CN101804464A - Kinetic parameter identification method for machine-tool cone-fit fixing and combining part - Google Patents

Abstract

The invention discloses a kinetic modeling and model parameter identification method for a machine-tool cone-fit fixing and combining part. The method establishes a 32-node tool holder-spindle combining part kinetic model, wherein the nodes 1-8, 9-19, 17-24 and 25-32 are equant points, and the movement of the cone-fit combining part unit is represented by the relative movement between node 1 and node 17, node 2 and node 18, node 3 and node 19,..., node 16 and node 32. Based on the modal test, by utilizing the theoretical characteristic that the product of frequency response matrix and impedance matrix are unit matrixes, the invention combines the stiffness matrix and mass matrix of the substructure obtained through the tested frequency response matrix and theory of finite elements, and identifies the model parameters by using an initial value cut-and-trial method and a non-linear least square fitting optimistic algorithm. The invention fully considers the coupling relation between the degrees of freedom of the tool holder-spindle taper combining part nodes, and has higher precision and universality.

Description

A kind of kinetic parameter identification method for machine-tool cone-fit fixing and combining part

Technical field

The invention belongs to Digit Control Machine Tool dynamics technology field, be specifically related to a kind of kinetic parameter identification method of machine-tool cone-fit fixing and combining part.

Background technology

Late 1960s, Kiel Sa Nuowa ^[1], Kirsanova ^[2]Cone-fit fixing and combining part is studied with regard to faying face normal direction and tangential characteristic Deng the people.They studies show that: have hysteresis phenomenon between the tangential loading of faying face and the unloading curve, even also like this under less than the situation of faying face maximum static friction force in circumferential load; The tangential contact stiffness and the faying face face of faying face are pressed into non-linear relation, and increase thereupon increasing.

Subsequently, on basis to traditional quantification descriptive statistics of rough surface microscopic appearance feature, Greenwood and Wmiamson ^[3]The application surface contourgraph is measured real surface, has proposed the GW model of surperficial contact after the analysis, has obtained the equivalent global stiffness of two surface contacts.MajumdarA ^[4]Deng the scholar contact stiffness model---MB model based on fractal theory has been proposed then, Machine Joint Surfaces is reduced to the contact problems of a rough surface and a true planar, single micro-bulge Approximate Equivalent on the rough surface is a spheroid, and the surface topography isotropism of hypothesis rough surface, interaction on the rough surface between each micro-bulge can be ignored, and has obtained to theoretical property the normal direction contact stiffness and the dimensionless contact stiffness of Machine Joint Surfaces on this basis.

Yet above scholar concentrates on to study fixing combination portion of machine tool in theory, progress and development along with computer science and technology, some foreign scholars afterwards then from the angle of experiment and theoretic finite element analysis combination, cooperate the joint portion dynamic characteristic to carry out more effective, more deep research to handle of a knife-main shaft awl.

T.R.Kim, S.M.Wu and K.F.Ehmann ^[5]The method that is considered to first utilization experiment has been studied the awl cooperation joint portion of main shaft-handle of a knife, and cooperates the rigidity and the damping parameter of joint portion to connect axial pre tightening force and awl.In the experiment test analysis the influences of three kinds of different axial pre tightening forces to joint portion rigidity and damping.

Rivin ^[6]The running status of cutter structure has been done a large amount of technical research, and sum up six important factor in order, comprising the influence of machined parameters to cutter life and stability, the contact-making surface of handle of a knife and main shaft about processing, modularization cutter, and the cutter dynamic balancing under high-speed cutting.After Rivin proposes these important factor in order, Levina ^[7]Further studied angular deformation between handle of a knife-main shaft joint portion to the influence of the distortion of point of a knife.Levina has also studied the influence to the static rigidity of handle of a knife-main shaft joint portion of the pulling force of pull bar and handle of a knife taper error.S.Smith, W.R.Winfough and J.Halley ^[8]By discovering the increase along with the pulling force of pull bar, the quiet rigidity of handle of a knife-main shaft joint portion also increases thereupon Deng the people, and damping reduces thereupon.

It is later relatively that domestic correlative study is carried out.Do not possess objective only certainty in order to overcome classical GW model and WA model, Zhang Xueliang, topaz U.S. be based on the contact fractal theory, proposed to have the normal direction contact stiffness fractal model of the Machine Joint Surfaces of size independence first ^[9], calculated Machine Joint Surfaces normal direction contact stiffness theoretically, and the resolution ratio of this rigidity and sample length and instrument is irrelevant, this is the maximum feature of rough surface normal direction contact stiffness fractal model.In addition, they have also done contrast with the Digital Simulation result with relevant experimental studies results, have uniformity.Afterwards, topaz U.S., Wang Shijun ^[10]Proposed to adopt the contact performance of the isoparametric element simulation joint portion of six nodes, derived the stiffness matrix of six node osculating elements, set up the complete machine analytical model,, confirmed validity complete machine Rigidity Experiment result and result of calculation comparison.

The Xiao Yongshan of Central South University ^[11]Discern on the theoretical foundation in the joint portion parameter Deng the people, utilize the SCADAS mode testing arrangement and the poster processing soft LMS Test.Lab of LMS company that lathe joint portion connector has been carried out the mode test, and in finite element software, set up FEM model, simulate with spring unit between the joint portion, stiffness coefficient adopts trial and error procedure to obtain estimated value earlier, the relative least square deviation with the corresponding vibration shape of test of the vibration shape that obtains with finite element is a target again, spring rate is a design variable, optimize and identify spring rate, optimize identification back frequency accuracy than higher, shown that the experimental modal test combines with Finite Element Method, can solve the problem of obtaining of lathe joint portion parameter preferably.

Above-mentioned all is the spring damping model basically.Though the parameter of the spring-damper of model can be discerned by method theoretical and that experiment combines, reaches reasonable effect, the defective of this model maximum is:

One ignored the coupled relation between handle of a knife-spindle taper joint portion each free degree of node, so the result does not have generality.

