9.2.3 Converting Dimensions to Equal Bilateral Tolerances/ L5 O, e; }. @) I9 D8 I! }) ~
In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances
( ]% T2 u) C- Z. u- j/ e) Y$ |(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such
. j7 `+ \& |7 J5 E% |as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we1 j; D: k; o* Z0 q2 c7 g
could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length) R S; f1 \' v; q+ k- E
of the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,
5 L ^6 }7 {: Z# L1 `all of these methods perform the same function. They give a boundary within which the dimension is
3 _* a* Y$ C: o& }% {) V' K- M$ pacceptable.
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The designer might think that changing the nominal dimension has an effect on the assembly. For' E: @% H/ X* U
example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
S9 \3 B& y1 cfalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give
) K$ q0 T- u3 B2 p: K* f& S7 r) rpreference to any dimension within the tolerance range.3 h. y7 W8 q' ?* S
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension, v0 v% s& y% a5 L
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer
$ H6 m8 n0 p+ C$ {7 B' Daimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want; b8 z& M" T$ o9 T& X
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of1 X$ ` d1 W4 s( T, I9 L
good parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.
+ A- I4 |% A9 P; Q9 c- qThis allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the7 z$ f* B+ g: r8 n# h; D, w
manufactured parts would be outside the tolerance limits.
2 Q1 N* b: W; H- ]9 `; ?0 D& _As in the previous example, many manufacturing processes are normally distributed. Therefore, if we
+ a [ k5 s; Y( A9 O/ W. [ ~put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to: e9 b/ l6 m; P# d
a mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance
5 F- E: \4 r4 ^+ A! w4 ofollow.4 k; `5 v1 ?& |* t
! i- s4 K$ P) d, ?
: u f) v5 c5 u* ^1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/
' n2 g" R, H( v5 c-.009 has an upper limit of 3.031 and a lower limit of 3.019.)) _) M3 a8 t7 P. V/ i! T
2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)* U- G b8 q8 D
3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006) k2 L& s7 H5 |1 v
4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).. s; _8 s- i/ q, {: ^
Alternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025) b' Y i" N, u* h0 |% Z
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As a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
) R: [9 H7 X6 d& Y6 E8 pmay force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral& t9 g3 `+ H) ~ ]- @7 v9 P- W: \
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to8 G' {0 S9 S, O
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees$ H, g3 G o) v" }0 Y
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would/ r! Q/ H. J" N) } T
also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
$ b% Q% _1 H3 f1 W5 b7 S: Y: D Kthan the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.
5 z) R I& \2 q3 x TAs we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep2 q: g1 w' \0 Z N4 ]5 x/ [2 k. o
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-- G# [8 }! W9 E$ u# v
ances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-0 j' D' r# \6 s8 X9 ` m- Y
sary dimensions and tolerances to mean dimensions with equal bilateral tolerances.
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$ c- C. w5 y8 A1 G/ f6 }; K. y# O a9 ?9 b/ Z8 ]. I0 s
"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."7 v+ E& B q" O N$ y
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