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This paper proposes an efficient actual inverse kinematics method to compensate the geometric errors of five-axis machine tools. The analytical expressions of corrected numerical control (NC) code are derived according to the invertibility, associative law of multiplication, and block calculation of homogenous transformation matrix (HTM). No additional analysis and models are needed for the compensated expressions, appropriate conversion with the geometric error model based on HTM is sufficient. It is simple, convenient and universal for geometric error compensation. The corrected NC code can be obtained through algebraic operation, without time-consuming iteration, differential, or pseudo-inverse algorithm. Then compensation accuracy and efficiency of the method are simulated. And the results indicate higher efficiency compared to existing method. At last, the method is verified by cutting experiment on a five-axis machine tool. Both simulation and experiment results can validate the feasibility of the method. The proposed method significantly improves the computation efficiency and is considered more suitable for real-time compensation. [ABSTRACT FROM AUTHOR]

This paper presents the precision enhancement of five-axis machine tools according to differential motion matrix, including geometric error modeling, identification and compensation. Differential motion matrix describes the relationship between transforming differential changes of coordinate frames. Firstly, differential motion matrix of each axis relative to tool is established based on homogenous transformation matrix of tool relative to each axis. Secondly, the influences of errors of each axis on accuracy of tool are calculated with error vector of each axis. The sum of these influences is integration of error components of machine tool in coordinate system of tool. It endows the error modeling clear physical meaning. Moreover, integrated error components are transformed to coordinate frame of working table for integrated error transformation matrix of machine tools. Thirdly, constructed Jacobian is established using differential motion matrix of each axis without extra calculation to compensate the integrated error components of tool. It makes compensation easy and convenient with reuse of intermediate. Fourthly, six-circle method of ballbar is developed based on differential motion matrix to identify all ten error components of each rotary axis. Finally, the experiments are carried out on SmartCNC500 five-axis machine tool to testify the effectiveness of proposed accuracy enhancement with differential motion matrix. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a general and systematic approach for geometric error modeling of machine tools due to the geometric errors arising from manufacturing and assembly. The approach can be implemented in three steps: (1) development of a linear map between the pose error twist and source errors within machine tool kinematic chains using homogeneous transformation matrix method; (2) formulation of a linear map between the pose error twist and the error intensities of a machine tool; (3) combination of these two models for error separation. The merit of this approach lies in that it enables the source errors affecting the compensatable and uncompensatable pose accuracy of the machine tool to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for the accuracy improvement by suitable measures, i.e. component tolerancing in design, manufacturing and assembly processes, and error compensation. Two typical multi-axis machine tools are taken as examples to illustrate the generality and effectiveness of this approach. [Copyright &y& Elsevier]

Abstract: A unified cutting mechanics model is developed for the prediction of cutting forces in milling, boring, turning and drilling operations with inserted tools. The insert and its orientation on a reference tool body are mathematically modeled by following ISO tool definition standards. The material and cutting edge geometry-dependent friction and normal forces acting on the rake face are transformed into reference tool coordinates using a general transformation matrix. The forces are further transformed into turning, boring, drilling and milling coordinates by simply assigning operation specific parameters. The unified model is validated in cutting experiments. [Copyright &y& Elsevier]

The modelling of volumetric errors of machine tools has been widely used by the method of Homogeneous Transformation Matrix (HTM) based on rigid body kinematics analysis for a long time. Without spindle induced errors and thermal errors, to establish a closed-loop HTM for a three-axis machine tool, the total of 21 geometric errors are the primary elements to be known. It is well known that the measured points of translational errors are directly related to the volumetric error at the tool cutting point through rigid body kinematics. In the generalized HTM method, however, this relationship is missing. This report, therefore, proposes a new comprehensive approach to formulate the volumetric errors based on the famous Abbe principle in order to derive the error term in the motion direction, and Bryan principle to derive the error terms in orthogonal to the motion direction. The proposed methodology is simple in concept, rational in physical meaning and easy in implementation. Experimental results, including faster multi-degree-of-freedom error measurements, volumetric error analysis and compensation on a testbed of small machine tool, validate the correctness and effectiveness of this method. Image 1 • This new method is more physically reasonable than the popular Homogeneous Transformation Matrix method. • An embedded sensor system for detecting 5-DOF geometric errors of a linear stage has been developed and equipped into an investigated small NC machine tool. • Through error measurement and compensation experiments, the correctness and feasibility of this new model have been verified. [ABSTRACT FROM AUTHOR]