CN105068504A - Electric main shaft system modeling method taking features of combination portions into consideration - Google Patents

Abstract

The invention discloses an electric main shaft system modeling method taking features of combination portions into consideration. According to the method, first of all, based on a frequency response function method, the rigidity of the combination portion of an electric main shaft system is identified by use of a hammering experiment, then a finite element model of a main shaft-handle-cutter system is established through the mode of adding and deleting a transition unit at the tail end of a main shaft and a handle, and finally, bearing rigidity, and a rigidity matrix of a main shaft-bearing combination portion and a rigidity matrix of a main shaft-handle-cutter combination portion which are obtained through identification are added to the rigidity matrix of the electric main shaft system so that a complete electric main shaft system kinetic equation is obtained. According to the invention, the rigidity of the combination portions are identified by use of an experiment method, and a theoretical model of the electric main shaft system is established with the influences of the combination portions are taken into consideration, so that the influence rules of the rotating speed, the bearing rigidity, the rigidity of each combination portion and the like for the dynamic features of the electric main shaft system can be simultaneously analyzed. The method can provide guidance for design and application of an electric main shaft and also provides a theoretical basis for prediction of the cutting stability of the electric main shaft system.

Description

A kind of electric chief axis system modeling method considering joint portion characteristic

Technical field

The invention belongs to electric chief axis system dynamic analysis field, relate to a kind of electric chief axis system modeling method considering joint portion characteristic, the method has carried out identification to axis system joint portion rigidity, and consider main shaft-bearing combining part, main shaft-handle of a knife-cutter joint portion establishes complete electric chief axis system finite element dynamics.

Background technology

Electro spindle (MotorizedSpindle) is one of critical component of numerically-controlled machine.Be characterized in machine tool chief axis and spindle motor to unite two into one, machine tool chief axis, by built-in electric motor Direct driver, shortens to zero Machine Tool Main Drive chain, thus achieves the Zero-drive Chain of lathe.Electro spindle is supported by angular contact ball bearing usually, and front end is connected with handle of a knife, cutter by taper hole.In general electric chief axis system comprises main shaft, bearing, handle of a knife, cutter four part, wherein there are main shaft-bearing, main shaft-handle of a knife, handle of a knife-cutter three joint portions.Each several part joint portion can produce different impacts to electric chief axis system dynamics.In cutting stability is analyzed, each several part joint portion also can produce different impacts to the cutting stable region of electric chief axis system, and therefore the Dynamic Modeling of electric chief axis system joint portion and parameter identification are the key issues of research electric chief axis system dynamics.In common electric spindle design analysis, often have ignored the impact of joint portion, or just modeling analysis is carried out to a part of joint portion of wherein certain, but the theoretical modeling method of not complete all joint portions of consideration.Along with high speed and the precise treatment of electro spindle, be necessary to consider that all joint portion characteristics carry out complete theoretical modeling to electric chief axis system.

Summary of the invention

The object of this invention is to provide a kind of electric chief axis system modeling method considering joint portion characteristic, the method uses the method for finite element carry out modeling to electric chief axis system and consider the impact of main shaft-bearing combining part, main shaft-handle of a knife-cutter joint portion.First the method carries out identification to the rigidity of three joint portions existed in electric chief axis system respectively based on the experimental technique of frequency response function, then set up the finite element model of main shaft-handle of a knife-tooling system by the mode of adding at main shaft, handle of a knife end and delete excessive unit, the main shaft finally bearing rigidity, identification obtained-bearing combining part rigidity and main shaft-handle of a knife-cutter joint portion rigidity are added in the stiffness matrix of electric chief axis system kinetics equation and are obtained complete electric chief axis system kinetics equation.

The present invention adopts following technological means to realize:

1, based on the test method of frequency response function, utilize LMS signal acquiring system to carry out hammering experiment to main shaft-bearing, main shaft-handle of a knife-cutter joint portion, write Matlab program and experimental data is updated to identification formulae discovery and obtains joint portion rigidity.

