Calculation of overloads induced by indexing errors in spur gearboxes using multi-degree-of-freedom dynamical simulation

Abstract

Indexing errors are a cause of significant vibration and overloading in gearboxes and require much designer attention, especially in high-speed applications. Furthermore, the continuously varying elastic deflections of the meshing teeth contribute to vibration excitation and tooth profile corrections, which are usually employed to alleviate the ill effects of these errors and further complicate the modelling of the phenomenon. Current gear dynamical simulation models either do not consider indexing errors or do so in a simplified manner.To address this problem, in this article, the exact geometry of tooth meshing is used as a starting point for a comprehensive dynamical modelling of gear systems, seamlessly incorporating the effect of pitch errors, tooth separation, degree-of-freedom coupling, and profile corrections. The resulting model is fundamentally non-linear. A single-stage spur gear reducer is then simulated dynamically using various scenarios of error distributions and profile corrections, and the overload factor is calculated. The results show that there are optimal corrections, which can reduce overload by a factor of nearly 35 per cent; however, with bigger corrections, the benefit diminishes. The sensitivity of different design solutions to manufacturing tolerances is investigated and definitive trends are recognized. Finally, a new design recommendation for profile correction is made on the basis of these findings.

Modelling Dependencies and Couplings in the Design Space of Meshing Gear Sets

“…Most commonly, however, it is the stiffness function (the variation of stiffness with the angular position) that must be carefully designed, primarily to achieve a desired dynamical response [9].…”

“…It is a metric of the mesh self-excitations and it is generally desirable to minimise it, in order to reduce noise, vibrations and the fatigue loading of gears. It is strongly influenced by the stiffness function, and thereby by the contact ratio, any errors and profile modifications [9].…”

“…In [9] a study was presented to minimise the load factor by means of profile modifications in the form of tip relief. The recommendations were made based on dynamical simulations and took into account the existence of index errors of various magnitudes and of an optimal 'flat region' where sensitivity to the modification parameters is minimised.…”

Calculation of Spur Gear Dynamic Transmission Error in Consideration of the Progressive Engagement of Compliant Profile-modified Teeth

“…Almost all of the research conducted on gear dynamic behavior is limited to unmodified conjugate gears [2][3][4][5][6][7][8], thereby leaving these questions regarding the dynamic behavior of gears with profile modifications unanswered. It used to be that profile modifications were mostly considered at the level of static and/ or kinematic calculations [9][10]; however this trend is changing [11][12].…”

A Lightweight Model for Gear Mesh Dynamics Incorporating Variable Mesh Stiffness

“…The study of gear vibration has traditionally treated problems such as the determination of the primary resonant speeds of given gear mechanisms, or calculating the corresponding load factors [1][2][3][4][5]. However these models are typically either too simplistic in terms of how stiffness is modelled, or employ complex FEA analysis that is resource intensive.…”