## 12. Metrology Problems

Problem 12.1 Select gauge blocks from an 83 piece set to build up a dimension of 3.2265”

Problem 12.2 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. Problem 12.3 Find the Running Clearance fit category for the hole and shaft shown below. Problem 12.4 Set up a sine bar (with 5 inches between cylinder centers) 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).

Problem 12.5 If the scale below reads .48, label the bottom vernier scale. Problem 12.6 List four different reasons that a material like cheese would not be good for gauge blocks.

Problem 12.7 When using a dial indicator, is parallax or the principle of alignment more significant? Explain your answer.

Problem 12.8 How can you verify that a standard square is 90°?

Problem 12.9 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 gages.

Problem 12.10 Write the values displayed on the vernier scales below. Problem 12.11 If the thimble on a micrometer is made larger, does it affect the ‘radial arm’, or the ‘inclined plane’ principle?

Problem 12.12 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.

Problem 12.13 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.

Problem 12.14 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 gages be?

b) Using the gauge block set shown below, list the gauge block stacks required.

Problem 12.15 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? Problem 12.16 The hole shaft pair is assembled with an LN fit. a) Draw the tolerance diagram.

b) Determine what the LN fit number is.

Problem 12.17 A sine bar will be used to give an angle of 82°35’

a) If the sine bar has 5” centers, 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?

Problem 12.18 Draw the number on the vernier scale below if the reading is 1.12 Problem 12.19 Parallax effects are more important than the principle of alignment for flow type pneumatic comparators: TRUE or FALSE

Problem 12.20 Draw GO/NO-GO gages for the shaft below. Problem 12.21 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.

Problem 12.22 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?

a) transfer gauge

b) tool makers microscope

c) GO/NOGO gages

d) mechanical comparator

Problem 12.23 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.

d) none of the above.

Problem 12.24 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.

d) all are correct.

Problem 12.25 Which of the following physical principles is not used as a basis for comparators.

a) air pressure.

b) air flow.

d) none of the above.

Problem 12.26 Surface plates are,

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.

d) all of the above.

Problem 12.27 Sine bars,

a) are more accurate near 90°.

b) are more accurate near 0°.

c) are used with angular gauge blocks.

d) none of the above.

Problem 12.28 Given the diagram below, what will the average interference/clearance be?

a) 0.008”

b) 0.020”

c) 0.032”

d) none of the above Problem 12.29 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)

a) 1

b) 2 or 3

c) 4 or 5

d) more than 5

Problem 12.30 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.

d) none of the above.

Problem 12.31 Briefly describe the relationship between tolerance and accuracy.

Problem 12.32 Find a gauge block stack that gives a value of 1.2351°.

Problem 12.33 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.

Problem 12.34 Suggest a suitable comparator for measuring the diameter of a threaded nut.

Problem 12.35 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? Problem 12.36 For mass production the inspector will need a fast and accurate instrument for measurement in order to ensure that part dimensions are between acceptable limits. What kind of category of instruments will you choose? Explain why.

Problem 12.37 What kind of magnification does the micrometer use?

Problem 12.38 Gauge blocks are made to such high precision they wring. What does the term wring mean?

Problem 12.39 What would happen if the gauge blocks being lapped were first lapped in the pattern on the left, then second with the pattern on the right? Problem 12.40 A steel scale with 1mm divisions will have a vernier scale added to get readings to 0.1mm. Use a diagram to show this scale and number the divisions.

Problem 12.41 List five potential applications of standards.

Problem 12.42 Design Limit Gages (GO/NOGO) for the block with a hole in it. Assume that the hole is always perfectly centered. Problem 12.43 We are to measure a square hole that is to be measured at 25°C but when it is used at 40°C it is to be 2.000” exactly. Given that the coefficient of linear thermal expansion is 10-6K-1 for the part and 10-7K-1 for the gauge blocks (calibrated at 23°C) what height should the stack be?