Nominal diameter, clamp length and thread pitch analysis for bolt preload

INTERNATIONALMechanical Engineering and Technology (IJMET), ISSN 0976 –
International Journal of JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online) IJMET
Volume 4, Issue 2, March - April (2013), pp. 141-151
© IAEME: www.iaeme.com/ijmet.asp
Journal Impact Factor (2013): 5.7731 (Calculated by GISI) ©IAEME
www.jifactor.com

NOMINAL DIAMETER, CLAMP LENGTH AND THREAD PITCH
ANALYSIS FOR BOLT PRELOAD AUGMENTATION

Satish S. Kadam1, S. G. Joshi2
1
(Associate Professor, Mechanical Engineering Department, BharatiVidyapeeth Deemed
University College of Engineering, Pune 411043, Maharashtra (India)
2
(formerly Professor in Department of Mechanical Engineering, Walchand College of
Engineering, Sangli, Maharashtra, India)

ABSTRACT

Threaded fastening is used mainly for fastening together mechanical parts. Compared
to other types of jointing methods such as adhesion, welding, brazing and pressure insertion,
threaded fastening has a unique characteristic that elastic energy is built up inside the joint
members. Tension in the bolt and compression in the fastened parts are created as a product
of action and reaction. These forces can make the joint less susceptible to fatigue and
loosening when external load is applied or internal pressure is increased. Since the torque
applied to a fastener must overcome all friction before any loading takes place, the amount of
friction present is important. It is seen that approximately 50% of the torque applied will be
used to overcome bolt head-bearing friction and another 35% to overcome the thread friction
and approximately 5% is consumed by prevailing torque. Thus only 10% torque is available
to produce clamping force. In this paper, an analysis is presented to study the effect of
various parameters such as clamp length, nominal diameter and thread pitch on the preload
required for maintaining joint integrity. The suggested design guidelines are useful for proper
selection of threaded fasteners used in different assemblies of structures, machine elements
etc.

Keywords : Bolted Joints, Preload Augmentation

141

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –

I. INTRODUCTION

A screw thread is an extension of one of the basic machines, the inclined plane,
that has been wrapped around a shaft. When the thread is turned, it moves the mating part
or nut up the inclined plane. When increased turning force or torque is applied to the
shaft, the force exerted on the nut is increased. This force creates a tension in the bolt,
which clamps the mating parts together. Preload is the technical term for the tension
caused by tightening the fastener that holds the assembled parts together. Generating
sufficient preload force is the key to strong and reliable bolted joints that will not loosen
or break under load. Figure 1 shows the forces that act on a bolted joint.
Bolted joint design is an iterative process. To make some design decisions the
designer relies mostly on trial and error, past experience and personal judgment. The
designer is able to make better judgments regarding the effect of certain design
parameters and decisions with the increase in his experience and knowledge.
However, regardless of the size, application or operating parameters of a joint,
following some steps which are commonly followed in practice are:

1. Define the purpose of the joint: Define what the joint is designed to do, environmental
conditions, cost targets, size and operating parameters, desired life, critical nature,
potential failure modes etc. involved in the purpose of the joint.
2. Design the joint: Determine the layout of the joint, including joint members, size, shape
and material(s).
3. Estimate service loads: The static and dynamic loads to be considered include weight,
pressure, shock, inertial effects, thermal effects, etc.
4. Define bolts to be used: With the joint geometry and service loads established, the bolt
size, number and strength can be determined. Bolt selection should include material,
diameter, thread pitch, length, tensile strength, head style, drive style, thread style,
hardness and plating.
5. Determine required bolt preload and clamping force: The minimum clamping force
should be great enough to overcome vibration loosening, joint separation, slippage,
fatigue, leakage and other similar type failures. Maximum clamp force should not be
great enough to cause bolt yielding, joint crushing, stress cracking, fatigue failure, tensile
failure or other similar failures in service.
6. Determine tightening methods and assembly line accuracy: During assembly, there are
different fastener assembly methods and tightening strategies which must be considered.
Among the potential tightening strategies and their preload accuracy are: Torque: ± 35 %,
Torque-Angle: ± 15 %, Torque - to -Yield: ± 7 %
7. Finalize joint design: At this point, it may be necessary to make changes in joint
material, bolt preload range, bolt selection, tightening methods, etc. depending upon what
was determined during the other steps of the joint design process.

