Kinematic errors prediction for multi-axis machine tools’ guideways based on tolerance

Fan, Jinwei; Tao, Haohao; Wu, Changjun; Pan, Ri; Tang, Yuhang; Li, Zhongsheng

doi:10.1007/s00170-018-2335-9

Cited by 42 publications

(18 citation statements)

References 30 publications

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“…Fan et al proposed a kinematic errors prediction method for the machine tool's guideways based on tolerance by formulating the relationship between tolerance and geometric profile errors of guideways on the machine tools. This method is convenient for engineers to derive the distribution of kinematic errors in their design [22] The issue now is if we can consider the actual situation and use new ideas or theories to analyze and discuss the motion errors of the stage. During the research and development of parallel coordinate measuring machines, we found that many parallel mechanisms only have numerical solutions and cannot obtain analytical solutions.…”

Section: New Idea About Analysis Of Linear Motion Errormentioning

confidence: 99%

Analysis of Motion Errors of Linear Guide Pair Based on Parallel Mechanism

Lei

2021

Machines

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This paper systematically summarized the technical state of art and research results on the motion error of a linear guideway, corrected some misconceptions, and further clarified the relationship between the straightness error of the guide rail itself and the motion error of the linear stage. Moreover, a new method based on parallel mechanism is provided to study the motion errors of the linear guide pair. The basic idea is to abstract the structural relationship between the stage and the guide rail into a 4-bar parallel mechanism. Thus, the stage can be considered as a moving platform in the parallel mechanism. Its motion error analysis is also transferred to moving platform position analysis in the parallel mechanism. The straightness motion error and angular motion error of the stage can be analyzed simultaneously by using the theory of parallel mechanism. Some experiments were conducted on the linear guideway of a self-developed parallel coordinate measuring machine. The experimental data and analysis verify the feasibility and correctness of this method.

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Section: New Idea About Analysis Of Linear Motion Errormentioning

confidence: 99%

Analysis of Motion Errors of Linear Guide Pair Based on Parallel Mechanism

Lei

2021

Machines

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“…The verticality error is the deviation between the actual position and the ideal position of the axis of motion, and its magnitude is the difference between the actual angle between two adjacent axes and 90°. As the rotation axis rotates around the axis, its position will also affect the accuracy, and the position deviation of the rotation axis is the deviation between the actual rotation axis and the ideal axis, which is the position deviation [20][21][22][23]. Take axis B…”

Section: MMmentioning

confidence: 99%

Research on Geometric Error Modeling and Compensation Method of CNC Precision Cylindrical Grinder Based on Differential Motion Matrix and Jacobian Matrix

Fan¹,

Ye²

2021

Preprint

Self Cite

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In this paper, the geometric error modeling method of CNC cylindrical grinder based on the differential motion relationship between coordinate systems, the function fitting model method of basic geometric error terms based on cftool toolbox and the error compensation method based on Jacobian matrix are proposed. Firstly, the differential motion theory, which is widely used in the field of robot kinematics error modeling, is used to build the machine tool space machining error model of CNC cylindrical grinder. Different from the multi-body theory, this modeling method can clearly reflect the influence degree of each moving part on the grinding wheel cutter. Secondly, SJ6000 laser interferometer was used to measure and identify the geometric error terms of B2-K3032 CNC precision cylindrical grinder. MATLAB cftool toolbox was used to perform mathematical function fitting on the known error data, and the mathematical relationship between 24 geometric errors and machining instructions was found. Finally, combining with the 24 Sum of Sine function model, the known verticality error and position deviation, the differential motion matrix of each moving part in the tool coordinate system and the corresponding Jacobian matrix, the compensation quantity (dx dz db dc) of the comprehensive geometric error in the tool coordinate system by the CNC precision cylindrical grinder is obtained. In order to verify the feasibility of the above method, RA1000 series roundness meter was used to measure the radial circular runout error before and after the correction. The experimental results show that the precision of each shaft section is increased by 17.54%, 15.22%, 15.71%, 18.4%, 12.87%, respectively, and the average machining accuracy is increased by 15.948%. Therefore, the above methods are effective and reasonable for improving the precision of spindle workpieces, and can also be used for reference in the initial design stage of CNC cylindrical grinder manufacturing enterprises or improving the machining accuracy of existing machine tools.

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“…Different from Rameau et al [20], the three-step algorithm is intended for the evaluation of static structures (interpreted as overconstrained mechanisms). Fan et al [22] present a kinematic calibration of a multiaxis machine tool based on geometric errors of the guideways. The calibration performed mapping measured kinematic errors to the geometric profile of the guideways.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…The sensitivity analysis was used as a tolerance design tool by means of nonlinear constrained optimization. Common to Rameau et al [20], Zhao et al [21], Fan et al [22], and Ni et al [23] is the use of tolerance analysis as a keystone in the design process of mechanisms and machines with required performance (to guarantee mobility and assembly and to minimize positioning errors in machine tools and parallel robots).…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Tolerance Analysis of Planar Mechanisms Based on a Residual Approach: A Complementary Method to DLM

Tinoco

Durango

2019

Mathematical Problems in Engineering

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The kinematic performance of mechanisms is affected by different uncertainty sources involved in the manufacturing and assembling cycle; among these are the geometric variations. It is known that the effects of these variations produce position errors which are not usually included in the design process. With this objective, a complementary method for the tolerance analysis of planar mechanisms that incorporate geometric variations is presented in this paper. The approach is based on Direct Linearization Method (DLM) that does not consider all the kinematically admissible solutions. DLM naturally minimizes a residual functional ; however it is possible to maximize the residual by means of a proposed complementary method called H-Based Residual Method (RMH). From the proposed methodology, local and global error domains can be defined to predict the maximum and minimum position errors caused by the input variations. DLM and RMH were applied in a four-bar mechanism with dimensional and angular variations to estimate positioning errors. The results show intervals where output positions were invariant with respect to angular variations of the crank. These computations were performed through a distance ratio established with the output deviations determined with nominal angular variations. Furthermore, domain errors were predicted for a set of positions generated by a multivariate normal random algorithm with 1000 combinations of input variations (links lengths). These domains delimited all solutions created in each position stage. It means that by applying the proposed methodology it is possible to estimate the geometric errors of any combination of variations.

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Kinematic errors prediction for multi-axis machine tools’ guideways based on tolerance

Cited by 42 publications

References 30 publications

Analysis of Motion Errors of Linear Guide Pair Based on Parallel Mechanism

Analysis of Motion Errors of Linear Guide Pair Based on Parallel Mechanism

Research on Geometric Error Modeling and Compensation Method of CNC Precision Cylindrical Grinder Based on Differential Motion Matrix and Jacobian Matrix

Tolerance Analysis of Planar Mechanisms Based on a Residual Approach: A Complementary Method to DLM

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