# EE3901/EE5901 Sensor TechnologiesWeek 12 Tutorial

**Dr. Bronson Philippa**

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

All materials in that datasheet have tetragonal crystal symmetry, i.e. $d_{31}=d_{32}$ and $d_{15}=d_{24}$. 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 $T_{1}$, $T_{2}$ and $T_{3}$ 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 $V_3$ along axis 3.

(a) Calculate the voltage $V_{3}$ when $T_{1}=0$, $T_{2}=0$ and $T_{3}=1000\ \text{N/m}^{2}$.

(b) Calculate the voltage $V_{3}$ when $T_{1}=0$, $T_{2}=1000\ \text{N/m}^{2}$ and $T_{3}=0$.

(c) Calculate the voltage $V_{3}$ when $T_{1}=1000\ \text{N/m}^{2}$, $T_{2}=0$ and $T_{3}=0$.

(d) Determine the relationship between the stresses $T_{1}$, $T_{2}$ and $T_{3}$ that will guarantee $V_{3}=0$.

## 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 $V=100$ 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 $\boldsymbol{S}$ on a single layer of the actuator. Assume no mechanical load (i.e. the stress is given by $\boldsymbol{T}=0$).

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

**Hint:** Engineering shear strain has units of radians, shown in the figure by the angle $S_{5}$. 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?

## Question 4

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

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.