Keywords: bolt design, optimal pre-load, dynamic loading, damping effect, closure lift-off.

In this paper, the dynamic behaviour of a closure bolting system is predicted by the use of a spring-mass-damper model. The loading is assumed to be an initially peaked, exponentially decaying internal pressure pulse acting on the closure. Especial attention is paid to the effect of pre-stress and applied pressure levels on the maximum bolt displacement and stress. The main aim is to find proper values of pre-stress, which comply with the requirements of no closure lift-off and no bolt yielding.

Discussion of the conventional design of bolted joints is presented by Shigley and Mitchell[1]. The key point regarding bolted connections brought out in this reference is that at a bolted connection, both the bolt and the material being bolted behave as linear springs (to the point of yield). Due to pre-loading of the bolt, the bolted material is subjected to a compressive force while the bolt itself is in the state of tension. Equilibrium requires that the total tensile bolt load be equal in magnitude to the compressive load in the bolted material.

Much of the previous investigations on the bolted connections are based on comparative statics. That is, performing comparisons of the two static cases both before and after loading is imposed and the system settles in its static situation. However, bolted joints have elasticity and mass and therefore, like any other system consisting elasticity and mass, can vibrate. Dynamic analysis of bolted joint connections is performed mainly in order to achieve two goals. The first is to analyse dynamic loosening of joints due to alternating forces applied to the connection. In this way, the bolt pre-stress is found in such a way as to prevent loosening. The second aim is to investigate dynamic stresses in the connection in order to find optimal preload, which prevents bolt yielding, fatigue and the closure lift off.

Duffey[2] has implemented a simple model for closure bolting systems and analysed the dynamic behaviour of this model. This analysis is basically presented for short duration dynamic loading, such as the one occurs at bolted closures for vessels used to contain explosions. It is believed that presence of damping (that is ignored in[2]) can be very effective in reducing the maximum bolt displacement and stress, especially at low bolt pre-stress values and long duration dynamic loadings.

Recently, Lavabre, et al.[3] considered the dynamic behaviour of bolted joints subjected to harmonic loading. In this paper, the elements of the connection have been assumed to behave nonlinearly. The presented analysis is valid only in the static range.

In the present paper, the main assumptions implied in the modelling process may be stated in the following manner. The effects of closure bending response and the resulting bending stresses induced in the bolts are not considered in the simple model developed. The input excitation is assumed to be initially peaked exponentially decaying pressure pulse and acting on the flange in a direction parallel to the bolt axis. The damping in the joint due to structural damping and damping due to the sealing element, have been assumed to be expressible in the form of an equivalent viscous damping. Hence, the damping force is proportional to the velocity and the equation of motion would be linear.

The algorithm of computations can be presented as follows. The solution starts with first evaluating finding the values of the parameters of the model. Some value for pre-stress is assumed and the corresponding pre-load that should be applied to the bolt is computed. The equilibrium position of the joint without external loading is calculated. The corresponding closure lift-off displacement curve is plotted. Several time steps are considered and corresponding values of instantaneous bolt lengths are calculated. In this way, the occurrence of closure lift-off should be born in mind.

It has been observed that optimal pre-stress values that minimize the peak bolt deformation and stress exist for relatively high levels of applied force and low pre- stress. While low levels of pre-stress are recommended for the reduction of peak bolt deformation and stress, for closures in which sealing is a consideration, higher values of pre-stress are necessary in order to prevent closure lift-off. The danger of bolt yielding due to excessive deformation should also be born in mind. It was observed that existence of damping reduces the maximum bolt deformation and stress. The effect of damping was observed to be un-ignorable, especially when high natural frequencies of the considered system or long duration loading pulses exist. This effect is, however, of less importance at higher pre-stress levels.

1

J.E. Shigley and L.D. Mitchell, "Mechanical Engineering Design", 4th edition, McGraw-Hill, New York, 1983.

2

E T.A. Duffey, "Optimal bolt pre-load for dynamic loading", International Journal of Mechanical Sciences, 35, 257-265, 1993. doi:10.1016/0020-7403(93)90080-E

3

R. Lavabre, H. Aziz and B. Combes, "Non-linear harmonic response of a bolted assembly", Proceedings of the ASME ESDA Conference, 369-376, 2000.

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