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Abstract

The goal of the project is to investigate the influence of elastic mechanisms on technical, bipedal locomotion. In particular, the paper presents the parameter identification for a biologically inspired two-legged robot model. The simulation model consists of a rigid body model equipped with rubber straps. The arrangement of the rubber straps is based on the arrangement of certain muscle groups in a human being. The parameters of the elastic elements are identified applying numerical optimisation. Thus two optimisation algorithms are investigated and compared with respect to robustness and computing time. Moreover, different objective functions are defined and discussed. The behaviour of the resulting configuration of the system is explored in terms of biomechanics.

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Authors and Affiliations

Daniela Förg
Heinz Ulbrich
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Abstract

In this paper the analysis of backlash influence on the spectrum of torque at the output shaft of a cycloidal gearbox has been performed. The model of the single stage cycloidal gearbox was designed in the MSC Adams. The analysis for the excitation with the torque and the analysis with constant angular velocity of the input shaft were performed. For these analyses, the amplitude spectrums of the output torque for different backlashes was solved using FFT algorithm. The amplitude spectrums of the combined sine functions composed of the impact to impact times between the cycloidal wheel and the external sleeves were computed for verification. The performed studies show, that the backlash has significant influence on the output torque amplitude spectrum. Unfortunately the dependencies between the components of the spectrum and the backlash could not be expressed by linear equations, when vibrations of the output torque in the range of (350 Hz – 600 Hz) are considered. The gradual dependence can be found in the spectrum determined for the combined sine functions with half-periods equal impact-to-impact times. The spectrum is narrower for high values of backlash.
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Bibliography

