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3.9 Practice Problems
1. What are measurement standards?
ans. Standards are objects of known size, quantity, roughness, etc. These standards are used to calibrate 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 measuring 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 difference between two dimensions to allow for press fits, running fits, etc.
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 consistently. 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".
1. Calculate the CLA/Ra value for the wave form below.
2. What is the difference between surface texture and integrity?
ans. Surface integrity refers to all of the properties of the surface of a material, while surface texture on refers to the geometry of the surface.
3. Describe roughness, waviness and lay.
ans. Roughness is semi or completely random variation in the surface height, these are typically smaller in size. Waviness is a period or larger variation in surface height. This can be caused by warping or buckling, ripples, etc. Lay refers to a direction of a roughness pattern. For example when cutting with a lath the roughness will be different in the axial and radial directions.
4. What methods are used for measuring surface roughness?
ans. Surface roughness is normally measured with an instrument that drags a stylus across the surface (called a profilometer). The movement up and down is measured and used to calculate a roughness value.
ans. Cutoff is the length of the surface that the stylus of the profilometer is allowed to move over.
6. Two different surfaces may have the same roughness value. Why?
ans. A surface roughness value gives an indication of the rms value, but this can come in many forms. A regular looking roughness pattern may have the same roughness value as a shallower wave form with an occasional deep pit.
7. What will be the effect of a difference between the stylus path and the surface roughness?
ans. If the stylus path does not align with the lay of the roughness, then the roughness reading will be lower (or higher) than expected.
8. When is waviness a desirable and undesirable design feature?
ans. Waviness of a surface can be desirable when the surface is to have a rough appearance. If there is a moving mechanical contact between two surfaces waviness can lead to premature wearing of the parts.
9. Given the figure below indicating stylus height values for a surface roughness measurement, find the Ra and Rq value.
10. How are surface roughness and tolerance of the process related?
ans. Surface roughness is a good indication of the ability of a process to control final dimensions. Therefore if the process cannot control the surface roughness, it will be unlikely that the dimensions can also be controlled.
11. How are tolerances related to the size of a feature?
ans. The tolerance/surface roughness graph is based on an important concept in manufacturing. There is a relationship between the scale of a dimension and the scale of a tolerance. In other words, if we make two parts in the same machine, but one is twice the size of the other, then its tolerance must be twice the size. Here we can see the more precise processes are near the bottom with a ratio of tolerance to dimension of 1/10000, the highest is about 1/10. Note: polishing and lapping are used to finish the production of gage blocks.
1. Show that the vee block method exaggerates errors using a round that is deformed into a triangular shape.
1. Select gauge blocks from an 83 piece set to build up a dimension of 3.2265"
2. Use the Unilateral System for a GO/NO-GO gauge design if the calibrated temperature is 72°F and the actual room temperature is 92°F. The shape to be tested is shown below.
3. Find the Running Clearance fit category for the hole and shaft shown below.
4. Set up a sine bar (with 5 inches between cylinder centres) to provide an angle of 15°.
a) What height of gauge blocks is required?
b) Suggest an appropriate set of gauge blocks from an 81 piece set.
c) What is the actual angle of the sine bar?
d) If the room temperature is 95°F and the coefficient of expansion is .000001" per inch per °F, and the gauge blocks are calibrated to 68°F, what is the actual sine bar angle?
e) Suggest a new gauge block stack for the conditions in d).
5. If the scale below reads .48, label the bottom vernier scale.
6. List four different reasons that a material like cheese would not be good for gauge blocks.
7. When using a dial indicator, is parallax or the principle of alignment more significant? Explain your answer.
8. How can you verify that a standard square is 90°?
9. Design a GO/NO-GO gauge for a 5" by 7" square hole with tolerances of ±.1" on each dimension. Show the tolerances and dimensions for the gauges.
10. Write the values displayed on the vernier scales below.
1. If the thimble on a micrometer is made larger, does it affect the `radial arm', or the `inclined plane' principle?
12. When a comparator approaches a workpiece from one direction, it will read a different value than when it approaches from the other way. Explain why.
13. One type of fit is for Interchangeable Assemblies (it uses tolerances to ensure that parts can be made separately, but still fit together). What are the two other types of fits that were described in class? Describe why they are different.
14. A square hole has one dimension that will be checked with a GO-NOGO gauge set. The basic dimension is 2.005" ±0.003". The gauge and hole are used in a room temperature of 105°F, but they should be accurate when at 60°F. The gauge coefficient of linear thermal expansion is 0.000001", and the coefficient is 0.000002" for the material of the workpiece with the hole.
a) What sizes should the GO and NOGO gauges be?
b) Using the gauge block set shown below, list the gauge block stacks required.
