Piezo actuators operate on the inverse piezoelectric effect: when voltage is applied, the actuator contracts or expands. But when the actuator is blocked from moving (by a load applied in the direction of travel), it generates a force. This relationship between displacement and force in piezo materials is an inverse relationship. In other words, the more force an actuator must generate against a load, the less travel it can produce. A “free” actuator — one that experiences no resistance to movement — will produce its maximum displacement, often referred to as “free stroke,” and generate zero force.

Conversely, when an actuator is blocked from moving, it will produce its maximum force, which is referred to as the blocked, or blocking, force. Theoretically, when the actuator is blocked, it is working against a load with infinitely high stiffness. But materials with infinite stiffness don’t occur in the real world, so the blocking force is determined by applying a voltage to the actuator, with no load applied. This “free” operation, as described above, generates the actuator’s maximum displacement, or free stroke. A force is then applied to return the actuator to its original length. This force is measured and recorded as the blocking force.

The stiffness of the actuator is the ratio of blocking force to free stroke.

k_p = stiffness of piezo actuator

F_block = blocking force

ΔL_fs = free stroke (nominal displacement) with no external load

There are two types of load that can be applied to a piezo actuator: a spring load, which increases as the actuator moves, or a constant load, which does not vary. The actuator’s ability to produce displacement and force depends on the type of load.

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Piezo output force and displacement with a non-constant (spring) load

Many piezo applications, such as valve operation, introduce loads that vary with the piezo’s stroke — in other words, spring loads. When the stiffness of the applied spring load is low compared to the piezo stiffness, the piezo output force (F_eff) is small. In other words, a spring (load) with low stiffness provides very little “blocking” for the piezo to work against in order to generate a force. Therefore, the piezo output force is greatly reduced from its maximum, or blocking, force.

F_eff = force produced with spring load

k_e = stiffness of applied load

On the other hand, the spring reduces the actuator’s displacement only slightly:

ΔL = displacement 0f actuator with spring load

A low-stiffness spring load — typically no more than 10 percent of the piezo stiffness — is generally recommended for preloading a piezo actuator to ensure the displacement is not severely reduced.

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Piezo output force and displacement with constant load

When a constant load is applied, there is an initial deflection, or compression, of the actuator due to the load. This means the zero point of the working curve is offset, or shifted, but the actuator’s stroke is unaffected.

ΔL_N = offset of the zero point with constant load

F = applied load

Some force is generated when the load is applied, causing the initial deflection, but once the actuator responds to the application of the load, its remaining work goes into generating the displacement. The zero point of the blocking force (maximum force) is also shifted, but is magnitude is not affected.

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Feature image credit: Noliac

Piezo elements are used in a variety of configurations to provide rotary or linear motion in applications that require short strokes and fast response times. Piezo elements that are used to produce motion through the inverse piezoelectric effect are known as piezo actuators. These devices provide very small displacements with extremely high resolution. When one or more piezo elements are combined, the assembly is commonly referred to as a piezo motor. Piezo motors require more sophisticated drive electronics, but can provide longer travel lengths than piezo actuators.

Depending on the arrangement of the piezo elements and the type of movement they generate, piezo actuators can generally be grouped into four main types: longitudinal, shear, tube, and contracting. Despite their different configurations and uses, these piezo actuators all operate on the same basic principle: movement is directly proportional to the voltage applied. Because they operate solely on the solid-state dynamics of the piezoelectric material, with no mechanical parts, piezo actuators do not experience wear.

A piezo actuator can be integrated with frictionless flexures and levers to form a flexure guided piezo actuator. The flexures and levers multiply and translate the motion of the piezo stack to provide travel up to a few mm, in one or multiple axes. Because the motion of the flexures is based on elastic deformation of the material, there is no friction and no wear.

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Unlike piezo actuators, piezo motors typically incorporate mechanical elements to produce motion, which makes them susceptible to wear. Take ultrasonic piezo motors for example. They operate by electrically exciting a piezo actuator to produce high-frequency oscillations. The actuator is preloaded against a runner via a coupling element. Although the motion (oscillation) of the actuator does not create wear, the interface between the coupling and the runner presents a source of friction, and therefore, wear.

Piezo inertia motors – also referred to as “stick-slip” motors – also use a piezo actuator and runner to produce motion. But in this case, the actuator expands slowly and contracts rapidly. Through a coupling element, the runner is able to move along with the actuator during expansion, but during the rapid contraction, the runner slips on the coupling and effectively stays in place. For rotary motion, a variation on this design uses “jaws” that engage with a very fine thread screw and turns the screw as the actuator expands. In either design, the reliance on friction and the “stick-slip” effect makes wear inherent in piezo inertia motors.

A piezo motor design with little or no wear is the piezo stepper motor. Piezo steppers consist of multiple piezo actuators and operate by coordinating clamping and shear motions between the actuators and a runner. Unlike other piezo motor designs, because each of the actuators (also referred to as “legs” due to their walking-type motion) in a piezo stepper motor make contact and then lift off of the runner, friction is minimized and wear is virtually eliminated.

Resonance occurs when the resonant frequency (also referred to as the natural frequency) of an object or system is equal or very close to the frequency at which it is being excited. This causes the object or system to vibrate strongly and can result in unexpected – and sometimes catastrophic – behavior. 

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When one oscillating object or system (a piezo drive or controller) drives another system (a piezo motor or actuator) at or near the natural frequency of the second system, the second system will oscillate at a high amplitude at a specific frequency. When damping effects are small, the resonant frequency of the system is approximately equal to its natural frequency.

Where:

f₀ = resonant frequency (without load) (Hz)

k_T = piezo stiffness (N/m)

m_eff = effective mass (kg)

The resonant frequency of a piezo motor or actuator depends on its material composition, shape, and volume. For example, a thicker piezo element will have a lower resonant frequency than a thinner element of the same shape. In addition, attaching a load to a piezo motor or actuator reduces its resonant frequency – the higher the load, the more the resonant frequency is reduced. In manufacturer specifications, the resonant frequency given for a piezo actuator assumes that it is unloaded and one end is fixed or attached to a mass that is significantly larger than the actuator.

Where:

f₀‘ = resonant frequency with added mass (Hz)

m´_eff = m_eff + additional mass (kg)

In an electrical circuit representing the piezo element, the frequency at which the impedance of the circuit is at a minimum is the series resonant frequency, f_s. Conversely, the parallel resonant frequency, f_p, in the equivalent circuit occurs when impedance in the circuit is theoretically infinite (assuming mechanical losses are ignored). This is also known as the anti-resonant frequency, f_a.

The series and parallel frequencies are suitable approximations of the minimum and maximum impedance frequencies – f_m and f_n, respectively – and therefore are used to determine the parameters of the piezoelectric motor or system. Maximum response of a piezo system occurs between f_m and f_n. Piezo systems with a higher resonant frequency will have a better phase and amplitude response, which means that the operating frequency can be higher.

Theoretically, the resonant frequency is the operating frequency at which the piezo material vibrates most readily and converts electrical energy into mechanical energy most efficiently. However, piezo systems (especially actuators used for positioning) are often operated below their resonant frequencies in order to minimize the phase shift between the driving signal and the actuator.

When operated below their resonant frequencies, piezo actuators act like capacitors, with displacement being proportional to the stored charge. With a rapid increase in control voltage, a piezo system can typically reach its nominal displacement in 1/3 the period of its resonant frequency. However, this causes large overshoot, which must be compensated for by the controller.

Where: 

t_min = minimum rise time (s)

f₀ = resonant frequency (Hz)

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Feature image credit: Stack Exchange Inc.