2, by the method for finite element, Timoshenko beam element is adopted to carry out dividing elements to main shaft-handle of a knife-cutter, an excessive unit is increased at the end of main shaft and handle of a knife, its cross section parameter is any given, again to the finite elements serial number of main shaft, handle of a knife, cutter, the quality of group collecting system and stiffness matrix, finally delete the quality of excessive unit and stiffness matrix again.

3, main shaft-handle of a knife-cutter joint portion is reduced to distribution spring, derives the stiffness matrix of distribution spring, then the stiffness matrix of distribution spring is added in system stiffness matrix, obtain the kinetics equation of main shaft-handle of a knife-tooling system.

4, according to the series relationship of bearing rigidity and bearing combining part rigidity, bearing rigidity and main shaft-bearing combining part rigidity are added in system stiffness matrix, obtains the electric chief axis system kinetics equation of all joint portions of complete consideration.

Feature of the present invention is to adopt experimentally has carried out identification to joint portion rigidity, and consider that the impact of joint portion establishes the theoretical model of electric chief axis system, the affecting laws to electric chief axis system dynamic perfromance such as rotating speed, bearing rigidity, each joint portion rigidity can be analyzed simultaneously.Method provided by the invention can be the design of electro spindle and use provides guidance, also for the prediction of electric chief axis system cutting stability provides theoretical foundation.

By description below and accompanying drawings, the present invention can be more clear, and accompanying drawing illustrates for explaining the inventive method and embodiment.

Accompanying drawing explanation

Fig. 1 electric chief axis system finite element model schematic diagram

Fig. 2 joint portion schematic diagram

Fig. 3 rigidity identification experimental principle figure

Fig. 4 main shaft-handle of a knife-tooling system group collection schematic diagram

Fig. 5 main shaft-handle of a knife-cutter joint portion stiffness matrix group collection schematic diagram

Fig. 6 bearing combining part cross sectional representation

Embodiment

A kind of electric chief axis system modeling method considering joint portion characteristic of the invention process, below in conjunction with accompanying drawing, is specifically described enforcement of the present invention.

Fig. 1 is electric chief axis system finite element model schematic diagram.As shown in the figure, main shaft-handle of a knife-cutter shaft part adopts Timoshenko beam element to carry out finite element modeling.Main shaft-bearing combining part rigidity and bearing rigidity are series relationship, can according to series connection formulae discovery support stiffness.Main shaft-handle of a knife-cutter joint portion is reduced to distribution spring, and spring intervals and shaft part element length are consistent.Step (1), identification electric chief axis system joint portion rigidity

1.1 frequency response function methods

Frequency response function method of identification is the ultimate principle based on mechanical impedance.First by discrete for one-piece construction be several minor structures, application of mechanical impedance method, sets up the kinetics equation of each minor structure respectively.Then according to interstructural actual connection, displacement and the force constraint condition at faying face place is determined.Eventually through the constraint condition between minor structure, the equation of motion of each minor structure is integrated thus obtains the integrally-built equation of motion and kinematic behavior.

Be illustrated in figure 2 joint portion schematic diagram.Wherein, b is the joint portion of minor structure 1 and minor structure 2.A and c is respectively the non-bonded portion of minor structure 1 and minor structure 2.Can derive joint portion stiffness matrix by frequency response function method is:

$P_j={\left\{\begin{array}{c}\left[\begin{array}{cc}-{\mathrm{TT}}_{ba}^1& {\mathrm{TT}}_{bc}^2\\ -{\mathrm{RT}}_{ba}^1& {\mathrm{RT}}_{bc}^2\end{array}\right]\×{\left[\begin{array}{cc}{\mathrm{TT}}_{aa}-{\mathrm{TT}}_{aa}^1& {\mathrm{TT}}_{ab}\\ {\mathrm{TT}}_{ba}& {\mathrm{TT}}_{bb}-{\mathrm{TT}}_{bb}^2\end{array}\right]}^{-1}\×\left[\begin{array}{cc}{\mathrm{TT}}_{ab}^1& {\mathrm{TR}}_{ab}^1\\ -{\mathrm{TT}}_{cb}^2& -{\mathrm{TR}}_{cb}^2\end{array}\right]\\ -\left[\begin{array}{cc}{\mathrm{TT}}_{bb}^2+{\mathrm{TT}}_{bb}^1& {\mathrm{TR}}_{bb}^2+{\mathrm{TR}}_{bb}^1\\ {\mathrm{RT}}_{bb}^2+{\mathrm{RT}}_{bb}^1& {\mathrm{RR}}_{bb}^2+{\mathrm{RR}}_{bb}^1\end{array}\right]\end{array}\right\}}^{-1}---\left(1\right)$

In formula, subscript 1,2---represent minor structure 1 and minor structure 2 respectively; Subscript a, b, c---represent each region of minor structure respectively, first letter represents pickup response position, and second letter represents Position of Vibrating; In matrix, element T represents displacement, and R represents corner.

