Experimental and analytical evaluation of tool path error using computer integrated nonlinear kinematical modeling for a 4DOF parallel milling machine

ABSTRACT

Machining errors in parallel kinematic machines primarily depend on their extent of kinematic nonlinearity. In this paper, a computer integrated model of the kinematic nonlinearity and trajectory interpolation method for a 4DOF parallel milling machine is developed. The nonlinear errors prompted during various trajectory modes are analyzed. It is proved that in order to avoid significant non-linearity, the actuator and the end-effector space must possess identical order of trajectory. The effects of tool path length, its spatial location, and the Jacobian matrix properties on the kinematic nonlinearity error, are studied. Results showed that the path length is the governing factor for the nonlinear behavior of the mechanism. Moreover, the kinematic error is illustrated to have a reverse relationship with maximum singular values of the inverse Jacobian matrix. Experiments are conducted using digital dial indicators. Experimental results verified the accuracy of the proposed mathematical approach and confirmed its applicability in actual machining processes. Moreover, the proposed interpolation algorithm successfully limits the kinematic error under the machining tolerance by minimal segmentation. Finally, it is demonstrated that the proposed method is superior in terms of accuracy, to the median osculating circle (MOC) method.

KEYWORDS:

• Precision machining
• kinematic nonlinearity
• trajectory generation
• parallel mechanism
• Jacobian matrix
• forward kinematics

Disclosure of potential conflicts of interest

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.