Modeling of Bradley Tracked Vehicle Steering and Fuel Consumption with a Detailed Kinematic Model of the HMPT500-3 Transmission and Simplified Vehicle Dynamics

The HMPT500-3 is a split torque path hydrostatic / mechanical CVT used in the Bradley Fighting Vehicle. A previous paper detailed a linear algebraic approach to model forward operation of the HMPT500-3 without steering using a reduced equation set. This model was expanded to the full equation set to allow transmission operation with steering. The equations showed that opposite to a typical automotive “open” differential, the HMPT500-3 enforces a speed difference between the sprockets for steering, but does not have an inherent torque bias. The typical regenerative steering torque from the decelerated inside track must be provided by interfacing with a vehicle model. A simplified 2-D planar dynamics model of the Bradley was developed to explore vehicle performance and fuel consumption with steering. The integrated model showed that fuel consumption during minimum radius turns can double that of straight-ahead operation at the same speed. Commercial vehicle performance codes lack tracked steering models, so test courses are run as simple gradient vs. distance profiles which would result in underestimating fuel consumption. The Munson Fuel Loop course was selected to attempt to quantify the contribution of steering to total fuel consumption. Fuel consumption calculations with steering were found to be 9% to 14% higher than those without steering depending on lap speed, and compared more favorably with Bradley test data. INTRODUCTION 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 complex interaction of six planetary gear sets and two variable displacement hydrostatic pump / motor units (HSUs), connected through intermediate shafts and gears. A previous paper (GVSETS 2012, ref [1]) detailed a linear algebraic approach to model forward operation of the HMPT500-3 without steering using a reduced equation set. This model was expanded to the full 22 simultaneous speed / torque equations to allow transmission operation with steering to be modeled. The equation set showed that opposite to a typical automotive “open” differential, the HMPT500-3 as a hydrostatic controlled differential enforces a speed difference between the sprockets for steering, but does not have an inherent torque bias between the sprockets. The typical regenerative steering torque from the decelerated inside track must be provided by interfacing with a vehicle dynamics model. A simplified 2-D planar dynamics model of the Bradley was developed to allow the transmission model to be fully exercised. This model uses lumped inertias for the vehicle body, running gear and drivetrain. Longitudinal gradient, rolling and aerodynamic resistances are accounted for and steering lateral dynamics are handled by modified Merritt steering equations. The Merrittmodel provides a closed form solution for the required steering moment and longitudinal track slip for steady state turns at a given radius and vehicle speed based on simple vehicle geometry and terrain factors. Exercising the integrated transmission & vehicle model showed that fuel consumption during minimum radius turns can reach double that of straight-ahead operation at the same speed. Current commercial codes for vehicle performance and fuel consumption lack tracked steering models, so test courses are run as simple gradient vs. distance profiles. This would result in underestimating fuel consumption, so it was decided to attempt to quantify the contribution of steering to total fuel Proceedings of the 2015 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) Modeling of Bradley Tracked Vehicle Steering and Fuel Consumption with a Detailed Kinematic Model of the HMPT500-3. UNCLASSIFIED: Distribution A, Approved for Public Release. Page 2 of 8 consumption on a typical test course. The Munson Fuel Loop course was selected as full profile data was available, as well as actual Bradley fuel consumption data. Course gradient and curvature (inverse of radius) were calculated at each step along the course. Pending development of a PID driver sophisticated enough to reliably follow the course, the vehicle model was used to generate fuel burn rate lookup tables over a wide range of speeds, grades and turn radii from infinity (straight road) to the minimum radius capability. The course speed at each location was then determined as the minimum of the target lap speed, speed on grade, speed in turn or acceleration limited speed recovery capability. This allowed calculation of the time to complete each distance step, and fuel burn rates with and without steering. The resulting integrated fuel consumption and average speed were then compared to vehicle test results on the Munson course over a range of speeds. Fuel consumption calculations with steering were found to be ~ 9 14% higher depending on lapspeed than those that ignored the effect of steering, and compared more favorably with the test data. THE TRANSMISSION / DRIVETRAIN MODEL Details of the simultaneous speed and torque equations used to model the HMPT500-3 for forward operation are available in a previous paper [1]. The simplified model ignored the steering differential, which uses a double-pinion planetary gear to provide a true averaging of the Left / Right HSU outputs. As before, the planetary gear set is described by one speed and two torque equations. With N denoting the number of gear teeth, S rotational speed and T torque and subscripts 1 thru 3 denoting the sun, carrier and ring gear respectively: N1S1 + (N3 − N1)S2 − N3S3 = 0 (1) T1 N1 + T2 (N3 − N1) + 2T3 N3 = 0 (2) T1 N1 + T3 N3 = 0 and N3 = 2N1 (3) The resulting 22 simultaneous equations for speed can be solved for each range of transmission operation to determine left and right output speeds based on input (engine) speed and left / right HSU actuation strokes. The set of 22 simultaneous torque equations is however under-determined, and some additional relationship between left and right output torques is required. This suggests that the HMPT500-3 as a hydrostatic controlled differential has no inherent left-right output torque bias, even while enforcing a speed difference between the two outputs for steering. This behavior is opposite to a typical automotive “open” differential, which allows any output speed difference, while balancing the output torques. The complete steering performance of the transmission cannot be determined in isolation, and the typical regenerative steering torque from the decelerated inside track must be provided by interfacing with a vehicle dynamics model. The complete drivetrain model is comprised of the engine, transmission and final drives / running gear as shown in figure-1. The constant final drive ratio is included in the overall gear ratios between the engine and left / right outputs. Lumped rotating inertias are used for the engine at the transmission input and the sprocket-track system at the outputs.