Design Optimization Model for an Automotive Electric Water Pump

This report describes a design optimization model for an automotive water (coolant) pump driven by a DC electric motor. It is intended for use as an example problem for multidisciplinary design optimization (MDO) methods, and consists of several interacting analysis functions. These analysis functions are based on sets explicit algebraic equations, making this model easily reproduced for use in MDO studies. A similar model was presented in [1] that involved the design of a belt-driven electric sump pump. The model presented here is more sophisticated, and uses an alternative approach to solve for the steady state operating speed. In [1] the analysis functions generated torque-speed curves for the pump and motor, and then solved for the intersection of those curves to find the operating point. Generating these curves was costly, but eliminated some of the feedback coupling between analysis functions. In this model the operating speed is treated as a coupling variable [2], and instead of determining the operating speed via torque-speed curves, it is solved for as an unknown state variable. This results in strong coupling between analysis functions, but makes for a more interesting analysis structure for analysis of MDO methods. Traditional automotive water pumps are belt driven by the vehicle engine, constraining pump shaft speed speed to engine speed multiplied by the belt speed ratio. In some cases, such as idling after a period of high load, the water pump must provide flow and pressure sufficient to cool a hot engine at low shaft speeds. Pumps can be designed to operate efficiently at a specific operating point, but cannot be simultaneously efficient at high and low shaft speeds. An enginedriven pump operates at off-design flow conditions during much of its duty cycle due to large speed fluctuations, requiring more input power than a pump driven by a constant-speed source. A motor-driven pump can provide constant input speed, and also consumes less energy by only pumping when when needed. Traditional water pumps are run continuously and utilize a thermostat-controlled bypass when engine cooling is not required. Electrification of belt-driven automotive components is a promising means for improving fuel economy. Electrification of some components, such as cooling fans, has been incorporated for some time into production vehicles. Electrification of additional components is a more recent endeavor [3, 4, 5]. Surampudi et al. tested a speed-controlled electric water pump on a class-8 tractor and measured an 80% reduction in energy consumption [6]. The analysis model used in this design problem involves five interdependent analysis functions that compute performance metrics based on ten design variable values. These quantities are defined in Table 1. Design variables x1–x5 define motor geometry, and x6–x10 define pump geometry. The motor is a permanent magnet brushed DC electric motor with four pole pairs, and the pump is single-stage centrifugal with six impeller blades and a single diffuser vane (Fig. 1). The motor directly drives the pump, so their shaft speeds are identical: ωmotor = ωpump = ω.