SUPPRESSION OF SOMMERFELD EFFECT IN POWER TRANSMISSION SYSTEM EMPLOYING CARDAN SHAFT THROUGH PHASE ANGLE ARRANGEMENT
DOI:
https://doi.org/10.11113/jurnalteknologi.v86.21123Keywords:
Power transmission system, cardan shaft, speed capture, phase angle, universal jointAbstract
In a power transmission system with a cardan shaft, the Sommerfeld effect occurs, which is characterized by speed capture and release at the resonance range. Suppression of the Sommerfeld effect is critical for smooth and reliable operation. This study aims to suppress the Sommerfeld effect in a transmission system by compensating the phase angle between the two universal joints installed in the cardan shaft. The differential equations of motion representing the dynamics of the system are derived using the Lagrange equation. The responses are simulated numerically using the Runge–Kutta algorithm for scenarios with constant and gradually varying input torque. To suppress the Sommerfeld effect, the phase angle is set to 25%, 50%, 75% and 100% of the maximum twist angle observed in the subcritical speed range of the in-phase configuration. With the phase angle of 25%, the Sommerfeld effect is damped, where the output speed only deviates by 5% from the estimated value for both input torque scenarios. It is shown how the change of the phase angle attenuates the Sommerfeld effect and the system vibrations, which should be considered in the development and practical implementation.
References
Ding, J., Lin, J., Yu, S. 2015. Dynamic Unbalance Detection of Cardan Shaft in High-speed Train Applying Double Decomposition and Double Reconstruction Method. Measurement. 73: 111-120.
Yi, C., Lin, J., Ruan, T., Li, Y. 2015. Real Time Cardan Shaft State Estimation of High-speed Train based on Ensemble Empirical Mode Decomposition. Shock and Vibration. https://doi.org/10.1155/2015/912483.
Golafshan, R., Dascaliuc, C., Jacobs, G., Roth, D., Berroth, J., Neumann, S. 2021. Damage Diagnosis of Cardan Shafts in Mobile Mining Machines using Vibration Analysis. IOP Conference Series: Materials Science and Engineering. 1097: 012019.
Hu, Y., Zhang, B., Tan, A. C. 2020. Acceleration Signal with DTCWPT and Novel Optimize SNR Index for Diagnosis of Misaligned Cardan Shaft in High-speed Train. Mechanical Systems and Signal Processing. 140: 106723.
Huang, Q., Yan, X., Wang, Y., Zhang, C., Wang, Z. 2017. Numerical Modeling and Experimental Analysis on Coupled Torsional-longitudinal Vibrations of a Ship’s Propeller Shaft. Ocean Engineering. 136: 272-282.
Hu, Y., Lin, J., Tan, A. C. 2019. Failure Analysis of Gearbox in CRH High-speed Train. Engineering Failure Analysis. 105: 110-126.
Liu, J. S. P., Remisoski, N., Iqbal, J., Egenolf, R. 2017. CAE Predictions for Cardan Joint Induced Driveline NVH. SAE Technical Papers. https://doi.org/10.4271/2017-01-1136.
Kato, M., Ota, H. 1990. Lateral Excitation of a Rotating Shaft Driven by a Universal Joint with Friction. Journal of Vibration and Acoustics, Transactions of the ASME 112: 298-303.
Han, H. S., Lee, K. H. 2019. Experimental Verification for Lateral-torsional Coupled Vibration of the Propulsion Shaft System in a Ship. Engineering Failure Analysis. 104: 758-771.
Hu, Y., Chit Tan, A., Liang, C., Li, Y. 2021. Failure Analysis of Fractured Motor Bolts in High-speed Train Due to Cardan Shaft Misalignment. Engineering Failure Analysis. 122: 105246.
Zheng, Z., Lin, J., Hu, Y., Zhou, Q., Yi, C. 2022. Dynamic Unbalance Identification and Quantitative Diagnosis of Cardan Shaft in High-speed Train based on Improved TQWT-RBFNN-NSGA-II Method. Eng Fail Anal. https://doi.org/10.1016/j.engfailanal.2022.106226.
Tchomeni, B. X., Alugongo, A. 2020. Theoretical and Experimental Analysis of an Unbalanced and Cracked Cardan Shaft in the Vicinity of the Critical Speed. Mathematical Models in Engineering. 6: 34-49.