Its two, the number of the spring-damper between the joint portion does not have clear and definite quantity, therefore the number of different its spring-dampers of model is also inequality, does not have versatility.

List of references:

[1]M?P?Dolbey，R?Bell.The?Contact?Stiffness?of?Joints?at?Low?Apparent?InterfacePressure[C].In：Annals?of?CIRP，1970.

[2]Kirsanova?V?N.The?Shear?Compliance?of?Flat?Joints[J].Machines?and?Tooling，1967(7)：23.

[3]GreenwoodJa，Wmiamson?Jbp.Contact?of?Norminally?Flat?Surface[J]，roc.Roy.Soc.Lond，Sep.A，1966：295：300-31.

[4]Majumdar?A，Bhushan?B.Fractal?Model?of?Elastic-plastic?Contact?between?RoughSurfaces.[J].J.Tribol?ASME，1991，113(1)：1-11.

[5]T.R.Kim，S.M.Wu，and?K.F.Ehmann，Identification?of?Joint?Parameters?for?a?TaperJoint[J].Trans?of?ASME，Journal?of?Engg.for?Industry(v111，1989)，pp282-287.

[6]E.I.Rivin.Tooling?structure：interface?between?cutting?edge?and?machine?tool[Z]，Annals?of?CIRP?49/2(2000)591-634.

[7]Z.M.Levina.Stiffness?calculations?for?cylindrical?and?taper?joints[J]，Machines?andTooling?XL1(1970)5-10.

[8]S.Smith，W.R.Winfough，J.Halley，The?effect?of?drawbar?force?on?metal?removal?ratein?milling[Z]，Annals?of?CIRP?48/1(1998)293-295.

[9] Zhang Xueliang, topaz U.S., Han Ying. based on the Machine Joint Surfaces normal direction contact stiffness model [J] of contact fractal theory. Chinese mechanical engineering, 2000.7.727-728

[10] Wang Shijun, topaz U.S.. the FEM model of machine tool guideway joint portion [J]. Chinese mechanical engineering, 2004.9.1634-1636

[11] Xiao Yongshan, Wang Xing, Song Fumin. based on joint portion rigidity optimization identification [Z] .2006LMS first user conference collection of thesis of experimental modal, Suzhou, 2006.10.1-6

Summary of the invention

The object of the present invention is to provide a kind of kinetic parameter identification method for machine-tool cone-fit fixing and combining part, this method can improve modeling precision, and the versatility of model is strengthened.

The Dynamic Modeling of a kind of machine-tool cone-fit fixing and combining part provided by the invention and model parameter recognition methods is characterized in that this method comprises the steps:

The 1st step was set up the machine-tool cone-fit fixing and combining part kinetic model:

(1.1) on the circumference of the upper base disc of the cooperation conical surface of taper hole part, get 8 Along ents, sequence number is 1～8, on the circumference of the taper hole cooperation conical surface disc of going to the bottom partly, get 8 Along ents, sequence number is 9～16, on the circumference of axis of cone cooperation conical surface upper base disc partly, get 8 Along ents, sequence number is 17～24, gets 8 Along ents on the circumference of the axis of cone cooperation conical surface disc of going to the bottom partly, and sequence number is 25～32; In the order, 1～8 is corresponding one by one with 17～24, promptly put 1 with point 17 line by cooperating the center of conical surface upper bottom surface; Point 1 and characteristic on point 17 this geometry are called correspondence, and point 2 also has correspondence with point 18, and point 1～8 all has correspondence successively with point 17～24; Equally, 9～16 25～32 also have correspondence successively with point; Call corresponding 2 points to 2 with correspondence;

(1.2) i and m all represent node number, and the span of i is 1 to 32, and the span of m is 1 to 16, j, and the n value is 1,2,3, represents that respectively direction is x, y, z; Node 1 and 17,2 and 18,3 and 19 ..., the relative displacement between 16 and 32 is expressed as: δ _1n=(x _1n-x _17n), δ _2n=(x _2n-x _18n), δ _3n=(x _3n-x _19n) ..., δ _16n=(x _16n-x _32n), then the unit, joint portion be exactly one by δ _1n, δ _2n, δ _3n..., δ _16nThe dynamic systems that constitute of totally 48 freedoms of motion; X wherein _IjBe the displacement of node, nodal force { F} ^eAccording to formula

Ask for, wherein f _IjBe nodal force, k _Mn ^IjBe stiffness effect coefficient, δ _MnBe node m and node m+16 relative displacement in the n direction;

Utilize k _Mn ^IjThe stiffness matrix [K] that obtains in main shaft-handle of a knife tapering joint portion model parameter is:

$\left[K\right]=\left[\begin{array}{cc}\left[K^{\′}\right]& -\left[K^{\′}\right]\\ -\left[K^{\′}\right]& \left[K^{\′}\right]\end{array}\right]---\left(1\right)$

The cone-fit fixing and combining part parameter identification of the 2nd step:

(2.1) carry out mode experiment, obtain the preceding N rank intrinsic frequency f of cone-fit fixing and combining part experimental model ₁, f ₂..., f _N, N represents the exponent number of model frequency, value is a positive integer;

(2.2) use finite element analysis method, obtain the stiffness matrix [K of the machine tool chief axis minor structure of cone-fit fixing and combining part experimental model ₁], the mass matrix [M of main shaft minor structure ₁], the stiffness matrix [K of handle of a knife minor structure ₂], the mass matrix [M of handle of a knife minor structure ₂], the damping matrix [C of main shaft minor structure ₁], the damping matrix [C of handle of a knife minor structure ₂], [C ₁] and [C ₂] all adopt viscosity ratio damper model;

