• Basically, the line of the physical measurement should be such that it is coincident with the mea-surement axis of the instrument.
• If the measurement is out of line, it may lead to misreadings caused by deflections in the instru-ment.
M C
D---- πD pitch
---= where,
M = magnification from the moving head to the hand motion C = measuring diameter of the instrument
D = diameter of the thread
pitch = the number of threads per unit length
Radial Arm Principle of Magnification
Inclined Plane Principle of Magnification πD pitch
---= C D
----=
0 5 10 15
40 35 30 25
C D
pitch NOTE: magnification
can result in greater sensitivity of an insrument to control, and reading by a user.
• micrometers are generally better than sliding vernier calipers when considering this principle.
35.4.3 Dial Indicators
• Converts a linear displacement into a radial movement to measure over a small range of move-ment for the plunger.
0 5 10 15
40 35 30
misalignment is 25
slight, but may still cause errors.
• The radial arm magnification principle is used here.
• these indicators are prone to errors caused by errors that are magnified through the gear train.
Springs can be used to take up any play/backlash in the rack and pinion to reduce these errors.
• The gears are small, but friction can result in sticking, thus reducing accuracy
• A spring is used on the rack to return the plunger after depression.
• The problems mentioned earlier will result in errors in these instruments. If the dial indicator is used to approach a dimension from two different sides, it will experience a form of mechanical
0
10
20
30
40 50
60 70
80
90
rack
plunger
pinion indicator dial
gears
hysteresis that will bias the readings. An example of this effect is given below.
• In the graph shown, as the dial indicator is raised in height (taking care not to change direction), the errors are traced by the top curve. As the height of the dial indicator is decreased, the bot-tom curve is traced. This can be observed using gauge blocks as the known heights to compare the readings against.
• The causes of this hysteresis are bending strain, inertia, friction, and play in the instrument.
• Applications include,
- centering workpices to machine tool spindles - offsetting lathe tail stocks
- aligning a vise on a milling machine - checking dimensions
• These indicators can be somewhat crude for accurate measurements, comparators have a higher degree of sensitivity.
35.4.4 The Tool Makers Microscope
• Quite basically this is a microscope. But, it has lines added to the optics for visual reference, and micrometer dials, and angular verniers added to the stage to measure distances.
• Parts are put on the stage, and the microscope is focused. The stage can then be rotated, and translated precise distances to allow visually referenced measurements
• Such a microscope might have two micrometer heads for x-y translation of the stage. In addi-tion, the stage can be rotated, and angular positions measures.
+ve errors
-ve errors
maximum variance
as height is increased
as height is decreased
35.4.5 Metrology Summary
• We can discuss various instruments, and what they are used for.
Table 1: Fill in more later
Feature SizeRange Accuracy Instrument Comments
Angle 90° yes/no square
85°-95° -- cylindrical
square outside
dis-tance depth
35.5 PRACTICE PROBLEMS
1. What are measurement standards?ans. Standards are objects of known size, quantity, roughness, etc. These standards are used to cal-ibrate and verify measuring instruments. As a result, measured values are more accurate.
2. What effect will temperature variation have on precision measurements?
ans. Temperature control during measurement is important because as materials are heated they expand. Each material expands at a different rate. This leads to distortion of parts and measur-ing devices that results in measurement errors.
3. How can a vernier scale provide higher accuracy?
ans. A vernier scale uses a second elongated scale to interpolate values on a major scale.
4. What are dimensional tolerances, and what are their primary uses?
ans. Dimensional tolerances specify the amount a dimension may vary about a target value. These are supplied by a designer to ensure the correct function of a device. If these tolerances are controlled the final product will work as planned.
5. Why is an allowance different from a tolerance?
ans. A tolerance is the amount a single dimension can vary. An allowance is an intentional differ-ence between two dimensions to allow for press fits, running fits, etc.
6. What are fits?
ans. There are standard for different types of fits (e.g. press fit, running clearance). These specify the allowance of two parts, so that they may be made separately and then joined (mated) in an assembly.
7. What is the difference between precision and accuracy?
ans. Precision suggests a limit of technology, accuracy is the ability to achieve a value consis-tently. These are often interchanged because we are usually concerned with the accuracy when producing precision parts.
8. If a steel ruler expands 1% because of a temperature change, and we are measuring a 2” length, what will the measured dimension be?
ans. If we assume that only the steel rule expands, and not the steel part, we can calculate,
9. Draw the scales for a vernier micrometer reading 0.3997”.
lbar 100+1
--- lmeasures ---100
= lmeasures 100 2( )
---101 1.98in
= =
For the 0.3997 value
0 1 2 3
0 5
20 0
10
5
The vernier scale to the left is shown as flattened out. It would typically be found on the back of the micrometer.
ans.
35.5.0.1 - Interferometry (REWORK)
• Light waves can be used to measure various attribute, such as distance by generating interfer-ence patterns.
• In general, if we take a single beam of light, and split it, the two separated beams will have the same frequency, and phase. If the two beams take different length paths, but eventually inter-sect each other, then they will form interference patterns, much as is found in wave tanks.