Dynamic analysis and identification of unbalance and misalignment in a rigid rotor with two offset discs levitated by active magnetic bearings: a novel trial misalignment approach

Prabhat Kumar, Rajiv Tiwari *

Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

Abstract: Rotating machinery is an essential and crucial component of numerous mechanical systems in modern industries, transport vehicles, and in several other applications. Excessive vibrations on rotating equipment due to multiple faults may cause catastrophic failure in machines and lead to hazardous accidents. So, there is a need for perceiving the dynamic nature and identifying the faults for the safe, smooth and effective operation of machines. This paper proposes a novel trial misalignment approach to estimate the misalignment with a similar concept as the trial unbalance in the rotor balancing. Active magnetic bearing (AMB) misalignment with the rotor has been investigated with residual misalignment and additional trial misalignment cases. Additional trial misalignments are provided in addition to the unknown misalignments of the residual misalignment case. For the execution of this methodology, the dynamic model of a four-degree-of-freedom unbalanced and misaligned rigid rotor with two offset discs supported by two active magnetic bearings has been mathematically developed. The offset discs result in the gyroscopic effect at high rotor speeds. Equations of motion of the rotor-AMB system have been derived and solved to generate the time domain rotor displacement and controlling current responses at AMB positions. A fast Fourier transform technique has been utilized to convert the time domain responses into the frequency domain for estimation of unbalance eccentricities and phases together with force-displacement and force-current stiffnesses of misaligned AMBs as well as AMB’s constant forces using the developed identification algorithm. Identified values of AMB’s parameters for both residual and additional trial misalignment cases are evaluated to estimate the four unknown misalignments. Testing of the algorithm has also been carried out at multiple spin speeds against measurement signal noise in rotor responses and bias errors in rotor system parameters to check its effectiveness and robustness. The algorithm is found to be exhibiting excellent.

Keywords: Misalignment; Unbalance; Active magnetic bearing; Gyroscopic moment; Fast Fourier transform; Identification