Elastic deformation of a hypoid gearbox

High load carrying capacity in the gear mesh can be achieved when the contact load is well distributed. Designing an adequate tooth flank geometry requires a thorough calculation approach. This is particularly important for automotive hypoid gearboxes with aluminum housing. In this paper, the deformation analysis of housing, bearings and shafts for a hypoid gearbox is validated by measurements at a static test rig. The challenge of compensating friction effects to get high-quality measurement results is successfully met by the presented approach.

There are several computer programs to calculate the elastic deformation behavior of the system shaft-bearing-housing. Most of the calculation programs use analytical approaches. The advantage of these programs, in comparison to a full FEM approach, is an efficient parameterization of gears and a very short calculation time, while delivering high precision results. The deformation behavior of housings can be considered in different ways. The deformation behavior of a bearing seat can be modelled by its stiffnesses. For housings with lower stiffnesses (for example aluminum housings), crossover influences become more and more important. The deformation behavior of a housing can be taken into account by a stiffness matrix. The stiffness matrix of a housing can be determined by using the finite elements method. Therefore, the complex elastic deformation behavior of housings can be considered in analytical calculation approaches. Within the scope of a research project, investigations have been made to validate the calculated elastic deformations of the shaft-bearing-housing system. For this purpose, deformation measurements of a test gearbox were taken by using a 3D coordinate measuring machine. The test gearbox is static and consists of a hypoid gearbox for automotive applications. The input torque is provided by a lever mechanism. The elastic deformation of the test gear box has been measured and compared to calculation results. Therefore, different approaches of modelling the elastic deformation behavior of the housing can be validated and compared to each other.