CN105005673A - Whole machine static stiffness matching and designing method in view of machine tool top-down design - Google Patents

Abstract

The invention discloses a whole machine static stiffness matching and designing method in view of machine tool top-down design. The method comprises steps: static stiffness of each part of the machine tool in a difference place is defined; a static stiffness model for the whole machine is built; force analysis is carried out on each part of the machine tool, a force condition of each part is obtained, and normal forces and tangential forces of the machine tool body, a vertical column and a slide carriage are obtained through analysis; a function relation between deformation of each part of the machine tool and static stiffness of each part of the machine tool is built; the static stiffness model for the whole machine is built; and on the basis of the static stiffness model for the whole machine, static stiffness matching and designing are carried out. In the machine tool concept design stage, the whole machine static stiffness given by a user serves as a target, machine tool static stiffness design is carried out in a top-down mode, and in the condition in which static stiffness in three directions at the tail end of the whole machine tool is given, reasonable static stiffness for each part is obtained through matching and designing. The static stiffness of the machine tool can be estimated and controlled at the beginning of the design, the efficiency and the accuracy of design are improved, the processing precision of the machine tool is improved, product performance estimation can also be carried out, and the production cost and the manufacturing cost are reduced.

Description

A kind of complete machine Static stiffness adaptation design method towards lathe Top-Down Design

Technical field

The present invention relates to a kind of complete machine Static stiffness adaptation design method.Particularly relate to a kind of complete machine Static stiffness adaptation design method towards lathe Top-Down Design.

Background technology

Static stiffness is one of important indicator of Machine Tool design, and the Static stiffness improving lathe is conducive to the efficiency of raising lathe, machining precision and suface processing quality.In Machine Tool design in the past, after grinding machine structure design completes, finite element software is normally just adopted to calculate its Static stiffness.Designed machine tool structure often cannot meet the requirement of user to complete machine Static stiffness, causes the modifying and calculating repeatedly of designer in the design process, wastes a large amount of time and manpower.In addition, designer cannot control complete machine Static stiffness at the beginning of design, and neither one effectively estimates means to it.Therefore, it is possible to design at the beginning of just with user requirement complete machine Static stiffness for target, being obtained the Static stiffness of each parts by Static stiffness matched design, and carry out structural design as target to each parts, is very important.

Summary of the invention

Technical matters to be solved by this invention is, provides a kind of complete machine Static stiffness adaptation design method towards lathe Top-Down Design.

The technical solution adopted in the present invention is: a kind of complete machine Static stiffness adaptation design method towards lathe Top-Down Design, comprises the steps:

1) Static stiffness of each parts of lathe at difference place is defined;

2) the quiet distorted pattern of complete machine is set up;

3) force analysis is carried out to each parts of lathe, obtain the stressing conditions of parts, that is, analyze the normal force obtained suffered by lathe bed, column and slide carriage and tangential force;

4) funtcional relationship between each part distortion of lathe and each parts Static stiffness of lathe is set up;

5) the Static stiffness model of complete machine is set up;

Funtcional relationship between each for lathe part distortion and lathe each parts Static stiffness is updated in the middle of the quiet distorted pattern of complete machine, just obtains the funtcional relationship between parts Static stiffness and lathe end Static stiffness, be the Static stiffness model of complete machine;

6) Static stiffness matched design is carried out based on complete machine Static stiffness model, that is:

Using the Static stiffness model of complete machine as equation of constraint, the scope of the Static stiffness of each parts of lathe of the same type calculated by Finite Element Method is as the scope of design of Static stiffness design variable, make that the Z-direction rigidity of machine pillar is maximum is set to objective function, utilize the fmincon quadratic programming function in Matlab software, obtain the Static stiffness size of each parts when known lathe end Static stiffness.

Step 1) in for the Static stiffness of the column of lathe, lathe bed and slide carriage, be the Static stiffness at four the location point places corresponding to four slide blocks selecting them; For the Static stiffness of main shaft, leading screw and worktable, be they are regarded as an entirety, select described entirety to bear the Static stiffness at the location point place of cutting force.