The expansion damping matrix of cone-fit fixing and combining part is designated as [C ₃], [C ₃] be 348 * 348 dimension matrixes, be damping matrix [C] by cone-fit fixing and combining part _{96 * 96}Expansion obtains, and specifically is with [C] _{96 * 96}Be placed on [C ₃] the upper left corner, other element mends 0; The expansion stiffness matrix of cone-fit fixing and combining part is designated as [K ₃], [K ₃] be 348 * 348 dimension matrixes, be stiffness matrix [K] by cone-fit fixing and combining part _{96 * 96}Expansion obtains, and specifically is with [K] _{96 * 96}Be placed on [K ₃] the upper left corner, other element mends 0;

Further, the integral rigidity matrix of the FEM model after the assembling of machine tool chief axis minor structure and lathe handle of a knife minor structure is designated as [K ¹²], [K ¹²] be 348 * 348 dimension matrixes, also be designated as [K ¹²] _{348 * 348}The total quality matrix of the FEM model after machine tool chief axis minor structure and the assembling of lathe handle of a knife minor structure is designated as [M ¹²], [M ¹²] be 348 * 348 dimension matrixes, also be designated as [M ¹²] _{348 * 348}Integral damping after machine tool chief axis minor structure and the assembling of lathe handle of a knife minor structure is designated as [C ¹²], [C ¹²] be 348 * 348 dimension matrixes, also be designated as [C ¹²] _{348 * 348}, wherein, [C ¹²]=α [M ¹²]+β [K ¹²], wherein, α is and the relevant constant of system's external damping that β is and the relevant constant of system's internal damping that α and β are called the damping constant of handle of a knife main shaft;

(2.2.1) recognition methods of handle of a knife main shaft damping constant α, β is as follows:

The optimization aim function of formula (III) is set:

${\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HSA00000047373200011.png"\; state="\{\{state\}\}">Q</figure-callout>}}_1=\underset{k=1}{\overset{N_1}{\mathrm{\&Sigma;}}}{\left[\right|A(k,1)\mathrm{\&alpha;}+B(k,1)\mathrm{\&beta;}|-|D(k,1)(+1)\left|\right]}^2---\left(\mathrm{III}\right)$

Wherein, k ∈ [97,348], ω _T1For with the pairing driving frequency of k, A (k, 1)=J ω _T1[M ¹²] _k[H] _{348 * 1}, D (k, 1)=J ω _T1[K ¹²] _k[H] _{348 * 1}, D (k, 1)={ ω _T1 ²[M ¹²] _k-[K ¹²] _k[H] _{348 * 1}, wherein, [M ¹²] _kExpression [M ¹²] k capable, [K ¹²] _kExpression [K ¹²] k capable;

A(k，1)α+B(k，1)β＝D(k，1) (IV)

A(k，1)α+B(k，1)β＝D(k，1)+1(V)

N ₁Expression ω _T1Different value numbers, and Q ₁When the pairing point of (+1) expression k in the expression formula is not point of excitation, will object function be set according to formula (IV); When the pairing point of k is point of excitation, will object function be set, find the solution mathematical non-linear least square problem, promptly ask for Q according to formula (V) ₁Minimum of a value, identify the value of α, β;

(2.2.2) recognition methods of cone-fit fixing and combining part damping constant β ' is as follows:

Set up the object function of the optimization identification of formula (VI):

$Q_2=\underset{l=1}{\overset{N_2}{\mathrm{\&Sigma;}}}{\left[\right|C(l,1)|-|D(l,1)\left|\right]}^2---\left(\mathrm{VI}\right)$

Wherein, the sequence number of the row of l representing matrix, l ∈ [1,48], ω _T2For with the pairing driving frequency of l, N ₂Expression ω _T2Different value numbers, C (l, 1)=(J ω _T2β '+1) [K '] _l[H ₁-H ₂] _{48 * 1},

$D(l,1)=\{({{\mathrm{\&omega;}}_{t2}}^2-J{\mathrm{\&omega;}}_{t2}\mathrm{\&alpha;}){\left[M_u^{12}\right]}_l-(1+J{\mathrm{\&omega;}}_{t2}\mathrm{\&beta;}){\left[K_u^{12}\right]}_l\}{\left[H\right]}_{348\&times;1}$

Find the solution the mathematical non-linear least square problem of formula (VI), identify the value of β ';

(2.2.3) the identification awl cooperates the stiffness matrix [K] of joint portion:

Adopt the least square fitting algorithm, the unknown number to the 2-48 of formula (VII) in capable is found the solution the initial value [K '] of r-1 element before r (r ∈ [2, the 48]) row line by line _Rw=[K '] _Wr(w≤r-1), [K '] _RwBe the parameter of having discerned, the initial value [K '] of a back 49-r element _Rw(w 〉=r) gets the corresponding element in the matrix of initial value [K '], promptly identifies the stiffness matrix [K] that awl cooperates the joint portion, and wherein, r, w are positive integer;

The inventive method is based on finite element theory and vibration mechanics, set up a kind of model of new machine-tool cone-fit fixing and combining part, and introduced the recognition methods of a kind of corresponding parameters with it.This method has taken into full account the various influence factors of joint portion and the coupled relation between kinetic parameter, promptly take into full account the coupled relation between handle of a knife-spindle taper joint portion each free degree of node, avoid using the spring-damper of some to describe certain model, on this basis, product according to frequency response matrix and impedance matrix is this theoretical foundation of unit matrix, utilization MATLAB nonlinear least square fitting function lsqnonlin has carried out optimizing identification to the stiffness matrix and the damping matrix of cone-fit fixing and combining part, this method has improved modeling precision, and model has good versatility.

Description of drawings

Fig. 1 is a cone-fit fixing and combining part kinetic model schematic diagram;

Fig. 2 is that handle of a knife minor structure measuring point is divided schematic diagram;

Fig. 3 is that main shaft minor structure measuring point is divided schematic diagram;

Fig. 4 is a vibration-testing scheme schematic diagram.

