Tolerance Plot Development for Fitting Pairs, Study notes of Engineering Dynamics

Solutions for designing and developing tolerance plots for fitting pairs using the hole and shaft basic systems. It includes calculations for various fit types, nominal sizes, and tolerances. The document also discusses the concept of selective assembly and its importance in ensuring exact fits, particularly for interference fits.

Typology: Study notes

2012/2013

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Solution Set 1
Class Allowance Hole Tol Shaft Tol
1 0.0025*cubroot(d^2) 0.0025* cubroot(d) -0.0025*cubroot(d)
2 0.0014* cubroot(d^2) 0.0013* cubroot(d) -0.0013* cubroot(d)
3 0.0009* cubroot(d^2) 0.0008* cubroot(d) -0.0008* cubroot(d)
4 0 0.0006* cubroot(d) -0.0004* cubroot(d)
5 0 0.0006* cubroot(d) 0.0004* cubroot(d)
6 -0.00025*d 0.0006* cubroot(d) 0.0004* cubroot(d)
7 -0.0005*d 0.0006* cubroot(d) 0.0004* cubroot(d)
8 -.001*d 0.0006* cubroot(d) 0.0004* cubroot(d)
d โ‰ก Nominal Size
Problem 1: Design and develop a tolerance plot of a fitting pair using the Hole Basic system.
The required fit is a Medium Fit with a nominal size of 1.125 inch (Class 3).
MMChole = Nom. Size = 1.125โ€
LMChole = 1.125 + 0.0008*cubroot(1.125) = 1.125 + 0.0008*1.040 = 1.125 + .00083 = 1.1258โ€
Allowance: 0.0009*cubroot(d^2) = 0.0009*1.0817 = .00097โ€
MMCShaft = MMChole โ€“ Allowance = 1.125 โ€“ 0.00097 = 1.1240โ€
LMCshaft = MMCs โ€“ Tolerances = 1.1240 - .0008*cubroot(1.125) = 1.1240 - .00083 = 1.1232โ€
Problem 2: Design and develop a tolerance plot of a fitting pair using the Shaft Basic system.
The required fit is a Free Fit with a nominal size of 0.75โ€ (Class 2).
MMCs = Nom. Size = 0.750โ€
LMCs = 0.750 โ€“ 0.0013*cubroot(.750) = .750 - .00118 = .7488โ€
Allowance: 0.0014*cubroot(d^2) = 0.0014 * .8255 = .00116โ€
MMCh = 0.750 + Allow. = 0.750 + .00116 = 0.7512โ€
LMCh = MMCh + tolh = .7512 + .00118 = 0.7523โ€
Problem 3: Design and develop a tolerance plot of a fitting pair using the Hole Basic system.
The required fit is a Medium Force Fit with a nominal size of 1.875โ€ (Class 7).
MMCh = Nom. Size = 1.875โ€
LMCh = MMCh + 0.0006*cubroot(1.875) = 1.875 + 0.00074 = 1.8757โ€
Interference = 0.0005*1.875 (neg. allowance!) = .00094
MMCs = MMCh + Interference + Tols = 1.875 + 0.00094 + 0.0004*cubroot(1.875) =
= 1.875 + 0.00094 + 0.00049 = 1.8764โ€
LMCs = MMCh + Interference = 1.875 + 0.00094 = 1.8759โ€
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Solution Set 1

Class Allowance Hole Tol Shaft Tol 1 0.0025cubroot(d^2) 0.0025 cubroot(d) -0.0025cubroot(d) 2 0.0014 cubroot(d^2) 0.0013* cubroot(d) -0.0013* cubroot(d) 3 0.0009* cubroot(d^2) 0.0008* cubroot(d) -0.0008* cubroot(d) 4 0 0.0006* cubroot(d) -0.0004* cubroot(d) 5 0 0.0006* cubroot(d) 0.0004* cubroot(d) 6 -0.00025d 0.0006 cubroot(d) 0.0004* cubroot(d) 7 -0.0005d 0.0006 cubroot(d) 0.0004* cubroot(d) 8 -.001d 0.0006 cubroot(d) 0.0004* cubroot(d) d โ‰ก Nominal Size

Problem 1: Design and develop a tolerance plot of a fitting pair using the Hole Basic system. The required fit is a Medium Fit with a nominal size of 1.125 inch (Class 3). MMChole = Nom. Size = 1.125โ€ LMChole = 1.125 + 0.0008cubroot(1.125) = 1.125 + 0.00081.040 = 1.125 + .00083 = 1.1258โ€ Allowance: 0.0009cubroot(d^2) = 0.00091.0817 = .00097โ€ MMCShaft = MMChole โ€“ Allowance = 1.125 โ€“ 0.00097 = 1.1240โ€ LMCshaft = MMCs โ€“ Tolerances = 1.1240 - .0008*cubroot(1.125) = 1.1240 - .00083 = 1.1232โ€

Problem 2: Design and develop a tolerance plot of a fitting pair using the Shaft Basic system. The required fit is a Free Fit with a nominal size of 0.75โ€ (Class 2). MMCs = Nom. Size = 0.750โ€ LMCs = 0.750 โ€“ 0.0013cubroot(.750) = .750 - .00118 = .7488โ€ Allowance: 0.0014cubroot(d^2) = 0.0014 * .8255 = .00116โ€ MMCh = 0.750 + Allow. = 0.750 + .00116 = 0.7512โ€ LMCh = MMCh + tolh = .7512 + .00118 = 0.7523โ€

Problem 3: Design and develop a tolerance plot of a fitting pair using the Hole Basic system. The required fit is a Medium Force Fit with a nominal size of 1.875โ€ (Class 7). MMCh = Nom. Size = 1.875โ€ LMCh = MMCh + 0.0006cubroot(1.875) = 1.875 + 0.00074 = 1.8757โ€ Interference = 0.00051.875 (neg. allowance!) =. MMCs = MMCh + Interference + Tols = 1.875 + 0.00094 + 0.0004*cubroot(1.875) = = 1.875 + 0.00094 + 0.00049 = 1.8764โ€ LMCs = MMCh + Interference = 1.875 + 0.00094 = 1.8759โ€

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Problem 4: Design and develop a tolerance plot of a fitting pair using the Shaft Basic system. The required fit is a Tight Fit with a nominal size of 2.25โ€ (Class 6). MMCs = Nom. Size = 2.250โ€ LMCs = MMCs โ€“ Tols = 2.250 โ€“ 0.0004cubroot(2.250) = 2.250 โ€“ 0.000524 = 2.2495โ€ Interference = 0.000252.250 (neg. Allowance!) = 0.00056โ€ MMCh = MMCs โ€“ tols โ€“ Interference = 2.250 โ€“ 0.000524 โ€“ 0.00056 = 2.2489โ€ LMCh = MMCh + tolh = 2.2489 + 0.0006*cubroot(2.25) = 2.2489 + .00079 = 2.2497โ€ Note the LMC to LMC sizes!!!

Problem 5: Selective assembly is used when an โ€œEXACTโ€ fit design relationship โ€“ either for interference or clearance โ€“ is required between mating parts. It typically is used to inspect in exactness however by measuring and sorting fitting components extracted from a wider toleranced process to control costs. It is a must for interference fits since the two components are expected to carry or resist forces across the interface between the internal (smaller) and external (larger) sizes of the fitting pair. In clearance fits, it is somewhat less often seen since the internal size is always larger than the internal sized object. However it is indicated if a specific lubrication gap is being designed or a specific desired centering gap is required (like pistons and cylinder walls in gasoline or diesel IC engines).

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