9.2.3 Converting Dimensions to Equal Bilateral Tolerances8 r! A+ J& j# A ~) N8 o In Fig. 9-2, there were several dimensions that were toleranced using unilateral tolerances) l+ K8 q+ F* h. p2 _" b1 q6 G ?8 K (such as .375 +.000/-.031, 3.019 +.012/-.000 and .438 +.000/-.015) or unequal bilateral tolerances (such 6 d; J! n5 q+ @# a6 y9 N# N8 kas +1.500 +.010/-.004 ). If we look at the length of the shaft, we see that there are several different ways we) r. o* N# O8 l# L+ N7 R+ | could have applied the tolerances. Fig. 9-4 shows several ways we can dimension and tolerance the length" m2 a* p/ U( z' }" Q* f" k/ }- Z% U of the shaft to achieve the same upper and lower tolerance limits (3.031/3.019). From a design perspective,/ ~2 w& J0 G" P, B* D* d- t all of these methods perform the same function. They give a boundary within which the dimension is 5 W: H; m( F& i) ^4 ?' [7 l* tacceptable.; y4 g+ c& s0 @, P# z. ?1 ?( f
% Y0 \0 W2 F( H9 A& M' i1 dThe designer might think that changing the nominal dimension has an effect on the assembly. For( E0 d9 W+ Y; Y4 P example, a designer may dimension the part length as 3.019 +.012/-.000. In doing so, the designer may8 H1 J! E+ A/ q3 h' y falsely think that this will help minimize the gap for Requirement 1. A drawing, however, doesn’t give i2 I( X0 k( N4 T6 N9 rpreference to any dimension within the tolerance range. 8 q/ p) p6 L* U. F" P5 MFig. 9-5 shows what happens to the manufacturing yield if the manufacturer “aims” for the dimension# ]9 h+ J2 i6 U7 C. R v stated on the drawing and the process follows the normal distribution. In this example, if the manufacturer t+ ?) i8 j- O* c5 N# [: naimed for 3.019, half of the parts would be outside of the tolerance zone. Since manufacturing shops want2 ]9 T5 {& }" ^) k2 M to maximize the yield of each dimension, they will aim for the nominal that yields the largest number of 9 n/ R. @/ D* C \" V' xgood parts. This helps them minimize their costs. In this example, the manufacturer would aim for 3.025. & q+ R5 N% O+ LThis allows them the highest probability of making good parts. If they aimed for 3.019 or 3.031, half of the* v, a) D* j+ C; ]' A manufactured parts would be outside the tolerance limits. 3 J: S2 M- R8 Q" [As in the previous example, many manufacturing processes are normally distributed. Therefore, if we7 o7 y; Z' n- J' J) r9 s# ~& I' @ put any unilateral, or unequal bilateral tolerances on dimensions, the manufacturer would convert them to 7 ^4 S3 q+ M0 F; X9 e5 ra mean dimension with an equal bilateral tolerance. The steps for converting to an equal bilateral tolerance ' N! Y, X5 e8 |& B# Z6 jfollow. % E, ^" B( {: P$ k- p) Y( B: {% A- E6 y0 \: u+ Q* Y , W! B' U0 Y: [% b" R* g 1. Convert the dimension with tolerances to an upper limit and a lower limit. (For example, 3.028 +.003/% v/ M* E/ y8 l/ g -.009 has an upper limit of 3.031 and a lower limit of 3.019.) 2 z3 l H, k( V# ~ |+ E3 R4 W5 Y2. Subtract the lower limit from the upper limit to get the total tolerance band. (3.031-3.019=.012)- y1 S$ [# L: k+ Q 3. Divide the tolerance band by two to get an equal bilateral tolerance. (.012/2=.006) 7 C i% u A0 K4. Add the equal bilateral tolerance to the lower limit to get the mean dimension. (3.019 +.006=3.025). - @! B! O& I! F- R2 oAlternately, you could subtract the equal bilateral tolerance from the upper limit. (3.031-.006=3.025)0 E; h' B7 ?9 ^# D* Y& g* l
8 j7 |5 M0 L9 {8 SAs a rule, designers should use equal bilateral tolerances. Sometimes, using equal bilateral tolerances, d' ^( Y0 t/ B4 X1 I' w" ^ may force manufacturing to use nonstandard tools. In these cases, we should not use equal bilateral& d' V9 ]" c0 a; W4 ?- Z0 L7 Y tolerances. For example, we would not want to convert a drilled hole diameter from Æ.125 +.005/-.001 to6 G4 X1 N2 U2 X% x) ~ Æ.127 ±.003. In this case, we want the manufacturer to use a standard Æ.125 drill. If the manufacturer sees + n; }6 F3 w KÆ.127 on a drawing, he may think he needs to build a special tool. In the case of drilled holes, we would+ {) O' E3 {0 J also want to use an unequal bilateral tolerance because the mean of the drilling process is usually larger ; R- F( f. [. e' Cthan the standard drill size. These dimensions should have a larger plus tolerance than minus tolerance. 3 d* R- L4 n- ]% ]7 i2 QAs we will see later, when we convert dimensions to equal bilateral tolerances, we don’t need to keep9 X/ [( U' g; j track of which tolerances are “positive” and which tolerances are “negative” because the positive toler-0 e: u/ u! W6 d1 M- _ ances are equal to the negative tolerances. This makes the analysis easier. Table 9-1 converts the neces-7 z: M6 r/ _& Q% y" p0 Z sary dimensions and tolerances to mean dimensions with equal bilateral tolerances.6 U& y' h& T. f 8 K1 b' c, D, r& `
7 n9 Q( _- ^" {* }# u; Z7 u"Dimensioning and Tolerancing Handbook, by Paul J. Drake, Jr."3 k( u( D, N: ]' p
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