A detailed explanation of piezoelectric accelerometers

    Piezoelectric accelerometers are commonly used in vibration and shock testing. These devices are ideal for measuring high-frequency acceleration signals found in hydraulic and pneumatic disturbances, pulse (shock) forces, machinery and equipment vibrations, pyrotechnic shocks, etc.

    In this article, we will get familiar with the basic concepts of these sensors.

    Understanding Piezoelectric Sensors: The Piezoelectric Effect

    The first key aspect of a piezoelectric accelerometer is the piezoelectric effect. Generally speaking, piezoelectric materials can generate electrical energy when subjected to mechanical stress.

    Conversely, applying an electric field to a piezoelectric material can cause it to deform and generate small mechanical forces. Although most EEs are familiar with the piezoelectric effect, the details of this intriguing phenomenon are sometimes not completely clear.

    A deeper understanding of this effect can help us better understand how piezoelectric sensors work. Figure 1 shows the effect of external mechanical forces on piezoelectric materials.

    Figure 1. Piezoelectric material without mechanical stress (a) and with stress (b). Image (adapted) courtesy of Felix Levinzon

    As shown in Figure 1(a), in the absence of mechanical stress, the positive and negative charge centers of the molecule coincide, which means that the molecule is electrically neutral.

    As shown in Figure 1(b), applying a mechanical force deforms the structure and separates the centers of positive and negative charges of the molecules, creating many small dipoles in the material.

    As you can see, some fixed charges appear on the surface of the piezoelectric material. The amount of charge generated is proportional to the force applied.

    How piezoelectric materials generate electric current

    Piezoelectric materials are a class of dielectric materials. They are insulating or very poor conductors of electric current. However, by depositing two metal electrodes on opposite surfaces of a piezoelectric material, we can harness the electric field generated by the piezoelectric effect to generate electricity.

    If we connect the two electrodes together through a wire as shown in Figure 1(b), the free electrons in the conductor flow to the positively charged electrode and generate a current. This current accumulates free electrons at the positive electrode and generates an electric field in the opposite direction to the original electric field generated by the piezoelectric effect.

    This effect explains why the current generated by static force lasts only a short time. The current continues until the electric field generated by the accumulation of free electrons cancels the electric field generated by the piezoelectric effect.

    Now, if we remove the external force, the material returns to its original shape and the electric field created by the piezoelectric effect disappears, which means that current flows through the wire in the opposite direction.

    Structure of a piezoelectric accelerometer

    In a piezoelectric accelerometer, a piezoelectric element is used to attach a known amount of mass (often called a proof mass) to the body of the accelerometer.

    When the sensor frame is accelerated by an external force, the mass tends to "back off" due to its inertia and deforms the piezoelectric element slightly. This causes the piezoelectric element to produce a measurable charge output to determine the input acceleration.

    Some common mechanical designs for piezoelectric accelerometers are depicted in Figure 2. The three basic designs are compression mode, shear mode, and bending mode.

    Figure 2. Some mechanical designs of piezoelectric accelerometers. Image (adapted) courtesy of PCBPiezotronics

    The figure also illustrates the force exerted by the mass on the piezoelectric element and the acceleration applied to the sensor body.

    Advantages and Disadvantages of Accelerometer Mechanical Design Mode

    Mechanical configuration can affect sensor performance in several different ways. It can have an impact on sensor sensitivity, bandwidth, temperature sensitivity, and sensitivity to strain on the sensor base.

    For example, with a compression mode sensor, we have a rigid structure that provides a relatively high frequency range. However, in a compression mode sensor, the piezoelectric material is in close contact with the bottom of the housing, and the sensor is sensitive to bottom bending and thermal expansion.

    That’s why this type may not be suitable for use in thermally unstable environments or on metal structures that may bend.

    In a shear mode sensor, the piezoelectric element undergoes shear deformation when subjected to acceleration. This type also has a high frequency range while being less susceptible to base bending and temperature changes. Shear mode accelerometers are the most popular configuration.

    The bending type has a less rigid structure and therefore offers a lower frequency range. With this type, the piezoelectric element experiences a relatively large strain for a given value of acceleration. Therefore, this structure offers a higher sensitivity; however, it is relatively fragile. The following table provides a comparison of these three types.

    Table 1. Comparison of three piezoelectric accelerometer modes. Image courtesy of Felix Levinzon

    Piezoelectric Accelerometer Range: Upper Frequency Limit

    Just like MEMS accelerometers, piezoelectric accelerometers work based on Newton's second law of motion. The mass and piezoelectric element can be modeled by a mass-damper-spring structure.

    The mass displacement can be described by the classical second-order differential equation of motion. The resonant behavior of this mechanical system defines the upper frequency limit of the piezoelectric accelerometer, as shown in Figure 3.

    Figure 3. Resonant frequency of a MEMS accelerometer. Image courtesy of BKSV

    As a rule of thumb, if we limit the frequency of the input acceleration to less than one-third of the accelerometer's resonant frequency, the response error should be less than about 12%.

    To learn more about the frequency response of a mass-damper-spring system, see this article.

    Piezoelectric Accelerometer Range: Frequency Lower Limit

    As shown in Figure 4, piezoelectric accelerometers do not have true DC response capabilities and cannot perform true static measurements.

    Figure 4. Graph showing the frequency response of a piezoelectric accelerometer mounted with a resonant frequency of 10kHz. Image courtesy of Endaq

    The lower frequency limit of a piezoelectric accelerometer is determined by the lower cutoff frequency of the amplifier following the sensor.

    For voltage-mode amplifiers, the lower frequency is also affected by the piezoelectric element parameters and the capacitance of the cable between the accelerometer and the amplifier.

    A properly designed piezoelectric accelerometer can operate at frequencies below 1 Hz. However, it should be noted that these sensors do not provide a true DC response.

    For example, they cannot measure the force exerted by gravity. Although this may seem like a big problem at first glance, it should be noted that many applications do not require the measurement of acceleration signals in the fraction-of-hertz range. Therefore, in many applications, the lack of a true DC response is not really a disadvantage.

    It is important to note that, in addition to the lower cutoff frequency limitation of the amplifier, piezoelectric-based sensing is not inherently suitable for true DC measurements. This is because the internal resistance of the sensor (and the input resistance of the signal conditioning circuitry) creates a resistance in parallel with the sensor.

    This parasitic resistance creates an undesirable leakage path for the sensor's output current and sets a lower limit on the system's usable frequency range.