142


Figure 1 Bolted joint

II. TORQUE-TENSION RELATIONSHIP

The torque required to turn the nut can be related to the axial load in the bolt by the
following formula: [1]

T = Fi × d × K (1)
Where,

T = Torque required to develop desired bolt preload
Fi = Bolt preload (Equivalent to clamping force FC)
d = Bolt nominal diameter mm
K = Nut Factor

and, K = K 1 + K 2 + K 3
p rt × µ t rb × µ b
K1 = ; K2 = ; K3 =
2× πd d cosα d
K1 = Factor for torque contribution towards Joint compression and Bolt elongation (also
termed as geometric factor)
K2 = Factor for torque contribution for overcoming thread friction
K3 = Factor for torque contribution for overcoming bolt / nut under-head bearing friction
under head

143


 p r ×µ r ×µ 
∴ T = Fi × d + t t
+ b b 
(2)
 2 × π d d cosα d 
 

p = Thread pitch
α = Half thread flank angle (π/6 for ISO thread)
rt = Thread root radius
rb = Effective bearing radius
µt = Coefficient of friction between male and female threads
µb = Coefficient of friction between the bearing surfaces under the turning fastener head or
nut
As we know; T = T1 + T2 + T3 (100% Torque)
Where,
T1 = Torque contribution towards Joint compression and Bolt elongation
T2 = Torque contribution for overcoming thread friction N-m
T3 = Torque contribution for overcoming bolt / nut under-head bearing friction

 p 
T1 = Fi × d × K 1 = Fi × d   (3)
 2× πd 

 rt × µ t 
T2 = Fi × d × K 2 = Fi × d   (4)
 d cosα 
 

 rb × µ b 
T3 = Fi × d × K 3 = Fi × d   (5)
 d 
 

To get the values of rt and rb it is necessary to calculate thread stress area (AS) and Bearing
area (AC) under nut or bolt head respectively.

π
AS = (d − 0.9382 × p )2 (6)
4

 2 
π   d3 + d2


 2

AC =   − d1  (7)
4 
2 
 
 

d1 = Bolt hole diameter = d (for small clearance)
d2 = Nut head diameter = 1.5 d (for standard hexagonal headed bolts)
d3 = Fastener head outer bearing or bearing cone diameter
= d2 + L tan 300 = 1.5 d + L tan 300
Where, L = Clamp length

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π
∴ AC =
16
[5d 2 0 2
+ 6 d L tan 30 + L tan 30
2 0
]
2 2
∴ A C ≈ d + 0.68 d L + 0.065 L (8)
For comparing the performance of different bolted joints, the analysis of the effect of various
parameters such as coefficient of friction, clamp length, nominal bolt diameter, pitch etc. is
important. So the calculations are made for M12×1.25 size bolts which are commonly used in
number of engineering applications. On the basis of such an analysis the joint parameters
were suggested to obtain desired preload.

For M12×1.25 bolts, d = 12 mm; p = 1.25 mm; α = 300
Assuming, Clamping length, L = 30 mm
Putting above values in equations (6) and (8) one can get,
π
AS = [d − 0.9382 × p ]2 = π × rt2
4
π
= [12 − 0.9382 × 1.25]2 = 92.0717 mm
2

4
from which rt = 5.4136 mm
2 2
A C ≈ d + 0.68 d L + 0.065 L = π × rb2
= 12 + (0.68 × 12 × 30 ) + 0.065 × 30
2
( 2
) = 447.3 mm 2

from which rb = 11.9323 mm
The most important parameter is preload (Fi) produced by tightening torque (T). The
tightening torque (T) depends mainly upon thread friction and bearing friction. In the
following sections, the bolt preload influencing factors such as friction, diameter, pitch and
clamp length are discussed and analyzed in detail.

