9.2.3 Converting Dimensions to Equal Bilateral Tolerances
4 b8 E: ] A3 q# l) {In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances
7 j0 F4 P' @ Z. {( p u(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such
, K2 K) Q0 Q1 t+ W1 Xas +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we
) o/ `" R- ^/ F* A0 F2 w; |. pcould have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length& U$ A, I4 M7 m6 n) p
of the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,
5 ?$ G9 {) T p, V, T5 Tall of these methods perform the same function. They give a boundary within which the dimension is: E' f, ^: P, a" T) g6 G' c9 s# Q
acceptable.
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% S" T$ t0 e! ?5 t* R$ GThe designer might think that changing the nominal dimension has an effect on the assembly. For
3 p5 k L6 y2 S. h$ _. L$ I- {example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
+ d/ e4 Z- ^+ U1 _# s) M7 C' v+ X, wfalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give
, u n) Q% _/ i( z6 Z2 A) n: i& ]preference to any dimension within the tolerance range.
! J; V' f3 v& F4 `' N5 Z8 R# K5 }2 L+ CFig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension( r0 G' Q5 l' `; J& q: P
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer
6 D( q) `! k f) v0 Haimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want
5 x* N/ @0 p5 q8 ?0 R3 v b! ato maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
- B) t- y5 l9 r+ g& H5 p! T- D& igood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.
5 b H; ?- V/ r# U0 Q4 F0 YThis allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the `% X0 E7 c3 P2 ]- M9 o6 ]0 K9 ~
manufactured parts would be outside the tolerance limits.6 w# q4 A: N% E# A* s R- r# _' o
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we
# v( T2 I( ?( ^4 r! F) Q( ~put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to, n( `! Z1 k, o& Y% R
a mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance% F4 ^* N' T( P/ \3 w/ S0 o: X
follow.
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# e8 I( W3 q+ m/ z1 w% W3 Q1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/
4 c6 O v, w+ n0 @& [' o! Q-.009 has an upper limit of 3.031 and a lower limit of 3.019.)
9 b3 A, g& d, r: I+ m2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)
" o. L7 |7 y/ p3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)# t ?: L0 ^( d4 V* P
4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).
6 a v3 F/ F- F* x$ A/ }0 SAlternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)8 w5 U+ g- B( |* e, C, Y5 \
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As a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
& d; Y3 T6 L# ^, B; Y4 m' Hmay force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral) m( C. I# j% T, q3 s6 Y
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to0 E. B# |1 U$ e7 Y& c" S' M
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees
" l, H6 Q' C5 y- o( i0 T; uÆ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would
/ u# f6 A7 r5 e. n3 t% W3 e1 \also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
1 E; H8 R2 b# c% k( ethan the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.
4 Q" L- t) y0 {; k* [+ ZAs we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep( M$ D. V, A1 s% ]' ^
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
& _' }& ?$ D+ p |8 ?6 Gances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-
( y( V8 z* L! \+ ^" F8 ]sary dimensions and tolerances to mean dimensions with equal bilateral tolerances.
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"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."
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