9.2.3 Converting Dimensions to Equal Bilateral Tolerances3 ]# y3 x% N" {' |+ s0 m, l
In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances k& [0 @" b5 G4 f, x% ~% u* r
(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such. M4 N1 R/ [$ _9 q0 ?: [) @, f" a
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we* J: x) N/ v0 s z: W2 t
could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length
( R$ ^' C& k5 n, Q4 z8 i% Iof the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,* m/ q( o+ R6 z- Y5 M- Y; j0 l* S J6 W
all of these methods perform the same function. They give a boundary within which the dimension is
# o& B& v5 q E. U4 z6 o; T6 D0 Hacceptable.
5 f5 x; F' C4 Y6 H; `0 W$ J% _5 g( D! X: n+ T: f
The designer might think that changing the nominal dimension has an effect on the assembly. For
& }1 _! r2 t8 }7 p3 C, J4 wexample, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
7 ^7 S3 o9 } f0 V5 Tfalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give
J7 k# {6 }# D- { w* t% D3 Bpreference to any dimension within the tolerance range.! D _6 N% f" B
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension$ h$ a2 E9 ]1 c5 L& K6 y \# C
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer, n4 V+ J' ]3 A5 f7 u2 @
aimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want
2 G" v; q W2 y4 b0 nto maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
" n3 P3 K; L+ n* S9 Y* o/ igood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.
# O7 Y7 @& x( b1 QThis allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the
$ J( [8 V0 g: s( V* V7 `& i, K! fmanufactured parts would be outside the tolerance limits.
( V4 \- _$ h6 l0 t K) eAs in the previous example, many manufacturing processes are normally distributed. Therefore, if we
/ l" s* V' K1 e: uput any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
% {# d& ?+ ]3 S9 u* ]a mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance
r L* E5 k$ C3 f. afollow.
& a c3 z5 ^7 z$ w" ?$ j
) P* T5 C9 K" f
7 O$ }; w! l+ g1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/3 i* c5 @5 U+ c
-.009 has an upper limit of 3.031 and a lower limit of 3.019.)! F7 o% a) W @( l- X% j4 F
2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012), I/ x( z* A6 A& E* D8 a
3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)3 f2 j( ~7 ]* o4 |7 N9 l
4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).
/ L& x: ` f: T" [# UAlternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)) t% i t5 {/ F. P4 L( X
/ `" N1 R# m3 ?# g- f4 YAs a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
5 F" a# }! A# L. gmay force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral! E6 y) r! ~/ A z
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to" v8 h- ^2 D7 r5 k( [; V$ c# _
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees
2 z/ |- \8 o: SÆ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would. V1 f% Z( e" `% g# C
also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
% k. A: s# h* X# @6 P8 qthan the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.
9 M/ v9 d! `( J/ @; pAs we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep
) B/ W; t; v# c+ s+ J7 ftrack of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
+ Z( Y9 A/ a" b: r. E {5 w% Sances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-
& d% l5 V0 I4 ^1 [5 f9 N6 Nsary dimensions and tolerances to mean dimensions with equal bilateral tolerances.8 G# N9 Y- L! x* B& G% F
; k4 R, ]" E2 b5 ]
2 {4 o' ]2 a& H `1 _( q"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."4 K* g" P) t' ~5 v* h9 i
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发表于 2014-5-23 20:05:11
