Dimensioning and Tolerancing Handbook Episode 3 Part 6 ppt

Floating and Fixed Fasteners 22-1522.9 Projected Tolerance Zone When using fixed or double-fixed fasteners, a projected tolerance zone should be used regardless of whetherthe design is u

Floating and Fixed Fasteners 22-15

22.9 Projected Tolerance Zone

When using fixed or double-fixed fasteners, a projected tolerance zone should be used regardless of whetherthe design is using threaded fasteners or alignment pins Variation in the perpendicularity of the screw or pincould cause assembly problems If a threaded fastener was out of perpendicular by the total amount of thepositional tolerance of (∅.014), an interference problem could occur (see Figs 22-15 and 22-16)

Figure 22-15 Tapped hole out of

perpendicular by ∅ 014

Figure 22-16 Variation in

perpendicular-ity could cause assembly problems

Figure 22-14 Positional tolerance for

clearance holes and nut plate rivet holes

22-16 Chapter Twenty-two

Fig 17 shows how a projected tolerance zone corrects the interference problem shown in Fig

22-16 The projected tolerance zone is applied to the threaded fastener or the pressed pin The tolerance zonefor the tapped hole extends through the mating parts clearance hole, thereby assuring the mating parts willfit

22.9.1 Comparison of Positional Tolerancing With and Without a

Projected Tolerance Zone

This section compares two position tolerancing methods to locate size features for fixed fasteners In thefirst method, we use a projected tolerance zone and calculate the functional tolerance zone using the fixed

fastener formulas, as shown previously We consider this a functional method for the case of a fixed fastener In the second method, we convert the projected tolerance zone to a zone that is not projected, and consider this a nonfunctional method As a comparison, we then calculate how much tolerance is lost

when dimensioning nonfunctionally

Assuming a maximum orientation (perpendicularity) error, Fig 22-18 shows the relationships between

the functional (projected) tolerance zone, T f , and the nonfunctional tolerance zone, T nf (not projected)

)2/(

2/)

Where D is the depth of the nonfunctional tolerance zone, and P is the projected height of the

functional tolerance zone (see Fig 22-18)

Eq (22.1) reduces to:

Figure 22-17 Projected tolerance zone example

Floating and Fixed Fasteners 22-17

Figure 22-18 Projected tolerance zone

— location and orientation components

If we measure the orientation of a feature on a workpiece, we can verify the following relationship:

,,

,

,

D P

actual n orientatio f

T actual n

T f T imum

location

f

T

, ,

T nf T imum

location

nf

T

, ,

T nf T actual n orientatio f

T f T imum location nf T imum

location

f

, ,

max , , max

P actual

n orientatio f

T

f

T

D P

actual n orientatio f

T

D P f T actual n orientatio f

,

12

,,

12,

,

∆

∆

(22.7)

22-18 Chapter Twenty-two

22.9.2 Percent of Actual Orientation Versus Lost Functional Tolerance

Fig 22-19 demonstrates how much functional tolerance is lost as a function of actual orientation ance The Y-axis is the percent that the actual orientation tolerance contributes to the total tolerance TheX-axis is the ∆ value

toler-22.10 Hardware Pages

Figure 22-19 Lost functional tolerance

versus actual orientation tolerance

The following pages show recommended tolerances for clearance holes C’Bores, C’Sinks, C’Bore Depths,and fasteners See Tables 22-1, 22-2, and 22-3.) The following general notes apply as noted in Figs 22-20,22-21, and 22-22

3 Counterbore diameters and depths are calculated using a flat washer with a worst case (MMC)outside diameter, and a worst case thickness C’Bore diameters are calculated, and the nearest frac-tional drill diameter is used

4 Worst case flat head screw height above and below the surface is shown in Table 22-5, and iscalculated for a positional tolerance of ∅.014

5 Flat head screws are not recommended because of head height issues, and alignment issues

6 Floating fasteners are not recommended because of the additional hardware required, and because ofthe difficulty of assembly

