9.2.3 Converting Dimensions to Equal Bilateral Tolerances2 Q x3 ]5 A$ I7 \) d
In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances
( O# |2 o/ ]$ _, s% E, u(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such- d) P& Q" @% |
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we
6 E' g; T3 R3 Acould have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length
: n9 D& d- A7 ^! h7 Rof the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,* z$ w" [8 t! F# A f' v
all of these methods perform the same function. They give a boundary within which the dimension is: ^9 J% [2 m6 f3 z
acceptable.
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The designer might think that changing the nominal dimension has an effect on the assembly. For; b* I/ Z5 T. B0 a
example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may/ v/ p- a# V# ?! ^' V, d: x
falsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give
" T: q3 T2 U; s( ipreference to any dimension within the tolerance range.
5 b3 a& n$ }) a4 U0 X/ oFig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension
! A. v- F8 N- q! G9 R5 O3 Mstated on the drawing and the process follows the normal distribution. In this example, if the manufacturer: o& N3 Z" x: d* U) F1 v. j5 \
aimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want
. W1 {9 b9 ]! W0 I$ d d% ~to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
0 ` A4 l8 e" Xgood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.* u; S6 Z' S* y- z3 X; r2 d+ u( h
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the( ]" C( j+ E9 R+ k, s7 u. ?6 p) e- y
manufactured parts would be outside the tolerance limits.. t8 L' S9 D6 ]8 p# f
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we
' u$ O4 E* U8 m5 c5 D4 a9 Tput any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to1 p. O# `3 r* u: r4 N* S" h
a mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance* Z0 u! t. Z& D/ o$ j. @
follow.; g1 F2 h$ f( g( d8 `
# t' [& A8 j' m+ g' I. i+ q# M1 z! v. T+ ~. W |5 Y' t
1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/
. {, \ M- C4 T-.009 has an upper limit of 3.031 and a lower limit of 3.019.)
) K, g' M% O. l. y$ x2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)4 |' f: q' K/ R: I
3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)% ]( W& k. h+ G6 U/ |0 }
4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).
( j" ? O# J8 \) O2 N7 sAlternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025), w: @3 g2 Y. x7 @* ^
4 F; H2 p. |) kAs a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
8 P6 G# k/ I* @5 o2 Omay force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral3 |9 O: u7 d! g4 \1 _. u: g. E/ {
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to4 [" j6 [ |- t' a1 ~6 }
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees+ W! w" Z4 O* i! J4 r# J
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would5 ]' F( m3 a6 s- @3 a0 g: [* e7 k
also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger8 {6 {7 }& w( u2 [. i
than the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.
& h1 _4 F5 K- Q* t! n( oAs we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep
6 w3 z" Y' E# T& C0 I8 `4 `track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-6 H/ q$ Z7 K' g! A. p9 ]1 |5 H4 I
ances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-- i. W6 F6 ]# o& o3 O9 t* m% \: \
sary dimensions and tolerances to mean dimensions with equal bilateral tolerances., _8 A f9 p8 E2 e; b5 j
. \; H7 C8 ^+ V* i( Q" S
7 u C) [, J# {* u9 N
"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr." f1 H% B! s3 a% ~
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