Research on modified lumped parameter method in torsional vibration analysis of reciprocating compressor shaft

Abnormal vibrations often occur during the operation of reciprocating compressors under different load conditions. To efficiently and accurately calculate the torsional vibration response of the shafting under various working conditions, a modified lumped parameter method (MLPM) based on finite element mode modification is proposed. MLPM is derived from the lumped parameter method (LPM) and incorporates corrections to the stiffness matrix based on the multi-degree-of-freedom modal calculation using a finite element model. This allows MLPM to combine the high accuracy of finite element method (FEM) with the fast computing speed of LPM. To demonstrate the effectiveness of MLPM, an abnormal vibration compressor equipped with a stepless capacity control system is considered. MLPM is utilized to calculate the torsional natural frequency (TNF) and torsional torque response of the compressor's shafting. The computed 1st-order TNF error between MLPM and FEM is only 0.20%. In the time domain, the torque response error of MLPM is less than 3.07%, while in the frequency domain, it is less than 0.57%. Moreover, MLPM exhibits a significantly increased calculation speed of more than 95% compared to FEM. By comparing MLPM results with torsional vibration test data, the 1st-order TNF error is found to be less than 0.50%, and the frequency-domain torque response error is no more than 8.91%. Furthermore, MLPM is effectively applied to solve the abnormal vibration problem of the compressor. It proposes a modification plan for the shafting, which successfully avoids torsional resonance and reduces the peak value of the torque response by 54.77%. These results demonstrate that MLPM is highly suitable for practical engineering applications due to its combination of high accuracy and fast computing speed.