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PRESENTATION 4 Precision, Accuracy, and Tolerance

PRESENTATION 4 Precision, Accuracy, and Tolerance. RANGE OF A MEASUREMENT. Example: What is the degree of precision and the range for 2 inches? The degree of precision of 2 inches is to the nearest inch

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PRESENTATION 4 Precision, Accuracy, and Tolerance

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  1. PRESENTATION 4Precision, Accuracy, and Tolerance

  2. RANGE OF A MEASUREMENT • Example: What is the degree of precision and the range for 2 inches? • The degree of precision of 2 inches is to the nearest inch • The range of values includes all numbers equal to or greater than 1.5 inches or less than 2.5 inches

  3. RANGE OF A MEASUREMENT • Example: What is the degree of precision and the range for 2.00 inches? • The degree of precision of 2.00 inches is to the nearest 0.01 inch • The range of values includes all numbers equal to or greater than 1.995 inches or less than 2.005 inches

  4. ADDING AND SUBTRACTING • The sum or difference cannot be more precise than the least precise measurement number used in computations

  5. ADDING AND SUBTRACTING • Example: Add 15.63 in + 2.7 in + 0.348 in and round answer to degree of precision of least precise number • Since 2.7 in is the least precise measurement, round the answer to 1 decimal place

  6. SIGNIFICANT DIGITS • Rules for determining the number of significant digits in a given measurement: • All nonzero digits are significant • Zeroes between nonzero digits are significant • Final zeroes in a decimal or mixed decimal are significant • Zeroes used as place holders are not significant unless they are identified as significant (usually with a bar above it)

  7. SIGNIFICANT DIGITS • Examples: 812 has 3 significant digits • (all nonzero digits are significant) 14.3005 has 6 significant digits • (zeroes between nonzero digits are significant) 9.300 has 4 significant digits • (final zeroes of a decimal are significant) 0.008 has 1 significant digits • (zeroes used as place holders are not significant)

  8. ACCURACY • Determined by the number of significant digits in a measurement • The greater the number of significant digits, the more accurate the number • Product or quotient cannot be more accurate than the least accurate measurement used in the computations

  9. ACCURACY • Examples: • Number 2.09 is accurate to 3 significant digits • Number 0.1250 is accurate to 4 significant digits • Number 0.0087 is accurate to 2 significant digits • Number 50,000 is accurate to 1 significant digit • Number 68.9520 is accurate to 6 significant digits • Note: When measurement numbers have the same number of significant digits, the number that begins with the largest digit is the most accurate

  10. ACCURACY • Examples: • Product of 3.896 in × 63.6 in = 247.7856, but since least accurate number is 63.6, answer must be rounded to 3 significant digits, or 248 in • Quotient of 0.009 mm  0.4876 mm = 0.018457752 mm, but since least accurate number is 0.009, answer must be rounded to 1 significant digits, or 0.02 mm

  11. TOLERANCE (LINEAR) • Tolerance (linear) is the amount of variation permitted for a given length • Tolerance is equal to the difference between maximum and minimum limits of a given length

  12. TOLERANCE (LINEAR) • Example: The maximum permitted length (limit) of a tapered shaft is 134.2 millimeters. The minimum permitted length (limit) is 133.4 millimeters. Find the tolerance. • Tolerance = maximum limit – minimum limit = 134.2 mm – 133.4 mm = 0.8 mm

  13. UNILATERAL AND BILATERAL TOLERANCE • A basic dimension is the standard size from which the maximum and minimum limits are made • Unilateral tolerance means that the total tolerance is taken in only one direction from the basic direction • Bilateral tolerance means that the tolerance is divided partly above and partly below the basic dimension

  14. UNILATERAL AND BILATERAL TOLERANCE • When one part is to move within another, there is a clearance between the parts • When one part is made to be forced into the other, there is interference between parts

  15. UNILATERAL AND BILATERAL TOLERANCE • Example: This is an illustration of a clearance fit between a shaft and a hole using unilateral tolerancing. Refer to the diagram and determine: • Maximum and minimum shaft diameter • Maximum and minimum hole diameter • Maximum and minimum clearance

  16. UNILATERAL AND BILATERAL TOLERANCE • Maximum shaft diameter 1.385″ + 0.000″ = 1.385″ • Minimum shaft diameter 1.385″ – 0.002″ = 1.383″ • Maximum hole diameter 1.387″ + 0.002″ = 1.389″ • Minimum hole diameter 1.387″ – 0.000″ = 1.387″

  17. UNILATERAL AND BILATERAL TOLERANCE • Maximum clearance equals maximum hole diameter minus minimum shaft diameter 1.389″ – 1.383″ = 0.006″ • Minimum clearance equals minimum hole diameter minus maximum shaft diameter 1.387″ – 1.385″ = 0.002″

  18. PRACTICAL PROBLEM • Determine the maximum and minimum permissible wall thickness of the steel sleeve shown below.

  19. PRACTICAL PROBLEM • Maximum thickness: [(26.08 mm + 0.05 mm) – (20.50 mm – 0.01 mm)] ÷ 2 = (26.13 mm – 20.49 mm) = 5.64

  20. PRACTICAL PROBLEM • Minimum thickness: [(26.08 mm – 0.05 mm) – (20.50 mm + 0.01 mm)] = (26.03 mm – 20.51 mm) = 5.52

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