CN112001052B - Quantitative analysis method for precision design of high-precision multi-axis numerical control machine tool - Google Patents
Quantitative analysis method for precision design of high-precision multi-axis numerical control machine tool Download PDFInfo
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Abstract
The invention relates to a quantitative analysis method for precision design of a high-precision multi-axis numerical control machine tool, which can directly obtain the precision of the whole machine tool according to a given design scheme of the tolerance precision of the machine tool in the novel machine tool innovation design stage and comprises the following steps: analyzing the structural composition of the numerical control machine tool, and determining key parts of key parts closely related to the whole machine precision of the numerical control machine tool; establishing a relation model of the tolerance of key parts of the numerical control machine tool and geometric error source parameters of the numerical control machine tool; establishing a complete machine accuracy analysis model of the numerical control machine; establishing a standard sample processing error space model; the invention is a breakthrough to the traditional precision experience design method, and has important significance to promoting the explosive development of the innovative design of the multi-axis numerical control machine tool in China, thoroughly getting rid of the constraint of the precision experience design method, promoting the spanned development of the precision design level of the multi-axis numerical control machine tool in China and reaching the leading level in the world.
Description
Technical Field
The invention relates to the technical field of precision design of numerical control machine tools, in particular to a quantitative analysis method for precision design of a high-precision multi-axis numerical control machine tool.
Background
In the modern machinery manufacturing industry, the multi-axis numerical control machine tool can be used as a 'working machine tool' to realize multi-process and multi-surface compound processing, is widely applied to important industries such as aerospace, automobiles, ships, energy sources and the like, and the development level is an important mark for measuring the development level and the product quality of the national equipment manufacturing industry.
At present, although related research work is performed on the precision design of machine tools, the method mainly depends on a traditional experience precision design method. When developing a novel high-precision numerical control machine tool, a design engineer firstly determines required tolerance for each part of the machine tool according to the overall design scheme of the whole machine tool and the structure of the part, and then uses methods of continuous modification of foreign drawings, comparison with similar machine tools, past design experience and the like.
However, the precision design based on experience has a certain design blindness, which is easy to cause the problems of long design period and high cost, even causes the problems of extremely high tolerance precision requirement and extremely high manufacturing cost of machine tool parts, and finally the precision of the whole machine tool cannot be ensured, and the accumulation of design experience is seriously lacked in developed countries because the numerical control machine tool in China is a development way for introducing, digesting and absorbing.
Therefore, the traditional precision experience design method is not particularly suitable for China, severely restricts the innovative development of novel high-precision numerical control machine tools in China, and is also a main reason that the numerical control machine tools which are self-developed in China cannot guarantee that all varieties have high precision.
On the basis, the invention provides a quantitative analysis method for the precision design of the high-precision multi-axis numerical control machine tool.
Disclosure of Invention
Aiming at the situation, in order to overcome the defects of the prior art, the invention provides a quantitative analysis method for the precision design of a high-precision multi-axis numerical control machine tool.
The quantitative analysis method for the precision design of the high-precision multi-axis numerical control machine tool is characterized by comprising the following steps of:
analyzing the structural composition of a numerical control machine tool, and determining key parts of key parts closely related to the whole machine precision of the numerical control machine tool;
step two, establishing a relation model of the tolerance of key parts of the numerical control machine tool and geometric error source parameters of the numerical control machine tool;
step three, establishing a complete machine precision analysis model of the numerical control machine;
step four, establishing a standard sample processing error space model;
and fifthly, selecting and optimizing a precision design scheme of the numerical control machine tool.
Preferably, the specific steps in the second step are as follows:
firstly, establishing a relation model of the tolerance of key parts of a numerical control machine tool and the surface morphology errors of the key parts after the key parts are processed;
secondly, collecting critical part tolerance of a critical part and surface morphology error detection data after processing the critical part, establishing a relation model of the part tolerance and the surface morphology error of the part by using the combination of a monotonic function and a Fourier series cut-off function according to the concept of the part tolerance and the real law of the motion error of the part and by using the actual data obtained in the production, and determining the Fourier series cut-off order in the model by comparing the relation model with the actually measured data;
and finally, deducing the relation between the surface appearance errors of the parts and the corresponding geometric error source parameters of the numerical control machine according to the assembly relation of each part of the numerical control machine, thereby indirectly establishing a relation model of the tolerance of key parts of the numerical control machine and the geometric error source parameters of the numerical control machine.
