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Figure 3.1 shows the four standard formats for linear and angular dimensions and tolerances. Formats are included for U.S. inch and metric dimensioning and tolerancing. According to ASME Y14.5M-1994 and ASME Y14.5-2009, the rules for angular dimensions and tolerances are the same for drawings prepared using U.S. inch and metric units.

Limit dimensions do not specify a nominal value. A high (maximum) value and a low (minimum) value are specified. When a limit dimension is stated in a horizontal format, the smaller value precedes the larger value, with the values separated by a dash. When a limit dimension is stated in a vertical format, the larger value (upper limit) is placed above the smaller value (lower limit). It makes no difference whether the toler-anced feature is an internal feature or an external feature.

Equal-bilaterally toleranced dimensions specify a nominal value and the amount a dimension may deviate from nominal. The tolerance values are equal in each direction.

Unequal-bilaterally toleranced dimensions specify a nominal value and the amount a dimension may deviate from nominal. The tolerance values are not equal in each direction, and neither value is zero.

Unilaterally toleranced dimensions specify a nominal value and the amount a dimension may deviate from nominal in one direction only. The toler-ance is in one direction only, either larger or smaller. The other tolertoler-ance value is zero.

Regardless which of the above methods is selected, the nominal dimension value must be part of the tolerance range. To put it another way, the upper and lower limits must include the nominal dimension, even if it is at one extreme of the range. The tolerance range cannot ever be “off the part.”

As shown in Figure 3.1, there are four different methods to specify tolerances and ranges. Each method specifies an upper and lower limit, either directly or indirectly. Three methods include a “nominal” value and acceptable deviation limits from that “nominal,” while limit dimensioning gives only the range, the upper and lower limits for the dimension.

Several questions may come to mind: What is the real difference between these methods? Do any of the methods better communicate design intent? Do any of the methods alone guarantee that manufacturing will target the “nominal” value stated on the drawing in the manufacturing process?

26 Mechanical Tolerance Stackup and Analysis, Second Edition

Formatting Dimensions with Plus / Minus Tolerances

The examples above show the ways to specify dimensions and ± tolerances on drawings prepared using SI units or U.S. Customary units. The way to specify angular dimensions and tolerances is also shown.

Limit Dimension 8.75 8.25

Tolerancing with U.S. Customary Units:

(inches)

Same number of decimal places in both limits.

No leading zeroes for dimension values.

Trailing zeroes used where needed.

Same number of decimal places in both limits.

8.75

Number of decimal places may be different for dimension and tolerance.

Number of decimal places must be the same for dimension and tolerance.

8.50 ±.25 Equal Bilateral Tolerancing

Number of decimal places must be the same for dimension and both tolerances.

Unequal Bilateral Tolerancing

Number of decimal places may be different for dimension and tolerances. Both tolerances must

have the same number of decimal places.

Unequal Bilateral Tolerancing

Number of decimal places may be different for dimension and tolerances. The zero tolerance has no decimal places and is not preceded by a

+ or - sign.

0

Unilateral Tolerancing Unilateral Tolerancing

8.50+.25 -.00

Number of decimal places must be the same for dimensions and both tolerances.

Leading zeroes for dimensions and tolerances. Trailing zeroes only used in

certain applications, (marked ***).

Angular Dimensions and Tolerances

Angles may be specified using decimal degrees or degrees, minutes and seconds. If decimal degrees are used, the number of decimal places must be the same for the dimension and both tolerances.

Angular dimensions and tolerances follow the same rules on drawings prepared using either type of units.

FIgure 3.1 Plus/minus dimension and tolerance format (U.S. inch and metric).

Tolerance Format and Decimal Places 27

The short answer is no, as all these methods specify the same legal limits. (See Figure 3.2.) Given that these methods are legally equivalent, all that you can be sure of is that manufacturing will always shoot for what is in their best interest.

They must. Based on the factors discussed in Chapter 5, they will adjust the pro-cess to minimize their costs. All of the methods ultimately communicate the same information, and that information is limits. Every plus/minus tolerance commu-nicates a high limit and a low limit. However, depending on the manufacturing process, in some cases, the nominal value may be more important than in others.

For example, if a hole is to be drilled, it is common to select a standard drill size for the hole. Of course the size of the hole must be verified to work using tolerance analysis, but if a hole is to be drilled, it is very common to select a standard sized hole for drilling. There are several methods for tolerancing drilled holes, and each has been derived empirically, the data collected after drilling thousands of holes in sample stock. Typically, drilled-hole tolerances are unequal-bilateral. The tolerance range is biased toward larger holes, such as +.005/-.002 or +.004/-.001. In cases where a hole is drilled and the nominal hole

Tolerance Range Specified

The examples above show the five ways to specify the same dimensional limits using dimensions and ± tolerances. The

tolerance range is the same for all five examples.

9.00

by Plus / Minus Tolerances

FIgure 3.2 Five ways to specify limits using plus/minus dimensions and tolerances.

28 Mechanical Tolerance Stackup and Analysis, Second Edition

size on the drawing is a standard drill size, it is probably likely that manufactur-ing will target design nominal. However, it is not necessary for them to do so.

They may have some older drills on hand that because of wear and other factors may target a different value. As long as the hole is within the range specified on the drawing, it is within specification and must be accepted as a good part. There is also the possibility that the hole will be put in using a different process.

The water gets muddied a little when statistical process control (SPC) comes into the picture. Quality control methods such as SPC, combined with drawing specifications such as critical control characteristics, sometimes attempt to link

“design nominal” with “manufacturing nominal.” Perhaps in an environment where these are strictly implemented there can be direct linkage between “design nominal” and “manufacturing nominal.”

There is a theorem in statistics called the central limit theorem which states that sampled values (tolerances in this case) under certain conditions follow a normal or Gaussian distribution, and that it is more likely for a value to be in the center of a range than at the extremes. Figure 3.3 shows a normal distribu-tion. This idea is one of the bases for the idea of statistical tolerancing as pre-sented in Chapter 8. The idea of a dimension “centering” about the midpoint of its range seems to work well with equal-bilaterally toleranced dimensions, but causes some grief when considered for unequal-bilaterally or unilaterally toler-anced dimensions. In these cases, as in the example of the drilled hole presented earlier, the “nominal” dimension value stated on the drawing is not the midpoint of the tolerance range. This text will not attempt to sort out these potential sta-tistical inconsistencies.

Without SPC and the added controls it brings, we are back to the idea that a plus/minus dimension allows anything within its tolerance range. Worst-case tolerancing uses this as its basis and is presented in Chapter 7.

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7ROHUDQFHYDOXHVDUHPRUHOLNHO\WREHLQWKHFHQWHURIWKHUDQJH QHDUWKHPHDQWKDQDWWKHH[WUHPHVZLWKFRQWUROOHGSURFHVVHV

FIgure 3.3 Gaussian distribution and the central limit theorem.

Tolerance Format and Decimal Places 29

Designers may hope that stating a “design nominal” on the drawing will bias manufacturing toward the stated value, and it may. However, in a legal sense, it adds no more or less specific requirement. Using any of the above methods merely specifies acceptable limits. All manufacturing must do is ensure that their process lies within those limits.

31

4 Converting Plus/Minus