Comparators

A comparator is a precision instrument that compares the size of a workpiece with a known standard (master or slip gauge) and indicates the difference on a magnified scale. It does not give the absolute size. Principle: set the instrument to zero on a master of the basic size; the pointer reading when the work replaces the master gives the deviation.

Classification

1. Mechanical (dial indicator, reed-type, sigma comparator): amplification by levers, gears, reeds.
2. Optical (Zeiss Ultra-optimeter, optical projector): amplification by a light beam and mirrors.
3. Electrical / electronic (LVDT, capacitance, inductive): displacement converted to an electrical signal.
4. Pneumatic (Solex type): the change of air gap is measured through back pressure or flow.
5. Combinations: mechanical-optical, electro-pneumatic.

Comparison

Comparators are used for the inspection of large batches where the tolerance is small.

Derivation

Let the plunger move by $\delta$ and the mirror rotate by $\theta$ about the pivot, with the plunger acting at distance $x$ from the pivot:

$$\theta \approx \frac{\delta}{x}$$

A reflected ray turns through $2\theta$ when the mirror turns by $\theta$. On a scale at distance $L$ the spot moves by

$$y = 2\theta L = \frac{2L}{x}\,\delta$$ $$\text{Magnification } M = \frac{y}{\delta} = \frac{2L}{x} = \frac{2(250)}{5} = 100$$

Least count

$$\text{LC} = \frac{\text{scale division}}{M} = \frac{0.5}{100} = 0.005\ \text{mm}$$

Shaft size

The deviation from the master is $+3.2 \times 0.005 = +0.016$ mm, so

$$\text{size} = 25.000 + 0.016 = 25.016\ \text{mm}$$

Limits are $24.985$ to $25.015$ mm. The shaft is larger than the upper limit by $0.001$ mm, therefore it is not acceptable (oversize, can be reworked).

Answer: $M = 100$, LC = 0.005 mm, size = 25.016 mm, rejected (oversize by 0.001 mm).