9.2.3 Converting Dimensions to Equal Bilateral Tolerances# @( u& w9 |3 F* d1 U
In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances
: N3 K' ]$ C: n(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such$ P/ S5 I9 Y" b2 D8 H
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we9 X* N/ I3 k6 U0 U
could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length3 V( j2 |5 ] `/ j# k9 \
of the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,2 z$ T# |$ U" I0 B3 O" Y- {
all of these methods perform the same function. They give a boundary within which the dimension is6 X9 @# K! `- X9 Q4 u- y$ T
acceptable.) ^. @; n6 H/ r& ?
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The designer might think that changing the nominal dimension has an effect on the assembly. For. f! P( r8 U8 k. o4 Z
example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may( o0 P6 W0 R$ T' P$ H/ P
falsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give/ B( x4 D" B* B4 }
preference to any dimension within the tolerance range.
2 p( G& V. D' GFig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension {4 P5 k$ X" C0 M. n
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer/ v9 A8 q& g+ \. E/ Q$ M
aimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want- @- O( P+ t$ B* x+ H
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
0 a6 V& {) R# l. u+ w. Q+ |good parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.
% D! g. R! A* o, q$ `3 Q h* rThis allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the5 e* S- ]6 q& o0 T3 A
manufactured parts would be outside the tolerance limits.
) q1 g) z; e- H4 X8 S ?/ }# xAs in the previous example, many manufacturing processes are normally distributed. Therefore, if we9 ]6 E: V) }# }, S5 u; \
put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
; z5 i# u: s) c$ v( O- a Ha mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance
w3 ^5 m$ ], b: }. }& k% y# u2 pfollow.
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. }! _9 p7 L. G( S3 e D- a8 l3 t& A0 x0 M0 R& `5 V9 g' l" ~
1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/ w9 S% B0 l! a6 l t8 @; r" n) t
-.009 has an upper limit of 3.031 and a lower limit of 3.019.)) U- O6 _2 \4 E2 {8 E" ]
2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)
5 ^' d+ N2 }: ~. t) k, A3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)
6 f { p) m- t# f. Y" i4 b6 @4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).
: a" y9 w$ i/ o) p- {( ~Alternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)" W; n% e3 R. r8 l. \
( ]( R- J. e6 U3 OAs a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
; z+ X+ j" a* C$ N" a9 l' V9 [may force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral
) f' ^ M0 M7 Btolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to
, v; a+ \: g. }8 n0 m) yÆ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees$ Y6 d0 E6 ~- {
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would1 ^. [3 R3 U7 w6 x8 ^
also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
! w3 w f. b+ l7 T- s# uthan the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.
$ n" h3 J K0 H! D4 F* I7 C, ?As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep
9 s- e1 d# F$ l& ^8 ltrack of which tolerances are “positive” and which tolerances are “negative” because the positive toler-% C* _) Y3 p4 R% H- e
ances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-
3 N8 |$ w, L; o4 q8 c; K( K3 ?sary dimensions and tolerances to mean dimensions with equal bilateral tolerances.$ y/ m; q( F( r$ ^* r# H
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"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."
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发表于 2014-5-23 20:05:11