7 For C’Bore depths, (see Table 22-4) For 060-56 threaded holes, the C’Bore depth is calculated usingonly a flat washer For 086-56 through 500-20, the C’Bore depth is calculated using both a flat washerand a split washer

Floating and Fixed Fasteners 22-19

Fastener Clearance Clearance C’Bore C’Bore

Size Hole Hole Hole Hole

Diameter Size Diameter Size AAA Tolerance .BBB Tolerance

9 Hole-to-hole tolerance for clearance holes and for nut plate rivet holes must be calculated per section22.7

10 Projected tolerance zone (PTOL) is determined by the maximum thickness of the mating part

11 When using floating and nonfloating nut plates, projected tolerance issues could cause ability issues See section 22.9

interchange-Table 22-1 Floating fastener clearance hole and C’Bore hole sizes and tolerances

22-20 Chapter T

Figure 22-20 Floating fastener tolerance and callouts

Floating and Fixed Fasteners 22-21

Figure 22-21 Fixed fastener tolerance and callouts

22-22 Chapter Twenty-two

Table 22-2 Fixed fastener clearance hole, C’Bore, and C’Sink sizes and tolerances

Size Hole Hole Hole Hole Diameter Size

Diameter Size Diameter Size EEE Tolerance CCC Tolerance .DDD Tolerance

.060-56 UNF 0935 (#42) +.005/-.002 228 (#1) +/-.010 125 +/-.010

.086-64 UNF

.112-40 UNC 144 (#27) +.005/-.002 421 (27/64) +/-.010 230 +/-.010.112-48 UNF

.125-40 UNC 1562 (5/32) +.005/-.002 453 (29/64) +/-.010 255 +/-.010.125-44 UNF

.138-32 UNC 1695 (#18) +.005/-.002 484 (31/64) +/-.010 285 +/-.010.138-40 UNF

.164-32 UNC 1935 (#10) +.005/-.002 547 (35/64) +/-.010 335 +/-.010.164-36 UNF

.190-32 UNC 221 (#2) +.005/-.002 609 (39/64) +/-.010 390 +/-.010.190-36 UNF

.250-20 UNC 2812 (9/32) +.005/-.002 797 (51/64) +/-.010 510 +/-.010.250-28 UNF

.312 -18 UNC 3438 (11/32) +.005/-.002 938 (15/16) +/-.010 640 +/-.010.312-24 UNF

.375-16 UNC 4062 (13/21) +.005/-.002 1.063 (1 1/16) +/-.010 765 +/-.010.375-24 UNF

.438-14 UNC 4688 (15/32) +.005/-.002 1.188 (1 3/16) +/-.010 815 +/-.010.438-20 UNF

.500-13 UNC 5312 (17/32) +.005/-.002 1.328 (1 21/64) +/-.010 880 +/-.010.500-20 UNF

Floating and Fixed Fasteners 22-23

Figure 22-22 Double-fixed fastener tolerance and callouts

22-24 Chapter Twenty-two

Table 22-3 Double-fixed fastener clearance hole and C’Bore sizes and tolerances

.312 -18 UNC 3438 (11/32) +.005/-.002 640 +/-.010.312-24 UNF

.375-16 UNC 4062 (13/21) +.005/-.002 765 +/-.010.375-24 UNF

.438-14 UNC 4688 (15/32) +.005/-.002 815 +/-.010.438-20 UNF

.500-13 UNC 5312 (17/32) +.005/-.002 880 +/-.010.500-20 UNF

Floating and Fixed Fasteners 22-25 22.10.4 Counterbore Depths - Pan Head and Socket Head Cap Screws

Table 22-4 C’Bore depths (pan head and socket head)