15. A square is set up the two ways shown below, and a comparator is run from one end to the other. The resulting measurements result in the rises, or drops indicated. If the comparator is run over a total distance of 5" for both measurements, what is the angle of the squares A and B?
16. The hole shaft pair is assembled with an LN fit.
a) Draw the tolerance diagram.
b) Determine what the LN fit number is.
17. A sine bar will be used to give an angle of 82°35'
a) If the sine bar has 5" centres, what height will be needed?
b) Calculate the gauge block stack for the height in a).
c) What is the actual angle of the sine bar?
d) If the temperature in the room is 65°F at calibration, and 85°F at use, what change in angle does the sine bar have (coefficient of linear thermal expansion 0.000001 "/"°F for the sine bar, and 0.0000005 "/"°F for the gauge blocks)?
e) Could the sine bar be used with other instruments to improve accuracy?
18. Draw the number on the vernier scale below if the reading is 1.12
19. Parallax effects are more important than the principle of alignment for flow type pneumatic comparators - TRUE or FALSE
20. Draw GO/NO-GO gauges for the shaft below.
Select the most significant error that occurs when reading a scale that is properly used.
a) parallax errors where the scale is not parallel to the work.
b) change in the length of the scale due to a temperature change of 1°C.
c) reading with a scale that has a damaged end.
d) rounding off to the nearest division.
If we wanted to measure the diameter of the inside of a tip of a medical syringe (in the range of 0.005") what would be the best measuring instrument?
Which of the following statements is most correct?
a) vernier scales are used for linear measurements only.
b) micrometer scales are used for linear measurements only.
c) micrometer scales make vernier scales more accurate.
Which of the statements below is not correct?
a) the radial arm principle amplifies the rotation of a screw to a larger surface area and radial travel.
b) the inclined plane principle means that a small axial travel for a thread will be amplified to a much larger radial travel
c) the principle of alignment suggests that the dimension to be measured, and the measuring instrument should be aligned along the same axis.
Which of the following physical principles is not used as a basis for comparators.
a) a surface that can be used to measure flatness without other equipment.
b) can be used for measuring small angles without other equipment.
c) a surface that can be used for measuring large angles without other equipment.
a) are more accurate near 90°.
c) are used with angular gauge blocks.
Given the diagram below, what will the average interference/clearance be?
Given an 83 piece set of gauge blocks, how many different stacks 1.1117" in height can be built from the same set? (do not consider wear blocks)
Select the most appropriate statement.
a) dial indicators use the inclined plane principle.
b) dial indicators are a crude form of comparator.
c) the range of the dial indicator is generally less than standard comparators.
Briefly describe the relationship between tolerance and accuracy. (2%)
Find a gauge block stack that gives a value of 1.2351°. (3%)
a) given a metric gauge block set that is calibration grade (a tolerance of +0.00010mm to -0.00005mm) find the dimension and tolerance of a stack that is 3.2761cm in height. (4%)
b) If the stack found in a) is increased in temperature from the ambient of 23°C to a higher temperature of 41°C, what is the new dimension and tolerance? (assume the coefficient of linear thermal expansion is 10-7K-1. (8%)
Suggest a suitable comparator for measuring the diameter of a threaded nut. (3%)
Two blocks are stacked as shown below. In the first test we measure the drop in height (0.005") from one side to the other (5.000"). Then the block on top is turned 180° (left to right)and the new drop in height (0.015") is measured over a distance (4.000"). What are the angles of each of the blocks? (8%)
1. From the same set of gauge blocks build up the dimensions 3.2452" and 3.2462". You must not use the same gauge blocks twice. Use the 83 piece gauge block set.
1. Design Plug gauges for holes that are 1.500" +0.0025" - 0.000". (ans. GO limits are 1.50025"/1.5000" dia., NO GO limits are 1.50250"/1.50225" dia.)
2. Design a gap gauge to inspect shafts that are 0.875" +0.000" -0.008". (ans. GO limits are 0.8746"/0.8738" dia., NO GO limits are 0.8678"/0.8670" dia.)
3. Design GO and NO GO gauges for the hole shown below.
(ans. the three gauges are pictured below)
4. Design GO/NO GO gauges for an equilateral triangular hole that is to have each side 2.025"±0.002".
1. Determine what height is required to set up a 5" sine bar for an angle of 11°34'. Specify the gauge block stack required.
2. Why are different grades of gauge blocks used?
ans. There are different quality levels for gages blocks. The poorest sets are workshop grade and are more accurate than most machine tools. The best sets are very accurate, and must be kept in tightly controlled conditions. The bast sets are used for calibrating others.
3. How are a ring gauge and a plug gauge different?
ans. A plug gage goes into a hole, a ring gage surrounds a dimension.
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