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by Masaya HAGIWARA

Clamp Force – The Key to Making Bolted Joints Safe

IntroductionIn almost all machinery or mechanical constructions, there exists a great number of joints connected by threaded

fasteners. Such connections are generally called bolted joints. A bolted joint consists of at least two clamped members, one externally threaded fastener (bolt, screw or stud), and one internally threaded fastener (nut) or one

internal thread directly machined (drilled and tapped) to one of the clamped members. The primary objective to use threaded fasteners is, of course, to keep the clamped members tight.

This article depicts how the clamp force works in bolted joints. Concrete design information is also presented to make bolted joints safe. The terms “bolt” and “nut” are used in this article for referring to externally and internally threaded

fasteners, respectively.

The Roles of “Clamping” and “Clamp Force”Bolt/nut assembly is used to keep the clamped members tight by applying a compressive force to them. The action is

called clamping or tightening, and the compressive force applied to the clamped members is called “clamp force”. It works to prevent the separation at the interface between two clamped members called “contact plane”. If one solid component is used

in a structure instead of two clamped members, neither bolt/nut assembly nor clamping action is necessary. In such cases, no fastener failure is, of course, expected. This suggests that if the contact plane of a joint does not separate when external load is applied, and the clamped members act as a solid body, the fastener failure is less likely to occur. Actually, most of the fastener failures such as self-loosening and fatigue fracture are caused by the separation of the contact plane of a bolted joint. The separation of the contact plane normally brings the excessive stress condition on a bolt/nut assembly.

How to Control the Clamp Force?Figure 1 shows a simple bolted joint and its 2-D model for analyzing the behavior

in tightening procedure. In the model, the clamp force and the axial tension on the bolt F are represented by vertically placed spring elements Kc and Ks, and the torques Tth and Tb acting on the bolt shank and on the clamped members are transformed into lateral forces represented by horizontally placed ones Γs and Γc, respectively. In the practical tightening control activities, the tightening torque T and/or the rotation angle Θ are normally selected as indices for clamp force control since they can be easily measured and controlled outside.

We can easily understand from Fig. 1(b) that the coefficient of frictions μth and μb would affect the clamp force F obtained by controlling the tightening torque T, and the stiffness values of the springs Ks and Kc would affect the clamp force F

ødød2

Nut

Clamped members

Clamp force F Fixture

Tightening torque T(Rotation angle Θ)

β

φP

Bolt

øD b

βF

F

Θ

Nut

Bolt

φ

TighteningT

Loosening

F(Ks)

F(Kc)･･･ Underhead

Clamped members

Tth

(Γs)

Tb

(Γc) Contact plane (μc)

Mating threads (μth)

Bearing surface (μb)

Rotationangle

Tth +Tb =T

obtained by controlling the rotation angle Θ. Therefore, we have to know the real values of these influencing factors to determine the target values of the indices T and/or Θ.

The effectiveness of the other indices such as the elongation of a bolt used in pre-tensioning method or thermal heating method can also be explained by using this figure noticing that the elongation of a bolt is indicated as the shrinkage of the spring Ks.

How does Clamp Force Work to Prevent self-loosening?

Figure 2 shows the 2-D model similar to Fig. 1(b) subjected to various types of external loading. There are three contact surfaces where slippage

(b) 2-D model

Fig. 1 Bolted joint and corresponding 2-D model in tightening(a) Bolted joint

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ø dø d2

β

φP

ø Db

β

Mr

Mr

Mr

Wa Wa

Wa

Wtr

Wtr

WaFb

Fb

Mr

FcΘ

Nut

Bolt

φLoosening

(Ks)

(Kc)･･･ Underhead

Clampedmembers

(Γs)

(Γc) Contact plane (μc)

Mating threads (μth)

Bearing surface (μb)

Rotationangle

+ =0

Wa

Wtr Mr

Fb

Tth

Tth Fc

Wa

Tb

Tb

Fig. 2 Bolted joint and corresponding 2-D model subjected to external loading

(a) Bolted joint

(a) Single bolted joint

(a) Single bolted joint (b) Multi-bolted joint (b) Multi-bolted joint

Fig.3 Two types of bolted joints subjected to axial tensile force W

Fig.4 Haigh diagrams for bolted joints in Fig.3 subjected to fatigue loading (0-Wmax)