III. FRICTION

Lambert [6] states that the coefficient of friction depends on a number of factors such
as the method of manufacture and surface finish of the threads, the degree of lubrication and
nature of the lubricant and the number of times the bolt has been previously tightened. The
change in the coefficient of friction, under different conditions, can have a very significant
effect on the slope of the torque preload curve. Better the lubrication on the fastener the more
of the torque energy will be converted into actual clamping force. The type of lubricant used
has a definite effect on how much of the torque is needed to overcome friction. As such in
this section, the effects of variation in coefficient of friction µtand µbare discussed.
The values of T1, T2 and T3 based respectively on equations (3), (4) and (5) are obtained for
M12×1.25 sizes as;

T1 ≈ 0.2 × Fi (9)

T2 = 6.2511 × Fi × µ t (10)

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T3 = 11 .9323 × Fi × µ b (11)
∴ T = Fi (0.2 + 6.2511 µ t + 11.9323 µ b ) (12)

The equation (12) shows that to develop the desired bolt preload (Fi), torque (T) is required,
which is taken as 100%. As per VDI 2230, the values for µtand µbrange between 0.1 and 0.18.
s
To calculate the individual contributions of T1, T2 and T3 to give total torque T, putting the
average value of µt= 0.14 and µb= 0.14 in equation (12) one obtains;

T = Fi (0.2 + 0.8752 + 1.67 ) (13)

The individual contributions of T1, T2 and T3 in the total torque T are 7.28418%,
31.8739% and 60.8419% respectively. This shows that the bolt / nut under- under-head bearing
friction has the significant share in the total torque T (Fig.2 shows the distribution of T3 for
all the cases). Similarly for different combinations of µtand µbthe percentage contribution of
T1, T2 and T3 in the total torque T have been calculated.

Figure 2 Torque distribution against bearing friction and thread friction coefficient

For the case of minimum value of friction, i.e. µt= 0.1 and µb= 0.1;
T = 2.01834 Fi (14)

and for the maximum friction value, i.e. µt=0.18 and µb= 0.18,
T = 3.473012 Fi (15)

From the catalogue of standard fasteners, the recommended torque (T) is 88 N for Grade
N-m
8.8-M12×1.25. By putting these value in equations (14) and (15) respectively one can get the
.
extreme values of preload Fi, as 43600 N and 25360 N respectively, which shows the

146


variation of 18240 N (approximately 42%).
The individual contributions of T1, T2 and T3 in the total torque T, for all the values of µt and
µb in the range of 0.1 to 0.18 have been calculatedand its distributions are shown in Fig. 3.

Figure 3 Individual torque distribution
ure

Figure 3 exhibits the scatter of torque values required to overcome the friction and develop
the desired clamping force in the joint.

IV. NOMINAL DIAMETER

To ensure a Tensile strength of a bolt is represented by the material and size. T load
The
carrying capacity of a bolt is proportional to the square of the bolt diameter.The individual
diameter.The
contributions of T1, T2 and T3in the total torque T, for different values of nominal diameter
are calculatedusing equations (3), (4) and (5), and the results are presented in Table 1 and
using
Figure 4.

Table 1 Torque Contribution for Bolt Diameters
Bolt Diameter (%) Torque Contribution % Change % Change
(d) mm in Bolt in T1, T2 and T3
T1 T2 T3 Diameter T1 T2 T3
8 9.5376 26.46 64.01 33.33 24 17.02 4.90
10 8.2333 29.53 62.24 16.66 11.96 7.39 2.20
12 7.2484 31.88 60.86 0 0 0 0

147


Figure 4 Torque contribution against bolt nominal diameter

Figure 4 shows that, for smaller size bolts, increased capacity of torque T1 is available.
Torque T1 is required to develop desired preload.

V. CLAMP LENGTH

From equation (8), it is seen that the clamp length ‘L’ has the significant effect on the
bearing radius ‘rb’, which ultimately affects the value of T3, i.e. Torque contribution for
overcoming bolt / nut under-head bearing friction. For analyzing the role of clamp length in
the tightening process, it has been varied from 20 to 50 mm in the step of 5 mm. Putting these
values in equation (8), bearing radius ‘rb’ is calculated. With the help of equations (3), (4) and
(5), for µt= 0.14 and µb= 0.14; the torque contribution data of T1, T2 and T3 are calculated and
the results are presented in Table 2 and displayed in Figure 5.

