Mathematical Model of a CNC Rotary Table Driven by a Worm Gear

This paper proposes a mathematical model of a CNC rotary table driven by a worm gear. The CNC rotary tables are generally utilized as rotary axes of 5-axis machining centres. In this study, a mathematical model which can simulate dynamic behaviours of rotary table is proposed. The model consists of inertia of motor, spur and worm gears, and table. Axial displacement of the worm is also considered into the model. Various motions are measured and simulated to confirm effectiveness of the model. As the results show, the proposed model can simulate step response, rotational fluctuations, and influence of unbalanced mass. DOI: 10.4018/ijimr.2012100103 28 International Journal of Intelligent Mechatronics and Robotics, 2(4), 27-40, October-December 2012 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Saito (2003, 2004) proposed identification and compensation method for geometric errors of rotary axes in 5-axis machining centers. The method can identify the geometric errors, such as location and angular deviations of rotary axes rotational center using a ball-bar system. The method also can be applied to other types machine tools (Dassanayake et al., 2006, 2011). Bringmann and Knapp (2006) also proposed a calibration method for geometrical errors of rotary axes using R-test (Weikert, 2004). R-test is also applied to produce error maps of the rotary axes (Ibaraki et al., 2011). On the other hand, it had already been investigated that the dynamic behaviour of controlled axes is also an important factor to achieve higher performance in such machines (Tsutsumi et al., 2007; Sato & Tsutsumi, 2011). From this point of view, various research studies on the modelling and analysis for feed drive systems of linear axes were conducted (Ebrahimi & Whalley, 2000; Erkorkmaz & Altintas, 2001; Sato & Tsutsumi, 2005; Sato, 2011). On the rotary axes, however, the dynamic behaviours of the driving mechanism have not sufficiently investigated. Although, Zirn (2008) described modelling methods for machine manipulators including rotary axes, and Dassanayake et al. (2008, 2009) investigated the motion characteristics of the rotary axes. In this study, a mathematical model of a rotary table driven by a worm gear is proposed. Worm gear is one of the main mechanisms adopted for the rotary axes of 5-axis machine tools, because of its irreversibility and costs. Parameter identification method and effectiveness of the proposed model will be shown by comparing the measured and simulated results of various motions. Influence of unbalanced mass is also discussed in causes where the mechanism is utilized for the tilting axis.