Total harmonic distortion (THD) is a function versus frequency that helps quantify how well the output of a system replicates the input. The lower the THD values, the less the noise or distortion in the system output.
THD measurements are used in many applications by different industries. This article concentrates on the use of THD in closed loop vibration control systems.
In a closed loop vibration control system, there are many components: amplifier, shaker, test fixture, test object, and a control accelerometer (Figure 1). A low THD of each component, and of the combined system, is desirable.
A system with a low THD is easier to control. In a sine test, the THD will be different at each frequency, making some frequencies easier to control than others.
The THD of a system is determined by inputting a single frequency into a system, and measuring the output. The output may contain additional harmonic frequencies of the input frequency, as shown in Figure 2. For example, if a 100 Hertz sine was input into the system, the output may contain 100 Hz and multiples like 200, 300, and 400 Hz.
The THD is the ratio of the energy in the output signal that is not related to the input sine tone (Equation 1):
THD is usually calculated over a range of frequencies (for example, 20 to 2000 Hz). The input sine frequency is swept over the desired range and a THD value at each frequency is recorded.
In a digital spectral measurement, the energy referred to in Equation 1 is measured by calculating the RMS value over a frequency range or around the main harmonic.
The results for a THD test are plotted in Figure 3.
THD has a value between zero and one for each frequency tested:
THD can also expressed in percentage, from 0 to 100%, where 100% corresponds to 1.
In many applications, a low THD is desired. A low THD means that the system output is similar to the system input, with minimal distortion.
In practice, there are differences in how THD may be calculated for a given spectrum. For some methods, only the energy at harmonics are considered. Sometimes the calculation is limited to first five or ten harmonics of the output signal.
Other methods consider the total RMS of the output signal. These methods are sometimes designated as THD+N, because the noise between harmonics is included in the calculation. The N is short for noise.
THD in Vibration Control shaker systems
A THD function can be measured on components (amplifier, shaker, test structure) or on combinations of components for a shaker system.
For example, the quality of amplifiers is often specified using THD. An amplifier THD of 0.01 or lower is normal (less than 1%).
Mechanical systems, on the other hand, tend to have higher THD values than electronic amplifiers.
For example, measuring the THD of an amplifier and shaker (without a test structure) usually has THD values below 2%, with some spikes of about 10% (blue curve, Figure 4).
The THD of a complete shaker system (gold curve, Figure 4) is measured over:
Adding a test article and fixture to the shaker and amplifier system, can increase the THD significantly. It can be above 50% at certain frequencies. Frequencies with a high THD may be difficult to control during a test.
Causes of Harmonic Distortion in Vibration Control shaker systems
Where do these harmonics come from, when ostensibly, only one controlled sine frequency is being input into the shaker system?
As shown in the video, and in Figure 5, despite a single frequency input, several sinusoidal harmonics of the control are also generated.
An ideal sine wave has a single frequency in its spectrum, without harmonics. Harmonics are present when the sinusoidal vibration of the output does not replicate the pure sine wave of the input.
Examples of a pure sine wave versus a sinewave with harmonics is shown in Figure 6.
A shaker system may distort a perfect sine wave input in the following ways:
Of the two setups in Figure 7, the setup on the right, with an off-center test object, would have higher Total Harmonic Distortion (THD) values than the test setup on the left.
The off-center test object would create forces not aligned with the direction of main excitation.
THD and System FRF
In a closed loop vibration control system, vibration is reproduced on the test object. There is a target value for the vibration levels on the test object, and the SCADAS output is adjusted to achieve this level.
To adjust the level properly, a Frequency Response Function (FRF) of the shaker control system is used to predict the input and output levels. It is useful to consider both the THD and the FRF when evaluating a dynamic system.
The FRF or transfer function (with units of g/V for a shaker system) also quantifies the relationship between the input and output of a system. In control theory the FRF is called the system gain. The FRF of a shaker control system is overlaid with the THD function in Figure 8.
In Figure 8, the following can be observed about THD and the system FRF:
Trying to control a system with a high THD can be difficult. Typically a single frequency is being input into the system with a controlled amplitude. High amounts of harmonic distortion create vibration at other frequencies, which are not controlled. This increases the vibration amplitude levels on the test object in an uncontrolled, and therefore, unpredictable manner. There are seveal sine test control parameters that can be adjusted to try and overcome these test difficulties.
THD and the system FRF can be measured during a sine control test while using Simcenter Testlab.
Measuring THD and FRF in Simcenter Vibration Control
A THD and FRF function can be calculated both online and offline in Simcenter Testlab (formerly called LMS Test.Lab):
In Simcenter Testlab Sine Control, the ‘THD’ and ‘FRF’ measurements can be turned on in the lower right corner of the ‘Sine Setup’ worksheet as shown in Figure 9.
The THD and FRF functions will automatically be stored in the Simcenter Testlab project file during the test, as well as after the test is completed.
If a sine sweep test has already been performed, and the time data is available, the application “Offline Sine Data Reduction” can be used to calculate the THD. “Offline Sine Data Reduction” can be started from the “Simcenter Testlab Environmental” folder.
Understanding and measuring the Total Harmonic Distortion of a shaker system is helpful:
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