Efficiency analysis of spur gears with a shifting profile

A model for the assessment of the energy efficiency of spur gears is presented in this study, which considers a shifting profile under different operating conditions (40–600 Nm and 1500–6000 rpm). Three factors affect the power losses resulting from friction forces in a lubricated spur gear pair, namely, the friction coefficient, sliding velocity and load sharing ratio. Friction forces were implemented using a Coulomb’s model with a constant friction coefficient which is the well-known Niemann formulation. Three different scenarios were developed to assess the effect of the shifting profile on the efficiency under different operating conditions. The first kept the exterior radii constant, the second maintained the theoretical contact ratio whilst in the third the exterior radii is defined by the shifting coefficient. The numerical results were compared with a traditional approach to assess the results.The authors would like to acknowledge Project DPI2013-44860 funded by the Spanish Ministry of Science and Technology and the COST ACTION TU 1105 for supporting this research

Advanced model for the calculation of meshing forces in spur gear planetary transmissions

This paper presents a planar spur gear planetary transmission model, describing in great detail aspects such as the geometric definition of geometric overlaps and the contact forces calculation, thus facilitating the reproducibility of results by fellow researchers. The planetary model is based on a mesh model already used by the authors in the study of external gear ordinary transmissions. The model has been improved and extended to allow for the internal meshing simulation, taking into consideration three possible contact scenarios: involute–involute contact, and two types of involute-tip rounding arc contact. The 6 degrees of freedom system solved for a single couple of gears has been expanded to 6 + 3n degrees of freedom for a planetary transmission with n planets. Furthermore, the coupling of deformations through the gear bodies’ flexibility has been also implemented and assessed. A step-by-step integration of the planetary is presented, using two typical configurations, demonstrating the model capability for transmission simulation of a planetary with distinct pressure angles on each mesh. The model is also put to the test with the simulation of the transmission error of a real transmission system, including the effect of different levels of external torque. The model is assessed by means of quasi-static analyses, and the meshing stiffness values are compared with those provided by the literature.The authors would like to acknowledge Project DPI2013-44860 funded by the Spanish Ministry of Science and Technology

Prediction and experimental verification of the cutting forces in gear form milling

In this paper, a mathematical model is presented by which the cutting forces in gear form milling process are predicted using the mechanistic approach. To use this approach, a detailed description of the chip geometry is needed. Eccentricity and run-out tool errors are considered, which is of great importance as the chip thickness will by these errors vary for the subsequent cuts. The chip geometry is determined by comparing the path of the cutting edge with already removed material. The boundary of the chips is determinable from the cutting edge geometry, which is here derived in parametric form so spur and helical gears are manufactured correctly. Locally on the cutting edge, the cutting forces are resolved from orthogonal cutting data and on the basis that these forces are proportional to the instantaneous chip thickness. The load each individual cutting tooth experience in operation, as well as the complete load on the tool, are resolved by summing the forces along the cutting edge. In the model, all cut chips are determined for each machined gear tooth gap, with the gear blank boundaries considered. The paper ends with experimental validation using indexable insert milling cutters. It is shown that the model predicts the force shape well and the peak force levels within 12 %