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FITS AND TOLERANCES 27.9
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FITS AND TOLERANCES
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27.3 U.S. STANDARD INCH UNITS
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The fits described in this section are all on a unilateral hole basis. The kind of fit obtained for any one class will be similar throughout the range of sizes. Table 27.6 describes the various fit designations. Three classes, RC9, LC10, and LC11, are described in the standards [27.1] but are not included here. These standards include recommendations for fits up to a basic size of 200 in. However, the tables included here are valid only for sizes up to 19.69 in; this is in accordance with the AmericanBritish-Canadian (ABC) recommendations. The coefficients listed in Table 27.7 are to be used in the equation L = CD1/3 (27.5)
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where L is the limit in thousandths of an inch corresponding to the coefficient C and the basic size D in inches. The resulting four values of L are then summed algebraically to the basic hole size to obtain the four limiting dimensions. It is emphasized again that the limits obtained by the use of these equations and tables are only close approximations to the standards.
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27.4 INTERFERENCE-FIT STRESSES
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The assembly of two cylindrical parts by press-fitting or shrinking one member onto another creates a contact pressure between the two members. The stresses resulting from the interference fit can be computed when the contact pressure is known. This pressure may be obtained from Eq. (2.67) of Ref. [27.3]. The result is p= bA (27.6)
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where = radial interference and A is given by A= 1 b2 + a2 1 c2 + b2 + o 2 2 i + Ei b a Eo c2 b2 (27.7)
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The dimensions a, b, and c are the radii of the members, as shown in Fig. 27.3. The terms Ei and Eo are the elastic moduli for the inner and outer cylinders, respectively. If the inner cylinder is solid, then a = 0 and Eq. (27.7) becomes A= 1 1 c2 + b2 (1 i ) + + o Ei Eo c2 b2 (27.8)
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Sometimes the mating parts have identical moduli. In this case, Eq. (27.6) becomes p= E (c2 b2 )(b2 a2 ) 2b2 (c2 a2 ) b (27.9)
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This equation simplifies still more if the inner cylinder is solid. We then have p= E (c 2 b2 ) 2bc2 (27.10)
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FITS AND TOLERANCES 27.10
FASTENING, JOINING, AND CONNECTING
TABLE 27.6 Standard Fits
The maximum stresses occur at the contact surface. Here the stresses are biaxial, if the longitudinal direction is neglected, and for the outer member are given in Ref. [27.3] as ot = p c2 + b2 c2 b2 or = p (27.11)
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FITS AND TOLERANCES 27.11
FITS AND TOLERANCES
TABLE 27.7 Coefficients C for Use in Eq. (27.5)
where t and r designate the tangential and radial directions, respectively. For the inner member, the stresses at the contact surface are it = p b2 + a2 b2 a2 ir = p (27.12)
A stress-concentration factor may be needed for certain situations. A hub pressfitted to a shaft, for example, would be likely to have an increased pressure at the ends. So if either a brittle fracture or a fatigue failure is a possibility, then for such cases a stress-concentration factor in the range from 1.5 to 2 should be used. Example 2. A 11 2-in solid-steel shaft is fitted to a steel forging having an outside diameter of 21 2 in using a class FN3 fit. Determine the worst-condition stresses for each member.
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