Prediction of Thermal Deflection at Spindle Nose-tool Holder Interface in HSM

Transcription

1 Prediction of Thermal Deflection at Spindle Nose-tool Holder Interface in HSM V Prabhu Raja, J Kanchana, K Ramachandra, P Radhakrishnan PSG College of Technology, Coimbatore Abstract Loss of machining accuracy is a major problem in machine tool spindles under high speed machining (HSM) conditions due to thermal deflections of the spindle nose. Frictional losses in the spindle bearings which contribute for the temperature rise and hence thermal deflection of the spindle nose are estimated. A 2-D axisymmetric finite element model of high speed spindle assembly is developed using ANSYS to determine the temperature distribution considering oil-mist lubricated bearings. Spindle nose thermal deflection is determined by performing a sequential thermal-structural coupled field analysis. The effects of spindle speed and cooling on the spindle nose deflection are investigated so as to minimize the same. The effect of conduction through tool holder on spindle nose deflection is also investigated. Introduction: The introduction of new cutting tool materials with improved cutting properties and of new manufacturing processes has made it necessary to raise the speed of spindle assemblies and the power of drives. The majority of high speed machine tools employ rolling element bearing spindles. The heat generated by spindle bearings heats the bearings, structural components in which they are mounted and the spindle, all of which have a significant influence on both the work capability of the spindle assembly and on the machining accuracy (Segida.A.P, 1984). When predicting the quality and parametric reliability of various types of high-speed spindle units, it is necessary to assess the influence of thermal processes. Numerous investigations have shown that thermal deformations in machine tools form a substantial part (25-75%) of the total accuracy balance (Push. A.V, 1985).The effect of lubrication on the high speed capabilities of the spindle assembly has been studied (A.M. Figatner et al,1983). The effect of dual cooling jacket around spindle bearings with feed-forward temperature control system to decrease thermal deformation in the spindle head unit caused by a sudden change in spindle load has been presented (Ikuo Tanabe et al, 1996). The use of helical cooling jackets for effective forced cooling has been studied (I.S. Yavelov, 1983). This paper examines the effect of spindle speed and external cooling in order to determine and minimize the thermal deflections of high speed spindles. Problem Definition: This paper presents a thermal model for a high speed milling spindle. The modules of this paper are: 1) To develop an accurate mathematical model of heat generation in the spindle assembly. 2) To determine the temperature distribution and thermal deflection considering oil-mist lubrication. 3) To incorporate external cooling and predict thermal deflection so as to minimize the same. 4) To investigate the effect of conduction through tool holder on spindle deflection.

2 Friction Heat generation Model: The spindle considered for analysis (Figure 1) is supported by bearings that are arranged as tandem duplex sets (DT) with 15 0 contact angle, both at the front and rear ends to form an O arrangement in the spindle assembly. The front and rear end bearing types are 7914X2TAU (bore diameter 70mm) and 7912X2TAU (bore diameter 60mm) respectively. The spindle taper specification is ISO 40. Figure 1 - High speed spindle assembly The mechanism of bearing friction heat generation is extremely complicated, as numerous factors are involved (J.L.Stein et al,1994). These include elastic hysteresis in rolling elements, sliding friction between the rolling elements and the rings, sliding due to deformation of contacting elements, sliding between the cage and rolling elements, viscous drag of the lubricant on the rolling elements and cage, sliding between rollers and inner and/or outer ring flanges, and seal friction. These factors often are inter-coupled and cannot be easily distinguished from one another. Therefore, instead of attempting to construct an analytical friction model, an empirical formula of Palmgren is used for estimating total bearing friction torque (Tedric Harris, 1966). The total frictional moment (M) of the bearing is obtained by adding the load independent moment (M 0 ) and load dependent moment (M 1 ).

3 M f 2 / 3 3 ( νn) d m where f 0 ν n d m Factor depending on bearing type and lubrication, Viscosity of lubricant (mm 2 /s) Spindle speed (rpm) Mean diameter of the bearing (mm). M 1 f1 p1 a b d m where f 1 p 1 a, b Factor depending on bearing type and load Load determining the frictional moment (N) Exponents depending on the type of bearing Finite element modeling: The problem of determining the temperature distribution in the spindle assembly is considered as a steady state heat transfer problem in which a state of thermal equilibrium is reached after many cycles of revolution. The time needed for one revolution of the ball which is loaded at any instant in the spindle bearing is much smaller in comparison with the time needed for any change in the heat generation and hence the temperature rise in the bearing. Therefore the heat generation in the bearing inner and outer raceways can be assumed to be equal, so that one needs to consider only a radial section of the spindle assembly to determine the temperature distribution. Further the geometry of the spindle assembly is also axisymmetric with respect to the spindle axis. Hence a two dimensional finite element analysis is performed using axisymmetric quadrilateral elements (PLANE 78). The finite element mesh of the spindle assembly is shown in Figure 2.