1.2 joint portion rigidity identification experiments

Hammering experimental principle figure as shown in Figure 3.Experimental facilities comprises LMS vibration measurement instrument, handle of a knife-axis system, sensor, stress ga(u)ge, exciting force hammer, computing machine; Wherein, each sensor is arranged in handle of a knife-axis system surface, one end of exciting force hammer hammering handle of a knife-axis system, and the other end of handle of a knife-axis system is connected with stress ga(u)ge, and stress ga(u)ge, LMS vibration measurement instrument are connected with computing machine; Exciting force hammer, each sensor are connected with LMS vibration measurement instrument respectively;

According to rigidity identification formula, adopt the pickup of single-point-excitation, multiple spot, the method for excitation, multiple spot pickup carries out hammering experiment to electric chief axis system each several part, just can obtain the rigidity value of joint portion.

The layout of measuring point should follow following principle: 1. respond end points and different cross section place that pickup point should be arranged in tested object; 2. impacting point should be selected in the position near joint portion.

Utilize Matlab coding, being updated to testing the data recorded in rigidity identification formula (1), just can obtaining the stiffness parameters of each joint portion of electric chief axis system.

Step (2), sets up the finite element model of main shaft-handle of a knife-tooling system

Based on Timoshenko beam theory, consider that the degree of freedom in node 5 directions sets up the finite element model of main shaft-handle of a knife-tooling system.Consider main shaft and handle of a knife, between handle of a knife and cutter, there is no common node, therefore increase a transition element respectively at the end of main shaft and handle of a knife, and serial number is carried out to the finite elements of main shaft-handle of a knife-tooling system.The effect of excessive unit is coupled together by main shaft-handle of a knife-cutter, thus can generate the quality of main shaft-handle of a knife-tooling system and stiffness matrix by coding, and the cross section information of excessive unit is arbitrarily given.

As shown in Figure 4, suppose that main shaft comprises p unit, handle of a knife comprises q unit to the group collection process of main shaft-handle of a knife-tooling system, and cutter comprises r unit, then the nodes N=p+q+r+3 that system is total.The matrix dimensionality of each node is 5 × 5, so group integrate the total quality of afterwards system and stiffness matrix dimension as 5N × 5N.After group collection completes, in mass of system and stiffness matrix, delete the matrix information of excessive unit.

Step (3), adds main shaft-handle of a knife-cutter joint portion rigidity

Joint portion is divided into some multidiameters, by the joint portion characteristic between distribution spring analog main shaft-handle of a knife-cutter.Spring intervals and shaft part element length are consistent, and the stiffness matrix of every root spring can use k _crepresent:

In formula, n is switching node number, k _cpfor the coupling stiffness of joint portion, can be obtained by the rigidity discrimination method of step (1), concrete form is as follows:

$k_{cp}=\left[\begin{array}{ccccc}0& 0& 0& 0& 0\\ 0& k_{yy}& k_{yz}& 0& 0\\ 0& k_{zy}& k_{zz}& 0& 0\\ 0& 0& 0& k_{\mathrm{\θ}}& 0\\ 0& 0& 0& 0& k_{\mathrm{\θ}}\end{array}\right]---\left(3\right)$

By the stiffness matrix k of each spring unit _cadd to according to correspondence position shown in Fig. 5 in the stiffness matrix of step (2) and main shaft-handle of a knife-tooling system stiffness matrix can be obtained.