The specific embodiment

It is the topmost fit system of cutting tool for CNC machine system that awl cooperates.To be machine tool chief axis cooperate formed joint portion with handle of a knife contacting between the two to cone-fit fixing and combining part.The bellmouth that cooperates with handle of a knife on the machine tool chief axis is called spindle taper hole, abbreviates taper hole as.The part that cooperates with taper hole on the handle of a knife is called the handle of a knife tapering, for convenience described later, abbreviates the handle of a knife tapering as the axis of cone.The part that the axis of cone cooperates with taper hole is called the cooperation conical surface, cooperate the conical surface to fill upper bottom surface and bottom surface this, then formed the outer surface of the round platform on the geometry, the less relatively circular surfaces of diameter of round platform outer surface upper end is called the upper base disc, the relatively large circular surfaces of diameter of round platform outer surface lower end is called the disc of going to the bottom, what further, the axis of cone and taper hole were all corresponding has above-mentioned upper base disc and the disc of going to the bottom.In the model that the inventive method is set up, machine-tool cone-fit fixing and combining part is divided into two minor structures: handle of a knife minor structure and main shaft minor structure.Wherein, the handle of a knife minor structure comprises taper hole and corresponding accessory, and the main shaft minor structure comprises the axis of cone and corresponding accessory.(so-called annex is decided according to concrete subjects, cannot treat different things as the same.)

The inventive method is set up partial nodes such as 8 respectively at the upper base disc of the axis of cone and taper hole and the disc of going to the bottom, and adds up to 32 nodes, wherein 1～8,9～16,17～24,25～32 is Along ent, and each node has three translational degree of freedom, totally 96 frees degree; Afterwards, the frequency response matrix of experiment and stiffness matrix, the mass matrix of the minor structure that obtains of finite element theory are combined, the method of gathering by initial value examination, utilization nonlinear least square fitting optimization algorithm is discerned model parameter, the stiffness matrix that identifies is assembled into carries out finding the solution of characteristic value in the minor structure.Concrete implementation step is as follows:

(1) set up the machine-tool cone-fit fixing and combining part kinetic model:

Set up the joint portion kinetic model of 32 nodes, derive the joint portion stiffness matrix, point out that this stiffness matrix satisfies symmetry and separability, determine the number of joint portion model parameter identification.Detailed process is:

(1.1) set up partial nodes such as 8 respectively at the upper base disc of the axis of cone and taper hole and the disc of going to the bottom, add up to 32 nodes, the sequence number of point is represented with i, i=1, and 2 ..., 31,32.Each node has three translational degree of freedom, and respectively with j=1,2,3 replace explanation, and wherein j=1 represents the x direction translational free degree, and j=2 represents the y direction translational free degree, and j=3 represents the z direction translational free degree, totally 96 frees degree.The Along ent of being got, 1～8 is taken on the circumference of taper hole cooperation conical surface upper base disc partly, 9～16 are taken on the circumference of the taper hole cooperation conical surface disc of going to the bottom partly, 17～24 are taken on the circumference of axis of cone cooperation conical surface upper base disc partly, and 25～32 are taken on the circumference of the axis of cone cooperation conical surface disc of going to the bottom partly.In the order, 1～8 is corresponding one by one with 17～24, promptly put 1 with point 17 line by cooperating the center of conical surface upper base disc.Point 1 and characteristic on point 17 this geometry are called correspondence, and point 2 also has correspondence with point 18, and point 1～8 all has correspondence successively with point 17～24.Equally, point 9～16 also has correspondence successively with point 25～32, calls corresponding 2 points to 2 with correspondence.

(1.2) displacement of node i on j translational degree of freedom is called modal displacement, is designated as x _Ij, node i suffered power on j translational degree of freedom is called nodal force, is designated as f _Ij, i=1,2 ..., 31,32, j=1,2,3.If m represents taper hole and cooperates the sequence number of node on the disc of the upper and lower end of conical surface part, m=1,2 ..., the relative displacement of 16, the m node node corresponding with it (i.e. m+16 node) on n translational degree of freedom be designated as δ _Mn

M and i are relatively independent, and promptly their points of representing separately respectively to be replaced do not have influence each other, and for example m=1 represents node No. 1, but i this moment can represent in 1～No. 32 node any one.Equally, n also represents the direction of translational degree of freedom, and n=1 represents the x direction translational free degree, n=2 represents the y direction translational free degree, n=3 represents the z direction translational free degree, but n and j are separate, be that they represent the free degree direction that replaced separately, there is not influence each other, for example n represents the translational degree of freedom of x direction or some other directions, and this moment, j can represent x, y, the z any one party to translational degree of freedom, same, j represents the translational degree of freedom of x direction or some other directions, and this moment, n can represent x, y, the z any one party to translational degree of freedom.Node 1 and 17,2 and 18,3 and 19 ..., the relative displacement between 16 and 32 can be expressed as: δ _1n=(x _1n-x _17n), δ _2n=(x _2n-x _18n), δ _3n=(x _3n-x _19n) ..., δ _16n=(x _16n-x _32n), then the unit, joint portion be exactly one by δ _1n, δ _2n, δ _3n..., δ _16n, n=1,2,3, amount to 48 dynamic systems that freedom of motion constituted.

(1.3) make { δ } ^eThe vector that is assembled into for relative displacement is promptly with δ _MnBe the vector of component, { F} ^eThe vector that is assembled into for nodal force is promptly with f _IjBe the vector of component, according to the stiffness effect Y-factor method Y, can be by modal displacement { δ } ^eAsk nodal force { F} ^e, concrete computing formula is as follows:

$\underset{n=1}{\overset{3}{\mathrm{\&Sigma;}}}{k}_{1n}^{\mathrm{ij}}{\mathrm{\&delta;}}_{1n}+\underset{n=1}{\overset{3}{\mathrm{\&Sigma;}}}{k}_{2n}^{\mathrm{ij}}{\mathrm{\&delta;}}_{2n}+...+\underset{n=1}{\overset{3}{\mathrm{\&Sigma;}}}{k}_{16n}^{\mathrm{ij}}{\mathrm{\&delta;}}_{16n}=f_{\mathrm{ij}}---\left(1\right)$

In the following formula, k _Mn ^IjBe the stiffness effect coefficient, be called for short stiffness coefficient, its concrete implication is: only the n direction at node m and node m+16 produces the unit relative displacement, needs the power that applies in i node j direction.

