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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

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Front Mech Eng    2013, Vol. 8 Issue (4) : 409-419    https://doi.org/10.1007/s11465-013-0275-5
RESEARCH ARTICLE
An investigation into the vibration of harmonic drive systems
M. Masoumi1(), H. Alimohammadi2
1. School of Mechanical Engineering, Semnan University, Semnan 35195-363, Iran; 2. School of Engineering, Tarbiat Modares University, Tehran 14115-175, Iran
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Abstract

Harmonic drive systems are precise and specific transmission gear systems which are beneficial in terms of the high transmission ratio and almost zero backlash. These inherent and spectacular properties result in using this mechanism in robotic and space sciences where the precision and lightwieght play an important role. This paper presents a vibration analysis of harmonic drive systems using the shell theory. Equations of vibration for the flexspline and the circular spline of the system are derived and used to find the natural frequencies for both parts and, moreover, vibration response of the system under the operating condition is calculated. Also, obtained vibration equations are utilized to study the effects of different involved parameters such as the geometry of the flexspline and its gear tooth, eccentricity, and unbalancing on the vibrational behavior of the system.
Keywords harmonic drive system      strain wave gearing mechanism      vibration analysis      natural frequencies     
Corresponding Author(s): Masoumi M.,Email:m_masoumi@sun.semnan.ac.ir   
Issue Date: 05 December 2013
 Cite this article:   
M. Masoumi,H. Alimohammadi. An investigation into the vibration of harmonic drive systems[J]. Front Mech Eng, 2013, 8(4): 409-419.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-013-0275-5
https://academic.hep.com.cn/fme/EN/Y2013/V8/I4/409
Fig.1  The components of a harmonic drive system []
Fig.2  Mechanism of strain wave gearing: (1) initial step, (2) 90 degree rotation of the wave generator and moving the flexspline a half of a tooth on the circular spline in the opposite direction (3) 180 degree rotation of the wave generator and moving the flexspline a tooth on the circular spline in the opposite direction
Fig.3  Force elements applied on the flexspline
Part of the systemDensity/(kg?m-3)Poinsson’s ratioYoung’s modulus/GPaRadius/mmThickness/mm
Flexspline78650.28520020.7-
Circular spline78650.28520020.93.84
Tab.1  Properties of the flexspline and the circular spline
Natural frequency/kHzFirstSecondThirdFourthFifth
Flexspline5790128167206
Circular spline5689126165204
Tab.2  First fifth natural frequencies of the flexspline and the circular spline
Flexspline dataSystem information
Width of the teeth(B)Profile angle(α)Number of the teethModulus of the teethDepth of the teethThickness (h)Angle of the tooth engagement(β)Input speed(ωb)Torque(T)
13.5 mm25°2000.2070.38 mm0.425 mm30°6000 r?min-140 N?m
Tab.3  Flexspline data and system information
Fig.4  Vibration response of the harmonic drive system under the operating condition
Fig.5  Vibration response of the harmonic drive system for different values of under the operating condition
Fig.6  Vibration response of the harmonic drive system for different values of under the operating condition
Fig.7  Effects of eccentricity on the angle between the locations of the applied forces on the flexspline
Fig.8  Vibration response of the harmonic drive system for different values of eccentricity under the operating condition
Fig.9  Vibration response of the harmonic drive system for different values of unbalance mass under the operating condition
1 Rong H. Research on amplitude value of vibration in harmonic gear. Machine Tool & Hydraulics , 1995, 6: 336-339
2 Musser C W. Strain wave gear-species. US Patent, 1960
3 Tuttle T D. Understanding and modeling the behavior of a harmonic drive gear transmission. Technical report, MIT Artificial Intelligence Laboratory , 1992
4 Kokhanovskii G I, Polenov V S, Spiridonov V V. Calculating the stress and strain state of the flexible wheel of a wave toothed transmission. International Applied Mechanics , 1973, 9(12): 1355-1358
5 Shuvalov S. Calculation of harmonic drives with allowance for pliancy of links. Russian Engineering Journal , 1974, 54: 47-52
