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發(fā)表于 2014-5-26 23:12:49
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9.2.3 Converting Dimensions to Equal Bilateral Tolerances8 M8 `# I+ X5 M! X
In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances1 g' j1 X0 R! `& [0 @7 J
(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such
! s0 n# Y9 ^5 P& ^* J) O, ^: Ias +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we
( l; m1 N. t2 |- y$ Gcould have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length
0 ?- W& U- }: Y0 ?& Mof the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,5 J4 ^5 A& I2 @6 L
all of these methods perform the same function. They give a boundary within which the dimension is
& C) g+ R% ^4 q% x" d9 V2 t2 uacceptable.
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The designer might think that changing the nominal dimension has an effect on the assembly. For
6 f z: ^+ a1 l. s* d. b( R6 G2 [example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may' H8 [: B; H, F5 j& y) B5 t
falsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give
9 p; j. L& x8 P. g8 qpreference to any dimension within the tolerance range.+ \" A; I/ N4 ^! F" I* B
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension
$ W" `5 o. C3 @1 |stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer
9 F% t. N/ o6 {aimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want6 X3 j- `# o% |$ w: e0 n
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
, G/ D# Q3 S" S; d+ rgood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.# s; Z: r+ M; R% G9 o1 b6 z( j* d
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the: X8 E0 `/ c0 M% |4 j/ x/ _
manufactured parts would be outside the tolerance limits.6 a3 a5 R( }* Y
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we' K6 X* Q+ W6 T
put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to& u* S* {' G% h
a mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance
; V" p8 S/ e: j% a. |2 X% u, r- afollow.
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1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/
- M* h4 ]" u4 \3 V-.009 has an upper limit of 3.031 and a lower limit of 3.019.)# x m5 }: q/ c7 M+ u1 s
2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)
4 m2 Z" b/ r( t% b& h6 [3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)2 _: m7 K. F% M3 @9 O8 V- C
4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).
& c3 C) |% J6 Z- lAlternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)
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As a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
$ z% j, }) f" i& b- Amay force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral: \3 Q8 [2 x' y
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to. m8 b" e; ]6 o( R4 m5 r
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees# Z$ K5 s9 j3 h8 U3 t' e6 K
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would
( M, m3 L! w6 ~8 Q# {0 }also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger( [8 e4 ^' w4 {" t" F' y+ V
than the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.
% T" L3 @; r# L6 S! u0 O# hAs we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep
; A. Y: V* H& q+ N4 itrack of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
& w3 \; s( p- k& C6 oances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-" a, D/ y: ^. ^. F5 N( [9 R# g$ U
sary dimensions and tolerances to mean dimensions with equal bilateral tolerances.
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7 |" d$ M9 i+ q% z C8 X" ?"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."+ q9 `& Q! w- }$ M8 G' X# m
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