Linear Algebraic Modeling of Power Flow in the HMPT500-3 Transmission

The HMPT500-3 is a split torque path hydrostatic / mechanical continuously variable transmission used in the Bradley Fighting Vehicle. Power transmission and steering is accomplished through the interaction of six planetary gear sets and two variable displacement hydrostatic pump / motor units (HSUs). Power flow in the HMPT500-3 is extremely complex, with numerous feedback paths within the planetary gear train. Without a clearly defined power flow path from gear set to gear set, the analysis cannot be handled in the conventional stepwise manner. The complete speed and torque equation sets must be solved simultaneously for all components. A linear algebraic approach was developed to model forward operation of the HMPT500-3 without steering. The left and right HSUs are lumped in a single unit, and the steering differential is ignored. A reduced set of 14 simultaneous equations for speed and 14 simultaneous equations for torque enable modeling of the ideal (lossless) power flow in the transmission for all forward ranges. Transmission losses are then estimated based on the speed and torque for each individual component, allowing the transmission overall efficiency to be calculated.