Rotordynamics Analysis with a Hirth and Curvic Coupling: 3D Solid Finite Element and Efficient Beam Model

Abstract

Gas turbines and other machinery rotating assemblies are frequently manufactured as multiple components rather than as a single device due to cost and precision requirements. Butt joints, Hirth couplings, and Curvic couplings are widely used to connect the various components. Hirth couplings transmit high torques in the rotating assemblies of compressors and turbines. Curvic couplings are commonly utilized in aircraft engines and large gas turbines for high load capacity and precision centering of stacked components. Both Hirth and Curvic couplings have non-axisymmetric, complex mating contact surfaces, but a curved tooth profile only exists on a Curvic coupling. These complex-shaped contact surface profiles allow the couplings to transmit torque, moment, and force. However, the surface contacts in these couplings introduce non-beamlike behavior such as local lateral flexibility that affects natural frequencies, critical speeds, mode shapes, imbalance response, and vibration stability, making a conventional beam model inadequate.

3D solid finite elements and a GW contact model are presented to explain local deformations at couplings. The proposed approach is benchmarked against experimental measurements of free-free natural frequencies of a test rotor with Hirth and Curvic couplings. The rotor is instrumented with strain gauges for preload force measurements. The Hirth and Curvic couplings’ contact surface roughness is measured with a stylus-type surface profiler. Measured surface roughness is used for obtaining the GW parameters. An iterative computation algorithm is developed and utilized to calculate contact stiffness and contact pressure at complex-shaped contact surfaces. This new approach shows improved predictions compared to existing methods. The proposed approach is applied to an industrial rotor to illustrate the effects of the couplings on natural frequencies as well as critical speeds.

An equivalent beam modeling method is developed to incorporate three-dimensional modeling results into a more accurate and cost-effective beam-based shaft model. Equivalent Young’s modulus Ecoupling and equivalent transverse shear effect Φcoupling are obtained by incorporating 3D solid finite element rotordynamic results into the conventional beam-type finite element rotordynamics. The equivalent beam models are validated using a variety of axial contact models with butt joints, Hirth couplings, and Curvic couplings, with natural frequencies measured in relation to preloads. Experimental data are utilized to establish a relationship between the amplitude parameters and the GW parameters. A case study of an overhung-type rotor-bearing system is performed.