Stiffness of CNC Machine Tool Feed Drives
In this paper a model for the feed drive system with disturbance forces is given. Static and dynamic stiffness for the proposed model is analyzed. An equation for analytical calculation of the static stiffness is given. Correctness of the proposed equatio
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ofProduction Engineering, Faculty ofMechanical Engineering, University "Sv. Kiril i Metodij", Skopje, Republic ofMacedonia
KEYWORDS: stiffness, CNC machine tool, feed drives. ABSTRACT. In this paper a model for the feed drive system with disturbance forces is given. Static and dynamic stiffness for the proposed model is analyzed. An equation for analytical calculation of the static stiffness is given. Correctness of the proposed equation is experimentally verified. Simulation of the influence of some parameters on the static and dynamic feed drive stiffness is performed with simulation program MATLAB & SIMULINK.
1 INTRODUCTION Feed drives are widely applied to CNC machine tools, robots, manipulators, assembly machines etc. The feed drive stiffness may be defined as an influence of the disturbance force (torque) on the position (angular position) deviation. In the theory of the automatic control stiffness can be defined as reciprocal value of the stationary error of the position (angular position) caused by the disturbance force (torque) [6]. Investigations about feed drives are very seldom presented in the literature. The results of Nieniewski [5], Nieniewski and Bollinger [4], Losic [2,3], Kakino et al. [1], are of particular interest. The most of the previous articles don't take into the consideration influence of the mechanical transmission elements on the feed drive stiffness. The research [ 1] is more complete, but still has one imperfection, absence of analytical equation for estimation the feed drive static stiffness.
2 A MODEL OF THE FEED DRNE SYSTEM WITH DISTURBANCE FüRCES Fig.l and fig.2 show an original model ofthe feed drive with disturbance forces. All the relevant parameters in fig.l are given bellow: Kv-position loop gain 1/s, T-sampling period s, s-Laplace operator, kg-coefficient of transformation of rotation in translation m/rad, Ddamping of the electrical parts, co-nominal angular frequency of the electrical parts 1/s, kvk-total stiffness of the mechanical transmission elements N/m, F-disturbance force N, kf-disturbance force gain 1/s, kb-gain ofthe mechanical transmission damping m/Ns, m-mass ofthe mechanical transmission elements kg, b-damping quotient ofthe mechanical transmission elements Ns/m, kiintegrator gain s, Xi-input position, Xo-output position. Factors kf, kb and ki are always l. They are taken into the consideration, only to have dimensional correctness of the models, given on fig.l and fig.2. Published in: E.Kuljanic (Ed.) Advanced Manufacturing Systemsand Technology, CISM Coursesand Lectures No. 437, Springer Wien New York, 2002.
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Z. Pandilov, V. Dukovski
Transfer function between output position and disturbance force is given with equation ( 1). Xo(s) = kr ·G3(s)·Gis) F(s) 1+G2(s) · G3(s) +G1(s) · G2(s) ·Gis)· Gis)
(1)
With substituting the transfer functions Gl(s), G2(s), G3(s) and G4(s) from fig.2 in equation (1) we obtain Xo(s) = F(s)
b 3s 3 +b 2 s 2 +b 1s+b 0 a 6 s 6 +a 5 s 5 +a 4 s 4 +a 3s 3 +a 2 s 2 +a 1s+a 0
(2)
FIGURE I. Model ofthe feed drive system with d
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