9.2.3 Converting Dimensions to Equal Bilateral Tolerances
, N1 l- `; E& U/ ?( vIn Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances* c. G6 {* B7 b# P# U/ e
(such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such
4 _' k! S- `% e5 v1 @2 G( q1 t8 D2 Ias +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we- I r/ N; }* ^& k1 j
could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length/ P$ r( \% ~3 u! V [) E2 U! P! q
of the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,; i* i$ M9 Y2 L7 p
all of these methods perform the same function. They give a boundary within which the dimension is
/ C/ W2 Z7 D) d3 i7 X% G) e. e3 ?acceptable.# @# M+ y8 W9 u# e
; q$ C% Z. u8 CThe designer might think that changing the nominal dimension has an effect on the assembly. For1 \, N, m* i7 k1 g: _1 \6 q1 l: q
example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may
, a* r6 X$ H+ q" y1 v6 I9 X( Ofalsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give
0 T; Z/ {5 b/ L" P; xpreference to any dimension within the tolerance range.
+ J! a1 H2 u1 O+ S7 Z$ zFig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension( ~5 {) g. n/ X G
stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer2 c0 o! c/ X' F
aimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want
' }' G+ }0 {. r. `2 g; [3 Fto maximize the yield of each dimension, they will aim for the nominal that yields the largest number of
4 T) B) C- b. O5 }- J, kgood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025. n0 y. m* L- V% z/ {- b
This allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the
7 v" u# h7 U Y: N/ Amanufactured parts would be outside the tolerance limits.6 @8 j9 U: R# I/ g
As in the previous example, many manufacturing processes are normally distributed. Therefore, if we) G, B0 U* ?* r, b) T+ D
put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to
6 r. ~, R9 j1 [- Ra mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance
' f p+ S) x6 J0 Y9 }- `follow.
! s) I) l# u$ ~ r( |3 ]
; K6 N* F9 T: `. b/ w
$ l5 p4 P; Z, h% ]: F/ E1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/
6 R: [2 ]4 D# j1 ?' n7 G-.009 has an upper limit of 3.031 and a lower limit of 3.019.)0 ?) E p" {8 k6 ?
2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)! F+ g/ ?9 U% @+ A; `# x
3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006)
9 ~; E( x0 |2 W3 h0 _3 f: k4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025).% o$ s9 e8 u8 O9 [
Alternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)3 j- f) P6 k$ O O4 t+ D
; {' ]- \9 u7 F& x. a' y& ~As a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances' Y- H+ I% B z6 M5 `- d
may force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral
/ r$ o$ @# w$ y% z5 ~. F6 Otolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to
0 P# z6 {: v' [! n/ k3 q5 R/ F6 EÆ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees& I) y4 `; v; x" ]( }: S
Æ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would
- V5 x- M0 Y9 n: R# kalso want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger3 { L U+ K* Z, V, d
than the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance.* E$ v9 g5 y) }
As we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep0 V, o/ z: E: g: B7 X2 S6 N4 y
track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-
. Q, x. ^: X- W# wances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-, C- `4 `- C" C7 j" Q
sary dimensions and tolerances to mean dimensions with equal bilateral tolerances.: Z. E, p2 S, ?0 p
7 N( y4 m# M/ y
0 N' K+ P) J( Z g"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."
0 s* ^% F# Q' k5 j |
发表于 2014-5-23 20:05:11
