9.2.3 Converting Dimensions to Equal Bilateral Tolerances. ?8 K& a* e; I; W8 O
In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances
4 u- X, x: z+ M# `(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such7 S1 Q8 c; U! I3 C
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we
9 y* ~: H) \3 B8 scould have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length
( L9 `/ T/ |& v5 d6 Aof the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,
9 U% I( k/ R! z6 Uall of these methods perform the same function. They give a boundary within which the dimension is; e4 S* d1 [1 ]4 P. ]5 E" I4 ^
acceptable.) ?; h+ @9 E% J
/ f, }2 ]$ S; R: O& OThe designer might think that changing the nominal dimension has an effect on the assembly. For( L$ Z6 R: k" J
example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
( `9 ~) p; v L. G4 |: bfalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give
% {6 I' m% c- F' D; W# H \) k5 {3 _2 Dpreference to any dimension within the tolerance range.' P6 R3 F8 n- m5 Q4 O
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension9 ^3 [ E( m9 R/ ?
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer
- O8 Y# w' s- I1 |( Oaimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want
$ L' j; t6 u4 ^9 [- Pto maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
' j7 s$ J, x# z6 t' h+ u' B. j6 Egood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.6 f& R3 j- f, @( T4 Y" s
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the- ?# C& g4 D2 q" m8 Z1 V+ x
manufactured parts would be outside the tolerance limits.! K' s- Q6 V. }
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we
2 f$ k! [' P- Y3 [% [put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to, {3 Q' s% a1 c' W& }
a mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance0 {. u& q2 q- z6 \5 t4 S
follow.# m# ^: r; p7 A3 y" t& `
9 x9 T5 _& ^. `, h3 }1 q) K* t- L! i% M2 v+ x
1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/
8 ^7 A& d; r5 b/ G# H1 C4 k9 }# O-.009 has an upper limit of 3.031 and a lower limit of 3.019.)
1 [2 ]6 a4 {6 F. ]2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)% @7 j6 U7 j1 J# g
3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)
u0 S0 l( f* D9 }% Y# M4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).1 ]' i6 r7 {3 K/ I( a5 H
Alternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)6 G x5 @( f6 ?; h$ O4 e) |; g
. j. {# d! J. N/ u8 y/ L" r- VAs a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances3 f$ M, Y% r) M- K0 @% W) i4 V
may force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral9 G) j( I$ m( M$ n
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to1 b& X" F! }% o2 u3 v% }4 r' D
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees" ^1 G6 w# O, R+ E& v8 s
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would
/ ^- y$ \, V9 ]! q6 |6 salso want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
7 F! ~' q% Q; Ythan the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.& L) O7 B2 n$ I, |% t" \) I
As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep. G) x) \' p9 d* U
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-; o1 T. H2 z5 ?
ances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-+ E9 }2 m% ?+ ^0 v: a T
sary dimensions and tolerances to mean dimensions with equal bilateral tolerances.* l: N; }& ~$ N5 L
: n& }( C' i5 `: T/ E5 b
! Z; Y8 A! g: t7 L$ F1 ~"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."# b o* v- \4 C
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发表于 2014-5-23 20:05:11
