9.2.3 Converting Dimensions to Equal Bilateral Tolerances
s9 i3 H+ H, H: o; V; ?In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances
4 J6 a. j. R( {& {" t5 C! H- M$ t3 n+ \(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such6 G5 M3 f3 U& X/ N9 Z6 [
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we( `+ A2 m/ f9 ?
could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length
! i @6 y% U! w8 Fof the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,
* V, `6 B) L: D/ A+ M; ]0 Nall of these methods perform the same function. They give a boundary within which the dimension is
& Y( g% _+ d2 E5 C6 }acceptable.
I' U% N2 k6 q& [
* [: n3 }3 x$ Y8 Z3 ]8 B: X8 VThe designer might think that changing the nominal dimension has an effect on the assembly. For4 Q9 C' O7 V# z4 r, [
example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may. L' Z# N. Y7 S y8 `& i+ k3 k
falsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give. ?) i0 S+ o: p8 L
preference to any dimension within the tolerance range.2 X8 E& b5 ]2 A6 r$ j
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension, Z3 O/ p# X* o! S0 L
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer X B' X K. l2 B0 ]0 C7 t
aimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want; w. f$ t! Q7 u4 _2 w+ Z
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
/ z5 ?1 \, a! z/ E' A4 |good parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.
# p$ p8 q; o: I2 z& i' Z! {9 FThis allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the
! u# N) m" U- e6 z7 p& K j% zmanufactured parts would be outside the tolerance limits.4 U* n4 O2 \' S1 Z" B3 t* D5 }
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we
, z0 t7 p. d* R, i, t+ V1 v- n9 @ eput any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
* ]* u/ @5 N" K" Aa mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance6 I* x/ ]" p8 \8 [& m3 n- B
follow., w7 {7 i* u$ F5 Q) r+ N! h
- `5 U1 Z' h2 a4 c: G' z; F
7 ^; u+ d5 f3 O! R% ?3 \& r1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/! o, u% {5 W( p+ C1 ]" _
-.009 has an upper limit of 3.031 and a lower limit of 3.019.)/ y [# g0 ~! n
2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)1 V# e8 _, ?* a, A0 s
3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)
* y M$ ~/ |: R, n `& t4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).2 d4 C+ J' x* ]
Alternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)3 d1 k8 q: ]/ b8 F* E
& C; g, ^/ u- n0 q4 X) h" R2 }As a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances; ~; |# H! y! m6 K$ y
may force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral
& L+ K' f3 J% _3 Gtolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to7 [, Z& B2 G: f+ k$ M
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees3 S! p/ C0 z6 a0 u2 u
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would- O, `' ~' Y1 J: g+ Y
also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger1 z9 X2 {9 N& X- i
than the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.
+ c; w9 ^* z# q' N9 {As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep# ^4 C" Z9 r9 F
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
& D9 |; u8 k& S9 Gances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-7 |0 S7 L- I9 B5 i' n
sary dimensions and tolerances to mean dimensions with equal bilateral tolerances.& V, o7 U" E4 e" N5 V, v/ @: z N
1 D& v: q' ~; t$ R0 O; @! z# Z; ]' y5 p+ `& g
"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."
5 r8 {3 T2 ~, K& z( B: e/ T |
发表于 2014-5-23 20:05:11