With δ _MnSubstitution formula (1) obtains one 96 mechanical model of tieing up the joint surface unit of equation group, as the formula (2).

Convert equation group (2) form of matrix to, as the formula (3).

Further be expressed as

{F} ^e＝[K]{X} ^e (4)

(4) in the formula,

{ X} ^e=(x ₁₁, x ₁₂, x ₁₃X ₁₆₁, x ₁₆₂, x ₁₆₃, x ₁₇₁, x ₁₇₂, x ₁₇₃X ₃₂₁, x ₃₂₂, x ₃₂₃) ^TBe called the modal displacement vector;

{ F} ^e=(f ₁₁, f ₁₂, f ₁₃F ₁₆₁, f ₁₆₂, f ₁₆₃, f ₁₇₁, f ₁₇₂, f ₁₇₃F ₃₂₁, f ₃₂₂, f ₃₂₃) ^TBe called the nodal force vector;

[K] also is designated as [K] with [K] for cooperating the stiffness matrix of the conical surface _{96 * 96}, for above-mentioned [K], it has piecemeal, promptly

$\left[K\right]=\left[\begin{array}{cc}\left[K^{\&prime;}\right]& -\left[K^{\&prime;}\right]\\ -\left[K^{\&prime;}\right]& \left[K^{\&prime;}\right]\end{array}\right]---\left(5A\right)$

Wherein,

Therefore [K] is again symmetrical matrix simultaneously, as long as go up the value of triangle element in having obtained [K '], promptly identified the stiffness matrix [K] in main shaft-handle of a knife tapering joint portion model parameter.

(2) cone-fit fixing and combining part parameter identification

(2.1) mode experiment of machine-tool cone-fit fixing and combining part (Fig. 4)

This link is difference to some extent according to the difference of application, promptly at concrete machine-tool cone-fit fixing and combining part, needs the geomery according to this joint portion, make corresponding mock-up and test method.Following mock-up and test method, only for reference, be the case that the present invention uses.

(2.1.1) set up the mock-up that awl cooperates the joint portion experiment.Model mainly is made up of main shaft and BT-45 handle of a knife, and adds an additional mass in BT-45 handle of a knife lower end.Handle of a knife realizes and the connecting of main shaft that by tightening of nut its retaining part is reduced to the ring-type thin-walled, and 2 square sulculuses of thin-walled 180 degree directions symmetrical distributions play the role of positioning, and prevents between the handle of a knife and main shaft relative motion to take place in the hammering experimentation.The axial pre tightening force of handle of a knife-main shaft is by the realization of tightening of nut, and torque is read by the torque wrench dial.

(2.1.2) experimental model freely is suspended under the jenny by suspension ring and steel wire rope, circumferential measuring point place placement sensor paste block, 3 normal direction of sensor are parallel with reference axis respectively, measure the acceleration signal of change in coordinate axis direction.The jump bit of aluminium head hammer cap is carried in employing, carries out mode experiment with the method for single-point excitation multi-point sampler.

Test model has 112 measuring points (Fig. 2, Fig. 3), and 56 unit wherein belong to the joint portion and cooperate the measuring point of the conical surface to be numbered 1～32 altogether.Test model in this method and FEM model are also incomplete same, below this are done description below:

Test model is used for experiment in kind, promptly this model have a few in practice and can survey.FEM model then must be considered theoretic reasonability, therefore (put 17-24 at four octagons of measuring point model (Fig. 2), point 25-32, point 33-40, therefore some 41-48 all constitutes octagon, has four octagons) central point, get again a bit, be to have added four octagonal four central points in the FEM model, so total (112+4) the individual node of FEM model.

Testing the preceding 6 rank model frequencies of measured main shaft handle of a knife is designated as respectively: f ₁, f ₂, f ₃, f ₄, f ₅, f ₆6 rank model frequencies are designated as respectively before the handle of a knife minor structure that calculates by FEM model: f _D1, f _D2, f _D3, f _D4, f _D5, f _D6The main shaft minor structure 6 rank model frequencies that calculate by FEM model are designated as respectively: f _Z1, f _Z2, f _Z3, f _Z4, f _Z5, f _Z6

(2.2) identification of machine-tool cone-fit fixing and combining part kinetic parameter, detailed process is:

The stiffness matrix of machine tool chief axis minor structure is designated as [K ₁], the mass matrix of main shaft minor structure is designated as [M ₁], the stiffness matrix of handle of a knife minor structure is designated as [K ₂], the mass matrix of handle of a knife minor structure is designated as [M ₂], the damping matrix of main shaft minor structure is designated as [C ₁], the damping matrix [C of handle of a knife minor structure ₂], [C ₁With [C ₂] all adopt viscosity ratio damper model.The quality of ignoring cone-fit fixing and combining part, the stiffness matrix of cone-fit fixing and combining part is designated as [K ₃], [K ₃] be 348 * 348 dimension matrixes, also be designated as [K ₃] _{348 * 348}, by [K] _{96 * 96}Expanding, specifically is with [K] _{96 * 96}Be placed on [K ₃] the upper left corner, other element mends 0, [K] _{96 * 96}Stiffness matrix for cone-fit fixing and combining part.The damping matrix of cone-fit fixing and combining part is designated as [C ₃], [C ₃] be 348 * 348 dimension matrixes, also be designated as [C] _{348 * 348}, by [C] _{96 * 96}Expanding, specifically is with [C] _{96 * 96}Be placed on [C ₃] the upper left corner, other element mends 0, [C] _{96 * 96}Damping matrix for cone-fit fixing and combining part.[C is arranged simultaneously, ₃]=β ' [K ₃], β ' is and the relevant constant of system's internal damping to be called the damping constant of cone-fit fixing and combining part.

