Power transmission system, cardan shaft, speed capture, phase angle, universal joint


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.


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