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A displacement sensor (a dial indicator) measures the lateral displacement of a mandrel mounted on the taper hole inside a drill spindle. The mandrel axis is an extension of the drill spindle taper hole axis and the protruding portion of the mandrel surface is perfectly cylindrical. Measurements are taken with the sensor placed at two positions P and Q as shown in the figure. The readings are recorded as Rₓ = maximum deflection minus minimum deflection, corresponding to sensor position at X, over one rotation. If R_P = R_Q > 0, which one of the following would be consistent with the observation?

1. The drill spindle rotational axis is coincident with the drill spindle taper hole axis
2. The drill spindle rotational axis intersects the drill spindle taper hole axis at point P
3. The drill spindle rotational axis is parallel to the drill spindle taper hole axis
4. The drill spindle rotational axis intersects the drill spindle taper hole axis at point Q

Correct answer: The drill spindle rotational axis is parallel to the drill spindle taper hole axis

Solution

When the readings R_P and R_Q are equal and greater than zero, it indicates that the lateral displacement is consistent across both sensor positions, which occurs when the drill spindle rotational axis is parallel to the taper hole axis. This alignment prevents any variation in displacement measurements as the mandrel rotates.

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