9.2.3 Converting Dimensions to Equal Bilateral Tolerances& \) {" W: ^$ K5 t6 h1 b
In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances) G r9 D9 ~; e6 x+ J) U" u! N
(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such
; P8 w6 N) c% Q& k4 i/ e2 Las +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we' h+ p' s3 C3 `3 @ y- }0 J3 \, ~
could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length4 J' x0 X. [) }
of the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,
% n( I" G' a9 Q% v- M S( a" [all of these methods perform the same function. They give a boundary within which the dimension is
4 C L4 s3 S; A* _0 \7 s; ]# Sacceptable.* ]8 x+ L, l0 }+ Y8 a
. p( w6 _3 @- W& U8 p3 B; `The designer might think that changing the nominal dimension has an effect on the assembly. For( X' C$ A0 r; m5 w1 g) G4 F
example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
+ m$ c6 `7 l6 E+ v. C$ }falsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give% X! e) r7 y" [) }
preference to any dimension within the tolerance range.
- d5 l* W) C$ |8 p# x7 EFig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension
) Z* m t4 G9 @7 P; b+ Ostated on the drawing and the process follows the normal distribution. In this example, if the manufacturer
# T1 w7 M2 O, }2 paimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want6 D- y& k+ ]+ ]1 B2 \9 d k. o
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
/ [( a+ E. ^# ~2 o; x: ggood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.
9 O( ?- C5 G" BThis allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the8 e/ m; Z5 [! Z7 \
manufactured parts would be outside the tolerance limits.- k. i2 ]- j( u* t
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we E* p; V+ }7 O+ S: O' J/ E/ U
put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to! R8 a" e4 l8 a5 W9 V- F5 X# ]0 v
a mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance
) p) T: x1 U$ ufollow.
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1 u: c' ]; C4 C" @, v, J
1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003// {3 o, u! D% [* P+ b
-.009 has an upper limit of 3.031 and a lower limit of 3.019.)9 T4 R2 q5 T7 a# C) o9 H( }- h
2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)0 s& F( s4 a n3 [ D8 L
3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)
: e/ B/ J- Z) ^' V' [# `5 j4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).
; V+ X# L# i# T H3 @ ~2 xAlternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)) x$ l' R: e0 W
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As a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
7 ]- _. ~3 o x+ C8 |7 X( \may force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral1 i, \" t7 \/ H: p' f `2 Y5 S
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to
: x6 U1 ^" T. x3 m/ A! AÆ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees- _# ^9 D: @" m9 W
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would
O- \; d# O" m% I, b# T6 ralso want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
; v" X' l0 q: b4 uthan the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.) m. n; V+ m5 k9 ~: z- z
As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep( A# o* z" C8 B2 F& i1 z
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
! R; y0 L8 w2 x" r4 Uances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-
1 R4 E* g. J) ^, `& Q$ i7 Tsary dimensions and tolerances to mean dimensions with equal bilateral tolerances.
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o# A* [0 J5 @+ a3 S
% L$ u0 i2 s4 M$ P"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."
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发表于 2014-5-23 20:05:11