Further, the integral rigidity matrix of the FEM model after the assembling of machine tool chief axis minor structure and lathe handle of a knife minor structure is designated as [K ¹²], because described FEM model has 116 nodes, each node has 3 translational degree of freedom, so [K ¹²] be 348 * 348 dimension matrixes, also be designated as [K ¹²] _{348 * 348}The total quality matrix of the FEM model after machine tool chief axis minor structure and the assembling of lathe handle of a knife minor structure is designated as [M ¹²], because described FEM model has 116 nodes, each node has 3 translational degree of freedom, so [M ¹²] be 348 * 348 dimension matrixes, also be designated as [M ¹²] _{348 * 348}Integral damping after machine tool chief axis minor structure and the assembling of lathe handle of a knife minor structure is designated as [C ¹²], because described FEM model has 116 nodes, each node has 3 translational degree of freedom, so [C ¹²] be 348 * 348 dimension matrixes, also be designated as [C ¹²] _{348 * 348}Wherein, [C ¹²]=α [M ¹²]+β [K ¹²], wherein, α is and the relevant constant of system's external damping that β is and the relevant constant of system's internal damping.α and β are called the damping constant of handle of a knife main shaft.The global matrix of the FEM model after the so-called assembling promptly is to become as a whole after main shaft minor structure and the handle of a knife minor structure cooperation installation, and the matrix of the FEM model that this is whole promptly is a global matrix.

According to the Modal Parameter Identification theory, have following formula to set up:

$\{-{\mathrm{\&omega;}}^2[M^{12}]+\mathrm{J\&omega;}[C^{12}]+\mathrm{J\&omega;}[C_3]+[K_3]+[K^{12}\left]\right\}\left[H\right]=I_s=\left[\begin{array}{c}0\\ .\\ .\\ .\\ 0\\ 1\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]---\left(6\right)$

Wherein, ω is a driving frequency, and promptly the frequency of dynamic excitation (as exciting force) can be recorded by experiment.J is an imaginary unit, promptly

[H] is 348 * 1 dimension matrixes, also is designated as [H] _{348 * 1}, be row of frequency response matrix, its meaning is: encouraging in the point of excitation direction, is the column vector of element with the response of other each point.

I for formula (6) right-hand member _s, because point of excitation is after 96 row, so the column vector I of unit _sIn the position of element 1 also after 96 row, i.e. I _sIn the value of preceding 96 elements inevitable all be 0.

(6) in the formula, [M ¹²] by [M ₁] and [M ₂] assemble and get; [C ¹²] by [C ₁] and [C ₂] assemble and get; [K ¹²] by [K ₁] and [K ₂] assemble and get.[M wherein ₁], [M ₂], [C ₁], [C ₂], [K ₁], [K ₂] all get by the finite element theory modeling.

(2.2.1) recognition methods of handle of a knife main shaft damping constant α, β is as follows:

Formula (6) is written as following form again:

{Jω[C ₃]+[K ₃]}[H]＝I _s+{ω ²[M ¹²]-[K ¹²]-Jω(α[M ¹²]+β[K ¹²])}[H](7)

(7) the preceding 96 row equation left sides of formula comprise the parameter that will discern, and two unknown numbers of α, β are contained on the right; The equation left side is 0 after 96 row.Therefore, after 96 row for formula (7), get that wherein k is capable, the sequence number of the row of matrix in the k expression (7), k ∈ [97,348].Then

a _k+{ω _t1 ²[M ¹²] _k-[K ¹²] _k-Jω _t1(α[M ¹²] _k+β[K ¹²] _k)}[H] _348×1＝0(8)

In the following formula, a _kBe I _sK component, ω _T1Be corresponding driving frequency, make A (k, 1)=J ω _T1[M ¹²] _k[H] _{348 * 1}, B (k, 1)=J ω _T1[K ¹²] _k[H] _{348 * 1}, D (k, 1)={ ω _T1 ²[M ¹²] _k-[K ¹²] _k[H] _{348 * 1}, wherein, [M ¹²] _kExpression [M ¹²] k capable, [K ¹²] _kExpression [K ¹²] k capable.

Can obtain by (8) formula:

When the pairing point of k is not point of excitation, a _k=0, then

A(k，1)α+B(k，1)β＝D(k，1)(9)

When the pairing point of k is point of excitation, α _k=1, then

A(k，1)α+B(k，1)β＝D(k，1)+1(10)

Following optimization aim function is set:

${\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HSA00000047373200011.png"\; state="\{\{state\}\}">Q</figure-callout>}}_1=\underset{k=1}{\overset{N_1}{\mathrm{\&Sigma;}}}{\left[\right|A(k,1)\mathrm{\&alpha;}+B(k,1)\mathrm{\&beta;}|-|D(k,1)(+1)\left|\right]}^2$

N ₁Expression ω _T1Different value numbers, and Q ₁When the pairing point of (+1) expression k in the expression formula is not point of excitation, will object function be set according to (9) formula; When the pairing point of k is point of excitation, will object function be set, find the solution mathematical non-linear least square problem, promptly ask for Q according to (10) formula ₁Minimum of a value, promptly identified the value of α, β thus.

