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Determining of model similarity for flexspline of harmonic drive with the use of FEM and extensometer method

Budzik G., Kozik B., Pacana J.

Journal of KONES

2009

Vol. 16, No. 2

55-60

This paper presents an analysis of the feasibility of using the model similarity method in engineering design. The analysis applies to virtual and physical models of the flexspline body of harmonic gear drive. The task consisted in determining stress distribution in the virtual models of the flexspline by means of the finite element method (FEM) and next its verification during bench tests by the extensometer method. The values of stresses calculated by the FEM method and the extensometer method were compared with each other with the aim ofdefming model similarity. The numerical calculations were made by means of the ADINA application which uses FEM with the use of contact elements. Stress distribution calculations applied to simplified virtual models of the flexspline. By the simplification of models a great number of finite elements used for the discretisation process were limited and because of that the time of calculations was shortened. The simplified model was precise enough to determine the stresses in the flexspline body. The subject of this analysis was the impact of different values of the torque moment T2 on the stresses in the flexspline body of the harmonie drive. The results of numerical calculations were checked against the standing tests of the real drive by applying the extensometer method. During the work of the gear, the values of relative elongation were measured and, based on them, the values of stresses were determined and compared to the results of the numerical calculations by FEM in the analogous cross-sections of the flexspline. The comparability of the results received by both methods proves both that the models used in the numerical calculations were properly designed and that the assumptions as well as the calculation were properly made. The determining of model similarity for the examined harmonie drive will make it possible to carry out analyses of stress calculations by FEM on virtual models without the necessity to verify them by laboratory standing tests each time.

Modeling of torsional vibration in harmonic drives

Leniowski R.

Archives of Acoustics

2007

Vol. 32, No. 4

923--931

Harmonic Drives (HD) play a considerable role in industrial applications and precise medical equipments. They offer unique features, such as high gear ratios, high torque capacities, compact geometry, zero backslash and high efficiency. However, the torsional flexibility, friction and nonlinear hysteresis lead to complex dynamic behavior of the system, which reveals as torsional vibrations. Hence, to improve the performance of new machines, the transmission compliance and internal friction mechanism must be analyzed. This paper is concerned with precise mathematical modeling of HD. The proposed model consists of three components: hysteresis, friction and torsion flexibility. The hysteresis has been modeled as weighted combination of individual Preisach cells to form global operator, which generates adequate hysteresis curve due to measured data. Friction model includes a lubricated contact force and dynamic behavior developed by Bliman & Sorine. The last component of the HD model describes the flexspline flexibility (the flexspline is a flexible cylinder made of steel with outer teeth), that produces substantial transmission torsion. Original proposition assumes that the flexspline can be modeled as cylindrical shell FEM model (n x m degree of freedom mass-spring-damper system), based on 16 directional mesh (four neareststretch springs, four diagonal-shear springs and eight next-nearest neighbors, nonlinear bend spring). The flexspline is loaded on both sides by the various forces which are tangent to the flexspline surface. The friction torques has been taken into account on both sides of HD: one in the input side, another on the output side. Simulation results show that the developed model has satisfactory features and accuracy and can be used in ongoing research to develop variant of MRAC-type controllers for vibration cancellation.