Derivation of Machine Tool Error Models and Error Compensation Procedure for Three Axes Vertical Machining Center Using Rigid Body Kinematics


Volumetric positional accuracy constitutes a large portion of the total machine tool error during machining. In order to improve machine tool accuracy cost-effectively, machine tool geometric errors as well as thermally induced errors have to be characterized and predicted for error compensation. This paper presents the development of kinematic error models accounting for geometric and thermal errors in the Vertical Machining Center (VMC). The machine tool investigated is a Cincinnati Milacron Sabre 750 3 axes CNC Vertical Machining Center with open architecture controller. Using Rigid Body Kinematics and small angle approximation of the errors, each slide of the three axes vertical machining center is modeled using homogeneous coordinate transformation. by synthesizing the machine's parametric errors such as linear positioning errors, roll, pitch and yaw etc., an expression for the volumetric errors in the multi-axis machine tool is developed. The developed mathematical model is used to calculate and predict the resultant error vector at the tool-workpiece interface for error compensation.


Mechanical and Aerospace Engineering


National Science Foundation (U.S.)

Keywords and Phrases

CNC Machine Tool Accuracy; Error Modeling; Error Prediction and Compensation; Thermal and Geometrical Errors

Document Type

Article - Journal

Document Version


File Type





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