9.2.3 Converting Dimensions to Equal Bilateral Tolerances3 V: o a0 ^# p
In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances
2 [& i) k+ a& c3 [(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such+ ^, @% W8 h% }
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we
/ B l l8 [2 r0 k8 B! Icould have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length
7 M( u5 Y4 y6 s. Y9 ~: e. Vof the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,
% a' U- M) Y) c Aall of these methods perform the same function. They give a boundary within which the dimension is$ B8 n i% X1 A Q# ~& c- v
acceptable.8 T" D$ r$ t; m7 B
+ {% v0 f4 t8 J1 H% d0 a! t+ a& RThe designer might think that changing the nominal dimension has an effect on the assembly. For
8 \9 l4 j+ ] y/ rexample, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
: u+ Y1 u! a( M* ?7 p9 v* Ofalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give0 R* Y' a+ w( s& c% k7 }
preference to any dimension within the tolerance range.+ l6 y# W( ^5 r: H
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension+ I. f1 u& A6 ]0 I
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer
9 H4 Z' Q, G4 H" z* y8 A/ ^' xaimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want$ c8 z0 h1 j7 V6 x6 ~, E
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
& J) \* h( C. `1 Xgood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025. |' X2 j. t. P. W- |3 R. ]$ Q) p/ J
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the
3 E' D1 a A9 ^" u& N. Amanufactured parts would be outside the tolerance limits.
) w: ^4 Z# h2 a. GAs in the previous example, many manufacturing processes are normally distributed. Therefore, if we6 {) ^ b& w' H% P+ N6 _
put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to% k5 k6 m6 f; ?% E- x- E3 W
a mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance
1 }' m% ~7 _ D: s, z( e6 s( {follow.
+ M. }! z, y+ o, j( P) x8 }/ A; O4 ?( F3 E- m% Z
# b6 w- N3 b2 L5 ?- @" B1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/
8 \. |; e3 n7 Y% _ g- [- L# f-.009 has an upper limit of 3.031 and a lower limit of 3.019.)
, U3 E. _4 {& ^# {: i: s2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)$ S4 d4 k! \% M$ S7 E
3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)
1 ?% I: H9 {3 @7 t2 S& G2 `0 P4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).
( c) u$ f+ w/ `: L* L& sAlternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)
. @; B, l9 j8 n4 s: u. r
+ d& y+ c: @$ y: u4 Z4 I8 wAs a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances7 h( C* y5 c* o5 {. O% d+ Z: O" x+ e
may force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral7 v% o0 J' q" z) F
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to
. @" b! D( u j- b7 `" N! d* O1 AÆ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees
0 Y" N: {0 p9 h5 n1 ZÆ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would
7 w( u2 N# L8 X+ l3 Talso want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
# f, s, R9 B# l0 a5 b1 _5 ^- k& jthan the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.- c8 w" ^- S1 T* ]( M1 D3 u0 l
As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep
! g1 k# |, x" dtrack of which tolerances are “positive” and which tolerances are “negative” because the positive toler-# G& J0 J9 U& _0 L+ a
ances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-
% |! L: t+ C6 G$ i& U" S2 ^sary dimensions and tolerances to mean dimensions with equal bilateral tolerances.
6 N0 `, ^# |8 J: C
5 J, r5 u" U/ V, C' |- \$ u( h7 y. r9 f& W8 e1 I1 X
"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."7 d; n4 J, R) Z# q8 d
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发表于 2014-5-23 20:05:11
