Research Papers

Piezoelectric Injectors for Automotive Applications: Modeling and Experimental Validation of Hysteretic Behavior and Temperature Effects

[+] Author and Article Information
Leonardo Altieri

e-mail: leonardo.altieri@polito.it

Andrea Tonoli

e-mail: andrea.tonoli@polito.it
Mechatronics Laboratory,
Politecnico di Torino,
Corso Duca degli Abruzzi 24,
I-10129 Torino, Italy

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 23, 2010; final manuscript received March 30, 2012; published online October 30, 2012. Assoc. Editor: Eric J. Barth.

J. Dyn. Sys., Meas., Control 135(1), 011005 (Oct 30, 2012) (8 pages) Paper No: DS-10-1378; doi: 10.1115/1.4006627 History: Received December 23, 2010; Revised March 30, 2012

Direct acting piezoelectric injectors seem to be a promising alternative to the electromagnetic ones because they permit a continuous control of the aperture. This characteristic can improve the performances and minimize the emissions of diesel engines. To exploit the potentialities of this kind of actuation, it is necessary to minimize the effects of the hysteretic behavior of piezoelectric materials. For this reason, the behavior of the actuator has to be modeled taking this effect into account. Additionally, the effects of the temperature must be considered, given the particularly critical position of the injectors near the engine. A modeling approach of piezoelectric injectors, including hysteresis and temperature effects as well as the electromechanical dynamic, is described in this paper. The model is based on a linear finite element (FE) discretization of the piezoelectric stack and the injector case. The hysteretic behavior is included in a second step by means of additional nonlinear state equations while the temperature effects are taken into account considering the temperature dependence of the material characteristics. A dedicated test bench has then been realized and experimental tests have been performed on piezoelectric injectors, with driving voltages and temperatures commonly used in automotive environment. The collected data allow to tune the model and to verify its validity even out of the tuning conditions.

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Fig. 2

Injector elements for FEM analysis. Piezoelectric injector actuator stack (gray), housing (white), stack tip (node 1), external force acting on the tip (Fext), and tip displacement (qpzt).

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Fig. 1

Piezoelectric element. The electrodes of the layers included in the element are mechanically in series and electrically in parallel.

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Fig. 3

Impedance of piezoelectric stack with case: comparison between experimental data (black), FEM (gray), and FEM reduced to the lowest five modes (dashed-dotted)

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Fig. 5

Experimental test bench of piezoelectric injectors. (1) Laser sensor, (2) injector support, (3) temperature PID controller, (4) injector heater jacket, (5) injector, (6) thermocouple, (7) sensor controller, (8) sensor signal conditioning block, and (9) XYZ linear stages.

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Fig. 4

Scheme of the piezoelectric injector model

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Fig. 8

(a) Stack tip displacement: experimental (black line), model with hysteresis (gray), and model without hysteresis (dotted); (b) absolute (black line) and relative (gray) errors between measured displacement and simulations; (c) absolute (black line) and relative (gray) errors between measured charge and simulations with respect to time. The relative error is computed considering the maximum values of the measured displacement and charge during a cycle with Vmax = 150 V and T = 20 °C.

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Fig. 6

Hysteresis loop characterization. Experimental results (black lines) and simulation (gray). Voltage-driven piezoelectric with a triangular wave shape, Vmax = 70–90–110–130–150 V, T = 20 °C.

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Fig. 7

Example of driving voltage used for experimental tests and simulations

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Fig. 9

Multiplier factors δd and δɛ related to temperature. Experimental (dots) and linear models (lines). Linear models correspond, respectively, to kd=2.154·10-3( °C-1) and kɛ=3.846·10-3( °C-1).

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Fig. 10

Hysteresis loop and temperature effects characterization. Experimental results (black lines) and simulation (gray). Voltage-driven piezoelectric with a triangular wave shape, Vmax = 150 V at temperatures T = 20–55–85 °C.




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