Loosening and sliding behaviour of bolt-nut fastener under transverse loading

The aim of this present research is to clarify the mechanical behavior of bolted joints under transverse loadings, Abstract Considering the efficient productivity and maintainability, most of machine and products has many joints (e.g., fastening, welding and adhesive joints). Especially, the bolted joints have been frequently used for these purposes as machine elements. However, many troubles such as loosening or fatigue failure of bolted joints were often experienced. More attentions must be paid on the improvement of the strength and the reliability of these bolted joints. It is generally said that the relative slippage between nuts and fastened body under the transverse loading will generate the rotation of nuts and cause the loosening of bolted joints. [1, 2]. For example, the thermal expansion due to temperature change between jointed members may cause these slippage and loosening problems. The aim of this present research is to clarify the mechanical behavior of bolted joints under transverse loadings, and present the critical relative slippage ( S cr ), more than this slippage the loosening will occur. To derive this critical relative slippage ( S cr ), at first the resistant bending moment between bolt/nut contact interface ( M n ),and equivalent stiffness on bolt head/fastened body contact interface( k w ) were derived.. Then the validity of resistant bending moment between bolt/nut contact interface ( M n ),and equivalent stiffness on bolt head/fastened body contact interface( k w ) were confirmed by the quasi-static loading test. Finally, the validity of critical relative slippage ( S cr ) was confirmed by the repeated cyclic loading test.


Introduction
Most of machines and products have various joint portions (e.g.fastening, welding and adhesive joints) for the effective productivity and maintainability.And bolt-nut joint, one of the joint structures is widely used as it's easiness to install and remove, produces big fastening power with small force and low price in production.However, several troubles on their strength and reliability occurred at these portions as illustrated in Fig. 1.So, serious attention must be paid to improve the strength and reliability of these portions.External load acting on the bolt-nut joint comes in two types.First, if the line of action of the forces on the joint is more or less parallel to the axes of the bolt, the joint is known to 14th International Conference on Experimental Mechanics nuts if the relative slippage on the interfaces between nuts and fastened body goes beyond a certain critical limit [3].This critical relative slippage (S cr ) that prescribes the upper limit for preventing the loosening behaviour has been estimated according to the theoretically obtained equation considering the bending deformation of bolt and the geometrical constraint condition.In this paper, firstly we present the equation for estimating the (S cr ) based on the fundamental cantilever deformation model.Then we present the investigated results of the deformation behaviour of bolt-nut joint under transverse loading condition considering the reaction moment by nut (M n ).Finaly we can confirmed that these estimated results of critical relative slippage coincided well with the experimental results [4,5].

