9.2.3 Converting Dimensions to Equal Bilateral Tolerances
3 V3 ]6 p% b4 O; S( M$ v( fIn Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances
8 h% W: }1 p, a* T4 g3 U3 q(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such
& M/ d. @* O, Nas +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we* S1 Q6 x2 ?3 j, x
could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length
5 t. b+ Y* v" T1 M$ S# |+ Iof the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,$ _7 _; z1 d7 W5 P) i
all of these methods perform the same function. They give a boundary within which the dimension is
9 y3 {7 \! n' H. C* O& qacceptable.
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8 O$ J7 Q) S9 A. x& ^* [The designer might think that changing the nominal dimension has an effect on the assembly. For
, W8 T2 j* j+ T/ p8 H. B; A+ |2 ^! dexample, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
- M3 K4 b* C5 \; Pfalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give
5 V* o7 n! |. z- vpreference to any dimension within the tolerance range. l3 K5 N! }& m* Q! [" b
Fig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension( J7 `2 I. e& G. o% F* ?- ^
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer
/ A0 F$ o. W& h9 v9 B. Taimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want( \# ]1 h/ P" t& z/ S2 a9 ^% D! x9 a
to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of# ?% Y' U7 O; \: |/ V
good parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025., _8 J3 V# I2 h9 [6 I
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the
" M8 a. s% r, vmanufactured parts would be outside the tolerance limits.
! v% V3 x+ o" R& T `8 _As in the previous example, many manufacturing processes are normally distributed. Therefore, if we5 a5 F. {7 S X; O/ t( m
put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
; @# H I2 ~$ S8 U, Ya mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance
) e6 Z& g' Z+ ~- [' q- Z* N7 ~$ ufollow.
6 J" D) E5 k! e+ K& B; y5 K V2 A) F9 r i: U+ @3 ?9 h8 h
7 W6 U% d6 k8 Y; t( J0 Z
1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/
, ^( D' r( m; t. ]/ f7 A-.009 has an upper limit of 3.031 and a lower limit of 3.019.): y3 P9 Z, {5 {) e: R: y! ^
2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)
! D7 }2 N% ^6 G5 i9 q2 u& n8 V3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)
' U4 F8 C3 R1 ]4 D0 E$ M4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).5 \7 v. i+ O {" O# K$ s
Alternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)( |6 T6 O) P% N! Y# j0 n, }
9 I0 S9 L$ I1 p7 q- ]7 ZAs a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances) h' Q* U, F0 C# q1 [6 t) b
may force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral
" {- f& K2 ]4 k7 b; `tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to" p( [+ [+ ]$ D% K }+ o# @
Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees2 w0 O; y( p" V9 N+ |
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would" r! E* C* ?, Z0 m# k$ G2 G
also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger
2 S& u9 }' B. { q$ d6 ~2 v/ \than the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.9 S7 ?. o% H$ _0 t* e3 w4 G
As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep
7 }' p" H0 Z2 Z# ]+ Mtrack of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
2 Y, y4 ~! Q7 C* G! O8 A% T! o hances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-0 f! Z% e! i( s1 ?, u
sary dimensions and tolerances to mean dimensions with equal bilateral tolerances.- E/ g4 S" H5 i7 g, Y B- H
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6 ?* i( {, c" f
"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."
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发表于 2014-5-23 20:05:11
