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a minimum assembly gap and the resultant dimension loop diagram.
Minimum Gap = Nominal Gap - Tolerance
Minimum Gap = [b + .5(p - tp) - .5(h + th) - a] - [(.5ta + th) + (.5tb + tp)]
which simplifies to:
Minimum Gap = (b - a) - .5(h - p) - .5(ta + tb) - 1.5(th + tp) (23.1)
Note that Eq. (23.1) gives the minimum gap if the parts touch as shown in Fig. 25-6. Since the minimum
gap 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 + th) - (p - tp).
23-6 Chapter Twenty-three
Figure 23-6 Fixed fastener minimum
assembly gap
Fig. 23-7 shows the two parts shifted to a maximum assembly gap and the resultant dimension loop
diagram.
Figure 23-7 Fixed fastener maximum
assembly gap
Maximum Gap = Nominal Gap + Tolerance
Maximum Gap = [b - .5(p - tp) + .5(h + th) - a] + [(.5ta + th) + (.5tb + tp)]
which simplifies to:
Maximum Gap = (b - a) + .5(h - p) + 1.5(th + tp) + .5(ta + tb) (23.2)
Note that Eq. (23.2) gives the maximum gap if the parts touch as shown in Fig. 23-7. Since the maximum
gap occurs when the pin and hole are both at LMC, the parts may be manually shifted to decrease this gap.
The amount the parts can shift is (h + th) - (p - tp).
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 and
equations for the assembly variation at the gap. This method defines one equation for the total variation
at the gap.
Fixed and Floating Fastener Variation 23-7
A radial plus and minus value can express the assembly shift in the fixed fastener example. This value
is the maximum diametrical amount of clearance between the fixed pin or fastener, and the clearance hole
divided by two. As the mating features depart from their respective virtual conditions, the assembly shift
increases. The maximum assembly shift occurs when the pin and hole have perfect form and orientation
at Least Material Condition (LMC).
From Fig. 23-5, the fixed fastener LMC assembly shift (ASfix ) is:
ASfix = .5[h + th - (p - tp)] (23.3)
where
h + th = Clearance hole LMC size
p - tp = Pin (fastener) LMC size
23.4.3 Fixed Fastener Equation
As previously stated, the most variation within a fastened interface occurs when the mating features are
at LMC. This allows additional (bonus) tolerance to accumulate. From the fixed fastener example in Fig.
23-5 the additional (bonus) tolerance contributors are:
2(th) = Clearance hole size tolerance
2(tp) = Total pin (fastener) size tolerance
Other contributors in the tolerance study are location tolerances for each feature. From Fig. 23-5, the
location tolerance contributors are:
ta = Cylindrical tolerance zone for the clearance hole
tb = Cylindrical tolerance zone for the pin
The total tolerance variation (tv) at the gap is:
tv = 2th + 2tp + ta + tb
The +/- or radial tolerance variation (rtv) at the gap is:
rtv = tv/2
rtv = th + tp + .5ta + .5tb (23.4)
Combining Eqs. (23.3) and (23.4) gives the gap variation (gv) with assembly shift included.
gv = ASfix + rtv
gv = .5[h + th - (p tp)] + th + tp + .5ta + .5tb
This reduces to:
gv = .5(h - p) + .5(ta + tb) + 1.5 (th + tp) (23.5)
23.4.4 Fixed Fastener Gap Analysis Steps
Using Eq. (23.5), only one dimension loop diagram is needed to understand the minimum and maximum
assembly gap. The diagram identifies the mean assembly dimension and Eq. (23.5) gives the variation from
the mean.
First, construct the dimension loop diagram. The dimension loop diagram rules do not change when
a fastener becomes part of the stackup. The diagram is drawn the same, except a vector is drawn to and
from the centerline of the fastened interface, continuing until the right hand side of the gap is reached.
The diagram does not trace the pin and hole as if one part was shifted relative to the other.
23-8 Chapter Twenty-three
The dimension loop diagram for Fig. 23-5 is shown in Fig. 23-8.
Figure 23-8 Centered fixed fastener
dimension loop diagram
The Gap equation is: Gap = (b - a) +/- gv
This equals: Gap = (b - a) +/- .5(ta + tb) + .5(h - p) + 1.5 (th + tp)
This gives the same minimum and maximum gap in Eqs. (23.1) and (23.2).
23.4.5 Floating Fastener Gap Analysis Steps
We can construct the floating fastener dimension loop diagram in the same manner as the fixed fastener
example. In the floating fastener application (Fig. 23-9), the assembly shift calculation uses the two
clearance holes and fastener. In this case, the fastener shifts within both clearance holes.
Figure 23-9 Floating fastener assembly
Fixed and Floating Fastener Variation 23-9
As previously stated, the most variation within a fastened interface occurs when the mating features
are at LMC. This allows additional (bonus) tolerance to accumulate. From Fig. 23-9 the equation for
assembly shift at LMC is:
ASfloat = .5(h1 + th1 + h2 + th2) - (p - tp) (23.6)
where
h1 = Mean clearance hole 1 size
th1 = Equal bilateral clearance hole 1 size tolerance
h2 = Mean clearance hole 2 size
th2 = Equal bilateral clearance hole 2 size tolerance
p = Mean pin (fastener) size
tp = Equal bilateral pin (fastener) size tolerance
From Fig. 23-9, the additional (bonus) tolerance contributors are:
2(th1) = Clearance hole 1 size tolerance
2(th2) = Clearance hole 2 size tolerance
Other contributors in the tolerance study are location tolerances for each feature. The location
tolerance contributors are:
ta = Cylindrical tolerance zone for clearance hole 1
tb = Cylindrical tolerance zone for clearance hole 2
The total tolerance variation (tv) at the gap is:
tv = 2th1 + 2th2 + ta + tb
The +/- or radial tolerance variation (tvr) at the gap is:
tvr = tv/2
tvr = th1 + th2 + .5ta + .5tb (23.7)
Combining Eqs. (23.6) and (23.7) gives the gap variation (gv) with assembly shift included.
gvfloat = ASfloat + tv
gvfloat = (h1 + th1 + h2 + th2)/2 - (p - tp) + th1 + th2 + .5ta + .5tb
This reduces to:
gvfloat = .5(ta + tb)+ 1.5(th1 + th2) + .5(h1 + h2) - (p - tp)
The gap equation is:
Gap = (b - a) +/- gvfloat
Gap = (b - a) +/- .5(ta + tb) + 1.5(th1 + th2) + .5(h1 + h2) - (p - tp)
23.5 Summary
This chapter demonstrates a process to perform worst case tolerance analysis on fixed and floating
fasteners. The methodology described extends the conventional tolerance analysis methodology by
introducing the concepts of virtual and resultant condition. This methodology can be used on any feature
having dependent size and location tolerance. The concepts are further used to develop one equation to
find minimum and maximum assembly conditions by understanding assembly shift within a fastened
interface. Maximum assembly shift occurs when both features of the fastened interface are at least material
condition. Although the fixed and floating fastener rules ensure a worst case fit, they also allow a part
23-10 Chapter Twenty-three
position to float when worst case conditions are not present. Many designs minimize or eliminate assem-
bly shift by using tooling or assembly instruction to  shift out the variation.
23.6 References
1. Cuba, Chris and Paul Drake. 1992. Mechanical Tolerance Analysis of Fixed and Floating Fasteners. Texas
Instruments Technical Journal. Nov-Dec: 58-65.
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. [ Pobierz całość w formacie PDF ]