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9.2.3 Converting Dimensions to Equal Bilateral Tolerances# m+ x) }, w, F! j4 d* X0 I
In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances8 z0 O- v/ R. Z
(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such6 u4 D! H: c5 ~) F& Q9 T- |
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we' r6 K9 }/ I2 j' g$ Z# v
could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length
, C6 J! n# ^0 B$ A# m9 T! Cof the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,& Y3 F6 ?/ ]! c' \, z+ c
all of these methods perform the same function. They give a boundary within which the dimension is
1 @2 e, B# Q0 }acceptable.& k( _, D) Y8 g0 i: S
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The designer might think that changing the nominal dimension has an effect on the assembly. For
. T: }5 F6 @/ ^example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
+ c2 }5 E5 K0 A% Y+ z2 \/ Zfalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give6 o* u- `0 V0 u# i V- B# U- x4 m7 }
preference to any dimension within the tolerance range.! p1 w& [* j" \" N% E. a
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension' [. H( }" \: V5 k# d7 J
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer6 O( x( `' \% x
aimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want6 ~3 q! G, u. u5 W2 J) p
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of$ o0 t; s; N: Z: e8 T1 o+ A
good parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.. N3 S& J- b) Y/ k
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the
4 B" q" s$ @! G6 Q1 D, B' zmanufactured parts would be outside the tolerance limits.
6 {8 z. Q. Y4 {6 r) qAs in the previous example, many manufacturing processes are normally distributed. Therefore, if we
2 y% E+ v, o4 J5 D, D3 t0 O& Lput any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
- Y! g" T. }. xa mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance) F8 B% o( u4 [' ^' U! u7 D
follow.
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1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/2 T, E8 P0 |6 v$ J3 j
-.009 has an upper limit of 3.031 and a lower limit of 3.019.)
9 P2 i$ g6 G7 g+ ]- {+ ~9 b2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)* M# O3 d8 x; j( u0 T
3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006). y k( Y9 i* ?8 T' ]
4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).
# e" o; Y, x7 s8 @: gAlternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)
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As a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances9 o, y, E( _3 @- Z" f# E9 u3 v
may force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral/ P5 \) `" l C; |" C1 R7 {1 D
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to
. m! R9 x! g2 {. j2 E6 m, v8 H- l- PÆ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees% P# J9 _% Z2 S% _( R/ L
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would
* n$ \( v% q. falso want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
, G4 H3 [% V* k. cthan the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.
* T5 z! H @* ?3 {( C; |' uAs we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep
0 B" T3 T+ X/ ]/ _track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
0 Z6 A4 ^! {/ I; |( iances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-
& @3 [% w0 S. v7 l& wsary dimensions and tolerances to mean dimensions with equal bilateral tolerances.
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"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr.") J9 u% E9 a. M- @
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