9.2.3 Converting Dimensions to Equal Bilateral Tolerances B+ `9 [' [5 R# W0 r
In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances
! w1 T4 N* M( U: n# l; y: i(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such* }2 x$ M0 l( `+ l9 M
as +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we. t. ?! P9 e7 C; \% R4 F0 Z, {: e6 _
could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length
* Y! r( a5 {" K/ G. yof the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,& \. `5 ?" k1 C/ G" b A- z% c5 r# u
all of these methods perform the same function. They give a boundary within which the dimension is
# C! A% d t8 P7 ~' Uacceptable.! @- G) @0 r, X8 A5 r2 G& U
+ }- d) S/ L' e( H. `! U8 C/ V; _
The designer might think that changing the nominal dimension has an effect on the assembly. For7 R$ Q# z+ A' |- O
example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
, s+ y: e; l! q8 K6 p* m8 G$ Tfalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give& E+ r; [7 w+ I1 F" @) ?7 @
preference to any dimension within the tolerance range.
# V# }3 S$ I, w- a2 o1 m% a( EFig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension
/ B" K+ |" m7 U* ]# Kstated on the drawing and the process follows the normal distribution. In this example, if the manufacturer
9 M. J$ R& B) i1 W! n7 N& Zaimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want
* B9 \/ D" V" |: cto maximize the yield of each dimension, they will aim for the nominal that yields the largest number of5 q1 p% o0 }5 G/ |" W
good parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025.
9 Q( {" u4 y" x+ `This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the8 Q3 G) _# Q3 R7 ?! b' {
manufactured parts would be outside the tolerance limits.+ [ S& f/ t p; h) n0 V( F
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we) Z) T$ ^/ }7 ]- i
put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
4 o8 R6 \, n5 T8 ea mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance: p5 r5 o3 _% ~
follow.' q2 ^2 w$ l( M8 n5 A; h" v- ]/ I
9 u9 P0 n' r2 P& c4 j6 |
+ c* O; P! E* e8 a& T' h1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/
9 h# o6 q; r, W% Q k( }2 ~-.009 has an upper limit of 3.031 and a lower limit of 3.019.)
1 S* g) X, Q2 p% ]2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012): _9 Z: k" A% y, U
3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)0 ~0 h6 q, I7 d
4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).& ^. u9 B% E/ n7 c0 b! |8 H h/ y
Alternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)
' ?0 E4 y+ S N# a) Y
7 P4 N) @1 O1 sAs a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances
M- g1 d0 v' v6 g5 K3 Ymay force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral7 g g3 s9 u) p2 o: N" \
tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to
; g7 s1 S; E# t0 bÆ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees9 B9 n' o7 L2 Q) ^
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would
" j' g/ Z& Z) [/ ~also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger7 b1 t9 z# S1 N! n7 F
than the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.3 s B0 ? h" B {7 a
As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep ?& P$ j# P: S9 [3 R5 d
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
% F1 V4 A4 l. Sances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-, {, q4 w# m* b# D6 x! g8 R4 s
sary dimensions and tolerances to mean dimensions with equal bilateral tolerances. h- g( h" v6 n& b5 c) P
8 {$ p' {' i# J1 A4 `9 i' c3 U
9 G/ @4 P) E' j( N( Z% X/ H"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."/ N, s/ q5 b4 `
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发表于 2014-5-23 20:05:11
