Unified error model based spatial error compensation for four types of CNC machining center: Part I—Singular function based unified error model

• HTM-based comprehensive error models for four types of CNC machining were established.
• The regularity of the HTM for four types of CNC machining center was found in this paper.
• A unified error model for four types of CNC machining center was established.

To unify the error model for four types of CNC machining center, the comprehensive error model of each type of CNC machining center was established using the homogenous transformation matrix (HTM). The internal rules between the HTMs and the kinematic chains were analyzed in this research. The analysis results show that the HTM elements associated with the motion axes which are at the rear of the reference coordinate system are positive value. On the contrary, the HTM elements associated with the motion axes which are at the front of the reference coordinate system are negative value. To express these internal rules, the singular function was introduced to the HTMs. And a unified error model for four types of CNC machining center was established based on the HTM and the singular function. The unified error model includes 18 error elements which are the main factors affecting the machining accuracy of CNC machine tools. The practical results show that the unified error model is not only suitable for vertical machining center but also suitable for horizontal machining center.