Step (4), adds bearing and bearing combining part rigidity

Bearing combining part and bearing belong to and are connected in series, as shown in Figure 6.According to series connection formula:

$\left\{\begin{array}{c}\frac{1}{K_{br}}+\frac{1}{K_{jr}}=\frac{1}{K_{rr}^s}\\ \frac{1}{K_{b\mathrm{\θ}}}+\frac{1}{K_{j\mathrm{\θ}}}=\frac{1}{K_{\mathrm{\θ}\mathrm{\θ}}^s}\end{array}\right.---\left(4\right)$

In formula, K _jrand K _{j θ}be respectively bearing combining part radial rigidity and angular rigidity; with be respectively system supporting radial rigidity and angular rigidity, the frequency response function discrimination method by step (1) obtains; K _brand K _{b θ}be respectively bearing radial rigidity and angular rigidity, can be tried to achieve by theoretical calculation method.

Finally will k _br, K _{b θ}substitution formula (4) can obtain the rigidity value K of bearing combining part _jr, K _{j θ}:

$\left\{\begin{array}{c}{K}_{jr}=\frac{K_{rr}^s{K}_{br}}{K_{br}-K_{rr}^s}\\ K_{j\mathrm{\θ}}=\frac{K_{\mathrm{\θ}\mathrm{\θ}}^s{K}_{b\mathrm{\θ}}}{K_{b\mathrm{\θ}}-K_{\mathrm{\θ}\mathrm{\θ}}^s}\end{array}\right.---\left(5\right)$

Bearing rigidity and bearing combining part rigidity are added to the electric chief axis system kinetics equation that can obtain all joint portions of complete consideration in main shaft-handle of a knife-tooling system stiffness matrix:

$\[M\]\left\{\stackrel{\·\·}{X}\right\}+\mathrm{\Ω}\[G\]\left\{\stackrel{\·}{X}\right\}+(\[K\]-Q^2\[M_R\])\left\{X\right\}=0---\left(6\right)$

In formula, [M] is total system mass matrix, [M]=[M _s]+[M _a]; [M _s] be axle system gross mass matrix, [M _s]=[M _t]+[M _r]; [M _t] be axle system total displacement mass matrix; [M _r] be the total gyrating mass matrix of axle system; [M _a] be other additional mass matrix of main shaft; [G] is the total gyroscopic matrix of axle system; [K] is system global stiffness matrix, comprises main shaft-handle of a knife-cutter shaft system global stiffness, bearing rigidity, bearing combining part rigidity, main shaft-cutter handle combining part rigidity and handle of a knife-cutter joint portion rigidity five part; Ω ²[M _r] be the total centrifugal force matrix of axle system.

Claims (1)

1. consider the electric chief axis system modeling method of joint portion characteristic for one kind, the step that the method comprises is as follows, 1) based on the test method of frequency response function, utilize LMS signal acquiring system to carry out hammering experiment to main shaft-bearing, main shaft-handle of a knife-cutter joint portion, write Matlab program and experimental data is updated to identification formulae discovery and obtains joint portion rigidity;

2) by the method for finite element, Timoshenko beam element is adopted to carry out dividing elements to main shaft-handle of a knife-cutter, an excessive unit is increased at the end of main shaft and handle of a knife, its cross section parameter is any given, again to the finite elements serial number of main shaft, handle of a knife, cutter, the quality of group collecting system and stiffness matrix, finally delete the quality of excessive unit and stiffness matrix again;

3) main shaft-handle of a knife-cutter joint portion is reduced to distribution spring, derives the stiffness matrix of distribution spring, then the stiffness matrix of distribution spring is added in system stiffness matrix, obtain the kinetics equation of main shaft-handle of a knife-tooling system;

4) according to the series relationship of bearing rigidity and bearing combining part rigidity, bearing rigidity and main shaft-bearing combining part rigidity are added in system stiffness matrix, obtains the electric chief axis system kinetics equation of all joint portions of complete consideration;

It is characterized in that: the specific implementation process of the method is as follows,

In electric chief axis system finite element model, main shaft-handle of a knife-cutter shaft part adopts Timoshenko beam element to carry out finite element modeling; Main shaft-bearing combining part rigidity and bearing rigidity are series relationship, according to series connection formulae discovery support stiffness; Main shaft-handle of a knife-cutter joint portion is reduced to distribution spring, and spring intervals and shaft part element length are consistent;