Preferably, the specific steps in the third step are as follows:
1) According to the structural composition of the numerical control machine tool, decomposing the numerical control machine tool into a multi-body system consisting of a plurality of bodies;
2) According to the theory of the motion of the multi-body system, under the condition of considering errors, any point in any body K in the multi-body system can be obtainedThe position matrix in the inertial coordinate system is:
wherein: [ SSV ]]＝[SSV] p [SSV] pe [SSV] s [SSV] se ；
V＝L t (K),S＝L t (V),L 0 (K)＝K，L u (K) =1, u, t is a natural number;
[SSV] p -an ideal transformation matrix of the relative position of the volume V with respect to the volume S;
[SSV] pe -a relative position error transformation matrix of volume V with respect to volume S;
[SSV] s -the relative motion of the volume V with respect to the volume S is an ideal transformation matrix;
[SSV] se -a relative motion error transformation matrix of volume V with respect to volume S;
p v -coordinates of the origin of coordinates of the volume V in an inertial coordinate system;
p ve -an error vector of the actual position of the body V with respect to the ideal position;
s v -displacement vector of body V;
s ve -displacement error vector of body V;
3) Deducing a pose error matrix of the center of a machine tool cutter in a workpiece coordinate system;
in general, a numerical control machine has two branches, one from the machine bed to the spindle tool and one from the machine bed to the workpiece coordinate system, the tool center point in the tool coordinate systemThe position matrix to the machine tool body coordinate system is as follows:
wherein V is the t-th low-order sequence number of the cutter M, S is the low-order sequence number of the V, L u (M)＝0，
At the same time, unit vectors along the arbor direction in the tool coordinate systemThe projection in the machine tool body coordinate system is:
similarly, the ideal center of the tool at the point to be processed can be obtained in the coordinate system of the workpieceNormal vector of workpiece surface->The position matrix and projection in the machine coordinate system are respectively:
the numerical control machine tool space tool position error and attitude error can be expressed as:
E P ＝P T -P W ；
E n ＝N T -N W ；
for this purpose, a tool center position error matrix of the machine tool in the workpiece coordinate system is determined:
4) Substituting the relation mode established in the second step into a numerical control machine tool center pose error matrix in a workpiece coordinate system, and establishing an internal relation analysis model of the numerical control machine tool part tolerance and the numerical control machine tool overall accuracy.
Preferably, in the fourth step:
generating a cutter processing path based on the processed standard sample model; then calculating the machining tool path of the standard sample piece according to the position of the tool center point in the tool path and the tool shaft vector; and finally substituting the processing tool path into the analysis model in the third step, so as to establish a standard sample processing error space model.
Preferably, in the fifth step:
firstly, randomly giving a design scheme of the tolerance of a numerical control machine tool part, and using a standard sample processing error space model in the fourth step, if the requirement of the standard sample processing precision is not met, re-executing the processes in the second to fourth steps until the standard sample processing precision meets the requirement, so as to obtain a machine tool precision design scheme of initial screening;
and then sorting the precision design schemes affecting the machining precision of the standard sample according to the initially selected machine tool precision design scheme, and selecting a final machine tool precision design scheme according to the sorting result.
The invention enables engineers to quantitatively analyze the whole machine precision of the machine tool by setting the tolerance parameters of the parts in the innovative design stage of the machine tool, and can also obtain the optimized value of the tolerance parameters of each part of the machine tool by taking the whole machine precision of the machine tool as a target, thereby rapidly improving and adjusting the whole machine precision of the machine tool, and guiding the real precision design of the novel high-precision numerical control machine tool.
The invention is a breakthrough to the traditional precision experience design method, has important significance for promoting the vigorous development of the innovative design of the multi-axis numerical control machine tool in China, thoroughly getting rid of the constraint of the precision experience design method, promoting the spanned development of the precision design level of the multi-axis numerical control machine tool in China and reaching the leading level of the world.
The machine tool developed by the invention has reliable whole machine precision, so that the indirect social and economic values brought by the machine tool in the production and the subsequent use are difficult to estimate.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a diagram of the five-axis numerical control machine tool of the present invention.
Fig. 3 is a diagram of a motion chain of the multi-body system of the present invention.
Fig. 4 is a tolerance parameter input interface of key parts of the five-axis numerical control machine tool of the invention.
Fig. 5 shows the X-axis straightness error and the C-axis tilt error of the present invention.
Fig. 6 is a topological structure diagram of the present invention.
FIG. 7 is a drawing of a master part tooling part of the present invention.
