The dynamics of tilting table behaves differently during five-axis machining due to the constant changes of the position of its center of mass which leads to different forces acting on parts of the transmission system. In this research, the lumped parameter method is used to model the dynamics of tilting table driven by worm and worm wheel in the tilting direction, where the varying stiffness of the transmission system at different tilting angles is considered. The impact testing experiments of tilting table system with tilting angles from 0° to 90° are also performed to verify the analytical model. The results from sensitivity analysis show that the three stiffnesses have a great effect on the variation of system natural frequency in the tilting direction, including the equivalent tangential meshing stiffness of worm and worm wheel, the torsional stiffness of worm wheel shaft, and the axial stiffness of worm supporting bearings. Moreover, the variations of system natural frequency with the three stiffnesses at different tilting angles are further investigated.
BohezELJ. Five-axis milling machine tool kinematic chain design and analysis. Int J Mach Tools Manuf2002; 42: 505–520.
2.
WeckMKrugerPBrecherC. Limits for controller settings with electric linear direct drives. Int J Mach Tools Manuf2001; 41: 65–88.
3.
AlbertelliPCauNBianchiG. The effects of dynamic interaction between machine tool subsystems on cutting process stability. Int J Adv Manuf Technol2012; 58: 923–932.
4.
LinSYFangYCHuangCW. Improvement strategy for machine tool vibration induced from the movement of a counterweight during machining process. Int J Mach Tools Manuf2008; 48: 870–877.
5.
TsutsumiMSaitoA. Identification and compensation of systematic deviations particular to 5-axis machining centers. Int J Mach Tools Manuf2003; 43: 771–780.
6.
Dassanayake KMM, Tsutsumi M, Sato R, et al. Motion characteristics of high performance rotary tables for CNC machines. In: 2008 ASME international mechanical engineering congress and exposition, Boston, MA, 2009, pp.27–36. New York, USA: ASME.
7.
SatoR. Mathematical model of a CNC rotary table driven by a worm gear. Int J Intell Mech Robot2012; 2: 27–40.
8.
GuHFHongRJ. Simulation and dynamic performance analysis on rotation platform of NC machine. Mach Tool Hydraul2008; 36: 216–219.
9.
YehTJWuFK. Modeling and robust control of worm-gear driven systems. Simul Model Pract Theory2009; 17: 767–777.
10.
WangJHowardI. The torsional stiffness of involute spur gears. Proc IMechE, Part C: J Mechanical Engineering Science2004; 218: 131–142.
11.
ChenZGShaoYM. Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack. Mech Mach Theory2013; 62: 63–74.
12.
del RinconAFViaderoFIglesiasM. A model for the study of meshing stiffness in spur gear transmissions. Mech Mach Theory2013; 61: 30–58.
13.
ParkerRVijayakarSImajoT. Non-linear dynamic response of a spur gear pair: modelling and experimental comparisons. J Sound Vib2000; 237: 435–455.
14.
KuangJHLinAD. Theoretical aspects of torque responses in spur gearing due to mesh stiffness variation. Mech Syst Signal Proc2003; 17: 255–271.
15.
WalhaLFakhfakhTHaddarM. Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash. Mech Mach Theory2009; 44: 1058–1069.
16.
SudohJTanakaYMatsumotoS. Load distribution analysis method for cylindrical worm gear teeth. JSME Int J Ser C-Dyn Control Robot Des Manuf1996; 39: 606–613.
17.
SimonVV. Influence of tooth errors and shaft misalignments on loaded tooth contact in cylindrical worm gears. Mech Mach Theory2006; 41: 707–724.
18.
FalahAHAlfaresMAElkholyAH. Localised tooth contact analysis of single envelope worm gears with assembly errors. Int J Adv Manuf Technol2013; 68: 2057–2070.
19.
ZhangYQZhangGHQiuXY. The contact stress of the planar double enveloping hourglass worm gears. J Sichuan University (Eng Sci Edn)2011; 43: 247–251.
20.
YangFSuDGentleCR. Finite element modelling and load share analysis for involute worm gears with localized tooth contact. Proc IMechE, Part C: J Mechanical Engineering Science2001; 215: 805–816.
21.
YuCJHuangXDFangCG. Optimizing dynamic characteristics of NC rotary table based on electromechanical-hydraulic coupling. J Mech Sci Technol2013; 27: 1081–1088.
22.
HernotXSartorMGuillotJ. Calculation of the stiffness matrix of angular contact ball bearings by using the analytical approach. J Mech Des2000; 122: 83–90.
23.
Lee H and Tesar D. An analytical stiffness analysis between actuator structure and principal bearings used for robot actuators. In: ASME 2011 international design engineering technical conferences and computers and information in engineering conference, Washington, DC, 2011, pp.1167–1176. New York, USA: ASME.
24.
GuoYParkerRG. Stiffness matrix calculation of rolling element bearings using a finite element/contact mechanics model. Mech Mach Theory2012; 51: 32–45.
25.
WangJDHowardI. Finite element analysis of high contact ratio spur gears in mesh. J Tribol-Trans ASME2005; 127: 469–483.
26.
ShigleyJEMischkeCR. Mechanical engineering design, New York: McGraw-Hill, 2001.
27.
HarrisTAKotzalasMN. Advanced concepts of bearing technology: rolling bearing analysis, Boca Raton, Florida: CRC Press, 2006.
28.
LiRFWangJJ. Dynamics of gear system: vibration, shock and noise, Beijing: Science Press, 1997.
29.
HeylenWLammensSSasP. Modal analysis theory and testing, Beijing: Beijing institute of technology press, 2001.
