Variable Reluctance Tachometer Output Frequency Calculation

A variable reluctance tachometer is a device used to measure the rotational speed of a shaft. It operates on the principle of changing magnetic reluctance, which generates a series of pulses as teeth on a rotating disc (rotor) pass by a magnetic pickup coil. The frequency of these pulses is directly proportional to the speed of rotation and the number of teeth on the rotor.

Understanding the Variable Reluctance Tachometer Principle

When the teeth of the rotor pass the magnetic pick-up, the air gap between the teeth and the pick-up changes. This change in the air gap causes a variation in the magnetic flux linking the coil. According to Faraday's law of electromagnetic induction, this changing magnetic flux induces a voltage (or pulse) in the coil. Each tooth passing generates one pulse. Therefore, the total number of pulses per unit time (frequency) depends on how many teeth pass the coil in that time.

Given Parameters for Tachometer Output

To calculate the frequency of the output pulses from the variable reluctance tachometer, we are provided with the following information:

• Number of teeth on the rotor, \(N_t = 180\) teeth
• Speed of the shaft, \(N = 1800\) revolutions per minute (rpm)

Formula for Output Pulse Frequency

The frequency (\(f\)) of the output pulses from a variable reluctance tachometer can be calculated using the following formula:

$$f = \frac{N_t \times N}{60}$$

Where:

• \(f\) is the frequency of output pulses in Hertz (Hz)
• \(N_t\) is the number of teeth on the rotor
• \(N\) is the speed of the shaft in revolutions per minute (rpm)
• The division by 60 converts the speed from revolutions per minute to revolutions per second, ensuring the frequency is in Hertz.

Step-by-Step Calculation of Output Frequency

Let's substitute the given values into the formula to find the frequency of the output pulses:

Given:

• \(N_t = 180\)
• \(N = 1800\) rpm

Applying the formula:

$$f = \frac{180 \times 1800}{60}$$

First, simplify the division:

$$f = 180 \times \frac{1800}{60}$$

$$f = 180 \times 30$$

Now, perform the multiplication:

$$f = 5400 \text{ Hz}$$

Conclusion on Tachometer Pulse Frequency

The calculated frequency of the output pulses from the variable reluctance tachometer is 5400 Hz. This result indicates that the tachometer generates 5400 electrical pulses every second given the specified number of teeth and shaft speed.