Torsional vibration analysis of lathe spindle system with unbalanced workpiece

Abstract

For the purpose of analyzing the torsional vibration caused by the gravitational unbalance torque arisen in a spindle system when it is machining heavy work piece, a 10-DOF lumped parameter model was made for the machine tool spindle system with geared transmission. By using the elementary method and Runge-Kutta method in Matlab, the eigenvalue problem was solved and the pure torsional vibration responses were obtained and examined. The results show that the spindle system cannot operate in the desired constant rotating speed as far as the gravitational unbalance torque is engaged, so it may cause bad effect on machining accuracy. And the torsional vibration increases infinitely near the resonant frequencies, so the spindle system cannot operate normally during these spindle speed ranges.

Keywords

unbalanced work piece / gravitational unbalance torque / torsional vibration / spindle system / geared transmission

References

[1] SaravananN., CholairajanS., RamachandranK. I.. Vibration-based fault diagnosis of spur bevel gear box using fuzzy technique [J]. Expert Systems with Applications, 2009, 36(2): 3119-3125

[2] GaoW.-z., HaoZ.-yong.. Active control and simulation test study on torsional vibration of large turbo-generator rotor shaft [J]. Mechanism and Machine Theory, 2010, 45(9): 1326-1336

[3] YuanZ.-w., ChuF.-l., LinY.-li.. External and internal coupling effects of rotor’s bending and torsional vibrations under unbalances [J]. Journal of Sound and Vibration, 2007, 299(1/2): 339-347

[4] ChenR.-l., ZengQ.-y., ZhangJ.-yan.. New algorithm applied to vibration equations of time-varying system [J]. Journal of Central South University of Technology, 2008, 15(1): 57-60

[5] HsiehS. C., ChenJ. H., LeeA. C.. A modified transfer matrix method for the coupled lateral and torsional vibrations of asymmetric rotor-bearing systems [J]. Journal of Sound and Vibration, 2008, 312(1/2): 563-571

[6] HuangD. G.. Characteristics of torsional vibrations of a shaft with unbalance [J]. Journal of Sound and Vibration, 2007, 308(3/4/5): 692-698

[7] LeesA. W.. Misalignment in rigidly coupled rotors [J]. Journal of Sound and Vibration, 2007, 305(1/2): 261-271

[8] PatelT. H., DarpeA. K.. Vibration response of misaligned rotors [J]. Journal of Sound and Vibration, 2009, 325(3): 609-628

[9] NeugebauerR., DenkenaB., WegenerK.. Mechatronic systems for machine tools [J]. Journal of CIRP Annals-Manufacturing Technology, 2007, 56(2): 657-686

[10] CHOI Y H, PARK S K, JUNG T S, KIM C S. A case study on the vibration and noise reduction in a gearbox for a lathe [C]// Proceedings of the Inter Noise, Seogwipo, 2003: 3543–3550.

[11] WiddleR. D., KrousgrillC. M., SudhoffS. D.. An induction motor model for high-frequency torsional vibration analysis [J]. Journal of Sound and Vibration, 2006, 290(3/4/5): 865-881

[12] WuJ.-jang.. Torsional vibration analyses of a damped shafting system using tapered shaft element [J]. Journal of Sound and Vibration, 2007, 306(3/4/5): 946-954

[13] CharlesP., SinhaJ. K., LidstoneG. L., BallA. D.. Detecting the crankshaft torsional vibration of diesel engines for combustion related diagnosis [J]. Journal of Sound and Vibration, 2009, 321(3/4/5): 1171-1185

[14] WhalleyR., AbdulA. A.. Contoured shaft and rotor dynamics [J]. Mechanism and Machine Theory, 2009, 44(4): 772-783

[15] PatelT. H., DarpeA. K.. Experimental investigations on vibration response of misaligned rotors [J]. Mechanical Systems and Signal Processing, 2009, 23(7): 2236-2252

[16] SingiresuS. R.Mechanical vibrations [M], 2004, New Jersey, Pearson: 381-540

[17] XueD.-yu.Computer aided control systems design using MATLAB language [M], 2006, Beijing, Tsinghua University Press: 17-63