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CN-121980777-A - Five-degree-of-freedom motion error analysis method for crossed ball guide rail workbench

CN121980777ACN 121980777 ACN121980777 ACN 121980777ACN-121980777-A

Abstract

The invention provides a five-degree-of-freedom motion error analysis method for a cross ball guide rail workbench, which comprises the steps of establishing a skin model based on tolerance information and plane characteristic information of parts, obtaining displacement rotation through constraint registration simulation, establishing a jacobian matrix based on an assembly structure, establishing a jacobian skin model by combining rotation information, calculating to obtain pose offset information of left and right guide rails and sliding rails in a guide rail pair, determining the space pose of a guide rail system in a global coordinate system by combining measured raceway shape errors, substituting the spatial pose in the global coordinate system into a cross ball guide rail error model established based on a Hertz contact theory and static balance, obtaining the five-degree-of-freedom motion error of a sliding table through iterative solution, and finally carrying out key error sensitivity analysis by adopting Monte Carlo simulation and a difference method. The method can accurately analyze the error transfer relation from the base to the functional point of the workbench, reveal the influence degree of the tolerance of parts on the motion precision, and provide important reference basis for the design and assembly of the precise workbench.

Inventors

  • LU WENLONG
  • XIE TAO
  • CHANG SUPING
  • ZHOU LIPING

Assignees

  • 华中科技大学

Dates

Publication Date
20260505
Application Date
20260108

Claims (10)

  1. 1. The five-degree-of-freedom motion error analysis method of the cross ball guide rail workbench is characterized by comprising the following steps of: acquiring tolerance information and plane characteristic information of assembled parts, and establishing a skin surface model of the parts; Dividing an internal pair and a kinematic pair according to the matching relation between the parts, and carrying out constraint registration simulation on the corresponding matching skin surface of the internal pair or the kinematic pair to obtain displacement rotation corresponding to the assembly pair; Based on the position information among the characteristics of all parts of the cross ball guide rail workbench assembly, establishing a jacobian matrix related to the ideal positions of the characteristics; establishing a jacobian skin surface model based on jacobian matrix information and corresponding displacement rotation information, and calculating to obtain pose offset of a left guide rail, a right guide rail, a left slide rail and a right slide rail in the crossed ball guide rail pair, wherein the pose offset deviates from an ideal position; acquiring the straightness error information of the raceways of the crossed ball guide rail and the sliding rail through measurement, and combining the pose offset to obtain the space pose offset of the raceways of the guide rail and the sliding rail in a global coordinate system; Establishing a crossed ball guide rail error model based on a Hertz contact theory and a static force balance theory, and calculating five-degree-of-freedom motion errors of the workbench at different stroke positions by combining the space pose offset; and carrying out key error sensitivity analysis based on Monte Carlo simulation and a difference method.
  2. 2. The method of claim 1, wherein the specific manner of creating the skin surface model comprises: Describing the planar characteristics of the parts as basic function superposition of different scales based on discrete cosine transformation, and And adding direction tolerance and position tolerance constraint to the generated skin surface to obtain a horizontal skin surface, an inclined skin surface and a vertical skin surface set meeting tolerance requirements.
  3. 3. The five-degree-of-freedom motion error analysis method of the cross ball guide table according to claim 1, wherein the dividing of the internal pair and the kinematic pair according to the fitting relationship between the components, the registration constraint simulation is performed on the corresponding fitting skin surface of the internal pair or the kinematic pair, to obtain a series of rotations corresponding to the fitting pair, includes: Analyzing an assembly structure of the cross ball guide rail workbench, wherein the assembly structure comprises a sliding table, a guide rail support, a guide rail base and a base; the kinematic pair describes the error transfer relationship of different characteristic surfaces of different parts, and the internal pair describes the error transfer relationship of different characteristic surfaces of the same part; and calculating displacement rotations of the internal pair and the kinematic pair by a point cloud constraint registration method.
  4. 4. The method for analyzing five degrees of freedom motion errors of a cross ball guide table according to claim 1, wherein the establishing method of the jacobian matrix comprises: And establishing a local coordinate system according to the characteristic plane of each part in the assembly body, and generating a corresponding jacobian matrix based on the position information of each local coordinate system relative to the coordinate system of the sliding table.
  5. 5. The method of claim 1, wherein the mathematical expression of the jacobian surface model is constructed based on a product of jacobian matrix and displacement rotations for calculating the functional required pose offsets for the left rail, the right rail, the left rail, and the right rail.
  6. 6. The method for analyzing five-degree-of-freedom motion errors of a cross ball guide table according to claim 1, wherein the cross ball guide table error model is established based on the hertz contact theory and the static force balance theory, and the five-degree-of-freedom motion errors of the table at different travel positions are calculated by combining the spatial pose offset, and the method specifically comprises the following steps: establishing a relation between the sliding rail-guide rail approach quantity of the crossed ball guide rail pair and the load based on the Hertz point-surface contact theory: ; Wherein, the In order to be subjected to normal pressure by the rolling bodies, For the equivalent modulus of elasticity, the elastic modulus, For the radius of the rolling bodies, Is the contact deformation; Taking shape errors of the guide rail and the guide rail roller path into consideration, establishing approaching amounts between guide rail-ball contact points and guide rail-ball contact points which change along with displacement distance y Change relation: ; Wherein, the Indicating the distance of the ith rolling element from the midpoint of the rail, Representing the shape error function of the slide rail, Representing a shape error function of the guide rail; considering that the crossed ball guide pair has a certain pretightening force, the approaching amount change relation between the guide rail-ball contact point and the guide rail-ball contact point can be expressed as: ; Wherein, the Representing the approach amount under the pretightening force; based on the static balance principle, the displacement error of the sliding table on five degrees of freedom is solved through iteration.
  7. 7. The method for analyzing five-degree-of-freedom motion errors of a cross ball guide table according to claim 1, wherein the specific manner of analyzing the key error sensitivity is as follows: aiming at a certain tolerance parameter, setting a plurality of groups of numerical value changes, carrying out Monte Carlo simulation, and calculating an error sensitivity index based on a difference method; The sensitivity index is the ratio of the tolerance variation to the motion error variation.
  8. 8. The method of five degree-of-freedom motion error analysis of a cross ball guide table of claim 1, further comprising: for the multi-feature matched assembly pair, the primary matching surface and the secondary matching surface are combined into a virtual pair, and assembly chain calculation is simplified through constraint registration.
  9. 9. The method of claim 6, wherein the raceway shape error function is expressed in a fourier series to fit periodic geometric errors of the rail surface.
  10. 10. The method of claim 1, wherein the five-degree-of-freedom motion errors include a horizontal straightness error, a vertical straightness error, a yaw error, a roll error, and a pitch error, and parameters having high tolerance sensitivity are preferentially controlled by the error sensitivity analysis.