6 Shuvalov S. Calculation of forces acting on members of a harmonic gear drive. Russian Engineering Journal , 1979, 59(10): 5-9
7 Sinkevich Y B. Effect of teeth on the rim rigidity of the flexible gear wheel of a harmonic drive. Russian Engineering Journal , 1978, 58(7): 19-22
8 Emel’yanov A. Calculation of the kinematic error of a harmonic gear transmission taking into account the compliance of elements. Soviet Engineering Research , 1983, 3(7): 7-10
9 Margulis M, Volkov D. Calculation of the torsional rigidity of a harmonic power drive with a disc generator. Soviet Engineering Research , 1987, 7(6): 17-19
10 Hashimoto M. Robot motion control based on joint torque sensing. In: Proceedings of IEEE International Conference on Robotics and Automation . Japan, 1989, 256-261
11 Karlen J P, Thompson J M, Vold H I, Farrell J D, Eismann P H. A dual-arm dexterous manipulator system with anthropomorphic kinematics. In: Proceedings of IEEE International Conference on Robotics and Automation . USA, Cincinnati, 1990, 368-373
12 Thompson B R. The PHD: A Planar, Harmonic Drive Robot for Joint Torque Control. Technical Report, Massachusetts Institute of Technology Cambridge Artificial Intelligence Laboratory , 1990
13 Legnani G, Faglia R. Harmonic drive transmissions: the effects of their elasticity, clearance and irregularity on the dynamic behaviour of an actual SCARA robot. Robotica , 1992, 10(4): 369-375
doi: 10.1017/S0263574700008201
14 Tuttle T D, Seering W. Kinematic error, compliance, and friction in a harmonic drive gear transmission. In: proceedings of ASME Design Technical Conferences: 19th Advances in Design Automation . USA, New Mexico, 1993, 319-324
15 Tuttle T D, Seering W. Modeling a harmonic drive gear transmission. In: Proceedings of IEEE International Conference on Robotics and Automation . USA, Atlanta, 1993, 624-629
16 Tuttle T D, Seering W. A nonlinear model of a harmonic drive gear transmission. IEEE Transactions on Robotics and Automation , 1996, 12(3): 368-374
doi: 10.1109/70.499819
17 Kircanski N M, Goldenberg A A. An experimental study of nonlinear stiffness, hysteresis, and friction effects in robot joints with harmonic drives and torque sensors. International Journal of Robotics Research , 1997, 16(2): 214-239
doi: 10.1177/027836499701600207
18 Rong H. Research About Vibration of Harmonic Drives. Mechanical Transmission , 1995, 1: 33-36
19 Taghirad H D, Belanger P. Torque ripple and misalignment torque compensation for the built-in torque sensor of harmonic drive systems. IEEE Transactions on Instrumentation and Measurement , 1998, 47(1): 309-315
doi: 10.1109/19.728840
20 Hashimoto M, Kiyosawa Y, Paul R P. A torque sensing technique for robots with harmonic drives. IEEE Transactions on Robotics and Automation , 1993, 9(1): 108-116
doi: 10.1109/70.210802
21 Jeon H S, Oh S H. A study on stress and vibration analysis of a steel and hybrid flexspline for harmonic drive. Composite Structures , 1999, 47(1): 827-833
doi: 10.1016/S0263-8223(00)00060-X
22 Ghorbel F H, Gandhi P S, Alpeter F. On the kinematic error in harmonic drive gears. Journal of Mechanical Design , 2001, 123(1): 90-97
doi: 10.1115/1.1334379
23 Gandhi P S, Ghorbel F H. Closed-loop compensation of kinematic error in harmonic drives for precision control applications. IEEE Transactions on Control Systems Technology , 2002, 10(6): 759-768
doi: 10.1109/TCST.2002.804119
24 Dhaouadi R, Ghorbel F H, Gandhi P S. A new dynamic model of hysteresis in harmonic drives. IEEE Transactions on Industrial Electronics , 2003, 50(6): 1165-1171
doi: 10.1109/TIE.2003.819661
25 Xu L, Zhu C, Qin L. Parametric vibration for electromechanical integrated electrostatic harmonic drive. Mechatronics , 2007, 17(1): 31-43
doi: 10.1016/j.mechatronics.2006.07.003
26 Rhéaume F, Champliaud H, Liu Z. Understanding and modelling the torsional stiffness of harmonic drives through finite-element method. Proceedings of the Institution of Mechanical Engineers. Part C, Journal of Mechanical Engineering Science , 2009, 223(2): 515-524
doi: 10.1243/09544062JMES949
27 Dong H, Zhu Z, Zhou W, Chen Z. Dynamic Simulation of Harmonic Gear Drives Considering Tooth Profiles Parameters Optimization. Journal of Computers , 2012, 7(6): 1429-1436
doi: 10.4304/jcp.7.6.1429-1436
28 www.assiotdirectory.com
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