[1] M. Blagojević, M. Matejić, and N. Kostić. Dynamic behaviour of a two-stage cycloidal speed reducer of a new design concept. Tehnički Vjesnik, 25(2):291–298, 2018, doi: 10.17559/TV- 20160530144431.
[2] M. Wikło, R. Król, K. Olejarczyk, and K. Kołodziejczyk. Output torque ripple for a cycloidal gear train. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(21–22):7270–7281, 2019, doi: 10.1177/0954406219841656.
[3] N. Kumar, V. Kosse, and A. Oloyede. A new method to estimate effective elastic torsional compliance of single-stage Cycloidal drives. Mechanism and Machine Theory, 105:185–198, 2016, doi: 10.1016/j.mechmachtheory.2016.06.023.
[4] C.F. Hsieh. The effect on dynamics of using a new transmission design for eccentric speed reducers. Mechanism and Machine Theory, 80:1–16, 2014, doi: 10.1016/j.mechmachtheory.2014.04.020.
[5] R. Król. Kinematics and dynamics of the two stage cycloidal gearbox. AUTOBUSY – Technika, Eksploatacja, Systemy Transportowe, 19(6):523–527, 2018, doi: 10.24136/atest.2018.125.
[6] K.S. Lin, K.Y. Chan, and J.J. Lee. Kinematic error analysis and tolerance allocation of cycloidal gear reducers. Mechanism and Machine Theory, 124:73–91, 2018, doi: 10.1016/j.mechmachtheory.2017.12.028.
[7] L.X. Xu, B.K. Chen, and C.Y. Li. Dynamic modelling and contact analysis of bearing-cycloid-pinwheel transmission mechanisms used in joint rotate vector reducers. Mechanism and Machine Theory, 137:432–458, 2019, doi: 10.1016/j.mechmachtheory.2019.03.035.
[8] D.C.H. Yang and J.G. Blanche. Design and application guidelines for cycloid drives with machining tolerances. Mechanism and Machine Theory, 25(5):487–501, 1990, doi: 10.1016/0094-114X(90) 90064-Q.
[9] J.W. Sensinger. Unified approach to cycloid drive profile, stress, and efficiency optimization. Journal of Mechanical Design, 132(2):024503, 2010, doi: 10.1115/1.4000832.
[10] Y. Li, K. Feng, X. Liang, and M.J. Zuo. A fault diagnosis method for planetary gearboxes under non-stationary working conditions using improved Vold-Kalman filter and multi-scale sample entropy. Journal of Sound and Vibration, 439:271–286, 2019, doi: 10.1016/j.jsv.2018.09.054.
[11] Z.Y. Ren, S.M. Mao, W.C. Guo, and Z. Guo. Tooth modification and dynamic performance of the cycloidal drive. Mechanical Systems and Signal Processing, 85:857–866, 2017, doi: 10.1016/j.ymssp.2016.09.029.
[12] L.X. Xu and Y.H. Yang. Dynamic modeling and contact analysis of a cycloid-pin gear mechanism with a turning arm cylindrical roller bearing. Mechanism and Machine Theory, 104:327–349, 2016, doi: 10.1016/j.mechmachtheory.2016.06.018.
[13] S. Schmidt, P.S. Heyns, and J.P. de Villiers. A novelty detection diagnostic methodology for gearboxes operating under fluctuating operating conditions using probabilistic techniques, Mechanical Systems and Signal Processing, vol. 100, pp. 152–166, 2018, doi: 10.1016/j.ymssp.2017.07.032.
[14] Y. Lei, D. Han, J. Lin, and Z. He. Planetary gearbox fault diagnosis using an adaptive stochastic resonance method. Mechanical Systems and Signal Processing, 38(1):113–124, 2013, doi: 10.1016/j.ymssp.2012.06.021.
[15] Y. Chen, X. Liang, and M.J. Zuo. Sparse time series modeling of the baseline vibration from a gearbox under time-varying speed condition. Mechanical Systems and Signal Processing, 134:106342, 2019, doi: 10.1016/j.ymssp.2019.106342.
[16] G. D’Elia, E. Mucchi, and M. Cocconcelli. On the identification of the angular position of gears for the diagnostics of planetary gearboxes. Mechanical Systems and Signal Processing, 83:305–320, 2017, doi: 10.1016/j.ymssp.2016.06.016.
[17] X. Chen and Z. Feng. Time-frequency space vector modulus analysis of motor current for planetary gearbox fault diagnosis under variable speed conditions. Mechanical Systems and Signal Processing, 121:636–654, 2019, doi: 10.1016/j.ymssp.2018.11.049.
[18] S. Schmidt, P.S. Heyns, and K.C. Gryllias. A methodology using the spectral coherence and healthy historical data to perform gearbox fault diagnosis under varying operating conditions. Applied Acoustics, 158:107038, 2020, doi: 10.1016/j.apacoust.2019.107038.
[19] D. Zhang and D. Yu. Multi-fault diagnosis of gearbox based on resonance-based signal sparse decomposition and comb filter. Measurement, 103:361–369, 2017, doi: 10.1016/j.measurement.2017.03.006.
[20] C. Wang, H. Li, J. Ou, R. Hu, S. Hu, and A. Liu. Identification of planetary gearbox weak compound fault based on parallel dual-parameter optimized resonance sparse decomposition and improved MOMEDA. Measurement, 165:108079, 2020, doi: 10.1016/j.measurement.2020.108079.
[21] W. Teng, X. Ding, H. Cheng, C. Han, Y. Liu, and H. Mu. Compound faults diagnosis and analysis for a wind turbine gearbox via a novel vibration model and empirical wavelet transform. Renewable Energy, 136:393–402, 2019, doi: 10.1016/j.renene.2018.12.094.
[22] R. Król. Resonance phenomenon in the single stage cycloidal gearbox. Analysis of vibrations at the output shaft as a function of the external sleeves stiffness. Archive of Mechanical Engineering, 68(3):303–320, 2021, doi: 10.24425/ame.2021.137050.
[23] MSC Software. MSC Adams Solver Documentation.
[24] MSC Software. MSC Adams View Documentation.
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Authors and Affiliations