Table 2 Torque Contribution for Clamp Length
Clamp (%) Torque Contribution % Change % Change
Length in Clamp Length in T1, T2 and T3
(L) mm T1 T2 T3 T1 T2 T3
20 7.9461 34.77 57.28 0 0 0 0
25 7.5980 33.25 59.15 20 4.58 4.58 3.163
30 7.2842 31.87 60.84 33.33 9.08 9.08 5.8484
35 6.9989 30.63 62.37 42.85 13.53 13.53 8.16
40 6.7381 29.48 63.77 50 17.93 17.93 10.1821
45 6.4982 28.43 65.07 55.55 22.28 22.28 11.96
50 6.2765 27.46 66.26 60 26.6 26.6 13.55

148


Figure 5 Torque contribution against clamp length

VI. PITCH

The thread pitch is linked with the stress induced in the bolt. The cross-sectional area
used for stress calculations is the thread tensile stress area which is different for coarse and
fine threads. The torque recommendations, therefore, are slightly higher for fine threads than
for coarse threads to induce the same stress. Choice between coarse or fine screw threads
requires a compromise or balancing of the advantages and disadvantages of each thread series
for the specific application.
M12×1.25, 1.5 and 1.75 bolt sizes are taken for calculation. Corresponding values of pitch p
are used in equations (3), (4) and (5), and with µt= 0.14 and µb= 0.14; the torque contributions
T1, T2 and T3 are obtained. The results are given in Table 3 and displayed in Figure.6.

Table 3 Torque Contribution for Thread Pitch

Pitch (%) Torque Contribution % Change % Change in T1, T2 and T3
(p) mm in Pitch
T1 T2 T3 T1 T2 T3
1.25 7.2484 31.88 60.86 0 0 0 0
1.5 8.6326 30.96 60.41 16.66 16.03 2.90 0.75
1.75 9.9961 30.05 59.95 28.57 27.48 5.76 1.49

149


Figure 6 Torque contribution against pitch

VII. CONCLUSIONS

(i) Controlling the friction between the mating surfaces must be the highest priority while
assembling the joint. Section III of the paper highlights the scattered nature of the torque-
tension relationship arrived due to variation in the values of coefficient of friction.
(ii) Bolt nominal diameter plays an important role in the strength consideration of the
threaded fastener, for a given joint. More number of slender (small diameter) bolts are
preferred, instead of a small number of large size bolts.
(iii) With the increase in the joint length, the value of torque T1 (required for developing
preload) increases and potential loss of preload is decreased.
(iv) The proper selection of bolt diameter and grip length (d/L = aspect ratio) is desired to
achieve the required preload.
(v) It is seen that large pitch values help to achieve more clamping force due to lesser
frictional resistance. However, the larger the pitch value, smaller is the effective tensile stress
area. In general, both coarse and fine threads are capable of providing sufficient strength for
most applications.

REFERENCES

[1] J. H. Bickford, Design and analysis of bolted joints (Marcel and Dekker, 1995).
[2] E. Dragoni, “Effect of thread pitch and frictional coefficient on the stress concentration in
metric nut bolt connections,” Transactions ASME Journal OMAE, 116(1), 1994, 21-27.
[3] J. F. Ferrero et. al. “Analysis of a dry friction under small displacements: applications to a
bolted joint,” Wear, 256, 2004, 1135-1143.

150


[4] T. H. Lambert, “Effect of variation in the screw thread coefficient of friction on the
clamping force of bolted connections,” Journal Mechanical Engineering Science, 4(4),
1962, 401-403.
[5] A. F. Luscheret. al., “Increasing abutment friction at bolted joint interfaces through
particle enhanced sealants,” International Journal of Vehicle Design, 29(3), 2002, 288-
306.
[6] S. A. Nassaret. al., “Bearing friction torque in bolted joints,” STLE Tribology
Transactions, 48, 2005, 69-75.
[7] S. A. Nassaret. al., “Thread friction torque in bolted joints,” ASME Journal of Pressure
Vessel Technology, 127, 2005, 387-393.
[8] M. P. Oliver. (2003). Thread and under head friction. Fastener Technology. Available:
http://www.delphi.com
[9] W. G. Waltermire, “Coarse or fine threads,” Machine Design, 32(6), 1960, 134-140.
[10] A. I. Yakushev, Effect of manufacturing technology and basic thread parameters on
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29th IEEE Conf. on Decision and Control, San Francisco, CA, 1990, 500-506.

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Nominal diameter, clamp length and thread pitch analysis for bolt preload

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Nominal diameter, clamp length and thread pitch analysis for bolt preload