An, K., Wang, W. 2017. Transmission Performance and Fault Analysis of a Vehicle Universal Joint. Advances in Mechanical Engineering. https://doi.org/10.1177/1687814017707478.
Fischer, I. S., Paul, R. N. 1991. Kinematic Displacement Analysis of a Double-cardan-joint Driveline. Journal of Mechanical Design, Transactions of the ASME. 113: 263-271.
Wu, G., Shi, W., Chen, Z. 2013. The Effect of Multi-universal Coupling Phase on Torsional Vibration of Drive Shaft and Vibration of Vehicle. SAE Technical Paper.
Sundar Dasgupta, S. 2022. Dynamics of a Non-Ideal Gyroscopic Rotor System with Translational-Rotational Coupling Effect of External and Internal Damping. Mechanics of Solids. 57: 604-616.
Bharti, S. K., Samantaray, A. K. 2021. Resonant Capture and Sommerfeld Effect due to Torsional Vibrations in a Double Cardan Joint Driveline. Communications in Nonlinear Science and Numerical Simulation. 97: 105728.
Yao, W., DeSmidt, H. 2021. Nonlinear Coupled Torsion/Lateral Vibration and Sommerfeld Behavior in a Double U-Joint Driveshaft. Journal of Vibration and Acoustics. 143: 1-15.
Sinha, A., Bharti, S. K., Samantaray, A. K., Bhattacharyya, R. 2020. Sommerfeld Effect in a Single-DOF System with base Excitation from Motor Driven Mechanism. Mech Mach Theory. https://doi.org/10.1016/j.mechmachtheory.2020.103808
Sinha, A., Samantaray, A. K. 2023. Escape through Parametric Instabilities in a Non-ideal Motor Driven Geared Rotor Shaft Driveline. Mechanism and Machine Theory. 180: 105166.
Bharti, S. K., Sinha, A., Samantaray, A. K., Bhattacharyya, R. 2021. Dynamics of a Rotor Shaft Driven by a Non-ideal Source through a Universal Joint. Journal of Sound and Vibration. 499: 115992.
Jha, A. K., Dasgupta, S. S. 2020. Suppression of Sommerfeld Effect in a Non-ideal Discrete Rotor System with Fractional Order External Damping. European Journal of Mechanics, A/Solids. https://doi.org/10.1016/j.euromechsol.2019.103873.
Jha, A. K., Dasgupta, S. S. 2019. Attenuation of Sommerfeld Effect in an Internally Damped Eccentric Shaft-disk System via Active Magnetic Bearings. Meccanica. 54: 311-320.
SoltanRezaee, M., Ghazavi, M. R., Najafi, A., Rahmanian, S. 2018. Stability of a Multi-body Driveshaft System Excited through U-joints. Meccanica. 53: 1167-1183.
Zají˘ Cek, M., Dupal, J. 2014. Analytic Solution of Simplified Cardan’s Shaft Model.
Schmelz, F., Seherr-Thoss, CH-C., Aucktor, E. 1992. Universal Joints and Driveshafts. Universal Joints and Driveshafts. https://doi.org/10.1007/978-3-662-02746-2.
Chaban, A., Łukasik, Z., Popenda, A., Szafraniec, A. 2021. Mathematical Modelling of Transient Processes in an Asynchronous Drive with a Long Shaft Including Cardan Joints. Energies (Basel). https://doi.org/10.3390/en14185692.
Xia, Y., Pang, J., Yang, L., Zhao, Q., Yang, X. 2019. Nonlinear Numerical and Experimental Study on the Second-order Torsional and Lateral Vibration of Driveline System Connected by Cardan Joint. JVC/Journal of Vibration and Control. https://doi.org/10.1177/1077546319889846.
Murawski, L., Dereszewski, M. 2020. Theoretical and Practical Backgrounds of Monitoring System of Ship Power Transmission Systems’ Torsional Vibration. Journal of Marine Science and Technology (Japan). 25: 272-284.
Downloads
Published
Issue
Section
License
Copyright of articles that appear in Jurnal Teknologi belongs exclusively to Penerbit Universiti Teknologi Malaysia (Penerbit UTM Press). This copyright covers the rights to reproduce the article, including reprints, electronic reproductions, or any other reproductions of similar nature.