Roman Król
1
ORCID: ORCID

  1. Faculty of Mechanical Engineering, Kazimierz Pulaski University of Technology and Humanities in Radom, Poland
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Abstract

In this paper a versatile analysis of the cycloidal gearbox vibrations and the resonance phenomenon was performed. The objective of this work was to show resonance phenomenon and vibrations study in the multibody dynamics model and in the finite element model of the cycloidal gearbox. The output torque was analyzed as a function of the external sleeves stiffness.
The results from the multibody dynamics model were verified in the finite element model using natural frequency with load stiffening, direct frequency response and direct transient response analyses.
It was shown that natural frequencies of the cycloidal gearbox undergo changes during motion of the mechanism. The gearbox passes through the thresholds of the increased vibration amplitudes, which lead to excessive wear of the external sleeves.
The analysis in the multibody dynamics model showed, that the increase in the external sleeves stiffness increases frequency of the second-order fluctuation at the output shaft. Small stiffness of the external sleeves guarantees lower frequency of the second order vibrations and higher peak-to-peak values of the output torque.
The performed research plays important role in the cycloidal gearbox design. This work shows gearbox dynamics problems which are associated with wear of the external sleeves.
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Bibliography

[1] M.Blagojević, M. Matejić, and N. Kostić. Dynamic behaviour of a two-stage cycloidal speed reducer of a new design concept. Technical Gazette, 25(Supplement 2):291–298, 2018. doi: 10.17559/TV-20160530144431.
[2] M. Wikło, R. Król, K. Olejarczyk, and K. Kołodziejczyk. Output torque ripple for a cycloidal gear train. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(21–22):7270–7281, 2019. doi: 10.1177/0954406219841656.
[3] N. Kumar, V. Kosse, and A. Oloyede. A new method to estimate effective elastic torsional compliance of single-stage Cycloidal drives. Mechanism and Machine Theory, 105:185–198, 2016. doi: 10.1016/j.mechmachtheory.2016.06.023.
[4] C.-F. Hsieh. The effect on dynamics of using a new transmission design for eccentric speed reducers. Mechanism and Machine Theory, 80:1–16, 2014. doi: 10.1016/j.mechmachtheory.2014.04.020.
[5] R. Król. Kinematics and dynamics of the two stage cycloidal gearbox. AUTOBUSY – Technika, Eksploatacja, Systemy Transportowe, 19(6):523–527, 2018. doi: 10.24136/atest.2018.125.
[6] K-.S. Lin, K.-Y. Chan, and J.-J. Lee. Kinematic error analysis and tolerance allocation of cycloidal gear reducers. Mechanism and Machine Theory, 124:73–91, 2018. doi: 10.1016/j.mechmachtheory.2017.12.028.
[7] L. X. Xu, B. K. Chen, and C.Y. Li. Dynamic modelling and contact analysis of bearing-cycloid-pinwheel transmission mechanisms used in joint rotate vector reducers. Mechanism and Machine Theory, 137:432–458, 2019. doi: 10.1016/j.mechmachtheory.2019.03.035.
[8] A. Robison and A. Vacca. Multi-objective optimization of circular-toothed gerotors for kinematics and wear by genetic algorithm. Mechanism and Machine Theory, 128:150–168, 2018. doi: 10.1016/j.mechmachtheory.2018.05.011.
[9] R. Król, M. Wikło, K. Olejarczyk, K.Kołodziejczyk, and A. Zieja. Optimization of the one stage cycloidal gearbox as a non-linear least squares problem. In: T. Uhl (ed.) Advances in Mechanism and Machine Science. Proceedings of the 15th IFToMM World Congress on Mechanism and Machine Science, pages 1039–1048, Cracow, Poland, 15-18 July, 2019. doi: 10.1007/978-3-030-20131-9_103.