22-26 Chapter Twenty-two

22.11 References

1 Orberg, Erik, Franklin D Jones, and Holbrook L Horton 1979 Machinery’s Handbook 21st ed New York,

NY: Industrial Press, Inc

2 The American Society of Mechanical Engineers 1995 ASME Y14.5M-1994, Dimensioning and Tolerancing.

New York, New York: The American Society of Mechanical Engineers

22.10.5 Flat Head Screw Head Height - Above and Below the Surface

Table 22-5 Flat head screw head height above and below the surface

Flat Head Screw Head Height Above and Below Surface for 100 Degree Flat Head

.060-56 UNF Above Surface 019

Below Surface -.021.086-56 UNC Above Surface 018.086-64 UNF Below Surface -.025.112-40 UNC Above Surface 022.112-48 UNF Below Surface -.023.125-40 UNC Above Surface 020.125-44 UNF Below Surface -.026.138-32 UNC Above Surface 022.138-40 UNF Below Surface -.027.164-32 UNC Above Surface 020.164-36 UNF Below Surface -.031.190-32 UNC Above Surface 022.190-36 UNF Below Surface -.032.250-20 UNC Above Surface 020.250-28 UNF Below Surface -.040.312 -18 UNC Above Surface 022.312-24 UNF Below Surface -.040.375-16 UNC Above Surface 020.375-24 UNF Below Surface -.053.438-14 UNC Above Surface 020.438-20 UNF Below Surface -.060.500-13 UNC Above Surface 022.500-20 UNF Below Surface -.064

Mr Cuba currently works as a member of the Mechanical Tolerancing and Performance Sigma Team at Raytheon Systems Company As a Six Sigma Black Belt, his responsibilities include dimensional man- agement consulting, Six Sigma mechanical tolerance analysis and allocation, and mechanical tolerancing training He graduated from Oklahoma State University with a bachelor’s degree in me- chanical design.

23.1 Introduction

This chapter describes an approach to understanding the inherent assembly shift and manufacturingvariation contributors within a fastened interface In most cases, the fastened interface must meet tworequirements: The parts must fit together and provide minimal assembly variation, and the variationallowed from the fastened interface should relate to a product performance requirement

In this chapter, each variable of the fastened interface is broken down to understand its contribution

to the total assembly variation

• First, the chapter shows a worst case tolerance study on features of size that are located using aposition feature control frame to understand the virtual and resultant condition boundaries

• Next, features of size are used in an assembly to understand variation within a fixed and floatingfastener

Chapter

23

23-2 Chapter Twenty-three

23.2 Hole Variation

Fig 23-1 shows an example dimensioned using a position feature control frame to locate the hole Thefeature control frame locates the hole using the maximum material condition (MMC) modifier When usingthe MMC modifier, tolerance may be added to the location tolerance as the actual feature size departs fromMMC Thus, the feature’s size tolerance and location tolerance are dependent This dependency must betaken into account in the tolerance study

Figure 23-1 Feature located using

Virtual Condition Hole = Feature MMC Size − Position Tolerance at MMC

For the example in Fig 23-1, the virtual condition of the hole (VCH) is:

Resultant Condition Hole = Feature LMC Size + Position Tolerance at LMC

Fixed and Floating Fastener Variation 23-3

For the example in Fig 23-1, the resultant condition of the hole (RCH) is:

To calculate the gap, the inner and outer boundaries (virtual and resultant condition) of the feature

are converted to a radial value, with an equal bilateral tolerance (r +/− t) See Chapter 9.

t = equal bilateral tolerance of r

The radial value used in the dimension loop diagram is:

r +/− t

Substituting into these equations, we get:

r = 5(h + t h) +/− (t h + 5t a)

which equals:

LMC/2 +/- (size tolerance + 1/2 feature control frame tolerance)

Fig 23-2 shows the dimension loop diagram for the gap in Fig 23-1

The gap equation equals: Gap = [x −.5(h + t h)] +/−(t h +.5t a)

