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Abstract

This article presents the results of investigating the influence of tooth contact ratio in helical cylindrical gears on vibroactivity of the gearbox. Based on the measurements carried out on a laboratory test stand, time-domain and frequency-domain start-up characteristics of vibrations and acoustic pressure were determined, and vibroactivity was assessed for a gearbox in which 4 pairs of gears were successively mounted with different face contact ratios equal to, respectively, epsilon beta=1,001; 1,318; 1,574; 2,636.

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Authors and Affiliations

Tomasz Figlus
Andrzej Wilk
Henryk Madej
Bogusław Łazarz
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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

In this article, the frequency characteristics of the forces and torques in the various cycloidal gearbox designs were investigated. The aim of the article is the search for frequency patterns that could be used in the formulation of a fault diagnosis methodology. Numerical analysis was performed in the cycloidal gearbox without defects as well as in cycloidal gearboxes with lobe defects or with removed lobes. The results of the numerical analysis were obtained in the multibody dynamics model of the cycloidal gearbox, implemented in Fortran and using the 2nd-order Runge-Kutta method for the integration of the motion equations. The used model is planar and uses Hunt and Crossley’s nonlinear contact modelling algorithm, which was modified using the Heaviside function and backlash to fit cycloidal gearbox model convergence demands. In the analysis of fault diagnosis methods, the coherence function and Morris minimum-bandwidth wavelets were used. It is difficult to find a unique pattern in the results to use in the fault diagnosis because of the random characteristics of the torques at the input and output shafts. Based on obtained results, a promising, low-vibration cycloidal gearbox design with removed 7 lobes of the single wheel was studied using the FFT algorithm.
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Bibliography

[1] Y. Fu, X. Chen, Y. Liu, C. Son, and Y. Yang. Gearbox fault diagnosis based on multi-sensor and multi-channel decision-level fusion based on SDP. Applied Sciences, 12(15):7535, 2022. doi: 10.3390/app12157535.
[2] F. Xie, H. Liu, J. Dong, G. Wang, L. Wang, and G. Li. Research on the gearbox fault diagnosis method based on multi-model feature fusion. Machines, 10(12):1186, 2022. doi: 10.3390/machines10121186.
[3] I. Komorska, K. Olejarczyk, A. Puchalski, M. Wikło, and Z. Wołczyński. Fault diagnosing of cycloidal gear reducer using statistical features of vibration signal and multifractal spectra. Sensors, 23(3):1645, 2023. doi: 10.3390/s23031645.
[4] R. Król. Analysis of the backlash in the single stage cycloidal gearbox. Archive of Mechanical Engineering, 69(4):693–711, 2022. doi: 10.24425/ame.2022.141521.
[5] 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.
[6] R. Król and K. Król. Multibody dynamics model of the cycloidal gearbox, implemented in Fortran for analysis of dynamic parameters influenced by the backlash as a design tolerance. Acta Mechanica et Automatica, 17(2):272–280, 2023. doi: 10.2478/ama-2023-0031.
[7] R. Król. Cycloidal gearbox model for transient analysis implemented in Fortran with constant time step 2nd order integrator. In: A. Puchalski, B.E. Łazarz, F. Chaari, I. Komorska, Z. Zimroz (eds) Advances in Technical Diagnostics II. ICTD 2022. Applied Condition Monitoring, pp. 63–74, vol. 21. Springer, Cham 2023. doi: 10.1007/978-3-031-31719-4_7.
[8] R. Król. Software for the cycloidal gearbox multibody dynamics analysis, implemented in Fortran. (Purpose: presentation of the results in the scientific article), 2023. doi: 10.5281/ZENODO.7729842.
[9] 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.
[10] 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.
[11] 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.
[12] 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.
[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, 100:152–166, 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. . 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] D. Abboud, S. Baudin, J. Antoni, D. Rémond, M. Eltabach, and O. Sauvage. The spectral analysis of cyclo-non-stationary signals. Mechanical Systems and Signal Processing, 75:280–300, 2016. doi: 10.1016/j.ymssp.2015.09.034.
[23] J.M. Morris and R. Peravali. Minimum-bandwidth discrete-time wavelets, Signal Processing, vol. 76, no. 2, pp. 181–193, 1999. doi: 10.1016/S0165-1684(99)00007-9.
[24] R. Król. Software for the cycloidal gearbox multibody dynamics analysis, implemented in Fortran. (Purpose: presentation of the results in the scientific article), 2022. doi: 10.5281/ZENODO.7221146.
[25] P. Flores and H.M. Lankarani. Contact Force Models for Multibody Dynamics, vol. 226, Springer, 2016. doi: 10.1007/978-3-319-30897-5.
[26] MATLAB documentation, https://www.mathworks.com/help/signal/ref/mscohere.html.
[27] MATLAB documentation, https://www.mathworks.com/help/wavelet/ug/wavelet-families-additional-discussion.html.
[28] X. Shi and A.A. Polycarpou. Measurement and modeling of normal contact stiffness and contact damping at the meso scale. Journal of Vibration and Acoustics, 127(1):52–60, 2005. doi: 10.1115/1.1857920.
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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

Reliable monitoring for detection of damage in epicyclic gearboxes is a serious concern for all industries

in which these gearboxes operate in a harsh environment and in variable operational conditions. In this

paper, autonomous multidimensional novelty detection algorithms are used to estimate the gearbox’ health

state based on vectors of features calculated from the vibration signal. The authors examine various feature

vectors, various sources of data and many different damage scenarios in order to compare novel detection

algorithms based on three different principles of operation: a distance in the feature space, a probability

distribution, and an ANN (artificial neural network)-based model reconstruction approach. In order to compensate

for non-deterministic results of training of neural networks, which may lead to different network

performance, the ensemble technique is used to combine responses from several networks. The methods are

tested in a series of practical experiments involving implanting a damage in industrial epicyclic gearboxes,

and acquisition of data at variable speed conditions.

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Authors and Affiliations

Ziemowit Dworakowski
Kajetan Dziedziech
Adam Jabłoński
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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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