Step 2) set up the quiet distorted pattern of complete machine, comprising:

(1) adopt theory of multi body system, complete machine is abstracted into typical body, and represents complete machine relevance with topology diagram;

(2) the desired characteristics matrix T between each typical body of lathe and adjacent body is established _ijwith deformation behaviour matrix △ T _ij, wherein, i, j ∈ [0,1,2,3,4,5,6,7];

(3) 1 Q in main shaft coordinate system is got _t(x _t, y _t, z _t), by carrying out homogeneous coordinate transformation between adjacent body, described some Q _t(x _t, y _t, z _t) coordinate can represent with worktable coordinate system,

In the ideal situation, described some Q _t(x _t, y _t, z _t) be expressed as Q with worktable coordinate system _w(x _w, y _w, z _w), Q _w(x _w, y _w, z _w) computing method as follows:

[x _w,y _w,z _w,1] ^T＝T ₃₇[x _t,y _t,z _t,1] ^T(1)

T ₃₇＝T ₆₇T ₅₆T ₄₅T ₀₄T ₁₀T ₂₁T ₃₂(2)

In formula, T ₆₇, T ₅₆, T ₄₅, T ₀₄, T ₁₀, T ₂₁, T ₃₂it is desired characteristics matrix;

When exposed to external forces, described some Q _t(x _t, y _t, z _t) change to physical location Q ' _w(x ' _w, y ' _w, z ' _w), Q ' _w(x ' _w, y ' _w, z ' _w) computing method as follows:

[x _w′,y _w′,z _w′,1] ^T＝T′ ₃₇[x _t,y _t,z _t,1] ^T(3)

T′ ₃₇＝T′ ₆₇T′ ₅₆T′ ₄₅T′ ₀₄T′ ₁₀T′ ₂₁T′ ₃₂(4)

Wherein T ' _ij=T _ij△ T _ij(5)

Q will be put _w(x _w, y _w, z _w) and some Q ' _w(x ' _w, y ' _w, z ' _w) do the quiet distorted pattern that namely difference obtains complete machine tool:

$\left(\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}y\\ \mathrm{\Δ}z\end{array}\right)=\left(\begin{array}{c}{B}_z{\mathrm{\Δ\β}}_{01}+B_y{\mathrm{\Δ\γ}}_{01}-{\mathrm{\Δx}}_{01}-{\mathrm{\Δx}}_{12}-{\mathrm{\Δx}}_{23}+{\mathrm{\Δx}}_{45}+{\mathrm{\Δx}}_{56}+R_f{\mathrm{\Δ\β}}_{45}+{\mathrm{\Δx}}_{67}+R_c{\mathrm{\Δ\β}}_{04}\\ {\mathrm{\Δy}}_{56}-R_c{\mathrm{\Δ\α}}_{04}-{\mathrm{\Δy}}_{01}-{\mathrm{\Δy}}_{12}-{\mathrm{\Δy}}_{23}-R_f{\mathrm{\Δ\α}}_{45}-B_z{\mathrm{\Δ\α}}_{01}+{\mathrm{\Δy}}_{67}+{\mathrm{\Δy}}_{04}\\ {\mathrm{\Δz}}_{04}+{\mathrm{\Δz}}_{45}-{\mathrm{\Δz}}_{01}-{\mathrm{\Δz}}_{12}-{\mathrm{\Δz}}_{23}-B_y{\mathrm{\Δ\α}}_{01}+{\mathrm{\Δz}}_{67}+{\mathrm{\Δz}}_{56}\end{array}\right)---\left(6\right)$

Wherein, △ x=x _w-x ' _w, △ y=y _w-y ' _w, △ z=z _w-z ' _w;

△ x _ijbe parts X to distortion, △ y _ijthe distortion of parts Y-direction, △ z _ijthe distortion of parts Z-direction, wherein, i, j=0,1,2,3,4,5,6,7;

△ α _ijthat parts are out of shape around X-axis, △ β _ijparts are out of shape around Y-axis, wherein, and i=0,4, j=1,4,5;

△ γ _ijthat parts are out of shape around Z axis, wherein, i=0, j=1;

R _fslide carriage and main shaft Z-direction distance, R _cslide carriage and main shaft Z-direction distance, B _ylathe bed and main shaft Y-direction distance, B _zlathe bed and main shaft Y-direction distance.