Mechanics of Bolt-Nut Joints
The sliding behaviour of bolt-nut joint and reverse rotation of nut under transverse load is showed in Fig. 3.The deformation behaviour of bolt-nut joint is depends on the amount of transverse load level applied on the joint (2,3,4).When the load, W is low, bolt and fastened components (fixed plate and movable plate) are deformed as a unit (Fig. 3 (a)).
No slip generated at the bolt and nut bearing surface.Then, slip generated at the contact surface between fixed plate and movable plate when W exceeded the frictional force (Where frictional force = number of bolts, n friction coefficient, Ǵ initial axial tension, F b ) is given to the joint.However, as shown in Fig. 3(b) when relative displacement, S between upper and lower plate is still small, by the bending deformation of the bolt, sliding at the bolt and nut bearing surface is not generated.Then, load and relative displacement between plates increased and at one stage (relative displacement exceeded ǍS (Fig. 3(c)), slip is also occurs at the bolt and nut bearing surface.This slip leads to the reverse rotation of the nut and decrease the axial tension.The loosening behaviour of bolt-nut joint shows the same occurrence if the transverse load applied in the opposite direction.When transverse cyclic load applied to the joint, bolt axial tension slowly decreases and at the worst stage, not only loosening occurs but also the fatigue failure of the bolt.So, it is important to evaluate both loosening behaviour and fatigue failure of the bolt-nut joint Concerning the loosening rotation of nut under transverse loading, Yamamoto and Kasei [6] proposed the equation that evaluates the critical relative slippage, S cr .Derivation of evaluation equation is given as below.
Intended bolt and nut is shown in Fig. 4. Consider that contact surface is exists between movable plate surface and nut bearing surface.Initial axial tension of bolt is set as F b .
When bolt-nut joint is subjected to shear direction external force, transverse load, W r and reaction moment, M n act at the thread portion.Here, we can calculate the bolt shank's deflection that caused by both transverse load and reaction moment by considering the bolt as a beam.Furthermore, bolt bearing surface is inclines since it is not fixed and proportional to the bending moment of bolt head.Bolt shank̉s deflection ,ǍaF that caused by transverse load, W r is shown in following equation : where, E = Young Modulus of bolt Ig = second moment of area of bolt's cylindrical portion Ip = second moment of area of thread portion Then, bolt shank̉s deflection, ǍaM that caused by reaction moment, M n is shown as below : And inclination angle of bolt head is defined as : (3) T where kw = bolt head's inclination compliance kw indicates the easiness of bolt head to incline during transverse loading.Displacement magnitude, Ǎaǰ at bolt head caused by bending stress is shown in following equation: So, displacement magnitude of load point at thread portion, ǍS which is sums of ǍaF, ǍaM, Ǎaǰ is shown in equation below : reaches relative slippage at the nut bearing surface occurs and critical relative slippage, S cr is defined as below : Yamamoto and kase [6] present the estimation equation of reaction moment as follows by using the mechanical model as shown in Fig. 4(a).
where Ǵ b = coefficient friction of bolt bearing surface In this model they assumed that the contact pressures between bolt and nut are uniformly distributed on 4 corners.But the contact pressure between bolt nut will distributed on each thread, so in this paper we present new estimation equation of reaction moment using the mechanical model as shown in Fig. 4(b), as follows.In this equation reaction moment on each thread M j is shown as follows. (10)

Comparison with the Experimental results
To confirm the validity of these estimation models we performed quasi-static loading tests as follows.

Experimental methods
Medium carbon steel plates were used for fastened components.The ordinary bolt made of carbon steel, M6, M10, M16 are used for the fastening.The mechanical properties of each bolt sizes are given in Table 1.Bolt-nut joint and sensors are shown in Fig. 5.The fastening and bending stress of bolts are measured using strain gage mounted at the vicinity of bolt neck as shown in Fig. 6.

Comparing results and Discussions
Fig. 8 show the relationships between transverse load which applied to the joint vs. relative displacement between fastened plates.From these quasi static test results we can obtain the experimental critical slippage S cr and these values coincided well with that of obtained from the experimental loosening behaviour under repeated load cycle as shown in Fig. 9.By comparing these experimental critical slippage S cr for each fastening force with the Eq. ( 7), we can obtain the experimental reaction moment M n as shown in Fig. 10.These experimental results coincided well with the estimated results from Eq. (9) as shown in this figure.

Conclusions
1.In this paper we introduced the estimation model of critical slippage S cr for bolt loosening under transverse loadings.2. In this estimation method we present new prediction equation for reaction moment M n based on the bolt/nut jointing model.3. Using these estimation methods we can predict critical slippage on each fastening conditions such as bolt sizes, bolt lengths, fastening force and so on.And these methods can be used for the CAE design tool for each machine structures.

Fig. 3
Fig. 3 Behavior of the bolt-nut joint in different load condition.

14th
International Conference on Experimental MechanicsCoefficient friction of nut bearing surface is set as Ǵw.When transverse load, W r

3
Derivation of Nut Reaction Moment M n Model of yamamoto and kase (b) Model in this study Fig.4Force and moment at each interface.

Fig. 7
Fig. 7 Experimental apparatus tension and relative displacement of fastened plates which is the difference displacement between fixed plate and movable plate are measured by sensors and load cell.

Fig. 8 Fig. 10
Fig.8 Dependence of transverse load Fig.9 Dependence of dF/dN on relative on relative displacement displacement.

Table 1
Material properties of M6, M10 and M16 boltFatigue testing machine with hydraulic pump is used in the order to generate transverse cyclic loading.Experimental apparatus is illustrated in Fig.7.In this experiment, static loading (tension only) is applied to the joint which is fastened by various axial tensions (depend on bolt size) and the critical load when sliding occurs between bolt bearing surface and fixed plate is examined.Transverse load, bolt axial