Budynas-Nisbett:Shigley's I.Basics 1.Introduction to T©The McGraw-Hill Mechanical Engineering Mechanical Engineering Companies,2008 Design,Eighth Edition Design 20 I Mechanical Engineering Design EXAMPLE 1-3 A shouldered screw contains three hollow right circular cylindrical parts on the screw before a nut is tightened against the shoulder.To sustain the function,the gap w must equal or exceed 0.003 in.The parts in the assembly depicted in Fig.1-4 have dimen- sions and tolerances as follows: a=1.750±0.003in b=0.750±0.001in c=0.120±0.005in d=0.875±0.001in Figure 1-4 An assembly of three cylindrical sleeves of lengths a,b,and c on a shoulder bolt shank of length a.The gap w is of interest. All parts except the part with the dimension d are supplied by vendors.The part con- taining the dimension d is made in-house. (a)Estimate the mean and tolerance on the gap w. (b)What basic value of d will assure that w>0.003 in? Solution (a)The mean value of w is given by Answer 0=a-b-c-d=1.750-0.750-0.120-0.875=0.005in For equal bilateral tolerances,the tolerance of the gap is Answer tm=1=0.003+0.001+0.005+0.001=0.010in all Then,w=0.005±0.010，and "mar=i+1w=0.005+0.010=0.015in wmin=币-tw=0.005-0.010=-0.005in Thus,both clearance and interference are possible. (b)If wmin is to be 0.003 in,then,=wmin+=0.003 +0.010=0.013 in.Thus, Answer a=a-b-c-i=1.750-0.750-0.120-0.013=0.867in The previous example represented an absolute tolerance system.Statistically,gap dimensions near the gap limits are rare events.Using a statistical tolerance system,the probability that the gap falls within a given limit is determined.This probability deals with the statistical distributions of the individual dimensions.For example,if the distri- butions of the dimensions in the previous example were normal and the tolerances,t,were See Chapter 20for a description of the statistical terminology.Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition I. Basics 1. Introduction to Mechanical Engineering Design 26 © The McGraw−Hill Companies, 2008 20 Mechanical Engineering Design EXAMPLE 1–3 A shouldered screw contains three hollow right circular cylindrical parts on the screw before a nut is tightened against the shoulder. To sustain the function, the gap w must equal or exceed 0.003 in. The parts in the assembly depicted in Fig. 1–4 have dimen￾sions and tolerances as follows: a = 1.750 ± 0.003 in b = 0.750 ± 0.001 in c = 0.120 ± 0.005 in d = 0.875 ± 0.001 in Figure 1–4 An assembly of three cylindrical sleeves of lengths a, b, and c on a shoulder bolt shank of length a. The gap w is of interest. a b c d w All parts except the part with the dimension d are supplied by vendors. The part con￾taining the dimension d is made in-house. (a) Estimate the mean and tolerance on the gap w. (b) What basic value of d will assure that w ≥ 0.003 in? Solution (a) The mean value of w is given by Answer w¯ = ¯a − b¯ − ¯c − d¯ = 1.750 − 0.750 − 0.120 − 0.875 = 0.005 in For equal bilateral tolerances, the tolerance of the gap is Answer tw =  all t = 0.003 + 0.001 + 0.005 + 0.001 = 0.010 in Then, w = 0.005 ± 0.010, and wmax = ¯w + tw = 0.005 + 0.010 = 0.015 in wmin = ¯w − tw = 0.005 − 0.010 = −0.005 in Thus, both clearance and interference are possible. (b) If wmin is to be 0.003 in, then, w¯ = wmin + tw = 0.003 + 0.010 = 0.013 in. Thus, Answer d¯ = ¯a − b¯ − ¯c − ¯w = 1.750 − 0.750 − 0.120 − 0.013 = 0.867 in 10See Chapter 20 for a description of the statistical terminology. The previous example represented an absolute tolerance system. Statistically, gap dimensions near the gap limits are rare events. Using a statistical tolerance system, the probability that the gap falls within a given limit is determined.10 This probability deals with the statistical distributions of the individual dimensions. For example, if the distri￾butions of the dimensions in the previous example were normal and the tolerances, t, were