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發(fā)表于 2014-5-26 23:12:49
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9.2.3 Converting Dimensions to Equal Bilateral Tolerances
1 x$ {& o3 ^, \In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances
" z$ f! ^. Q* G(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such. D- W% p' Q h$ M
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we9 \1 M3 x5 E9 k5 ?9 {
could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length
. u3 |* e% { G" ?, n1 E( H' Iof the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective, q8 T Q9 r8 M" f
all of these methods perform the same function. They give a boundary within which the dimension is
) R4 u6 ^' N0 B$ Y; {. d/ zacceptable., p5 r' J- b, a$ M1 ^! J% Z
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The designer might think that changing the nominal dimension has an effect on the assembly. For# ?4 H& x$ b) S" j; L" c
example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may; K# V" H6 M6 b2 C& t$ ?
falsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give
* Q/ i1 o% s6 n, p# Y+ I+ w; ^preference to any dimension within the tolerance range.- T9 m) Z3 V; R/ ]
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension' g" B( [, B! }! _4 R$ M! w& k/ K
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer" u, M" j! i! ^
aimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want/ \4 k* x$ ]4 X3 d
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
! P J; q9 V" ^4 |good parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.6 P7 I [! c$ R& n" V* \8 H
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the
4 \: Q% [( ^, k" V1 u7 R! t& p, Mmanufactured parts would be outside the tolerance limits.8 l- Y# z1 w1 m" T" j/ ]. ?* _) w
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we
+ D h3 @2 n# S I6 zput any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
3 v! }/ N3 {. z% e9 D E8 }; D1 Ga mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance) G. h+ m1 X+ U9 j# |
follow.
1 M1 F" P8 Z+ f2 [/ u% U9 i7 p
) w# c0 D7 {% y2 R T- I
- i$ k. c7 p; G) U. `1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/4 l' _' n4 M$ c# c
-.009 has an upper limit of 3.031 and a lower limit of 3.019.)' c& ~# c8 I$ [
2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)
3 f2 T2 y8 Y7 j3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006); V+ g' n3 K# x1 q8 t
4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).
- o. l8 I. d* q( E) ^$ HAlternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)6 Z/ ~% Q% D+ ]0 Z3 q5 }- q0 E6 o+ ~( j
( { j. X% L+ a/ y. ?& ~8 ?" E% kAs a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances# g+ z9 l/ R5 J) E& v" z0 C
may force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral7 g0 {: f+ ]0 B2 f+ d9 u3 U
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to/ H/ s( M a! ^9 f3 c: l
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees' s$ @& H- t/ @% a, r& m' A
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would
/ i; O& t1 s5 aalso want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
: o( E) o: C! ?! J8 @: hthan the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance. C$ R2 A( D7 T% U# A" B, W
As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep
! W( {, l- n5 l8 @" S1 N4 Ntrack of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
1 H- Y/ ` R: I3 I) v7 h1 X) wances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-1 j y" _$ a, X2 s I
sary dimensions and tolerances to mean dimensions with equal bilateral tolerances.* D3 B6 S+ a# V0 A7 v
5 _, {) }+ N* k4 K9 d/ X- j
* d4 |/ f6 z7 U ]- k `"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."
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