Calculate the resolution in linear travel of the tape

In summary, the conversation discusses the use of a 24V DC motor with an optical encoder to measure the linear travel and velocity of a tape drive. The resolution in linear travel is determined by dividing the circumference of the pulley by the number of pulses per revolution. The velocity of the tape when the motor is supplied with 24V is calculated using a motor speed vs. voltage graph. The question regarding accuracy is ambiguous, but it is suggested that the smallest deviation the encoder can measure is determined by finding the closest number of revolutions per second that the counter/timer can count and doubling it to create a tolerance band.
  • #1
polyperson
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Nobody replying, so I’ve reframed the question

A 24V DC motor has an optical encoder with 500 divisions which outputs the pulse frequency to an electronic counter/timer. The motor has a flat pulley of 31.827mm diameter used as a tape drive.

(a) Calculate the resolution in linear travel of the tape

(b) Determine the velocity of the tape if the motor is supplied with 24V

(c) To what accuracy can the velocity be determined?

Right (a) is simple:

Resolution = smallest distance that can be measured = linear travel of the tape per revolution divided by the number of pulses per revolution

Circumference = pi x 31.827 = 100mm

Therefore, Resolution = 100 ÷ 500 = 0.2mm per pulse

For (b) I had to use the Motor speed vs. voltage graph that we had to create as part of the experiment. I ended up with a value of 1608.56 rev/min which is 28.009 rev/s, so:

28.009 rev/sec x 100e-3m = 2.8009 m/s

But on (c) I am stuck. It's not very clear what he is asking. I think he means what is the smallest deviation from 2.8009 m/s that the encoder can measure.

Is the answer along the lines of:

If the counter/timer can't count in fractions of 1Hz (and that's merely an assumption) then surely it couldn't measure 28.009 rev/sec...so you need to find the number of rev/sec closest to 28.009 that it can measure and double it to give a tolerance band?
 
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  • #2
Ping upwards
 
  • #3


To determine the accuracy of the velocity, we need to consider the limitations of the electronic counter/timer. If it cannot count in fractions of 1Hz, then the closest value it can measure is 28 rev/sec. This would result in a velocity of 2.8 m/s, which is 0.0009 m/s off from the actual velocity of 2.8009 m/s. Therefore, the accuracy of the velocity can be determined to be within 0.0009 m/s. However, if the counter/timer can measure fractions of 1Hz, then the accuracy could potentially be even higher. Further testing and analysis would be needed to determine the exact accuracy of the velocity measurement.
 

1. What is the definition of resolution in linear travel of the tape?

The resolution in linear travel of the tape refers to the smallest measurable distance that the tape can move in a linear direction. It is typically measured in millimeters or inches.

2. How is the resolution in linear travel of the tape calculated?

The resolution in linear travel of the tape is calculated by dividing the total length of the tape by the number of increments on the measuring scale. For example, if a tape is 100 inches long and has 1000 increments on the measuring scale, the resolution would be 0.1 inches.

3. What factors can affect the resolution in linear travel of the tape?

The resolution in linear travel of the tape can be affected by a few factors, such as the precision of the measuring scale, the condition of the tape (e.g. stretching or warping), and the skill of the person using the tape (e.g. parallax error). It is important to properly maintain and use the tape to ensure accurate measurements.

4. Can the resolution in linear travel of the tape be improved?

Yes, the resolution in linear travel of the tape can be improved by using a tape with a finer measuring scale (e.g. more increments per unit of length) or by using a measuring tool with a higher precision. However, it is important to note that the resolution can only be improved to a certain extent and may also depend on the skill of the person using the tape.

5. How significant is the resolution in linear travel of the tape in scientific measurements?

The significance of the resolution in linear travel of the tape in scientific measurements depends on the precision required for the specific experiment or study. In some cases, a high resolution may be necessary for accurate results, while in others, a lower resolution may suffice. It is important to consider the required precision and choose the appropriate measuring tool accordingly.

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