Dynamic modeling of a piezoelectric fuel injector during rate shaping operation

Abstract

Piezoelectric fuel injectors provide a means to lower emissions, noise, and fuel consumption in advanced internal combustion engines by enabling complex injection rate profiles—referred to as “rate shaping.” Consideration of flow rate nonlinearities, piezostack hysteresis, and hydromechanical dynamics is required to achieve precise control of rate shaping. The goal of the effort described here was to develop, and experimentally validate, a dynamic, physically based model of a piezoelectric fuel injector during rate-shaping operating conditions. The model prediction captures the rate shape and demonstrates injected fuel errors of less than 5.2%.

Model-based estimation of piezoelectric fuel injector parameters

“…These experiments were conducted in an off-engine injector test rig, and the resulting A 1 (x 2 ) = A 1,0 curve was assumed to be accurate for all injectors. Since A 1 essentially quantifies how open or closed the nozzle is, it plays a critical role in determining the flow rate of fuel spraying out of the injector (especially during the toe, when the model is particularly sensitive [6]). As such, it would be beneficial to determine the A 1 (x 2 ) relationship for any given injector on-engine.…”

“…Since the parameter estimation in this paper was done entirely in a simulation environment, the dynamic injector model described and validated in [6] was used in the "Injector Simulation Model" block to simulate a real injector. This model contains eleven states and its outputs to the rest of the strategy are the total injected fuel per injection and the body pressure (which would be referred to as the line pressure on a real injector).…”

“…Additionally, A 1 (x 2 ) may change over the life of an injector if the needle happens to incur cavitation damage as it ages. In [6], A 1 (x 2 ) was determined by performing a series of experiments on a single injector. These experiments were conducted in an off-engine injector test rig, and the resulting A 1 (x 2 ) = A 1,0 curve was assumed to be accurate for all injectors.…”

“…Previous efforts by the co-authors and their colleagues have resulted in simulation models of the piezoelectric fuel injector during multi-pulse [5] and rate shaping [6] conditions. In addition, model-based fuel flow estimators for both cycle-tocycle and within-a-cycle control were developed in [7] and [8], respectively.…”

Study of the filling mechanism and parameter optimization method for vacuum casting

“…To calculate the temperature field using the finite difference method [10], a partition into layers comprising triangular cells and circular tubular cells along the thickness and radial directions respectively was created. The resulting finite difference form of the transient terms at the Nth node and jth layer is…”