(2.2.2) recognition methods of cone-fit fixing and combining part damping constant β ' is as follows:

For preceding 96 row of formula (7), because point of excitation is got I not at preceding 96 row _sPreceding 96 row elements are formed 96 * 1 new dimensional vector I _S1I is then arranged _S1=0, with [C ₃]=β ' [K ₃] substitution formula (7), and get preceding 96 row, obtain

{Jω _t2β′+1}[K] _96×96[H] _96×1＝{ω _t2 ²[M ¹²] _96×348-[K ¹²] _96×348-Jω _t2(α[M ¹²] _96×348

+β[K ¹²] _96×348)}[H] _348×1(11)

Utilize the piecemeal of [K] described in (1.3), then with matrix [H] _{96 * 1}, [M ¹²] _{96 * 348}, [K ¹²] _{96 * 348}All make average up and down piecemeal and handle, establish

The l that substitution formula (11) is got in preceding 48 row is capable, the sequence number of the row of matrix shown in the l expression (11), because preceding 48 capable calculating in the modus ponens (11) herein, so: l ∈ [1,48], abbreviation gets

$(J{\mathrm{\&omega;}}_{t2}{\mathrm{\&beta;}}^{\&prime;}+1){\left[K^{\&prime;}\right]}_l{[H_1-H_2]}_{48\&times;1}=\{({{\mathrm{\&omega;}}_{t2}}^2-J{\mathrm{\&omega;}}_{t2}\mathrm{\&alpha;}){\left[M_u^{12}\right]}_l-$

$(1+J{\mathrm{\&omega;}}_{t2}\mathrm{\&beta;}){\left[K_u^{12}\right]}_l\}{\left[H\right]}_{348\&times;1}---\left(12\right)$

In the following formula, [K '] _lThe l of representing matrix [K '] is capable, [M _u ¹²] _lRepresenting matrix [M _u ¹²] l capable, [K _u ¹²] _lRepresenting matrix [K _u ¹²] l capable.

(5A) knows by formula, as long as identified [K '], promptly identified [K] _{96 * 96}

For formula (12), make C (l, 1)=(J ω _T2β '+1) [K '] _l[H ₁-H ₂] _{48 * 1},

$D(l,1)=\{({{\mathrm{\&omega;}}_{t2}}^2-J{\mathrm{\&omega;}}_{t2}\mathrm{\&alpha;}){\left[M_u^{12}\right]}_l-(1+J{\mathrm{\&omega;}}_{t2}\mathrm{\&beta;}){\left[K_u^{12}\right]}_l\}{\left[H\right]}_{348\&times;1},$

That is:

C(l，1)＝D(l，1)(13)

The preceding 6 rank model frequency f of main shaft handle of a knife for gained in (2.1.2) ₁, f ₂, f ₃, f ₄, f ₅, f ₆, about these 6 peak value model frequencies are equal, respectively choose 15 frequency values, be spaced apart 1Hz, obtain N ₂Individual value is then with ω _T2Be taken as this N ₂Individual value.

Set up the object function of optimizing identification:

$Q_2=\underset{l=1}{\overset{N_2}{\mathrm{\&Sigma;}}}{\left[\right|C(l,1)|-|D(l,1)\left|\right]}^2$

Find the solution mathematical non-linear least square problem, by asking for Q ₂Minimum of a value, identify the value of β '.

(2.2.3) method of the identification of awl cooperation joint portion stiffness matrix is as follows:

According to the symmetry of [K '], with the element below the corresponding element replacement leading diagonal more than the leading diagonal, i.e. [K '] _Rw=[K '] _Wr, therefore second of [K '] row only needs the value of 47 elements of identification, and the like, r (r=2～48) row only needs to discern the value of (49-r) individual element, and r represents the sequence number of the row of [K '], and w represents the sequence number of the row of [K '].

Adopt the least square fitting algorithm, the unknown number to the 2-48 of formula (5B) in capable is found the solution the initial value [K '] of r-1 element before r (r ∈ [2, the 48]) row line by line _Rw=[K '] _Wr(w≤r-1), [K '] _WrBe the parameter of having discerned.The initial value [K '] of a back 49-r element _Rw(w 〉=r) gets the corresponding element in the matrix of initial value [K '], can identify awl and cooperate stiffness matrix.Wherein, r, w are positive integer.

The present invention not only is confined to the above-mentioned specific embodiment; persons skilled in the art are according to embodiment and the disclosed content of accompanying drawing; can adopt other multiple specific embodiment to implement the present invention; therefore; every employing project organization of the present invention and thinking; do some simple designs that change or change, all fall into the scope of protection of the invention.

Claims (1)

1. the Dynamic Modeling of a machine-tool cone-fit fixing and combining part and model parameter recognition methods is characterized in that, this method comprises the steps:

The 1st step was set up the machine-tool cone-fit fixing and combining part kinetic model:

(1.1) on the circumference of the upper base disc of the cooperation conical surface of taper hole part, get 8 Along ents, sequence number is 1～8, on the circumference of the taper hole cooperation conical surface disc of going to the bottom partly, get 8 Along ents, sequence number is 9～16, on the circumference of axis of cone cooperation conical surface upper base disc partly, get 8 Along ents, sequence number is 17～24, gets 8 Along ents on the circumference of the axis of cone cooperation conical surface disc of going to the bottom partly, and sequence number is 25～32; In the order, 1～8 is corresponding one by one with 17～24, promptly put 1 with point 17 line by cooperating the center of conical surface upper bottom surface; Point 1 and characteristic on point 17 this geometry are called correspondence, and point 2 also has correspondence with point 18, and point 1～8 all has correspondence successively with point 17～24; Equally, 9～16 25～32 also have correspondence successively with point; Call corresponding 2 points to 2 with correspondence;

(1.2) i and m all represent node number, and the span of i is 1 to 32, and the span of m is 1 to 16, j, and the n value is 1,2,3, represents that respectively direction is x, y, z; Node 1 and 17,2 and 18,3 and 19 ..., the relative displacement between 16 and 32 is expressed as: δ _1n=(x _1n-x _17n), δ _2n=(x _2n-x _18n), δ _3n=(x _3n-x _19n) ..., δ _16n=(x _16n-x _32n), then the unit, joint portion be exactly one by δ _1n, δ _2n, δ _3n..., δ _16nThe dynamic systems that constitute of totally 48 freedoms of motion; Wherein xij is the displacement of node, nodal force { F} ^eAccording to formula

Ask for, wherein f _IjBe nodal force, k _Mn ^IjBe stiffness effect coefficient, δ _MnBe node m and node m+16 relative displacement in the n direction;

Utilize k _Mn ^IjThe stiffness matrix [K] that obtains in main shaft-handle of a knife tapering joint portion model parameter is:

