9.2.3 Converting Dimensions to Equal Bilateral Tolerances# J# j$ \0 j3 z2 H8 {8 J
In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances! V% d* H( B& F [
(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such
V$ l w7 p k2 M/ t9 {as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we
8 p, O- N6 x3 T. K2 {could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length" x7 v2 h: D7 J8 H& |- S
of the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,
7 \ n4 d8 Q. m: \$ Oall of these methods perform the same function. They give a boundary within which the dimension is$ S, L J! `+ i+ s/ {2 p4 ?8 O
acceptable.6 b# L3 O% @4 a. q5 b& Z
K) U. W# ^# z7 @$ dThe designer might think that changing the nominal dimension has an effect on the assembly. For2 d) a* w, Q) L, z% n' d' B
example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
% G( W, W2 A. g+ j0 ^5 i; v, H- cfalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give1 v9 F2 O7 p8 u( g4 S8 ~( R
preference to any dimension within the tolerance range.9 F" C3 ~( G, h7 L9 j- w
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension
: w* K8 \4 r" b2 sstated on the drawing and the process follows the normal distribution. In this example, if the manufacturer
9 U3 r; U( y" F* f4 Jaimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want+ S* O1 G1 Q4 l: `
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of# z* G$ M* s6 x9 [. m0 R. d
good parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.: W) O. G3 f& T) G# ^
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the
% \2 J7 d1 ^0 G7 Q, Pmanufactured parts would be outside the tolerance limits./ T, o+ M. n3 J
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we5 @7 ~0 J+ a1 i& n
put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to: \3 B2 [: D7 L; D$ t2 @) h* o4 L+ Z- H1 z
a mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance! ~" T4 } z9 @, h
follow.
% D7 j4 u: `9 `7 x9 p( Q# x* L! \$ J) F+ ]6 h$ ^# W4 N
) p Q" n. j, s0 I$ c& _% p( k5 h& q1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/* y2 ^' J, x2 [8 _! a) n% ?7 m/ Z M, ]
-.009 has an upper limit of 3.031 and a lower limit of 3.019.)
`$ t0 e v& z; P2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)
4 S* f1 a) G) W: q: s) s3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)4 R- e4 S3 i6 m/ l; k# @
4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).. l- j+ e" H( Z4 w* m* B
Alternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)# {: e8 B( T. @4 \8 o/ y
$ `4 K6 ]1 _5 ?& v K9 x
As a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
1 E: l/ e- x. b" U; ?1 imay force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral
. U' ~ p, r1 ^4 etolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to6 Q" R: _" n! v# F! T4 y. h$ J
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees
; y( a; r1 l$ v* O! yÆ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would7 u' I' \0 m. o% Q6 k
also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger: y, t. C' E* r, L! p/ }
than the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.
5 V% R y& p! {/ qAs we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep
! U8 Y; L/ U7 W. h6 Q& D' Itrack of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
# w- S _/ E: `/ ~' a# kances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-
0 u. w2 N7 `/ d: [' `4 tsary dimensions and tolerances to mean dimensions with equal bilateral tolerances.
* ]2 n; b; H6 R5 A, K- l( M
# |* g" h& ~/ }5 ^3 @% s
% b5 Q& i% W4 |" X, b3 C4 }"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr.") f/ Y, Z0 D# K$ d, {
|