4 Figure 2 - Finite element model of spindle Estimation of thermal deflection of spindle assembly: The finite element model of the spindle assembly is used to determine the temperature distribution and thermal deflection. The thermal deflection is determined by performing a sequential thermal-structural coupled field analysis using compatible PLANE 83 elements. The boundary conditions applied for determining the temperature distribution are, heat generation at the inner and outer races of the bearings, free convection between the housing and the atmospheric air and convection of oil at the raceways. In oil mist lubrication, oil of 31mm 2 /sec viscosity with compressed air is taken for analysis. Since oil acts as both lubricant and coolant, it is capable of removing considerable amount of heat generated in the bearings. Hence convection heat transfer coefficient for oil and air is estimated for external flow condition and applied on the ball outer and inner races, using the Nusselt number, Nu 0.25 Re 0.6 Pr 0.38 where, Re Reynolds number of the lubricant Pr Prandtl number of the lubricant The expression for h is given by,

5 h Nu k / d where k Thermal conductivity of lubricant. Thus the temperature rise and thermal deflections are estimated for various operating speeds of the spindle. Minimisation of thermal deflection: From the previous analysis, the temperature rise and thermal deflections are high at higher operating speeds and hence forced cooling of the spindle assembly is required. Since the temperature rise at the front end bearings leads to thermal deflections at the spindle nose which in turn affects the machining accuracy, an external forced cooling through an annular passage is provided around the front end bearings. The convective heat transfer coefficient for external cooling is estimated and applied as boundary condition over the annular passage. Nusselt number of the coolant for laminar flow condition with uniform heat flux at the wall corresponding to Prandtl number greater than 0.6 is given by [ Pr/ [ x / ] Nu 1.3 Re D where x Length of the coolant passage in mm. D Diameter of the annular passage in mm. The thermal deflection of the spindle nose is estimated for various operating speeds considering external cooling. Estimation of thermal deflection of spindle with tool holder: The spindle is modeled with tool holder as shown in Figure 3 and temperature distribution and thermal deflections are determined for different operating speeds, with and without external cooling.

6 Figure 3 - Spindle with tool holder Results and discussion: Temperature rise in the front bearing is more than the rear bearing as shown in Figure 4. Figure 5 shows the maximum temperature rise of the front end bearing for different speeds, whose allowable limit is 70 0 C for oil-mist lubrication. Hence the spindle can be run upto rpm safely. On providing external cooling, the speed can be raised up to rpm.

7 Figure 4 - Temperature rise in front and rear bearings Figure 5 - Temperature rise in front bearing

8 The deflected shape of the spindle nose is shown in Figure 6 for rpm. The thermal deflection at the spindle nose varies from 10 µm to 28µm in the radial direction and from 24 µm to 67 µm in axial direction for a speed range of 2000 rpm to rpm without cooling. Figure 7 shows the axial deflection of spindle nose for different operating speeds. When external cooling is incorporated, the axial and radial deflections reduce by 15 %and 14% respectively for the maximum speed of rpm. Figure 6 - Spindle nose deflection at rpm

9 Figure 7 - Axial deflection of spindle nose The temperature rise at the spindle nose decreases with tool holder attached owing to conduction heat transfer through tool holder. Considering tool holder attachment, the axial and radial deflections at spindle nose increase by 9% and 11% respectively for the speed of rpm. This is due to a higher temperature gradient between front bearing and spindle nose. Figure 8 shows the axial deflection of spindle nose at different speeds, with and without tool holder. The axial deflection at the tool holder nose is still more because of expansion of tool holder in addition to spindle and is found to be 116 µm. On the other hand, radial deflection at tool holder nose is 10 µm which is less than the corresponding spindle nose deflection. By providing cooling, axial and radial deflections at the tool holder nose are reduced by 15% and 20% respectively for a speed of 15000rpm.

10 Figure 8 - Axial deflection of spindle nose with tool holder Conclusions: A model of heat generation, temperature distribution and thermal deflection in spindle assembly under high speed machining conditions is developed. The results of temperature rise are used to determine the working speed of the spindle without bearing failure. Thermal deflections of spindle nose under various operating speeds for oil mist lubrication conditions are determined and compared. The effects of forced cooling of the spindle assembly towards minimization of thermal deflections are studied. Thermal deflections of spindle along with the assembled tool holder are determined for different operating speeds. Further investigation on experimental estimation of spindle nose deflection is being carried out for validation. The model developed can be used for predicting the thermal behavior accurately and can be used for design of high speed spindle assemblies References: A.M. Figatner et al, 1983, Ensuring the high speed capability of spindles with rolling element bearings, Soviet Engineering research, Vol. 3, No. 4, Ikuo Tanabe and Kazuhisa Yanagi, 1996 Dual cooling jacket around spindle bearings with feed forward temperature control system to decrease thermal deformation, JSME International Journal, Series C, Vol.39, No.1, Push.A.V.,1985 Prediction of thermal displacements in spindle units, Soviet Engineering research, Vol. 5, No. 5, RHP Precision, 1987 High precision bearings, Bearing manual. Segida.A.P.,1984 Calculation of the temperature field and thermal distortions of spindle assemblies and boxes, Soviet Engineering research, Vol. 4, No. 2,

11 J.L. Stein and J.F. Tu, 1994 A state-space model for monitoring thermally induced preload in anti-friction spindle bearings of high speed machine tools, Transactions of ASME, Jl. of dynamic systems, measurement and control, Vol, 116,