Step 4) described funtcional relationship is

Wherein, △ is part distortion value, and F is the stressing conditions of each parts of lathe, and k is the Static stiffness of each parts of lathe, thus obtains the funtcional relationship of each part distortion and described parts Static stiffness.

Step 4) in, consider the flexibility of each parts of lathe, be subject to the distortion that two onesize power produce in the position that each parts are adjacent simultaneously, be not equal to the twice that a position is subject to the distortion of same power, therefore add influence coefficients of deformation the funtcional relationship formula between each part distortion of lathe and each parts Static stiffness of lathe is revised, obtain:

Wherein, n is that finger location point is subject to produced distortion and the ratio due to stressed the produced distortion of adjacent position point.

Complete machine Static stiffness adaptation design method towards lathe Top-Down Design of the present invention, at lathe conceptual phase, with the given complete machine Static stiffness of user for target, the Static stiffness design carrying out lathe of " top-down ", when given complete machine tool end three direction Static stiffness, obtained the Static stiffness size of rational each parts by matched design.The present invention can estimate and control in design the Static stiffness of lathe beginning, improves efficiency and the accuracy of design, improves the machining precision of lathe, can also carry out the Performance Prediction of product, and reduce manufacturing cost.The present invention also extends to the design field of other similar physical constructions.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the present invention towards the complete machine Static stiffness adaptation design method of lathe Top-Down Design;

Fig. 2 is complete machine of the present invention each parts Static stiffness schematic diagram;

Fig. 3 is complete machine topological structure schematic diagram of the present invention.

In figure

1: lathe bed 2: turntable

3: worktable 4: column

5: slide carriage 6: main spindle box

7: main shaft 0: ground

Embodiment

Below in conjunction with embodiment and accompanying drawing, a kind of complete machine Static stiffness adaptation design method towards lathe Top-Down Design of the present invention is described in detail.

As shown in Figure 1, a kind of complete machine Static stiffness adaptation design method towards lathe Top-Down Design of the present invention, comprises the steps:

1) Static stiffness of each parts of lathe at difference place is defined; The Top-Down Design of lathe starts from conceptual phase, now only has total arrangement's scheme, and each parts only have basic physical dimension.Carry out the Top-Down Design of complete machine Static stiffness in this case, first will set up the Static stiffness model of complete machine.In order to describe the rigidity of parts and be convenient to set up Static stiffness model, the Static stiffness of component locations point is adopted to characterize the Static stiffness of parts.Wherein,

For the Static stiffness of the column of lathe, lathe bed and slide carriage, it is the Static stiffness at four the location point places corresponding to four slide blocks selecting them;

For the Static stiffness of main shaft, leading screw and worktable, be they are regarded as an entirety, select described entirety to bear the Static stiffness at the location point place of cutting force.

In the present invention, the Static stiffness of each position point in complete machine, be respectively the Static stiffness of lathe bed along X and Y-direction, turntable is along the Static stiffness in X, Y, Z tri-directions, worktable is along the Static stiffness in X, Y, Z tri-directions, and column is along the Static stiffness of Y and Z-direction, and slide carriage is along the Static stiffness of X and Z-direction, main spindle box is along the Static stiffness in X, Y, Z tri-directions, and main shaft is along the Static stiffness in X, Y, Z tri-directions.These Static stiffness as shown in Figure 2.

2) the quiet distorted pattern of complete machine is set up; The Static stiffness model of complete machine obtains by setting up the quiet distorted pattern of complete machine.Setting up the quiet distorted pattern of complete machine is exactly set up the funtcional relationship of being out of shape between the distortion of each parts and tool-workpiece.The situation of total arrangement's scheme is only had in order to meet conceptual phase, the present invention adopts theory of multi body system, complete machine is abstracted into lathe bed, turntable, worktable, column, slide carriage, main spindle box, these typical body of main shaft, and represents its relevance with topology diagram as shown in Figure 3.Specifically comprise:

(1) adopt theory of multi body system, complete machine is abstracted into typical body, and represents complete machine relevance with topology diagram;