Fig. 8 is a tool path of the present invention.
Fig. 9 is a graph of error values at the sample processing point of the present invention.
FIG. 10 is a graph comparing the results of the precision design of the present invention.
Detailed Description
The foregoing and other features, aspects and advantages of the present invention will become more apparent from the following detailed description of embodiments, which proceeds with reference to fig. 1-10. The following embodiments are described in detail with reference to the drawings.
Exemplary embodiments of the present invention will be described below with reference to the accompanying drawings.
A quantitative analysis method for precision design of a high-precision multi-axis numerical control machine tool comprises the following steps:
analyzing the structural composition of the numerical control machine tool, and determining key parts of key parts closely related to the whole machine precision of the machine tool.
And step two, establishing a relation model of the tolerance of key parts of the numerical control machine tool and geometric error source parameters of the numerical control machine tool.
Firstly, establishing a relation model of the tolerance of key parts of the numerical control machine tool and the surface morphology errors after the machining of the key parts.
And secondly, collecting the critical part tolerance of the critical part and the surface topography error detection data after processing, utilizing the actual data obtained in the production according to the concept of the part tolerance and the actual rule of the part motion error, establishing a relation model of the part tolerance and the surface topography error by utilizing the combination of a monotonic function and a Fourier series cut-off function, and determining the Fourier series cut-off order in the model by comparing the relation model with the actually measured data.
And finally, deducing the relation between the surface appearance errors of the parts and the corresponding geometric error source parameters of the numerical control machine according to the assembly relation of each part of the numerical control machine, thereby indirectly establishing a relation model of the tolerance of key parts of the numerical control machine and the geometric error source parameters of the numerical control machine.
And thirdly, establishing a complete machine accuracy analysis model of the numerical control machine tool.
1) And decomposing the numerical control machine into a multi-body system consisting of a plurality of bodies according to the structural composition of the numerical control machine.
2) According to the theory of motion of a multi-body systemIn theory, under the condition of considering errors, any point in any volume K in the multi-volume system can be obtainedThe position matrix in the inertial coordinate system is:
wherein: [ SSV ]]＝[SSV] p [SSV] pe [SSV] s [SSV] se ；
V＝L t (K),S＝L t (V),L 0 (K)＝K,L u (K) =1, u, t is a natural number;
[SSV] p -an ideal transformation matrix of the relative position of the volume V with respect to the volume S;
[SSV] pe -a relative position error transformation matrix of volume V with respect to volume S;
[SSV] s -the relative motion of the volume V with respect to the volume S is an ideal transformation matrix;
[SSV] se -a relative motion error transformation matrix of volume V with respect to volume S;
p v -coordinates of the origin of coordinates of the volume V in an inertial coordinate system;
p ve -an error vector of the actual position of the body V with respect to the ideal position;
s v -displacement vector of body V;
s ve -displacement error vector of body V.
3) Deducing a pose error matrix of the center of a machine tool cutter in a workpiece coordinate system;
generally, a numerical control machine has two branches, one from the machine bed to the spindle tool and one from the machine bed to the workpiece coordinate system. Tool center point in tool coordinate systemThe position matrix to the machine tool body coordinate system is as follows:
wherein V is the t-th low-order sequence number of the cutter M, S is the low-order sequence number of the V, L u (M)＝0。
At the same time, unit vectors along the arbor direction in the tool coordinate systemThe projection in the machine tool body coordinate system is:
similarly, the ideal center of the tool at the point to be processed can be obtained in the coordinate system of the workpieceNormal vector of workpiece surface->The position matrix and projection in the machine coordinate system are respectively:
the numerical control machine tool space tool position error and attitude error can be expressed as:
E P ＝P T -P W
E n ＝N T -N W
for this purpose, a tool center position error matrix of the machine tool in the workpiece coordinate system is determined:
4) Substituting the relation model established in the second step into a machine tool center pose error matrix in a workpiece coordinate system, and establishing an internal relation analysis model of machine tool part tolerance and numerical control machine tool complete machine precision.
And step four, establishing a standard sample processing error space model.
Generating a cutter processing path based on the processed standard sample model; then calculating the machining tool path of the standard sample piece according to the position of the tool center point in the tool path and the tool shaft vector; and finally substituting the processing tool path into the analysis model in the third step, so as to establish a standard sample processing error space model.
And fifthly, selecting and optimizing a precision design scheme of the numerical control machine tool.