[10] R. Król. Updated software for the one stage cycloidal gearbox optimization (MATLAB scripts) (2.0). Zenodo, 2021. doi: 10.5281/zenodo.4737264.
[11] L. X. Xu and Y. H. Yang. Dynamic modeling and contact analysis of a cycloid-pin gear mechanism with a turning arm cylindrical roller bearing. Mechanism and Machine Theory, 104:327–349, 2016. doi: 10.1016/j.mechmachtheory.2016.06.018.
[12] M. Pfabe and C. Woernle. Reducing torsional vibrations by means of a kinematically driven flywheel – Theory and experiment. Mechanism and Machine Theory, 102:217–228, 2016. doi: 10.1016/j.mechmachtheory.2016.03.011.
[13] Y. Chen, X. Liang, and M. J. Zuo. Sparse time series modeling of the baseline vibration from a gearbox under time-varying speed condition. Mechanical Systems and Signal Processing, 134:106342, 2019. doi: 10.1016/j.ymssp.2019.106342.
[14] R. Yang, F. Li, Y. Zhou, and J. Xiang. Nonlinear dynamic analysis of a cycloidal ball planetary transmission considering tooth undercutting. Mechanism and Machine Theory, 145:103694, 2020. doi: 10.1016/j.mechmachtheory.2019.103694.
[15] W. He, B. Chen, N. Zeng, and Y. Zi. Sparsity-based signal extraction using dual Q-factors for gearbox fault detection. ISA Transactions, 79:147–160, 2018. doi: 10.1016/j.isatra.2018.05.009.
[16] D. Zhang and D. Yu. Multi-fault diagnosis of gearbox based on resonance-based signal sparse decomposition and comb filter. Measurement, 103:361–369, 2017. doi: 10.1016/j.measurement.2017.03.006.
[17] C.U. Mba, V. Makis, S. Marchesiello, A. Fasana, and L. Garibaldi. Condition monitoring and state classification of gearboxes using stochastic resonance and hidden Markov models. Measurement, 126:76–95, 2018. doi: 10.1016/j.measurement.2018.05.038.
[18] C. Wang, H. Li, J. Ou, R. Hu, S. Hu, and A. Liu. Identification of planetary gearbox weak compound fault based on parallel dual-parameter optimized resonance sparse decomposition and improved MOMEDA. Measurement, 165:108079, 2020. doi: 10.1016/j.measurement.2020.108079.
[19] W. Teng, X. Ding, H. Cheng, C. Han, Y. Liu, and H. Mu. Compound faults diagnosis and analysis for a wind turbine gearbox via a novel vibration model and empirical wavelet transform. Renewable Energy, 136:393–402, 2019. doi: 10.1016/j.renene.2018.12.094.
[20] Y. Lei, D. Han, J. Lin, and Z. He. Planetary gearbox fault diagnosis using an adaptive stochastic resonance method. Mechanical Systems and Signal Processing, 38(1):113–124, 2013. doi: 10.1016/j.ymssp.2012.06.021.
[21] L. Hong, Y. Qu, J. S. Dhupia, S. Sheng, Y. Tan, and Z. Zhou. A novel vibration-based fault diagnostic algorithm for gearboxes under speed fluctuations without rotational speed measurement. Mechanical Systems and Signal Processing, 94:14–32, 2017. doi: 10.1016/j.ymssp.2017.02.024.
[22] S. Schmidt, P. S. Heyns, and J. P. de Villiers. A novelty detection diagnostic methodology for gearboxes operating under fluctuating operating conditions using probabilistic techniques. Mechanical Systems and Signal Processing, 100:152–166, 2018. doi: 10.1016/j.ymssp.2017.07.032.
[23] T. Wang, Q. Han, F. Chu, and Z. Feng. Vibration based condition monitoring and fault diagnosis of wind turbine planetary gearbox: A review. Mechanical Systems and Signal Processing, 126:662–685, 2019. doi: 10.1016/j.ymssp.2019.02.051.
[24] S. Schmidt, P. S. Heyns, and K. C. Gryllias. A methodology using the spectral coherence and healthy historical data to perform gearbox fault diagnosis under varying operating conditions. Applied Acoustics, 158:107038, 2020. doi: 10.1016/j.apacoust.2019.107038.