(2) the present invention with lathe under the operating mode of reality issuable static(al) deformation for according to setting each parts distortion.In order to the coordinate transform be described in ideally and between body under stressing conditions, establish the desired characteristics matrix T between each typical body of lathe and adjacent body _ijwith deformation behaviour matrix △ T _ij, wherein, i, j ∈ [0,1,2,3,4,5,6,7], described desired characteristics matrix T _ijwith deformation behaviour matrix △ T _ijas table 1:

Table 1

Wherein, △ x _ij(i, j=0,1,2,3,4,5,6,7) be parts X to distortion, △ y _ij(i, j=0,1,2,3,4,5,6,7) are the distortion of parts Y-direction, △ z _ij(i, j=0,1,2,3,4,5,6,7) are the distortion of parts Z-direction, △ α _ij(i=0,4, j=1,4,5) are that parts are out of shape around X-axis, △ β _ij(i=0,4, j=1,4,5) parts are out of shape around Y-axis, △ γ _ij(i=0, j=1) is that parts are out of shape around Z axis, Y _ij(i, j=0,1,2,3,4,5,6,7) be adjacent between Y-direction distance, Z _ij(i, j=0,1,2,3,4,5,6,7) are Z-direction distances between adjacent body.

(3) 1 Q in main shaft coordinate system is got _t(x _t, y _t, z _t), by carrying out homogeneous coordinate transformation between adjacent body, described some Q _t(x _t, y _t, z _t) coordinate can represent with worktable coordinate system,

In the ideal situation, described some Q _t(x _t, y _t, z _t) be expressed as Q with worktable coordinate system _w(x _w, y _w, z _w), Q _w(x _w, y _w, z _w) computing method as follows:

[x _w,y _w,z _w,1] ^T＝T ₃₇[x _t,y _t,z _t,1] ^T(1)

T ₃₇＝T ₆₇T ₅₆T ₄₅T ₀₄T ₁₀T ₂₁T ₃₂(2)

In formula, T ₆₇, T ₅₆, T ₄₅, T ₀₄, T ₁₀, T ₂₁, T ₃₂it is desired characteristics matrix;

When exposed to external forces, described some Q _t(x _t, y _t, z _t) change to physical location Q ' _w(x ' _w, y ' _w, z ' _w), Q ' _w(x ' _w, y ' _w, z ' _w) computing method as follows:

[x _w′,y _w′,z _w′,1] ^T＝T′ ₃₇[x _t,y _t,z _t,1] ^T(3)

T′ ₃₇＝T′ ₆₇T′ ₅₆T′ ₄₅T′ ₀₄T′ ₁₀T′ ₂₁T′ ₃₂(4)

Wherein

T′ _ij＝T _ij△T _ij(5)

Q will be put _w(x _w, y _w, z _w) and some Q ' _w(x ' _w, y ' _w, z ' _w) do the quiet distorted pattern that namely difference obtains complete machine tool:

Wherein, △ x=x _w-x ' _w, △ y=y _w-y ' _w, △ z=z _w-z ' _w.

3) force analysis is carried out to each parts of lathe, obtain the stressing conditions of parts, that is, analyze the normal force obtained suffered by lathe bed, column and slide carriage and tangential force;

In order to set up the relation between part distortion and parts stiffness coefficient, need to carry out force analysis to each parts.When lathe end is subject to X, Y, Z tri-direction unit forces respectively, respectively using structural members such as lathe bed, column, slide carriages as research object, set up the respective equation of static equilibrium.Solving equation, can obtain the normal force suffered by structural member such as lathe bed, column, slide carriage and tangential force.

4) funtcional relationship between each part distortion of lathe and each parts Static stiffness of lathe is set up;

Described funtcional relationship is

Wherein, △ is part distortion value, and F is the stressing conditions of each parts of lathe, and k is the Static stiffness of each parts of lathe, thus obtains the funtcional relationship of each part distortion and described parts Static stiffness.

Consider the flexibility of each parts of lathe, be subject to the distortion that two onesize power produce in the position that each parts are adjacent simultaneously, be not equal to the twice that a position is subject to the distortion of same power, therefore add influence coefficients of deformation the funtcional relationship formula between each part distortion of lathe and each parts Static stiffness of lathe is revised, obtain:

Wherein, n is that finger location point is subject to produced distortion and the ratio due to stressed the produced distortion of adjacent position point.