(b) 2-D model

ø11

M10

ø53

20

20

W

W

W

40

20

2×M10

120150

20

F =10 kN

F =20 kN

F =30 kN

F =40 kN

AB

Fatigue limit（ p =50%）

0

Mean stress σm MPa

400200 600 800 1000

600

Stre

ss a

mpl

itude

σa M

Pa

400

200

σmax = σ0.2σmin= 0

Wmax=40kN Wmax=30kN

Wmax=20kN

Fatigue limit（ p =50%）

σmax = σ0.2 σmin= 0

Wmax=40kN Wmax=30kN

Wmax=20kN

F =10 kN

F =20 kN

F =30 kN

F =40 kN

0

Mean stress σm MPa

　 400200 600 800 1000

600

Stre

ss a

mpl

itude

σa M

Pa　

400

200 A

B

or relative displacement may occur. To consider the self loosening problem, it is important to notice the equilibrium of torques. Supposing that, as an extreme case, the coefficients of friction μth and μb become zero alternately under repeated loading, two springs Γs and Γc, will act as “a pair of pistons” to keep the relationship Tth+Tb=0. During the loading cycles, the nut will move to the right direction step by step to decrease the clamp force F. This is the simplest explanation of self-loosening mechanism of bolt/nut assembly. If neither slippage nor separation occurs at the contact plane, the slippage on the other contact surfaces is hardly ever expected since the additional forces or stresses on the bolt/nut assembly are normally very small. Thus, the higher clamp force would work to prevent self-loosening by keeping the contact plane tighter as well as increasing directly the resistances of slippage between the mating threads and between the bearing surfaces.

Design Consideration to Prevent Fatigue FractureAs mentioned before, the higher the clamp force, the smaller the additional forces or stresses acting on bolt/nut assemblies

by the external load. It should be noted that the separation at the contact plane is more likely to occur when bending moment is applied.

Figure 3 shows two types of bolted joints, (a) concentrically loaded single bolted joint and (b) multi-bolted joint having the same bolt(s) and nut(s) subjected to the same magnitude of the external tensile force W.

Figure 4 shows Haigh diagrams to consider the risk of fatigue fracture (1). Assuming that the external tensile force fluctuates from zero to Wmax=30kN, the bolt in both bolted joints will fail by fatigue with 100% probability if the clamp force F is 10 kN since the stress amplitude acting on the bolt (point A) is much higher than the fatigue limit shown by the solid line. If the clamp force F is raised to 30 kN (Point B), the bolt in the single-bolted joint will be free from fatigue since the stress amplitude acting on the bolt becomes negligibly small. On the other hand for the multi-bolted joint, the point B is just above the fatigue limit line, and there is still more than 50% risk of fatigue fracture even though the number of bolts is doubled. The higher stress comes from prying action of the clamped members for the bolted joint as shown in Fig.3 (b). To avoid this, the offset or eccentricity of the bolt axes should be minimized.

What Should We do for Bolted Joints Unable to Apply Sufficient Clamp Force?There are some cases where enough clamp force cannot be applied due to the constraint of the strength

and/or the rigidity of clamped members. In such cases, “double nuts” would be one of the most effective countermeasures to prevent both self-loosening and fatigue fracture. The locking force acting between two nuts generates the resistant force against the slippage between the mating threads, and at the same time it improves the stress concentration on the first thread root of a bolt mated with the lower nut. The fatigue strength of a bolt mated with double nuts may reach 150% of that of a same bolt mated with single regular nut (2).

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(a) Initial tightening (b) Secondary tightening (c) LockingFig. 5 Typical tightening procedure for bolt/double nuts assembly

TighteningTorque

TighteningTorque

LockingTorque

Clamp force Clamp force

Lockingforce

Lower nut

Upper Nutød ød2

ød ød2

ød ød2

T1 TlocFloc

T2 ≈ T1

F’ ≈ FF

The locking force should be as high as possible. Therefore, the use of two regular nuts is recommended. In the case where thin nut has to be used due to the constraint of length, size or weight, it should be used as a lower nut closer to the bearing surface of a clamped member since the loadability of bolt/thin nut assembly for thread stripping is lower than that of bolt/regular nut assembly. Figure 5 summarizes the procedure to make bolt/double nuts assembly.

Concluding RemarksThe importance of the clamp force is emphasized in this article. Please don’t misunderstand the significance of so called “high

strength bolts” with property classes 10.9 and 12.9. They are not designed to endure the severe service conditions, but are lined up simply to be able to apply higher clamp force. Higher clamp force leads to realizing safer bolted joints.

References (1) Hagiwara, M. and Yoshimoto, I.: Experimental Mechanics, Vol. 27, No. 4 (1987), pp. 398-403.

(2) Hagiwara, M. et. al.: Trans. JSME Series C (in Japanese), Vol. 79, No. 800 (2013), pp. 1189-1195.