Firstly, randomly giving a design scheme of the tolerance of the numerical control machine tool parts, and if the machining error space model of the standard sample in the fourth step does not meet the machining precision requirement of the standard sample, re-executing the processes in the second to fourth steps until the machining precision of the standard sample meets the requirement, thereby obtaining the machine tool precision design scheme of initial screening.
And then sorting the precision design schemes affecting the machining precision of the standard sample according to the initially selected machine tool precision design scheme, and selecting a final machine tool precision design scheme according to the sorting result.
The following describes the specific procedure of the above method in connection with a specific example:
a quantitative analysis method for precision design of a high-precision multi-axis numerical control machine tool is shown in figure 1. For a five-axis AC double-swing gantry numerical control milling machine, as shown in fig. 2, the following steps are used for description:
step one, as shown in fig. 2 and 3, the five-axis AC double-swing gantry numerical control milling machine mainly comprises a workbench, a cross beam (X axis), a saddle (Y axis), a ram (Z axis), a rotary swing head (C axis), a rotary swing head (a axis), a cutter and a workpiece. Critical parts and parts, which are closely related to the whole machine precision of the numerical control machine, are as follows: screw rods and guide rail pairs of all translation parts; bearing holes in front and back of the case of the rotating member, bearing support parts in front and back of the rotating shaft, and the like. The kinematic chain of the numerical control machine tool is decomposed into two branched chains consisting of a plurality of rigid bodies: workpiece branches and tool branches, in each of which every two adjacent bodies are connected to each other.
And step two, according to fig. 4 and 5, randomly giving tolerance parameters of key parts of the machine tool, and obtaining error source parameters of the machine tool.
The machine tool error source parameters which are irrelevant to the position are not changed along with the change of the movement position of the machine tool, and the errors are direct reflection of tolerances, such as non-perpendicularity errors of a Y axis and an X axis, and are direct reflection of non-perpendicularity tolerances. Whereas position-dependent machine tool error source parameters, such as rail surface topography errors of the translation axis, can be fitted to the variation of the error curve by a first order fourier series; and then acquiring error source parameters of the machine tool based on the tolerance according to the assembly relation of the guide rail pair of the machine tool.
Step three, as shown in fig. 6, calculating a machine tool center pose error matrix in a workpiece coordinate system:
wherein (x, y, z, C, A) is the tool path.
Step four, as shown in fig. 7 and 8, a tool path is generated according to the machined part diagram of the standard sample cone frustum, and the tool path is calculated.
Referring to fig. 7 and 8, the actual position vector of the center point of the tool in the workpiece coordinate system is calculated according to the installation position of the cone frustum:
wherein, gamma is the rotation angle of the cone frustum in an inertial coordinate system.
Then, calculating a truncated cone machining error vector:
in the formula (P) wx P wy P wz ) T The position coordinates of the conical frustum processing point in the workpiece coordinate system.
As shown in fig. 9, the machining error value at the position of the truncated cone to be machined is calculated from the machining error vector of the truncated cone.
And fifthly, as shown in fig. 7, 9 and 10, calculating the roundness, coaxiality and inclination of the position to be machined according to the machining error value of the position to be machined of the cone frustum, comparing the roundness, coaxiality and inclination with standard precision requirements, and meeting the precision requirements, so that the tolerance precision design scheme of the machine tool is feasible.
The invention enables engineers to quantitatively analyze the whole machine precision of the machine tool by setting the tolerance parameters of the parts in the innovative design stage of the machine tool, and can also obtain the optimized value of the tolerance parameters of each part of the machine tool by taking the whole machine precision of the machine tool as a target, thereby rapidly improving and adjusting the whole machine precision of the machine tool, and guiding the real precision design of the novel high-precision numerical control machine tool.
The invention is a breakthrough to the traditional precision experience design method, has important significance for promoting the vigorous development of the innovative design of the multi-axis numerical control machine tool in China, thoroughly getting rid of the constraint of the precision experience design method, promoting the spanned development of the precision design level of the multi-axis numerical control machine tool in China and reaching the leading level of the world.
The machine tool developed by the invention has reliable whole machine precision, so that the indirect social and economic values brought by the machine tool in the production and the subsequent use are difficult to estimate.