Step (1), identification electric chief axis system joint portion rigidity

1.1 frequency response function methods

Frequency response function method of identification is the ultimate principle based on mechanical impedance, first by discrete for one-piece construction be several minor structures, application of mechanical impedance method, sets up the kinetics equation of each minor structure respectively; Then according to interstructural actual connection, displacement and the force constraint condition at faying face place is determined; Eventually through the constraint condition between minor structure, the equation of motion of each minor structure is integrated thus obtains the integrally-built equation of motion and kinematic behavior;

Wherein, b is the joint portion of minor structure 1 and minor structure 2; A and c is respectively the non-bonded portion of minor structure 1 and minor structure 2; Can derive joint portion stiffness matrix by frequency response function method is:

$P_j={\left\{\begin{array}{c}\left[\begin{array}{cc}-{\mathrm{TT}}_{ba}^1& {\mathrm{TT}}_{bc}^2\\ -{\mathrm{RT}}_{ba}^1& {\mathrm{RT}}_{bc}^2\end{array}\right]\×{\left[\begin{array}{cc}{\mathrm{TT}}_{aa}-{\mathrm{TT}}_{aa}^1& {\mathrm{TT}}_{ab}\\ {\mathrm{TT}}_{ba}& {\mathrm{TT}}_{bb}-{\mathrm{TT}}_{bb}^2\end{array}\right]}^{-1}\×\left[\begin{array}{cc}{\mathrm{TT}}_{ab}^1& {\mathrm{TR}}_{ab}^1\\ -{\mathrm{TT}}_{cb}^2& -{\mathrm{TR}}_{cb}^2\end{array}\right]\\ -\left[\begin{array}{cc}{\mathrm{TT}}_{bb}^2+{\mathrm{TT}}_{bb}^1& {\mathrm{TR}}_{bb}^2+{\mathrm{TR}}_{bb}^1\\ {\mathrm{RT}}_{bb}^2+{\mathrm{RT}}_{bb}^1& {\mathrm{RR}}_{bb}^2+{\mathrm{RR}}_{bb}^1\end{array}\right]\end{array}\right\}}^{-1}---\left(1\right)$

In formula, subscript 1,2---represent minor structure 1 and minor structure 2 respectively; Subscript a, b, c---represent each region of minor structure respectively, first letter represents pickup response position, and second letter represents Position of Vibrating; In matrix, element T represents displacement, and R represents corner;

1.2 joint portion rigidity identification experiments

Experimental facilities comprises LMS vibration measurement instrument, handle of a knife-axis system, sensor, stress ga(u)ge, exciting force hammer, computing machine; Wherein, each sensor is arranged in handle of a knife-axis system surface, one end of exciting force hammer hammering handle of a knife-axis system, and the other end of handle of a knife-axis system is connected with stress ga(u)ge, and stress ga(u)ge, LMS vibration measurement instrument are connected with computing machine; Exciting force hammer, each sensor are connected with LMS vibration measurement instrument respectively;

According to rigidity identification formula, adopt the pickup of single-point-excitation, multiple spot, the method for excitation, multiple spot pickup carries out hammering experiment to electric chief axis system each several part, just can obtain the rigidity value of joint portion;

The layout of measuring point should follow following principle: 1. respond end points and different cross section place that pickup point should be arranged in tested object; 2. impacting point should be selected in the position near joint portion;

Utilize Matlab coding, being updated to testing the data recorded in rigidity identification formula (1), just can obtaining the stiffness parameters of each joint portion of electric chief axis system;

Step (2), sets up the finite element model of main shaft-handle of a knife-tooling system

Based on Timoshenko beam theory, consider that the degree of freedom in node 5 directions sets up the finite element model of main shaft-handle of a knife-tooling system; Consider main shaft and handle of a knife, between handle of a knife and cutter, there is no common node, therefore increase a transition element respectively at the end of main shaft and handle of a knife, and serial number is carried out to the finite elements of main shaft-handle of a knife-tooling system; The effect of excessive unit is coupled together by main shaft-handle of a knife-cutter, thus can generate the quality of main shaft-handle of a knife-tooling system and stiffness matrix by coding, and the cross section information of excessive unit is arbitrarily given;