$\left[K\right]=\left[\begin{array}{cc}\left[K^{\&prime;}\right]& -\left[K^{\&prime;}\right]\\ -\left[K^{\&prime;}\right]& \left[K^{\&prime;}\right]\end{array}\right]---\left(I\right)$

The cone-fit fixing and combining part parameter identification of the 2nd step:

(2.1) carry out mode experiment, obtain the preceding N rank intrinsic frequency f of cone-fit fixing and combining part experimental model ₁, f ₂..., f _N, N represents the exponent number of model frequency, value is a positive integer;

(2.2) use finite element analysis method, obtain the stiffness matrix [K of the machine tool chief axis minor structure of cone-fit fixing and combining part experimental model ₁], the mass matrix [M of main shaft minor structure ₁], the stiffness matrix [K of handle of a knife minor structure ₂], the mass matrix [M of handle of a knife minor structure ₂], the damping matrix [C of main shaft minor structure ₁], the damping matrix [C of handle of a knife minor structure ₂], [C ₁] and [C ₂] all adopt viscosity ratio damper model;

The expansion damping matrix of cone-fit fixing and combining part is designated as [C ₃], [C ₃] be 348 * 348 dimension matrixes, be damping matrix [C] by cone-fit fixing and combining part _{96 * 96}Expansion obtains, and specifically is with [C] _{96 * 96}Be placed on [C ₃] the upper left corner, other element mends 0; The expansion stiffness matrix of cone-fit fixing and combining part is designated as [K ₃], [K ₃] be 348 * 348 dimension matrixes, be stiffness matrix [K] by cone-fit fixing and combining part _{96 * 96}Expansion obtains, and specifically is with [K] _{96 * 96}Be placed on [K ₃] the upper left corner, other element mends 0;

Further, the integral rigidity matrix of the FEM model after the assembling of machine tool chief axis minor structure and lathe handle of a knife minor structure is designated as [K ¹²], [K ¹²] be 348 * 348 dimension matrixes, also be designated as [K ¹²] _{348 * 348}The total quality matrix of the FEM model after machine tool chief axis minor structure and the assembling of lathe handle of a knife minor structure is designated as [M ¹²], [M ¹²] be 348 * 348 dimension matrixes, also be designated as [M ¹²] _{348 * 348}Integral damping after machine tool chief axis minor structure and the assembling of lathe handle of a knife minor structure is designated as [C ¹²], [C ¹²] be 348 * 348 dimension matrixes, also be designated as [C ¹²] _{348 * 348}, wherein, [C ¹²]=α [M ¹²]+β [K ¹²], wherein, α is and the relevant constant of system's external damping that β is and the relevant constant of system's internal damping that α and β are called the damping constant of handle of a knife main shaft;

(2.2.1) recognition methods of handle of a knife main shaft damping constant α, β is as follows:

The optimization aim function of formula (III) is set:

$Q_1=\underset{k=1}{\overset{N_1}{\mathrm{\&Sigma;}}}{\left[\right|A(k,1)\mathrm{\&alpha;}+B(k,1)\mathrm{\&beta;}|-|D(k,1)(+1)\left|\right]}^2---\left(\mathrm{III}\right)$

Wherein, k ∈ [97,348], ω _T1For with the pairing driving frequency of k, A (k, 1)=J ω _T1[M ¹²] _k[H] _{348 * 1}, B (k, 1)=J ω _T1[K ¹²] _k[H] _{348 * 1}, D (k, 1)={ ω _T1 ²[M ¹²] _k-[K ¹²] _k[H] _{348 * 1}, wherein, [M ¹²] _kExpression [M ¹²] k capable, [K ¹²] _kExpression [K ¹²] k capable;

A(k，1)α+B(k，1)β＝D(k，1) (IV)

A(k，1)α+B(k，1)β＝D(k，1)+1 (V)

N ₁Expression ω _T1Different value numbers, and Q ₁When the pairing point of (+1) expression k in the expression formula is not point of excitation, will object function be set according to formula (IV); When the pairing point of k is point of excitation, will object function be set, find the solution mathematical non-linear least square problem, promptly ask for Q according to formula (V) ₁Minimum of a value, identify the value of α, β;

(2.2.2) recognition methods of cone-fit fixing and combining part damping constant β ' is as follows:

Set up the object function of the optimization identification of formula (VI):

$Q_2=\underset{l=1}{\overset{N_2}{\mathrm{\&Sigma;}}}{\left[\right|C(l,1)|-|D(l,1)\left|\right]}^2---\left(\mathrm{VI}\right)$

Wherein, the sequence number of the row of l representing matrix, l ∈ [1,48], ω _T2For with the pairing driving frequency of l, N ₂Expression ω _T2Different value numbers, C (l, 1)=(J ω _T2β '+1) [K '] _l[H ₁-H ₂] _{48 * 1},

$D(l,1)=\{({{\mathrm{\&omega;}}_{t2}}^2-J{\mathrm{\&omega;}}_{t2}\mathrm{\&alpha;}){\left[M_u^{12}\right]}_l-(1+J{\mathrm{\&omega;}}_{t2}\mathrm{\&beta;}){\left[K_u^{12}\right]}_l\}{\left[H\right]}_{348\&times;1}$

Find the solution the mathematical non-linear least square problem of formula (VI), identify the value of β ';

(2.2.3) the identification awl cooperates the stiffness matrix [K] of joint portion:

Adopt the least square fitting algorithm, the unknown number to the 2-48 of formula (VII) in capable is found the solution the initial value [K '] of r-1 element before r (r ∈ [2, the 48]) row line by line _Rw=[K '] _Wr(w≤r-1), [K '] _RwBe the parameter of having discerned, the initial value [K '] of a back 49-r element _Rw(w 〉=r) gets the corresponding element in the matrix of initial value [K '], promptly identifies the stiffness matrix [K] that awl cooperates the joint portion, and wherein, r, w are positive integer;

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