A semi-analytical approach to simulate strains in load sensing bearings using FEA

Abstract

The advancements in driver assistance systems in cars and the development of autonomous vehicles require more states of the car to be known than the conventional sensors can accurately determine. Load sensing bearings (LSBs) are under development that measure the wheel forces under dynamic load. Through sensor fusion, the addition of this sensor can increase the robustness and accuracy of the state estimators used in cars. An algorithm uses the strain measured on the surface of an instrumented LSB to calculate the forces on the bearing. The development of LSBs requires a tool that simulates the strain signals in a fast and accurate manner to gain insight into the bearing behavior.
Due to the complex nonlinear behavior of the bearing, there is not a fast, straightforward tool available that estimates its strains. This thesis presents a methodology that uses finite element analyses (FEA) to construct a model that calculates the strain in the outer ring of a wheel bearing for any given load. The FEA consists of a linear elastic model of the outer ring and a single loaded ball that is modeled by a Hertzian contact. Multiple simulations are done for different positions of the ball, such that a rotating bearing can be approximated. A nonlinear analytical bearing model in conjunction with a, from FEA constructed, outer ring flexibility model calculates the load on each bearing ball. A strain model, also built from the FEA, uses these loads to calculate the strain on the outer ring.
The simulated strains are validated with experiments performed on a bearing test rig of SKF. Measurements from a with strain gauges instrumented bearing show that the model predicts the observed behavior in the signals. Analyses of the simulated and measured signals in the frequency domain show a difference in gain and offset, which can be calibrated. Unexpected discrepancies are observed within the measured signals of symmetrically placed sensors on the LSB, which should give identical signals, that are likely caused by a distortion of the shape of the outer ring introduced by the manufacturing process or installation of the bearing.
The scope for future work should focus on further validation of the model and developing a calibration method to increase the accuracy. It is believed that the uncertainties in the model can be summarized into a small set of parameters that can be calibrated for a specific instrumented LSB with only a few measurements. Once accurate strains can be simulated, the model could be utilized in a state observer to convert actual strain measurements into loads, and it is possible to use it to optimize the design of the LSB and the location of the strain gauges.