9.2.3 Converting Dimensions to Equal Bilateral Tolerances
; }8 n4 b* u ]6 E/ [In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances/ i9 U' m. k' l' V% M6 g
(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such0 n, f7 P) B: g$ A! a
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we
; d' N4 ]" M9 |0 B) W7 t. b# Dcould have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length; G- t& }0 s/ W* |# \. U
of the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,
2 h! T: p' `9 kall of these methods perform the same function. They give a boundary within which the dimension is
+ H) Q8 h) b0 u8 i! g6 |) Oacceptable.
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The designer might think that changing the nominal dimension has an effect on the assembly. For
4 r8 @8 F5 u Z. @! [# Jexample, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
$ w* y; y/ h+ f b) z Yfalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give
/ R7 y* y0 n# C9 o6 l1 K& _preference to any dimension within the tolerance range.
) B' l- Z- ?% _$ O8 ~; [9 Q* NFig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension
5 C. @8 D6 z1 M, dstated on the drawing and the process follows the normal distribution. In this example, if the manufacturer0 P6 S2 i5 V$ J! i$ n9 f
aimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want1 c0 W& u9 C$ h& l
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
. o: \* e% a9 A& }5 k0 dgood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.' k$ v# E4 H, v" d' w% I0 U0 C
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the
4 L2 _2 x" j% F3 e- i# r; Wmanufactured parts would be outside the tolerance limits.
1 n# m; F, B; i7 _% m5 XAs in the previous example, many manufacturing processes are normally distributed. Therefore, if we
6 ]! ~3 A1 t9 j; Xput any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
+ _$ Q. |" \4 Fa mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance* T6 z8 d( H" [
follow.; r8 Y9 f" ~2 h# t9 S" G% h2 e
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z" p) c) w# [1 K7 u4 R6 r1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/* A( l8 y: _. k3 s5 ?: H
-.009 has an upper limit of 3.031 and a lower limit of 3.019.)
+ k2 j: l) F; I0 u4 d& d' d2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)
6 I6 k. Y! R4 M& c3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)
$ v5 y7 H+ O& G( g t' z4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).
; Z3 v5 j: S) ^Alternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)- b: o( W/ M# V- ?# ]
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As a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
# N6 a9 p0 a! ~3 ?8 M4 vmay force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral0 Z5 J. P) O# u/ m1 M
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to
5 ~: X. Z; h; u. [3 p' h2 e$ hÆ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees5 J4 Q6 W( D5 u4 ~
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would. y7 B8 E# C" g1 z) C
also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
$ d+ x/ }# }' [$ ^than the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.
# g& J' s- B% u" ^: \# E7 v) G. U" ~8 qAs we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep( `' {2 D$ Y( P! {" N. [$ ?$ z( w9 Y! |
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
6 S+ _* g. P1 Q. o5 p3 t! f9 Aances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-6 q0 O1 t. L0 Q
sary dimensions and tolerances to mean dimensions with equal bilateral tolerances.5 |$ G, d, Z* s, Z+ K; P: x7 Y. d- o
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' ]+ W9 C& o, U0 ^"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."
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