5) the Static stiffness model of complete machine is set up;

Funtcional relationship between each for lathe part distortion and lathe each parts Static stiffness is updated in the middle of the quiet distorted pattern of complete machine, just obtains the funtcional relationship between parts Static stiffness and lathe end Static stiffness, be the Static stiffness model of complete machine;

6) Static stiffness matched design is carried out based on complete machine Static stiffness model, that is:

Using the Static stiffness model of complete machine as equation of constraint, the scope of the Static stiffness of each parts of lathe of the same type calculated by Finite Element Method is as the scope of design of Static stiffness design variable, make that the Z-direction rigidity of machine pillar is maximum is set to objective function, utilize the fmincon quadratic programming function in Matlab software, obtain the Static stiffness size of each parts when known lathe end Static stiffness.

Although be described the preferred embodiments of the present invention by reference to the accompanying drawings above; but the present invention is not limited to above-mentioned embodiment; above-mentioned embodiment is only schematic; be not restrictive; those of ordinary skill in the art is under enlightenment of the present invention; do not departing under the ambit that present inventive concept and claim protect, can also make a lot of form, these all belong within protection scope of the present invention.

Claims (5)

1., towards a complete machine Static stiffness adaptation design method for lathe Top-Down Design, it is characterized in that, comprise the steps:

1) Static stiffness of each parts of lathe at difference place is defined;

2) the quiet distorted pattern of complete machine is set up;

3) force analysis is carried out to each parts of lathe, obtain the stressing conditions of parts, that is, analyze the normal force obtained suffered by lathe bed, column and slide carriage and tangential force;

4) funtcional relationship between each part distortion of lathe and each parts Static stiffness of lathe is set up;

5) the Static stiffness model of complete machine is set up;

Funtcional relationship between each for lathe part distortion and lathe each parts Static stiffness is updated in the middle of the quiet distorted pattern of complete machine, just obtains the funtcional relationship between parts Static stiffness and lathe end Static stiffness, be the Static stiffness model of complete machine;

6) Static stiffness matched design is carried out based on complete machine Static stiffness model, that is:

Using the Static stiffness model of complete machine as equation of constraint, the scope of the Static stiffness of each parts of lathe of the same type calculated by Finite Element Method is as the scope of design of Static stiffness design variable, make that the Z-direction rigidity of machine pillar is maximum is set to objective function, utilize the fmincon quadratic programming function in Matlab software, obtain the Static stiffness size of each parts when known lathe end Static stiffness.

2. a kind of complete machine Static stiffness adaptation design method towards lathe Top-Down Design according to claim 1, it is characterized in that, step 1) in for the Static stiffness of the column of lathe, lathe bed and slide carriage, be the Static stiffness at four the location point places corresponding to four slide blocks selecting them; For the Static stiffness of main shaft, leading screw and worktable, be they are regarded as an entirety, select described entirety to bear the Static stiffness at the location point place of cutting force.

3. a kind of complete machine Static stiffness adaptation design method towards lathe Top-Down Design according to claim 1, is characterized in that, step 2) set up the quiet distorted pattern of complete machine, comprising:

(1) adopt theory of multi body system, complete machine is abstracted into typical body, and represents complete machine relevance with topology diagram;

(2) the desired characteristics matrix T between each typical body of lathe and adjacent body is established _ijwith deformation behaviour matrix Δ T _ij, wherein, i, j ∈ [0,1,2,3,4,5,6,7];

(3) 1 Q in main shaft coordinate system is got _t(x _t, y _t, z _t), by carrying out homogeneous coordinate transformation between adjacent body, described some Q _t(x _t, y _t, z _t) coordinate can represent with worktable coordinate system,

In the ideal situation, described some Q _t(x _t, y _t, z _t) be expressed as Q with worktable coordinate system _w(x _w, y _w, z _w), Q _w(x _w, y _w, z _w) computing method as follows:

[x _w,y _w,z _w,1] ^T＝T ₃₇[x _t,y _t,z _t,1] ^T(1)

T ₃₇＝T ₆₇T ₅₆T ₄₅T ₀₄T ₁₀T ₂₁T ₃₂(2)

