9.2.3 Converting Dimensions to Equal Bilateral Tolerances
( I7 B5 S9 S9 y# g8 _- rIn Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances4 y9 F' o4 s& P
(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such) @% I( N. ?7 M/ R) l( Q0 `; y+ z4 }2 V
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we
# Q7 A {! q2 F4 C) i P* lcould have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length0 o& f: B8 m. Q- O! ]9 w
of the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,5 `* F$ ^5 w5 A
all of these methods perform the same function. They give a boundary within which the dimension is. A$ e! B7 n+ P+ g
acceptable.3 H' S$ Q; n: w/ C \' e
5 o( j$ l6 i" m" R9 n! I0 d( z& F( l9 B) cThe designer might think that changing the nominal dimension has an effect on the assembly. For
8 R$ n: V0 X% U. E- eexample, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may! a8 e- e/ V% l! c4 L( N
falsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give
" i* _' v* y3 Z% I5 X4 r0 \preference to any dimension within the tolerance range.+ Q3 W& h) @1 f' j
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension
( r; V4 F4 W0 f; i8 T: o6 P% Fstated on the drawing and the process follows the normal distribution. In this example, if the manufacturer" L2 k* U/ ?5 K, t8 c
aimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want- E; F. F9 e2 z# v+ Q0 W, _# k2 h
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of% `- F- I) |& v9 a5 O' {
good parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.2 ^4 i0 l. D# I. i0 X
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the# f* T2 A) R# _
manufactured parts would be outside the tolerance limits.* x. c4 p, n) f: `0 \" ^$ m
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we
4 q8 `6 X/ l# w8 bput any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
' B' L2 q( p1 U; {- Sa mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance
# I( S; R5 u- I6 T' ?follow.+ Y& u$ z- s2 G D7 G- @9 b9 F
! T7 c C k/ z) R( q
" \) D# A: Y$ T$ z+ |+ M% X" G1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/
2 ?+ u) F% }- Q, ]( E-.009 has an upper limit of 3.031 and a lower limit of 3.019.)3 P/ i1 G$ k5 Q1 a, G" s
2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)) X2 T; i( u" e- ~) k3 E
3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)( k8 G1 g9 }% w+ [# l! Y
4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).
; G3 J7 ] {: \' Z, `+ E. zAlternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)
& e% r" E7 O' o7 f3 f2 M
# U4 X4 C& y8 Z, j& @% v/ IAs a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
; x9 h0 u' K0 @. D. w5 D+ Vmay force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral3 e- t* f: p3 g/ k. Z
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to* C+ Y8 [. Z c0 j
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees
' [. ?! M }& Q; p+ {Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would2 o% |$ t% T/ ]+ C
also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger0 D& _5 g( J% [, L' W' e, q
than the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance./ b5 x- L; X5 @! k0 E. D/ z/ S% a
As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep! }/ a& I7 I# a+ g% l' p Z6 E
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
+ I- e, ^' X8 M, w- L! wances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-
; w. P; W) }5 wsary dimensions and tolerances to mean dimensions with equal bilateral tolerances.+ X5 z, f& ~5 |! ]9 M
% R$ X- x5 p$ ~0 F3 h- r" z1 v
# A" b$ _, V' m5 {. v+ \$ U3 \"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."" a7 K0 I! |& j8 Z3 G9 p9 \( e
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发表于 2014-5-23 20:05:11
