Thermal model of the spindle drive structure

Journal of Machine Engineering, Vol. 10, No. 4, 2010 machine tool, spindle unit temperature, thermal deformations, model Zdzisław WINIARSKI1 Zbigniew KOWAL1 Wojciech KWAŚNY1 Jae-Yong HA2 THERMAL MODEL OF THE SPINDLE DRIVE STRUCTURE A computation system dedicated for machine tool spindle drives is presented which integrates a FDM model with a FEM model. Modelling of heat exchange through coolers are discussed, as well as modelling of heat exchange between cooling-lubricating oil and gear transmissions, shafts and headstock walls. In modelling of heat exchange inside headstock, the use of additional elements - type "Fluid" and "Air" - is proposed. Sample modelling results are presented concerning a headstock from a drilling-milling machine tool for machining with high loads and are compared with experimental data. 1. INTRODUCTION Main drives of turning, milling and grinding machine tools, as well as machining centres are usually equipped in synchronous or asynchronous electric motors. Types of drive transmission from a motor to a machine tool spindle can be various. The introduction of a gear box between the motor and spindle allows, in a broad range, adjusting rotational speed and torque on the spindle for the needs of the technological process. While selecting drive parameters it is important to achieve required rotational speed quickly which requires high acceleration and at the same time suitable motor power surplus. In such solutions there is a possibility of the appearance of large radial forces, increased vibrations, noise and other unfavourable phenomena. At required high torques between the motor and the spindle, gear transmissions are applied. At lower torques such transmission is adequately shortened all the way to a direct integration of the motor with the spindle (electrospindle). There are also solutions of main drives with high-torque motors or motors coupled in series in order to increase torque on the spindle. Such solutions are however much more expensive from these described before. The selection of one of ways for transmitting drive will always be a compromise between the required torque value and rotational speed, precision and cost. ___________ 1 2 Institute of Production Engineering and Automation, Wroclaw University of Technology, Wroclaw, Poland DOOSAN Infracore Corporation, Korea 42 Zdzisław WINIARSKI, Zbigniew KOWAL, Wojciech KWAŚNY, Jae-Yong HA Difficulties in modelling main drives rise together with the complexity of their kinematic structure and the need of applying motor, bearing and transmission cooling systems. It also causes the rise of the amount and diversity of generated heat sources, which require proper computation models, as well as the rise of the complexity of modelling forced cooling of particular drive components. The possibility of using commercial FEM programs, such as: Nastran, Ansys, ABAQUS or Simdesigner for CATIA to simulate the behaviour of machine tool structures is limited, because they do not have many required boundary conditions, which enable taking into account significant interactions between the efficiency of internal heat sources and temperatures and deformations of the entire structure. This especially applies to bearing assemblies, gear transmissions, couplings, etc. placed in closed spaces, in which power losses are a relation of temperature with thermal and elastic dimension changes. In such situations, the best results are yielded by dedicated systems. In this paper, a dedicated system, called SATO[6], will be described, which has been elaborated and is still developed at the Wroclaw University of Technology, as well as thermal and elastic phenomena models used in it, enabling the analysis of complex kinematic structures of spindle drives in varying operational conditions and in transient thermal states. 2. DEDICATED SYSTEM SATO FOR THERMO-ELASTIC ANALYSES This system is designated to simulate thermal and static behaviour of machine tools. During its development, various methods were used, such as a Finite Element Method (FEM), Finite Difference Method (FDM), as well as a series of procedures supporting modelling of boundary conditions [5]. This system integrates computations of temperature and displacement distributions with determining power losses in kinematic links of drive systems (Fig. 1.). Such integration ensures high precision of simulations. It is especially important for the spindle assembly, where interactions take place between power losses, temperature and thermal dimensional changes. These can significantly change values of power losses in relation to these defined by simplified mathematical models without such conjugations. Boundary conditions included in the system ensure modelling of thermal and elastic phenomena taking place in the structure, as well as on stationary and mobile links between machine tool units and components. These include: radiation, natural convection and convection forced by the movement of elements, carrying of heat by means of coolant flow, contact conductivity and contact stiffness. Boundary conditions included in the system enable modelling of heat exchange with the environment, as well as in closed spaces inside housings, as it takes place e.g. inside headstock bodies. Internal procedures for computing power losses in subassemblies and kinematic pairs of a machine tool require preparation of input data in the initial (cold) state with help of external procedures. The most complex ones include procedures for ball bearings in the assembled state. Fig. 2 shows an algorithm for determining such input data concerning spindle angular contact bearings taking into consideration contact angle changes in a bearing according to ball bearing theory [2]. Thermal Model of the Spindle Drive Structure 43 Fig. 1. Dedicated SATO system general structure The result of the operation of such algorithm are: after-assembly load of a bearing set Fap or negative after-assembly clearance Lp, after-assembly contact angles αp, as well as resulting interferences or clearances between a bearing and housing W1p and between a bearing and spindle W2p. Fit W1p, W2p take into account not only dimensional deviations of a hole in a housing and spindle pin, but also surface quality expressed as roughness height Rz. Angular contact ball bearings are assembled in sets of two or more bearings, arranged in “X”, “O” arrangements or their combinations. Each of bearings in such set can have different assembly conditions, due to e.g. varying dimensions of a hole in the spindle or dimensions of the external diameter of a housing (Fig. 3). Thermal changes of bearings set node dimensions during operation disrupt the elastic force equilibrium on both sides of a set, taking place in an assembled bearing set, and lead to the establishment of a new equilibrium of axial forces, but on a different level. In special cases it can lead to partial or full unload of bearings. The consequence of such phenome (...truncated)