EE3901/EE5901 Sensor Technologies
Week 12 Tutorial

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College of Science and Engineering, James Cook University
Last updated: 10 May 2022

The first 3 questions require material data from PI Ceramic GmbH.

All materials in that datasheet have tetragonal crystal symmetry, i.e. d31=d32d_{31}=d_{32} and d15=d24d_{15}=d_{24}. The other piezoelectric constants that are not specified in the datasheet are zero.

Question 1

The material PIC153 from PI Ceramic GmbH is being used in a force sensing application, as shown in Figure Q1. The material is poled along axis 3. The device is a 1 cm ×\times 1 cm ×\times 1 cm cube. Normal strains T1T_{1}, T2T_{2} and T3T_{3} are applied as indicated. All shear strains are zero. Metal electrodes have been deposited onto the faces that lie in the 1-2 plane, allowing for voltage measurement V3V_3 along axis 3.

Figure Q1: The geometry of the device for Questions 1 and 2. Zoom:

(a) Calculate the voltage V3V_{3} when T1=0T_{1}=0, T2=0T_{2}=0 and T3=1000 N/m2T_{3}=1000\ \text{N/m}^{2}.

(b) Calculate the voltage V3V_{3} when T1=0T_{1}=0, T2=1000 N/m2T_{2}=1000\ \text{N/m}^{2} and T3=0T_{3}=0.

(c) Calculate the voltage V3V_{3} when T1=1000 N/m2T_{1}=1000\ \text{N/m}^{2}, T2=0T_{2}=0 and T3=0T_{3}=0.

(d) Determine the relationship between the stresses T1T_{1}, T2T_{2} and T3T_{3} that will guarantee V3=0V_{3}=0.

Question 2

Ceramic piezoelectric materials lose their inherent polarisation if they are heated above a temperature known as the Curie temperature. Suppose that the sensor in Question 1 needs to operate at 300 °C. Choose the material from the datasheet that will provide the highest sensitivity to strains along axis 3 (as per Figure Q1) but can tolerate these higher temperatures.

Question 3

A piezoelectric shear actuator is built using PIC151, as shown in Figure Q3. The height of an individual layer (when it is perfectly vertical) is 0.8 mm. The applied voltage is V=100V=100 V.

(a) Consider initially a device made from a single layer (of height 0.8 mm). Use the piezoelectric actuator equation


to calculate the strain S\boldsymbol{S} on a single layer of the actuator. Assume no mechanical load (i.e. the stress is given by T=0\boldsymbol{T}=0).

(b) Now consider the multi-layer structure shown in Figure Q3 (b). Let nn be the number of layers. Calculate ΔL\Delta L, which is the distance travelled by the tip of the actuator when the voltage is varied from V=0V=0 to V=100V=100 V.

Hint: Engineering shear strain has units of radians, shown in the figure by the angle S5S_{5}. You may approximate the geometry as that of a right-angled triangle.

(c) How many stacked actuator layers would be required to achieve a working range of 2 μm given an applied voltage range of 0 to 100 V?

Figure Q3: A piezoelectric shear actuator. (a) A single element with the shear greatly exaggerated for clarity. Applying a voltage in direction 1 causes a bending of the tip. (b) A complete actuator has multiple layers with each subsequent layer having an opposite polarisation direction and opposite voltage polarity. The overall movement distance is nΔLn\,\Delta L where nn is the number of layers. Zoom:

Question 4

A sample of quartz has a piezoelectric coefficient matrix of the form

[d11d12d13d14d15d16d21d22d23d24d25d26d31d32d33d34d35d36]=[2.32.300.670000000.674.6000000]×1012 C/N.\left[\begin{array}{cccccc} d_{11} & d_{12} & d_{13} & d_{14} & d_{15} & d_{16}\\ d_{21} & d_{22} & d_{23} & d_{24} & d_{25} & d_{26}\\ d_{31} & d_{32} & d_{33} & d_{34} & d_{35} & d_{36} \end{array}\right]=\left[\begin{array}{cccccc} -2.3 & 2.3 & 0 & -0.67 & 0 & 0\\ 0 & 0 & 0 & 0 & 0.67 & 4.6\\ 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right]\times10^{-12}\ \text{C/N}.

Also, the material has a relative permittivity of 4.5.

(a) Sketch a 3D cube and draw the axes 1, 2, and 3 arbitrarily on your figure. Make sure that you use a right-handed coordinate system (i.e. use your right hand to determine the polarity of each axis).

(b) You are designing a force sensor and want to maximise sensitivity to normal stresses. Choose two opposite faces of the cube to deposit metal electrodes. Indicate how you would connect a voltage meter in order to create a force sensor.

(c) Suppose your cube has dimensions 1 cm ×\times 1 cm ×\times 1 cm. Based on the geometry of part (b), you measure a voltage of 0.05 V. You know that the only stress acting on the quartz crystal is a normal stress along axis 1. Calculate the value of this stress.