{)=}2.5\right)\\ 2{\mathrm{\π}}^{-3/4}{\left(1n\mathrm{\γ}\right)}^{1/2}{G}^{1/2}{\mathrm{E\ψ}}^{1/4}{a}_l^{3/4}ln\left(\frac{a_l}{a_{1c}}\right)(D=2.5)& \end{array}\right.$

$F_{ep}=\left\{\begin{array}{cc}\frac{H_{G2}(D-1){\mathrm{\ψ}}^{(3-D)/2}{a}_l^{\′(D-1)/2}}{2(2.26-0.88D)}\·(a_{1c}^{\′(2.26-0.88D)}-a_{2c}^{\′(2.26-0.88D)})& D\≠113/44\\ \frac{69}{88}{H}_{G2}{\mathrm{\ψ}}^{19/88}{a}_l^{\′69/88}ln\left(\frac{a_{1c}^{\′}}{a_{2c}^{\′}}\right)& D=113/44\end{array}\right.$

$F_p=\frac{H(D-1)a_l^{\′(D-1)/2}}{3-D}{\mathrm{\ψ}}^{(3-D)/2}{a_{2c}^{\′}}^{(3-D)/2}$

Wherein H_G1,H_G2The coefficient related to material properties and faying face fractal parameter is,

Hardness of the H for softer material, H=2.8Y, Y are yield strength value；K is the parameter related to Poisson's ratio, k=0.454+ 0.41ν；a′_1c,a′_2cRespectively elasticity, elastoplasticity and plastic deformation between critical cross-section product；

Then the total normal load of faying face is represented by F=F_e+F_ep+F_p；

In normal stiffness modeling, it is respectively with elastic-plastic deformation region normal contact stiffness in elastic deformation：

$K_{ne}=\frac{2\sqrt{2}E(4-D)(D-1)}{3\sqrt{\mathrm{\π}}(3-D)(2-D)}{\mathrm{\ψ}}^{(3-D)/2}{a_l}^{\′(D-1)/2}({a_l}^{\′(2-D)/2}-{a_{1c}}^{\′(2-D)/2})$

$k_{nep}=\frac{{\mathrm{df}}_{ep}/{\mathrm{da}}^{\′}}{d\mathrm{\δ}/{\mathrm{da}}^{\′}}=\frac{H_{G2}{\mathrm{\π}}^{(3-D)/2}(1.76-0.38D)}{2^{3-D}{G}^{(D-2)}{\left(\ln \mathrm{\γ}\right)}^{1/2}(3-D)}{a}^{\′(0.26+0.12D)}$

In shear stiffness modeling, it is respectively with the tangential contact stiffness in elastic-plastic deformation region in elastic deformation：

$K_{te}=\frac{4G^{\′}(D-1)}{\sqrt{2\mathrm{\π}}}{\mathrm{\ψ}}^{(3-D)/2}{a}_l^{\′(D-1)/2}{\∫}_{a_{1c}^{\′}}^{{a_l}^{\′}}{a}^{\′(-D/2)}{(1-H_1{a}^{\′(D-2)/2})}^{1/3}{\mathrm{da}}^{\′}$

$K_{tep}=\frac{8G^{\′}(D-1)}{\sqrt{\mathrm{\π}}{H_{G2}}^{1/2}}{\mathrm{\ψ}}^{(3-D)/2}{a}_l^{\′(D-1)/2}{\∫}_{a_{1c}^{\′}}^{{a_l}^{\′}}{a}^{\′(-D/2)}{(1-H_2{a}^{\′(0.44-0.22D)})}^{1/3}{\mathrm{da}}^{\′}$

In formula G' be joint portion equivalent shear modulus, 1/G'=(2- ν₁)/G₁+(2-ν₂)/G₂；H₁,H₂By formulaObtain；

To sum up, faying face normal direction is respectively with tangential total contact stiffness：K_n=K_ne+K_nep, K_t=K_te+K_tep；

Step (2) Finite Element Static Analysis；

3-D geometric model is set up to sided locking knife handle-axis system, by contacting with CONTAC using TARGE object elements Unit is set up double combination face and contacts right, using mapping mode to two-sided handle of a knife grid division, carries out axial restraint to main shaft Constraint, applies broach force in handle of a knife small end, integrally applies rotating speed constraint to system, carries out static analysis；Divide in analysis result The node pressure values on conical surface faying face and end face faying face are indescribably taken, and is calculated in each node place grid place regional area Faying face pressure value；

Step (3) calculates the corresponding equivalent normal direction of each node on double combination face and shear stiffness；

By the conical surface and end face faying face node place partial pressure value substitute into faying face fractal method to shear stiffness model in, meter Calculate equivalent normal direction and shear stiffness value corresponding to each node on double combination face；

Step (4) calculations incorporated portion radial direction and torsional rigidity；

As taper faying face and end face faying face are rotationally symmetrical surf, thus set up respectively radial rigidity in the y-direction and Torsional rigidity model around y-axis is as follows：

$K_{TT}=K_{TT1}+K_{TT2}=\underset{i=1}{\overset{n_T}{\Σ}}(K_{ni}^T\·cos\mathrm{\α}+K_{ti}^T\·sin\mathrm{\α})\·{\mathrm{cos\θ}}_i+\underset{j=1}{\overset{n_E}{\Σ}}{K}_{tj}^E$

$K_{RR}=K_{RR1}+K_{RR2}=\underset{i=1}{\overset{n_T}{\Σ}}\[(K_{ni}^T\·\sin \mathrm{\α}+K_{ti}^T\·\cos \mathrm{\α})\·r_i^T\]+\underset{j=1}{\overset{n_E}{\Σ}}{K}_{nj}^E\·r_j^E$

N in formula_T, n_ERespectively taper-face contact face and end contact face interstitial content；Respectively conical surface faying face nodal method To rigidity and shear stiffness；Respectively end face faying face normal stiffness and shear stiffness；θ is contact surface node location Angle；r_i ^T,Respectively conical surface faying face and the distance between end face faying face node and x-axis；

Step (5) discloses rotating speed and impact of the broach force to joint portion rigidity；

Under the conditions of calculating different rotating speeds, joint portion is reversed and radial rigidity value, discloses effect tendency of the rotating speed to joint portion rigidity.