Figure 23-2 Dimension loop diagram for

Fig 23-1

23-4 Chapter Twenty-three

23.3 Assembly Variation

The previous discussion developed an understanding for an individual feature’s boundaries Theseboundaries define the amount of assembly shift within a fastened interface Assembly shift results fromthe amount of allowance defined between the fastener and clearance hole Many engineers design theallowance amount using the fixed or floating fastener rules within ASME Y 14.5 (Reference 2) Zeroassembly shift occurs when a virtual condition pin assembles into a virtual condition hole Maximumassembly shift occurs when the pin and hole have perfect form and orientation at LMC size

In most cases, the fastened interface must meet two requirements: The parts must fit together andprovide minimal assembly variation The assembly variation within the pin/hole interface can be analyzedseveral ways

• The mating parts can be shifted until touching provides a maximum and minimum assembly variation.(See Figs 23-3 and 23-4.)

• The assembly variation can be represented by a process capability This could be in the form of auniform, normal, or other known distribution

• Tooling, fixtures, or gravity can be used to minimize or eliminate assembly variation

This chapter looks at shifting the mating parts to understand the maximum and minimum assemblyvariation

23.4 Fixed and Floating Fasteners

There are two types of fastening systems used to assemble parts: fixed fasteners and floating fasteners.Fig 23-3 illustrates a fixed fastener This is defined as a fastener where one of the parts has restrainedfasteners such as screws in tapped holes or studs (Reference 2) A floating fastener is defined as a fastenerwhere two or more parts are assembled with fasteners such as bolts and nuts, and all parts have clearanceholes for the bolts (Reference 2) See Chapter 22 for more discussion on fixed and floating fasteners.The assembly variation within a fixed fastener occurs when one part shifts as shown in Fig 23-3 The floatingfastener assembly variation has two parts shifting that contribute to the variation as shown in Fig 23-4

Figure 23-3 Fixed fastener centered and

shifted

Figure 23-4 Floating fastener centered

and shifted

Fixed and Floating Fastener Variation 23-5 23.4.1 Fixed Fastener Assembly Shift

Fig 23-5 shows a fixed fastener within an assembly and uses the following notation to develop equationsfor assembly shift, minimum gap, and maximum gap The minimum and maximum gaps between datumsurfaces E and B occur when the locating features are at least material condition and using their maximumlocation tolerances The following summarizes these conditions

where

p = Pin mean size

t p = Equal bilateral pin size tolerance

t a = Cylindrical tolerance zone diameter (hole)

h = Hole mean size

t h = Equal bilateral hole size tolerance

t b = Cylindrical tolerance zone diameter (pin)

Shifting the parts to a maximum and minimum shows the worst case gap for each condition tionally, we draw a dimension loop diagram for each condition Fig 23-6 shows the two parts shifted for

Conven-a minimum Conven-assembly gConven-ap Conven-and the resultConven-ant dimension loop diConven-agrConven-am

Minimum Gap = Nominal Gap - Tolerance

Minimum Gap = [b + 5(p − t p) − 5(h + th) − a] − [(.5ta + t h ) + (.5t b + t p)]

which simplifies to:

Minimum Gap = (b − a) − 5(h − p) − 5(ta + tb) − 1.5(th + t p) (23.1)Note that Eq (23.1) gives the minimum gap if the parts touch as shown in Fig 25-6 Since the minimumgap occurs when the pin and hole are both at LMC, the parts may be manually shifted to increase this gap

The amount the parts can shift is (h + t) − (p − t)

Figure 23-5 Fixed fastener assembly

23-6 Chapter Twenty-three

Figure 23-6 Fixed fastener minimum

assembly gapFig 23-7 shows the two parts shifted to a maximum assembly gap and the resultant dimension loopdiagram

Maximum Gap = Nominal Gap + Tolerance

The amount the parts can shift is (h + t h) − (p − t p)

23.4.2 Fixed Fastener Assembly Shift Using One Equation and Dimension Loop

The following discussion describes an alternative method of defining two dimension loop diagrams andequations for the assembly variation at the gap This method defines one equation for the total variation

at the gap

Figure 23-7 Fixed fastener maximum

assembly gap