Dynamic simulation of high-pressure angle spur gears

Abstract

The present work dwells with the dynamic modeling of high-pressure angle spur gears ranging from 30 to 35 degrees. The benefits and potential of such gears in terms of dynamic performance is explored. A custom optimized spur gear tooth root geometry is used to construct the root area of the case studies presented and compared versus standardized ISO geometries. An extension of the closed-form load and position-dependent mesh stiffness previously developed by the authors is introduced to accommodate the hereby studied non-standard gear geometries. The non-linear load and position-dependent mesh stiffness is formulated in closed form using a hybrid polynomial/ logarithmic approximation and validated versus finite element results. The non-implicit single degree of freedom (DOF) dynamic model employed is discussed in detail and manages to successfully predict the dynamic transmission error of a gear pair as well as meshing nonlinearities including contact reversal and loss of contact. We present an extensive comparison of the dynamic behavior between standard 20-degre and high-pressure angle gears, for a wide range of rotational speed and transmitted torque values. A colormap with the peak-to-peak transmission error values indicates significant regions of gear operation where high-pressure angle geometries result to a favorable dynamic response. We further examine the transmission error response limit cycle by comparing phase diagrams of different geometries under specific rotational speed and torque conditions. Clear improvement of the transmission error values is demonstrated for the majority of the tested scenarios suggesting increased performance of high pressure angle gears versus conventional geometries.