Modelling thermal deformation of tilting rotary table with direct drive system

Journal of Machine Engineering, Vol. 10, No. 4, 2010 machine tool, tilting rotary table thermal deformation, model Andrzej BŁAŻEJEWSKI1 Wojciech KWAŚNY1 Jerzy JĘDRZEJEWSKI1 Tae-Weon GIM2 MODELLING THERMAL DEFORMATION OF TILTING ROTARY TABLE WITH DIRECT DRIVE SYSTEM Mathematical models representing power losses in tilting rotary tables with a direct drive system (increasingly often used in CNC machine tools) are presented. The process of creating an FEM model for computing the heating up and thermal deformation of tilting rotary tables is described. A simple way of verifying the FEM model on the basis of motor catalogue specifications is provided. Exemplary results of computations and thermal analyses carried out for a tilting rotary table with a synchronized two-sided direct drive system are reported. 1. INTRODUCTION Today multiaxis (five and more numerically controlled axes) machining is used in many branches of industry, particularly the aviation industry and the car industry. Its main advantage is that complicated shapes, undercuts and hard to reach angles can be machined under one workpiece setting. Such machining is possible thanks to five-axis machine tools which instead of a standard table have a tilting rotary table with controlled rotation axes: A, C or B. Typical configurations of machine tools with linear and rotation axes are shown in Fig. 1 [12]. In the case of one-sided drives, power losses on the motor side are greater, which results in the lack of thermal symmetry of the tilting table. Tilting tables with a synchronized two-side drive system have no such drawback. The additional rotation axes increase the flexibility of the machine tool, but at the same time they constitute an additional source of linear and angular errors. The errors are the sum of geometric, kinematic and thermal errors. This paper discusses problems connected with the modelling of the thermal behaviour of a two-axis tilting rotary table with a synchronized two-side drive system during an assumed duty cycle. The main objective was to develop a methodology and a tool based on ___________ 1 2 Institute of Production Engineering and Automation, Wroclaw University of Technology DOOSAN Infracore Corporation, Korea Modelling Thermal Deformation of Tilting Rotary Table with Direct Drive System 27 the finite element method for predicting the heating up and thermal deformation (the phenomena affecting the total machine tool error) of the table’s components. Fig. 1. Configuration of milling centre with rotation axes A, B & C, a) vertical centre, b) horizontal centre [12] 2. TILTING ROTARY TABLE DESIGNS Currently there are two main machine tool tilting rotary table designs, differing in their drive transmission: a worm gear or a synchronized one-sided or two-side drive (Table 1). Owing to their clear advantages, designs with torque motors begin to predominate, especially in new machine tool models. Their major advantages include: high speeds of rotation axes C and A, high accelerations, no clearances, motion fluidity and high positioning precision and speed. The mechanical drive transmission entails difficulties in achieving the rotational speeds and torques required by modern HSC machine tools, and motion errors due to friction in the mechanical gear and to reverse clearance [8]. Other advantages stemming from the use of direct drives (torque motors) are presented in Table 2. Torque motors eliminate the need to use gearboxes, worm gears and other mechanical ways of transmitting drive. They are also characterized by high dynamic response without hysteresis and a large gap (0.5-1.5 mm) between the stator and the rotor, which facilitates assembly. A major feature of the motors are their dimensions, i.e. large outside diameters at a relatively small length. For a diameter of over 2 m the motor’s length may be less than a few tens of mm. Also their inside diameters are equally large since the rotor is a thin ring with permanent magnets (Fig. 2). The use of permanent magnets guarantees high efficiency of the motors. Andrzej BŁAŻEJEWSKI, Wojciech KWAŚNY, Jerzy JĘDRZEJEWSKI, Tae-Weon GIM 28 Table 1. Typical tilting rotary table designs Type of motor Drive transmission Servomotor Worm gear View of tilting rotary table [6] Torque motor One-sided direct drive without support [11] One-sided direct drive with support Synchronized two-sided direct drive [10] [7] Table 2. Comparison of specifications of indirect and direct drive motors [1] Specification Cost (conventional drive = 100%) Mounting/assembly time Position index time Position repeatability Feedback system resolution Stiffness Conventional Mechanical Drive 100% 88 hr. 1 sec 2.5 arc sec 6 7.2x10 Nm/rad Direct Drive 97% 12 hr 0.33 sec 1 arc sec 0.18 arc sec 13x106 Nm/rad Modelling Thermal Deformation of Tilting Rotary Table with Direct Drive System 29 Fig. 2. Direct drive: a) torque motor [1], b) direct drive rotary Table Thanks to the large outside and inside diameter, high torques can be achieved, which is the main advantage of such motors. A model of the thermal behaviour of tilting rotary tables with a direct drive system should comprise (Fig. 3): - models of heat generation in bearings and motors, - a bearing stiffness model, - a cooling model, - a model of rotation and tilting axes operating conditions, - a geometrical model, - an FEM model. Fig. 3. Model of thermal behaviour of tilting rotary tables with direct drive 30 Andrzej BŁAŻEJEWSKI, Wojciech KWAŚNY, Jerzy JĘDRZEJEWSKI, Tae-Weon GIM 3. MODELLING OF THERMAL LOADS 3.1. AXIAL/RADIAL CYLINDRICAL BEARINGS Conventional axial/radial bearings, e.g. of type RTC and YRT, have two rows of rollers transmitting longitudinal forces and one row of rollers transmitting transverse forces (Fig. 4a). An axial/radial cross bearing, e.g. of type RU and SX, has two rows of rollers set perpendicularly to each other in one plane (Fig. 4b). The two varieties of bearings can be mounted in both axis C and axis A of the tilting rotary table. Fig. 4. Axial/radial bearings: a) conventional, b) cross For the modelling of the thermal output of such bearings one can use the total power losses in each of them. The total power losses in a bearing of this type are the sum of the losses in two or three rows of rollers. The bearings should be preloaded during assembly or in the case of cross bearings (class CC0), by the manufacturer. The power losses in the bearings can be calculated from the modified Palmgren formulas [5] or from the following relations: M ⋅n [W ] 9,55 (1) M = ∑ Mo + ∑ M1 (2) N= M o = f o ⋅ 10 −1 ⋅ (ν ⋅ n ) 2/3 M 1 = f 1 ⋅ P ⋅ d m [ Nm] ⋅ d m3 [ Nm] (3) (4) Modelling Thermal Deformation of Tilting Rotary Table with Direct Drive System 31 where: N – bearing power losses, M – the total moment of friction, Mo – the moment of hydrodynamic friction, M1 – the moment of load induced friction, dm – the mean diameter of the bearing [m], n – rotational speed [r (...truncated)