In the group collection process of main shaft-handle of a knife-tooling system, definition main shaft comprises p unit, and handle of a knife comprises q unit, and cutter comprises r unit, then the nodes N=p+q+r+3 that system is total; The matrix dimensionality of each node is 5 × 5, so group integrate the total quality of afterwards system and stiffness matrix dimension as 5N × 5N; After group collection completes, in mass of system and stiffness matrix, delete the matrix information of excessive unit;

Step (3), adds main shaft-handle of a knife-cutter joint portion rigidity

Joint portion is divided into some multidiameters, by the joint portion characteristic between distribution spring analog main shaft-handle of a knife-cutter; Spring intervals and shaft part element length are consistent, and the stiffness matrix of every root spring can use k _crepresent:

In formula, n is switching node number, k _cpfor the coupling stiffness of joint portion, can be obtained by the rigidity discrimination method of step (1), concrete form is as follows:

$k_{cp}=\left[\begin{array}{ccccc}0& 0& 0& 0& 0\\ 0& k_{yy}& k_{yz}& 0& 0\\ 0& k_{zy}& k_{zz}& 0& 0\\ 0& 0& 0& k_{\mathrm{\θ}}& 0\\ 0& 0& 0& 0& k_{\mathrm{\θ}}\end{array}\right]---\left(3\right)$

By the stiffness matrix k of each spring unit _cadd in the stiffness matrix of step (2) and main shaft-handle of a knife-tooling system stiffness matrix can be obtained;

Step (4), adds bearing and bearing combining part rigidity

Bearing combining part and bearing belong to and are connected in series; According to series connection formula:

$\left\{\begin{array}{c}\frac{1}{K_{br}}+\frac{1}{K_{jr}}=\frac{1}{K_{rr}^s}\\ \frac{1}{K_{b\mathrm{\θ}}}+\frac{1}{K_{j\mathrm{\θ}}}=\frac{1}{K_{\mathrm{\θ}\mathrm{\θ}}^s}\end{array}\right.---\left(4\right)$

In formula, K _jrand K _{j θ}be respectively bearing combining part radial rigidity and angular rigidity; with be respectively system supporting radial rigidity and angular rigidity, the frequency response function discrimination method by step (1) obtains; K _brand K _{b θ}be respectively bearing radial rigidity and angular rigidity, can be tried to achieve by theoretical calculation method;

Finally will k _br, K _{b θ}substitution formula (4) can obtain the rigidity value K of bearing combining part _jr, K _{j θ}:

$\left\{\begin{array}{c}{K}_{jr}=\frac{K_{rr}^s{K}_{br}}{K_{br}-K_{rr}^s}\\ K_{j\mathrm{\θ}}=\frac{K_{\mathrm{\θ}\mathrm{\θ}}^s{K}_{b\mathrm{\θ}}}{K_{b\mathrm{\θ}}-K_{\mathrm{\θ}\mathrm{\θ}}^s}\end{array}\right.---\left(5\right)$

Bearing rigidity and bearing combining part rigidity are added to the electric chief axis system kinetics equation that can obtain all joint portions of complete consideration in main shaft-handle of a knife-tooling system stiffness matrix:

$\[M\]\left\{\stackrel{\·\·}{X}\right\}+\mathrm{\Ω}\[G\]\left\{\stackrel{\·}{X}\right\}+(\[K\]-Q^2\[M_R\])\left\{X\right\}=0---\left(6\right)$

In formula, [M] is total system mass matrix, [M]=[M _s]+[M _a]; [M _s] be axle system gross mass matrix, [M _s]=[M _t]+[M _r]; [M _t] be axle system total displacement mass matrix; [M _r] be the total gyrating mass matrix of axle system; [M _a] be other additional mass matrix of main shaft; [G] is the total gyroscopic matrix of axle system; [K] is system global stiffness matrix, comprises main shaft-handle of a knife-cutter shaft system global stiffness, bearing rigidity, bearing combining part rigidity, main shaft-cutter handle combining part rigidity and handle of a knife-cutter joint portion rigidity five part; Ω ²[M _r] be the total centrifugal force matrix of axle system.