9.2.3 Converting Dimensions to Equal Bilateral Tolerances
* D% r' [% ~( x8 x0 [In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances
( o+ Z" c* U( ^3 @6 b# }% I(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such% f" g4 Q0 W0 t& P/ V* z/ }
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we
; S0 g* W5 U, b- ?: K' Y6 w( Q- wcould have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length
0 }1 U- ?/ R. {+ D. I' w- _: Q1 p& dof the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,
) Z* ], c! p# y2 {# M9 dall of these methods perform the same function. They give a boundary within which the dimension is) e" e0 `' j/ c$ h
acceptable.4 O. _8 r; {/ x
2 K( y( ~/ |' qThe designer might think that changing the nominal dimension has an effect on the assembly. For& L- P' H% Y9 [& S
example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
0 _( Y+ t4 a& o% u# y: `9 _4 e Xfalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give
P$ Q( u5 p! r% K& {+ spreference to any dimension within the tolerance range.* w' v# X! \7 D# P
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension
, B9 k" F! w; sstated on the drawing and the process follows the normal distribution. In this example, if the manufacturer
% z/ X' f- B. J# Jaimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want- D) n" r2 S$ j* p$ d' W. h& A( G8 e, X
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
# u! z* e- D1 i; w" Igood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.% y/ G' i$ f1 s8 f
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the
+ j" ~) \4 x2 a2 x1 ?+ rmanufactured parts would be outside the tolerance limits.! M3 P6 e8 Y( o! ^
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we0 x# v* g7 E# q( m% F/ x+ }* G, b
put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to9 H( Q. V" W% W2 k/ p3 D* p
a mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance
7 K, [6 `- x5 Pfollow.
4 @( t6 s* z- a4 f
/ g; l+ Z4 n: w$ s. ]
7 L: T( ~9 ]: i) p4 O h; L) ]1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/
% R" d% A1 v! U4 e* ^! g& _. C-.009 has an upper limit of 3.031 and a lower limit of 3.019.)
1 y6 p7 h% K$ ^! w4 O" O+ ^* `2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)
* V$ F, u2 H4 q+ p% R5 X3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)
3 R4 h& U1 x# v4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).
3 p7 d, k' c2 ~1 L9 zAlternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)
' w0 B% ^; Q+ t5 a S5 Y: c& N& e
As a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
) D8 k& g9 K, R. I- K" X4 f$ e. p1 Amay force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral3 b% A7 I9 D7 W4 d
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to) `) q, u3 D6 `) { O0 O
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees( D% k$ g( V3 s( }: F9 W+ U$ R
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would) v# v j' R. `, @
also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
" G. s6 L2 ^# ~# l+ x1 vthan the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.' _* Y3 W* T9 \6 d0 @
As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep, q8 s) _9 x6 {$ T6 ~! u0 m/ ]& Q
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
9 s. B, e( E" p7 O) M0 gances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-
$ E( R0 x, L! {; R8 v$ j4 gsary dimensions and tolerances to mean dimensions with equal bilateral tolerances.
% j2 m `- C& r9 x) N+ K+ z# C* d! p7 R
9 f0 a% A( @9 }0 X"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."5 D, @4 M Q1 ^7 ^( m3 r
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发表于 2014-5-23 20:05:11
