Summary:

Three multistage between bearing pumps were installed in a nuclear power plant in reactor charge application. The pumps are driven by a 1000 kW electrical motor with VFD through the gearbox. one of the pumps was found with shaft repetitive cracking failures initiated at the key-way stress concentration area, and coupling location between the high-speed shaft and pump speed.  Torsional vibration analysis is performed to find the root cause of this shaft cracking problem. all possible external excitations including; Gear meshing, Vaned frequency, line frequency, and 1x and 2x Pump and Motor speeds (4x,8x,12x) are considered. The torsional natural frequencies of the complete train are verified that at least 10 % above or 10 % below any possible excitation frequency within the specified range of operating speeds. The design has been changed to increase the torsional critical speeds. Few torsional resonances are observed to fall within the margin specified in API 610, Clause, 5.9.2.3. 

Stress analysis is performed to demonstrate that the resonances have no adverse effect on the complete train as per API 610, clause 5.9.2.4.

Methodology:

Problem Solving approach:

The entire gear train consists of VFD motor, gearbox (High-speed shaft and Low-speed shaft), the multistage pump is modeled in ANSYS Workbench. Coupling between VFD motor and Low-speed shaft, between high-speed shaft and pump shaft is replaced with equivalent torsional stiffness. Pinion and gear between the high-speed shaft and the low-speed shaft are replaced with mesh stiffness. Weights of rotating components of the pump shaft, motor shaft, and couplings are considered as point masses. All axial and lateral movements are constrained as boundary conditions. Steel 4145 is used for pump, motor, and gearbox shafts. Torsional critical speeds are computed and, and these results are compared with the theoretical approach( Holzer method) and found a good agreement. Campbell's diagram is developed by incorporating all external excitations in order to identify the interference points. As per API 610, clause 5.9.2.3, the torsional natural frequencies of the complete train shall be at least 10 % above or 10 % below any possible excitation frequency within the specified range of operating speeds.  From the analysis it is observed that the 2^nd mode is closure to 2x pump speed, 3^rd the mode is closure to vane passing frequency, and the higher modes are closure to gear mesh frequency.

Main Challenges:

We planned to attempt to increase the shaft dimensions to increase the 2^nd torsional critical speed. Our customer did not agree to modify the shaft dimensions as there are issues with clearances and space constraints.

Results Outcome:

We proceeded with modifying the coupling’s stiffness at high speed and low-speed shaft in order to increase 2^nd TCF, and recommended stiffness was provided to supplied to manufacture couplings. With the modified coupling design, 3^rd mode and higher modes are not changed. The torsional steady-state analysis is performed at vane passing frequency and gear mesh frequency to find the fatigue life of the gear train. Dynamics stresses and mean stresses are calculated from finite element analysis and plotted in a modified goodman's diagram. All points corresponding to mean stress and alternating stresses are fallen inside of the diagram. From the analysis results, it is observed that the design is safe with required modifications.

About the Author:

Dr. Joel Daniel is a principal consultant at Pythagoras Engineering, an engineering consulting firm in India.  He has over 17 years of experience in finite element theory, linear and nonlinear structural analysis, heat transfer analysis, composite life prediction, fracture mechanics, structural vibrations, and rotor dynamics.