9.2.3 Converting Dimensions to Equal Bilateral Tolerances- `: i( }: C1 u3 W3 C
In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances
. j3 e- C6 P3 V0 C4 d# l4 w(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such
$ w d0 g& q% o( b/ k: Uas +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we
1 w7 p9 Y9 P fcould have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length
3 h% E3 ~' W& t1 X5 C; p pof the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,# Y/ z# b- m7 h- p
all of these methods perform the same function. They give a boundary within which the dimension is1 D- Q# @7 m4 v4 m9 d$ o
acceptable.
# Q B! E6 x! X& J
0 V; K. r4 h) E, O& m3 L+ ]The designer might think that changing the nominal dimension has an effect on the assembly. For
z; e- p! R4 @" zexample, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may7 H% F" y- q. y& j
falsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give2 b( ]% w8 [+ ^1 |: j4 y
preference to any dimension within the tolerance range. h! z1 _( w" D& \/ N
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension
% r5 v& o; [& dstated on the drawing and the process follows the normal distribution. In this example, if the manufacturer
9 f4 t5 V! c" ~' _aimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want
1 U6 B8 T0 }- x: T7 o6 r/ Tto maximize the yield of each dimension, they will aim for the nominal that yields the largest number of0 c& s+ Z" o* L- j
good parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.! r+ ~" ~: u) U2 M( K
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the
$ q, u# P" Y! ~& jmanufactured parts would be outside the tolerance limits./ r( y# q( G; P/ @
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we0 X$ O* @: b9 x1 S3 f! d" e- y
put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
, ]) ?6 ?: T8 M) G: Ja mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance
7 A0 `4 W$ x2 g1 t/ \, N* Rfollow.4 t% `* {. ^* ], {' Z/ x2 X$ I6 R1 Y
( c3 O7 D) S; e4 T B3 s7 ~ ~, O
. Y* x: I+ _* `* l% Q! U1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/
4 T1 N2 B8 z6 q+ |% L& w Z+ B-.009 has an upper limit of 3.031 and a lower limit of 3.019.)
$ M/ E/ N% \- y6 f2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)
: p5 I. S/ n$ |3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)
5 m, T1 v' k6 q. s0 ]. }4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).9 w5 E9 P% _6 `
Alternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)+ e$ C( T% ?8 t) \% o! D4 ?; c
( z2 r6 Q. B, p7 g
As a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances q" `+ M/ `2 w, s/ p
may force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral3 q. p5 Q' I+ q' Z
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to) P" h" w! w0 ^% ]2 Z" R
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees
& w$ P5 m5 o* U% M: } N h/ }. O; J: IÆ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would
- f; t. h. [' E9 Qalso want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
# J. ~+ P* C: o/ pthan the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.
. }( X$ k- b+ \- _' F) |As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep) ^: L% Y- M; ^6 ]8 Y
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-. T- k; w! N1 B6 b# h9 F2 i6 }
ances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-
1 _! P, R0 L5 K) i# p! P" ~/ k' Tsary dimensions and tolerances to mean dimensions with equal bilateral tolerances.
, P& d5 s9 {' X! E- V% _, F
* y. P+ t' S0 d2 `" w* E' x4 w
/ g8 V1 `3 ?0 ?" d"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."4 b# _) k. K9 b) Z
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