In formula, T ₆₇, T ₅₆, T ₄₅, T ₀₄, T ₁₀, T ₂₁, T ₃₂it is desired characteristics matrix;

When exposed to external forces, described some Q _t(x _t, y _t, z _t) change to physical location Q ' _w(x ' _w, y ' _w, z ' _w), Q ' _w(x ' _w, y ' _w, z ' _w) computing method as follows:

[x _w′,y _w′,z _w′,1] ^T＝T′ ₃₇[x _t,y _t,z _t,1] ^T(3)

T′ ₃₇＝T′ ₆₇T′ ₅₆T′ ₄₅T′ ₀₄T′ ₁₀T′ ₂₁T′ ₃₂(4)

Wherein

T′ _ij＝T _ijΔT _ij(5)

Q will be put _w(x _w, y _w, z _w) and some Q ' _w(x ' _w, y ' _w, z ' _w) do the quiet distorted pattern that namely difference obtains complete machine tool:

$\left(\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}y\\ \mathrm{\Δ}z\end{array}\right)=\left(\begin{array}{c}{B}_z{\mathrm{\Δ\β}}_{01}+B_y{\mathrm{\Δ\γ}}_{01}-{\mathrm{\Δx}}_{01}-{\mathrm{\Δx}}_{12}-{\mathrm{\Δx}}_{23}+{\mathrm{\Δx}}_{45}+{\mathrm{\Δx}}_{56}+R_f{\mathrm{\Δ\β}}_{45}+{\mathrm{\Δx}}_{67}+R_c{\mathrm{\Δ\β}}_{04}\\ {\mathrm{\Δy}}_{56}-R_c{\mathrm{\Δ\α}}_{04}-{\mathrm{\Δy}}_{01}-{\mathrm{\Δy}}_{12}-{\mathrm{\Δy}}_{23}-R_f{\mathrm{\Δ\α}}_{45}-B_z{\mathrm{\Δ\α}}_{01}+{\mathrm{\Δy}}_{67}+{\mathrm{\Δy}}_{04}\\ {\mathrm{\Δz}}_{04}+{\mathrm{\Δz}}_{45}-{\mathrm{\Δz}}_{01}-{\mathrm{\Δz}}_{12}-{\mathrm{\Δz}}_{23}-B_y{\mathrm{\Δ\α}}_{01}+{\mathrm{\Δz}}_{67}+{\mathrm{\Δz}}_{56}\end{array}\right)---\left(6\right)$

Wherein, Δ x=x _w-x ' _w, Δ y=y _w-y ' _w, Δ z=z _w-z ' _w;

Δ x _ijbe parts X to distortion, Δ y _ijthe distortion of parts Y-direction, Δ z _ijthe distortion of parts Z-direction, wherein, i, j=0,1,2,3,4,5,6,7;

Δ α _ijthat parts are out of shape around X-axis, Δ β _ijparts are out of shape around Y-axis, wherein, and i=0,4, j=1,4,5;

Δ γ _ijthat parts are out of shape around Z axis, wherein, i=0, j=1;

R _fslide carriage and main shaft Z-direction distance, R _cslide carriage and main shaft Z-direction distance, B _ylathe bed and main shaft Y-direction distance, B _zlathe bed and main shaft Y-direction distance.

4. a kind of complete machine Static stiffness adaptation design method towards lathe Top-Down Design according to claim 1, is characterized in that, step 4) described funtcional relationship is

Wherein, Δ is part distortion value, and F is the stressing conditions of each parts of lathe, and k is the Static stiffness of each parts of lathe, thus obtains the funtcional relationship of each part distortion and described parts Static stiffness.

5. a kind of complete machine Static stiffness adaptation design method towards lathe Top-Down Design according to claim 1, it is characterized in that, step 4) in, consider the flexibility of each parts of lathe, be subject to the distortion that two onesize power produce in the position that each parts are adjacent simultaneously, be not equal to the twice that a position is subject to the distortion of same power, therefore add influence coefficients of deformation the funtcional relationship formula between each part distortion of lathe and each parts Static stiffness of lathe is revised, obtain:

Wherein, n is that finger location point is subject to produced distortion and the ratio due to stressed the produced distortion of adjacent position point.