9.2.3 Converting Dimensions to Equal Bilateral Tolerances
3 F, _# Y* i1 D* j# p+ bIn Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances# n( k0 H6 O9 ]/ }0 o2 w
(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such4 D, A4 `9 `* P! {: B1 r( ~" l
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we
" L" T9 H! I( ~could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length: Y: y. G: S3 P
of the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,: A8 o* Y; H7 u/ a9 Y6 G- |2 x
all of these methods perform the same function. They give a boundary within which the dimension is
4 [; {6 N4 b0 q: r. i! Yacceptable.+ {/ }# m. W8 l- b9 j
8 |. D9 v8 R% y, U0 c. e( S5 sThe designer might think that changing the nominal dimension has an effect on the assembly. For
' O1 Z4 q$ s8 u' }- Yexample, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
7 E3 F: U4 a2 O/ K( e* ?falsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give( j& q, `& F4 Z, X
preference to any dimension within the tolerance range. w5 ]( r& [( T9 Q6 @% A- \# x' |
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension7 X# i) T& }4 r# r
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer5 l' D! l( i7 P& Y$ o a
aimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want/ ?* E5 p6 ^; q4 R" V2 o
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
C0 H1 A) G1 w% q( V5 vgood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.
0 J5 k6 t; s5 F% e2 ]+ @4 ], KThis allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the
( w# S' X% x! Q9 }+ B8 M6 y+ i8 Wmanufactured parts would be outside the tolerance limits.0 l8 D1 |% x/ R# x9 e: h
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we; [: x4 Q) x1 z% N
put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
7 u# E) e' [9 m/ `, S7 Da mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance' H1 I+ c7 F t0 W9 U( A; e8 Y* O$ D
follow.
; u# ^& w& ^) z; f4 w8 e& R0 a3 l3 a- `0 C4 r
# |/ E( e( M" D5 Y
1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/7 [ P1 \9 d, r# j7 m! I" U+ M4 D
-.009 has an upper limit of 3.031 and a lower limit of 3.019.)
( k( O$ F- ~" m% w2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)
# J1 }) h( G- X; l5 \- J! s- ~3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)- E7 ^; q7 o; C+ J5 ?$ T
4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).* M$ M/ o& _6 i; M
Alternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)3 |( {4 P2 n/ g! M: t
# ^% b; c% R5 u/ G5 m+ I6 EAs a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
: R$ @- H1 j( x ]6 v4 F7 Cmay force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral
* {. \6 H4 d8 c3 ]! z/ ^0 S3 xtolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to! v! S# h# H5 J! ~5 c
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees" X3 s# m- u8 X; v9 U) g- O$ Y
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would) }3 d T2 ?0 g3 h$ z
also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
3 s+ `7 L8 U/ q6 ?than the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.- m/ X: y( h' D- Z. j n3 A
As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep7 K$ Q$ B* V/ r. E. P W# I
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
$ X( ^( \. s" p/ t# H- C7 ?ances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-) Q" n/ C+ I7 r* s
sary dimensions and tolerances to mean dimensions with equal bilateral tolerances. T/ d) Z+ L- A3 C& z
, @; @3 x2 k2 e7 b5 T! u ?/ S: i8 B0 p% u* [& G K8 A; t" {
"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."* f3 t% x" w1 y5 \9 H+ u P+ O4 h
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发表于 2014-5-23 20:05:11
