Chapter 2: Statistical Considerations

1
Chapter 2 Statistical Considerations

• BAE 417-Design of Machine Systems
• Fall 2006

2
Limits, Fits, and Tolerances(Sections 2-6 and
2-7)

• Capital letters refer to holes lowercase letters
  are used for shafts

3
Limits and Fits

• Basic Size- size to which limits or deviations
  are assigned
• Deviation- algebraic difference between size and
  corresponding basic size
• Upper deviation- indicates maximum difference
• Lower deviation- indicates minimum difference
• Fundamental deviation- which of the above is
  closer to the basic size

4
Limits and Fits

• Tolerance- difference between max. and min. size
  limits
• International tolerance grade numbers (IT)-
  designated groups of tolerances that vary
  depending on basic size
• Hole basis- system of fits corresponding to hole
  sizes (H is the fundamental deviation)
• Shaft basis- system of fits corresponding to
  shaft size (h is the fundamental deviation)
• See Table 2-8 for a Description of Preferred Fits
  Using the Basic Hole System

5
Conventions and Variable Definitions

• D- basic hole size
• d- basic shaft size
• d- deviation
• du- upper deviation
• dl- lower deviation
• dF- fundamental deviation
• DD- tolerance grade for hole
• Dd- tolerance grade for shaft

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• For holes
• Dmax D DD (Eq. 2-38)
• Dmin D
• For shafts with clearance fits c, d, f, g, and h
• dmax d dF (Eq. 2-39)
• dmin d dF Dd
• For shafts with interference fits k, n, p, s, and
  u
• dmin d dF (Eq. 2-40)
• dmax d dF Dd

7
Example

• Find the shaft and hole dimensions for a loose
  running fit with a 34-mm basic size.

8
Solution

• From Table 2-8 we find the ISO symbol to be
  34H11/c11
• From Table A-11 using the IT tolerance grade of
  11 (IT11) and a basic size of 34 (34 mm) we get
  DD Dd 0.160 mm
• Using Eq. 2-38 we get
• Dmax D DD 34 0.160 34.160 mm
• Dmin 0.160 mm

9
Solution

• Using Table A-12 we find the fundamental
  deviation (dF) for the 34c11 shaft to be
• dF -0.120 mm
• Using Eq. (2-39) we get
• dmax d dF 34 0.120 33.880 mm
• dmin d dF Dd 34 - 0.120 0.160 33.720
  mm

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Dimensions and Tolerances

• Nominal size - size for speaking of an element
  (i.e., ½ bolt or 3 pipe)
• Basic size exact theoretical size
• Limits stated maximum and minimum dimensions
• Tolerance difference between two limits
• Bilateral 1.005 0.002 in
• Unilateral in
• Natural tolerance plus and minus three standard
  deviations

11
Dimensions and Tolerances

• Clearance difference in dimensions (diametral
  or radial)
• Used only when the internal member is smaller
  than the external member
• Interference difference in dimensions
• Used when the internal member is larger than the
  external member
• Allowance minimum clearance or maximum
  interference

12
Tolerance Stacking

• The gap, grip, or interference of an
  assembly of mating parts is defined as
• where xs are right tending and ys are left
  tending displacements

13
Homework Assignment

• Do problems 2-25, 2-27, and 2-32 for next Tuesday.