Encoders are most commonly used to measure angles or linear distances, but they can also be used to perform speed or linear velocity measurements. This is because there is a linear relationship between the encoder's pulse frequency and its rotational speed. As the encoder rotates faster, the pulse frequency increases at the same rate.
Encoder speed can be determined by either of two methods: pulse counting or pulse timing.
Orthogonal coding
Incremental encoders typically output signals on two channels – often referred to as "A" and "B" – with the two phases offset by 90 degrees. The direction of rotation is determined by which channel comes first. Generally, if channel A comes first, the direction is clockwise, and if channel B comes first, the direction is counterclockwise. Quadrature output also allows for increased encoder resolution through the use of X2 or X4 decoding techniques. With X2 decoding, both the rising and falling edges of channel A are counted, doubling the number of pulses counted per revolution, thus doubling the encoder's resolution. With X4 decoding, both the rising and falling edges of channels A and B are counted, thus quadrupling the resolution.
In X4 encoding, both the rising and falling edges of channels A and B are counted.
Pulse counting
Pulse counting uses the sampling period (t) and the number of pulses counted within the sampling period (n) to determine the average time of a pulse (t/n). Knowing the number of pulses per encoder revolution (N), the speed can be calculated.
ω=2πn/Nt
in:
ω = angular velocity (rad/s)
n = number of pulses
t = sampling period (s)
N = pulses per revolution
At low speeds, the resolution of pulse counting is poor, so this method is best suited for high-speed applications.
Pulse time
The high-frequency clock signal is counted during one encoder cycle (the pitch or the interval between two adjacent rows or windows) using pulse counting. The number of clock signal cycles (m) divided by the clock frequency (f) gives the time of the encoder cycle (the time it takes for the encoder to rotate one pitch). If the encoder PPR is represented by N, the encoder angular velocity is given by the following formula:
ω=2πf/Nm
in:
ω = angular velocity (rad/s)
f = clock frequency (Hz)
m = number of clock cycles
N = pulses per revolution
At high speeds, the time between pulse timings (also known as pulse frequencies) may be too short to accurately measure the clock cycle, so this method is best suited for low-speed applications.
Accuracy of speed measurement
The accuracy of encoder speed measurements can be affected by various factors, including instrument error, phase error, and interpolation error.
Instrument errors include mechanical defects in the encoder and scale errors on the encoder disk or reticle, such as variations in the spacing between lines or windows. Instrument-related errors also include the flatness of the substrate, inaccurate sensor positioning, and lack of concentricity between the encoder and motor shafts.
Phase error stems from the fact that there is no information between pulses or readings. In other words, a quadrature encoder only reads the edges of the signal on one or two channels (A and B) and does not transmit information between these readings. Phase error is simply ±1/2 or a fixed number of measurement steps.
Interpolation errors only occur when the encoder resolution exceeds the electronic level inherent to the X4 decoding of a quadrature encoder. Interpolation errors tend to increase with encoder speed. Using an encoder with a higher line count or more windows can reduce interpolation and phase errors.
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