Xu, Y., Fujii, Y., Dai, E., McCallum, J. et al., "Piecewise 1st Order Hydraulic Actuator Model for Transient Transmission Simulations," SAE Technical Paper 2017-01-1140, 2017, doi:10.4271/2017-01-1140.
A transmission system model is developed at various complexities in order to capture the transient behaviors in drivability and fuel economy simulations. A large number of model parameters bring more degree of freedom to correlate with vehicular test data. However, in practice, it requires extensive time and effort to tune the parameters to satisfy the model performance requirements. Among the transmission model, a hydraulic clutch actuator plays a critical role in transient shift simulations. It is particularly difficult to tune the actuator model when it is over-parameterized. Therefore, it is of great importance to develop a hydraulic actuator model that is easy to adjust while retaining sufficient complexity for replicating realistic transient behaviors. This paper describes a systematic approach for reducing the hydraulic actuator model into a piecewise 1st order representation based on piston movement. The model is coupled with the planetary gear-train and clutches for demonstrating its performance in 6-speed transmission system simulations. The model is first tuned based on design values, and its hydraulic response is further refined for improved performance. Since the complex hydraulic response is decoupled from the physical parameters and represented with fewer time constants, the model is significantly easier to tune for capturing the transmission dynamics with an additional benefit of computational efficiency.