Claims (1)
1. The quantitative analysis method for the precision design of the high-precision multi-axis numerical control machine tool is characterized by comprising the following steps of:
analyzing the structural composition of a numerical control machine tool, and determining key parts of key parts closely related to the whole machine precision of the numerical control machine tool;
step two, establishing a relation model of the tolerance of key parts of the numerical control machine tool and geometric error source parameters of the numerical control machine tool;
step three, establishing a complete machine precision analysis model of the numerical control machine;
step four, establishing a standard sample processing error space model;
step five, selecting and optimizing a precision design scheme of the numerical control machine tool;
the specific steps in the second step are as follows:
firstly, establishing a relation model of the tolerance of key parts of a numerical control machine tool and the surface morphology errors of the key parts after the key parts are processed;
secondly, collecting critical part tolerance of a critical part and surface morphology error detection data after processing the critical part, establishing a relation model of the part tolerance and the surface morphology error of the part by using the combination of a monotonic function and a Fourier series cut-off function according to the concept of the part tolerance and the real law of the motion error of the part and by using the actual data obtained in the production, and determining the Fourier series cut-off order in the model by comparing the relation model with the actually measured data;
finally, deducing the relation between the surface morphology errors of the parts and the corresponding geometric error source parameters of the numerical control machine according to the assembly relation of each part of the numerical control machine, thereby indirectly establishing a relation model of the tolerance of key parts of the numerical control machine and the geometric error source parameters of the numerical control machine;
the specific steps in the third step are as follows:
1) According to the structural composition of the numerical control machine tool, decomposing the numerical control machine tool into a multi-body system consisting of a plurality of bodies;
2) According to the theory of the motion of the multi-body system, under the condition of considering errors, any point in any body K in the multi-body system can be obtainedThe position matrix in the inertial coordinate system is:
wherein: [ SSV ]]＝[SSV] p [SSV] pe [SSV] s [SSV] se ；
V＝L t (K),S＝L t (V),L 0 (K)＝K,L u (K) =1, u, t is a natural number;
[SSV] p -an ideal transformation matrix of the relative position of the volume V with respect to the volume S;
[SSV] pe -a relative position error transformation matrix of volume V with respect to volume S;
[SSV] s -the relative motion of the volume V with respect to the volume S is an ideal transformation matrix;
[SSV] se -a relative motion error transformation matrix of volume V with respect to volume S;
p v -coordinates of the origin of coordinates of the volume V in an inertial coordinate system;
p ve -an error vector of the actual position of the body V with respect to the ideal position;
s v -displacement vector of body V;
s ve -displacement error vector of body V;
3) Deducing a pose error matrix of the center of a machine tool cutter in a workpiece coordinate system;
in general, a numerical control machine has two branches, one from the machine bed to the spindle tool and one from the machine bed to the workpiece coordinate system, the tool center point in the tool coordinate systemThe position matrix to the machine tool body coordinate system is as follows:
wherein V is the t-th low-order sequence number of the cutter M, S is the low-order sequence number of the V, L u (M)＝0，
At the same time, unit vectors along the arbor direction in the tool coordinate systemThe projection in the machine tool body coordinate system is:
similarly, the ideal center of the tool at the point to be processed can be obtained in the coordinate system of the workpieceNormal vector of workpiece surface->The position matrix and projection in the machine coordinate system are respectively:
the numerical control machine tool space tool position error and attitude error can be expressed as:
E P ＝P T -P W ；
E n ＝N T -N W ；
for this purpose, a tool center position error matrix of the machine tool in the workpiece coordinate system is determined:
4) Substituting the relation mode established in the second step into a numerical control machine tool center pose error matrix in a workpiece coordinate system, and establishing an internal relation analysis model of the numerical control machine tool part tolerance and the numerical control machine tool overall accuracy;
in the fourth step:
generating a cutter processing path based on the processed standard sample model; then calculating the machining tool path of the standard sample piece according to the position of the tool center point in the tool path and the tool shaft vector; finally substituting the processing tool path into the analysis model of the third step, thereby establishing a standard sample processing error space model;
in the fifth step:
firstly, randomly giving a design scheme of the tolerance of a numerical control machine tool part, and using a standard sample processing error space model in the fourth step, if the requirement of the standard sample processing precision is not met, re-executing the processes in the second to fourth steps until the standard sample processing precision meets the requirement, so as to obtain a machine tool precision design scheme of initial screening;
and then sorting the precision design schemes affecting the machining precision of the standard sample according to the initially selected machine tool precision design scheme, and selecting a final machine tool precision design scheme according to the sorting result.
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| 陶浩浩 ; 范晋伟 ; 邬昌军.一种基于公差的机床导轨几何误差预测方法.工程科学与技术.2020,235-242. * |
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