9.2.3 Converting Dimensions to Equal Bilateral Tolerances
% i o, p) o& k9 v6 PIn Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances, C( M |; Q* d, B# h! I
(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such# b# Z- Q2 H, f* g& g
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we' Z! z" V& Q; [+ M( D. x
could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length3 A$ @8 Y# v- v: h4 |
of the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,
5 ?2 \/ Q9 w% call of these methods perform the same function. They give a boundary within which the dimension is8 ~( T* x5 `0 h: W* q9 N
acceptable.
; U- D* B4 B+ O4 n0 s U+ d
" b/ {5 D o/ W. n! t3 uThe designer might think that changing the nominal dimension has an effect on the assembly. For
- z6 ]- X# t9 P3 I# H& C3 I9 K. Nexample, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
: e: l# c/ T' u6 k8 o" Wfalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give( g i3 y5 M/ a7 |2 x
preference to any dimension within the tolerance range.5 \/ T- c4 K. {+ \" @ A! Q
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension* }8 {( e9 O# T6 O, d: ^# Z
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer
7 \2 \" w) d. e/ P$ m0 qaimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want7 r, u9 C0 \1 Y; m
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
% z9 A9 V" [6 X" I E8 V$ v, kgood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.8 q# v6 {: I/ t% ] @* Z
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the- e/ F7 g5 ^9 x6 i6 j, o2 B
manufactured parts would be outside the tolerance limits.
! `) v% g5 @" I, d! C: z9 {As in the previous example, many manufacturing processes are normally distributed. Therefore, if we9 J5 z" @0 p' [& p7 ^& B' c* ^
put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
+ o8 Z2 K0 q1 h1 B5 Da mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance$ a* p& ^# c5 P! P
follow.; w' } e; ], h) c) r
" K1 X/ s6 {: s
4 w- m% B; `+ s1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/9 O" I6 k5 F( W
-.009 has an upper limit of 3.031 and a lower limit of 3.019.)' ^( h% x$ H O( x9 E0 Q C
2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)
# Q! h* q/ \8 c. B3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)
) ?; w" Q- Y! _4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).8 s+ F/ q) `! @; s Q
Alternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)1 V3 T% f1 U6 \8 A m( F
5 R4 z I! X& L. c( Z
As a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
% B1 x& R1 \( \# g2 y8 E5 C5 `may force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral( `/ C1 e4 R* {8 F! x
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to9 D; O% v% g# ~2 v
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees
% J0 V: n- G( [; Z0 g0 b# CÆ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would
* d; d; W. Y6 w. kalso want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
' o! w# N( o1 W7 ]% V: D/ c6 _than the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.' @( [3 o f) F, J/ h6 e1 Q
As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep$ ~5 ^7 A I0 G% S+ [0 K. d* K* b# ?
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
2 F, o- _3 k! U4 ?/ l% U" n5 |, Fances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-
/ T2 T) w8 ?1 V- m( J' C) zsary dimensions and tolerances to mean dimensions with equal bilateral tolerances.$ {% o- o9 ^% n5 N
& ]! E/ y2 ]4 S! t
' p+ C' v" ]8 o) W- J" q( W: p" U
"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr.", [" ^& ^) g. V1 M" u$ ?$ `
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发表于 2014-5-23 20:05:11