[25] Y. Li, K. Feng, X. Liang, and M.J. Zuo. A fault diagnosis method for planetary gearboxes under non-stationary working conditions using improved Vold-Kalman filter and multi-scale sample entropy. Journal of Sound and Vibration, 439:271–286, 2019. doi: 10.1016/j.jsv.2018.09.054.
[26] S. Tong, Y. Huang, Y. Jiang, Y. Weng, Z. Tong, N. Tang, and F. Cong. The identification of gearbox vibration using the meshing impacts based demodulation technique. Journal of Sound and Vibration, 461:114879, 2019. doi: 10.1016/j.jsv.2019.114879.
[27] X. Chen and Z. Feng. Time-frequency space vector modulus analysis of motor current for planetary gearbox fault diagnosis under variable speed conditions. Mechanical Systems and Signal Processing, 121:636–654, 2019. doi: 10.1016/j.ymssp.2018.11.049.
[28] D.F. Plöger, P. Zech, and S. Rinderknecht. Vibration signature analysis of commodity planetary gearboxes. Mechanical Systems and Signal Processing, 119:255–265, 2019. doi: 10.1016/j.ymssp.2018.09.014.
[29] G. D’Elia, E. Mucchi, and M. Cocconcelli. On the identification of the angular position of gears for the diagnostics of planetary gearboxes. Mechanical Systems and Signal Processing, 83:305–320, 2017. doi: 10.1016/j.ymssp.2016.06.016.
[30] W. Żurowski, K. Olejarczyk, and R. Zaręba.Wear assessment of sliding sleeves in a single-stage cycloidal drive. Advances in Science and Technology Research Journal, 13(4):239–245, 2019. doi: 10.12913/22998624/114180.
[31] K. Olejarczyk, M. Wikło, K. Kołodziejczyk, R. Król, and K. Król. Theoretical and experimental verification of one stage cycloidal gearbox efficiency. In: T. Uhl (ed.) Advances in Mechanism and Machine Science. Proceedings of the 15th IFToMM World Congress on Mechanism and Machine Science, pages 1029–1038, Cracow, Poland, 15-18 July, 2019. doi: 10.1007/978-3-030-20131-9_102.
[32] M. Wikło, K. Olejarczyk, K. Kołodziejczyk, K. Król, and I. Komorska. Experimental vibration test of the cycloidal gearbox with different working conditions. Vibroengineering PROCEDIA, 13:24–27, 2017. doi: 10.21595/vp.2017.19073.
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Authors and Affiliations

Roman Król
1
ORCID: ORCID

  1. Kazimierz Pulaski University of Technology and Humanities in Radom, Faculty of Mechanical Engineering, Poland.
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Abstract

This paper presents the construction of adequate 3-D computer models for simulation research and analysis of dynamic aspects of caliper disc brakes, as well as of drum brakes, actuated by a short stroke electromagnet or a hydraulic thruster, when these brake types are used in the hoisting mechanism of cranes. The adequacy of the 3-D models has been confirmed by comparing their simulation results with results from an experiment and from classic computational models. The classic computational models, related to the study of main dynamic features of friction brakes, are layouts that are based on a number of assumptions, such as that the braking force instantly reaches its steady-state value, the clearance between the friction lining and the disc/drum is neglected, etc. These assumptions lead to a limitation of research options. The proposed 3-D computer models improve the research layouts by eliminating a number of the classic model assumptions. The improvements are related to the determination of the braking time, braking torque, normal force and other dynamic aspects of the brakes by performing simulations that take into account: the braking force as a function of time, the presence of clearance between the friction lining and the disc/drum, etc.
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Authors and Affiliations

Yanko Slavchev
Lubomir Dimitrov
Yavor Dimitrov

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