Description

Five-degree-of-freedom motion error analysis method for crossed ball guide rail workbench Technical Field The invention relates to the technical field of linear motion error analysis, in particular to a five-degree-of-freedom motion error analysis method for a cross ball guide rail workbench. Background Along with the development of semiconductor manufacturing, precise optical measurement technology and biomedicine, higher requirements are put forward on the motion precision of a precise motion platform, and the rolling linear guide rail pair workbench is widely applied to semiconductor manufacturing and detection equipment by virtue of the advantages of small motion resistance, high rigidity, small occupied space and the like. However, in the process of design, manufacture and assembly, non-ideal geometric characteristics and assembly errors of parts can introduce errors, so that the actual motion trail and posture of the rolling linear guide pair workbench deviate from an ideal state, the error transfer relation from a base to the workbench of the rolling linear guide pair workbench is unknown, and multilayer plastic source and compensation work for the motion errors of the workbench cannot be completed, therefore, the modeling work of the assembly error transfer relation of the rolling linear guide pair workbench is developed, and the method has important significance for improving the precision machining and detection of semiconductors. Disclosure of Invention The invention provides a five-degree-of-freedom motion error analysis method for a cross ball guide rail workbench, which aims to solve the problems in the prior art. The five-degree-of-freedom motion error analysis method for the cross ball guide rail workbench comprises the steps of obtaining tolerance information and plane characteristic information of assembled parts and establishing a skin model of the cross ball guide rail workbench, dividing internal pairs and kinematic pairs according to matching relations among the parts, carrying out registration constraint simulation on corresponding matching skin surfaces of the internal pairs or the kinematic pairs to obtain a series of rotations corresponding to the assembled pairs, establishing a series of jacobian matrixes related to ideal positions of the characteristics based on position information of the parts of the cross ball guide rail workbench assembly, establishing jacobian skin surface information based on the jacobian matrix information and the corresponding rotation information, calculating pose offset of left and right guide rail sliding rails in the cross ball guide rail pair, measuring the straightway error information of the cross ball guide rail and the sliding rail by a micrometer, combining the pose offset of the guide rail and the sliding rail, and obtaining the spatial pose information offset of the guide rail and the sliding rail relative to a global coordinate system, establishing an error model of the cross ball guide rail relative to the rolling rail based on Hertz theory and static balance, combining the pose information offset of the position of the cross ball guide rail and the sliding rail, and obtaining critical motion error analysis key error information based on the five-degree-of freedom motion error of the workbench. The specific mode of establishing the skin surface model comprises the steps of describing the plane characteristics of parts as basis function superposition of different scales based on discrete cosine transformation, and adding direction tolerance and position tolerance constraint to the generated skin surface to obtain a horizontal skin surface, an inclined skin surface and a vertical skin surface set meeting tolerance requirements. According to the five-degree-of-freedom motion error analysis method of the crossed ball guide rail workbench, the invention divides the internal pair and the kinematic pair according to the matching relation between the parts, carries out registration constraint simulation on the corresponding matching skin surface of the internal pair or the kinematic pair to obtain a series of rotations corresponding to the assembly pair, and concretely comprises the steps of analyzing the assembly structure of the crossed ball guide rail workbench, and obtaining the assembly of the workbench by a series of parts of a sliding table, a guide rail support, a guide rail base and a base, wherein the assembly comprises a series of internal pairs #、、And (d) sum) Motion pair @、、、、And). A series of rotation information can be obtained through point cloud constraint registration. The invention provides a five-degree-of-freedom motion error analysis method of a cross ball guide rail workbench, which is based on position information among characteristics of parts of an assembly body of the cross ball guide rail workbench, and establishes a series of jacobian matrixes related to ideal positions of the characteristics, and specifically comprises