Hobson Engineering Co Pty Ltd A.B.N. 38 000 289 958 technical paper 1 MECHANISMS AND PREVENTION OF VIBRATION LOOSENING IN BOLTED JOINTS * Saman Fernando Engineering, Research, Development and Innovations Manager Ajax Fasteners, Braeside, Victoria SUMMARY: Loosening of bolted joints under a vibratory environment has been an ongoing problem associated with many engineering applications. Total loss of the fastener or subsequent fatigue failure due to loss of bolt pre-tension are the predominant failure modes of vibration loosening. The present paper analyses two possible mechanisms of vibration loosening and identi es critical parameters in preventing loosening. The mathematical models developed shed light on the effect of various bolted–joint related parameters on vibration loosening and joint integrity. It also develops simple rules-of-thumb for the prevention of vibration loosening. Finally, based on the results of the above mathematical model the paper discusses the available locking devices and their correct usage and limitations. NOMENCLATURE m mass of the particle on the conveyor m1 mass of the transported component (bolt or D nominal bolt diameter nut) d0 amplitude of rectilinear vibration P effective downward force d0(t) cyclic rectilinear displacement applied on p thread pitch the conveyor R reaction force on the particle F friction force on the particle rt effective radius of the thread F0 friction force with respect to conveyor at relative rest of the particle rb effective radius of the head/nut bearing surface Fb bolt tension T tightening torque Fi pre-tension of the bolt Ti installation torque (initial tightening torque) f non-dimensional friction parameter (eqns (30, 58)) TI inertial torque G non-dimensional inertial parameter (eqns Tp Break-Loose torque (29, 57)) x displacement in x-direction g gravitational acceleration Greek Symbols: J polar moment of inertia α thread ank angle K nut factor (eqns (6, 7)) β inclined angle of the conveyor K1 thread pitch contribution of nut factor (eqn δ transformed time variable (eqn (40)) (2)) Γ non-dimensional inertial parameter K2 thread friction contribution of nut factor (eqn (31)) (eqn (3)) γ transformed time variable (eqn (39)) K bearing friction contribution of nut factor 3 λ (eqn (4)) pre-load factor (eqn (48)) μ * Paper M23/605 submitted 12/08/03 t thread friction coef cient Paper accepted for publishing 20/06/05 © Institution of Engineers, Australia 2005 Australian Journal of Mechanical Engineering, Vol 2, No.2 Since 1935 ... because quality matters 10 Clay Place Ph: +61 2 8818 0222 Eastern Creek NSW 2766 Fax: +61 2 9620 1850 www.hobson.com.au Hobson Engineering Co Pty Ltd A.B.N. 38 000 289 958 2 “Mechanisms and prevention of vibration loosening in bolted joints” – Fernando μb bearing friction coef cient In most situations, both of the above effects may occur in one joint. μI static friction coef cient of the conveyor surface It is common experience that vibration loosening of joints may occur when a bolted joint undergoes μ dry friction coef cient of the conveyor dynamic load uctuations.1 There are a large number surface of thread-locking devices available in the market in θ angle of the applied rectilinear vibration to order to alleviate joint loosening problems.4 However, the conveyor surface use of such devices needs to be done with care. It is very important to understand the root causes and τ non-dimensional time (eqn (27)) mechanisms behind the phenomenon of vibration τ0 non-dimensional time when the particle at loosening in order to decide the optimum method momentary rest of alleviating the problem. This paper discusses the mechanisms of loosening, mechanisms preventing τ1 non-dimensional time when the particle at momentary rest loosening, and guidelines on using various thread- locking devices commonly available in the market. ω angular velocity of rectilinear vibration ξ non-dimensional displacement (eqn (26)) 2 BREAK-LOOSE TORQUE ψ angular rotation of the wheel There are several de nitions related to loosening and Axis Systems: tightening of fasteners that need to be established. OXY inertial co-ordinate system placed on the Prevailing torque is the torque necessary to rotate the conveyor fastener relative to its mating component with the oxy relative co-ordinate system placed on the torque being measured while the fastener is in motion particle and with zero axial load in the assembly. Prevailing-on Derivatives: torque is measured when the fastener is advanced towards its seated position. Prevailing-off torque is . rst derivative with respect to time – measured when the fastener is being removed.5 velocity Break-loose torque is the torque, applied in a removal .. second derivative with respect to time direction, necessary to start the fastener in motion – acceleration from its fully preloaded installed position. For most locking fasteners, break-loose torque is higher than 5 Subscript: initial tightening torque (installation torque) Ti . mean time averaged The tightening torque is the torque applied on the fastener while generating axial-tension on the bolt. The tightening torque (T) of a bolted joint can be 1 INTRODUCTION represented as:2 Most bolted joints, especially the ones associated with machinery, are subject to signi cant vibration ⎡ p r μ r μ ⎤ = + t t + b b levels during their life span. Rotating or reciprocating T Fb .D.⎢ ⎥ machines, such as gas/steam turbines, electric motors ⎣2π D D cosα D ⎦ (1) and IC engines, are subject to vibration of relatively high frequency. Gyratory crushers, jack hammers and p K1 = so forth are subject to medium frequency vibrations. 2π D (2) Forging/stamping machines are subject to relatively low frequency, high amplitude vibrations. Certain rt μt dynamic structures (eg. bridges and buildings subject K2 = α (3) to wind and cyclonic loads) also undergo dynamic D cos load fluctuations. Cyclic temperature variations μ may also cause dynamic (very low frequency) load rb b K 3 = uctuations in bolted joints. Although the frequencies D (4) of these uctuations are spread over a wide spectrum, the general effects of dynamic loading on bolted joints are similar. The main effects are: T = Fb .D.(K1 + K2 + K 3 ) (5) a) loosening of the nut/bolt and K = K + K + K b) fatigue. 1 2 3 (6) Australian Journal of Mechanical Engineering Vol 2, No.2 Since 1935 ... because quality matters 10 Clay Place Ph: +61 2 8818 0222 Eastern Creek NSW 2766 Fax: +61 2 9620 1850 www.hobson.com.au Hobson Engineering Co Pty Ltd A.B.N. 38 000 289 958 “Mechanisms and prevention of vibration loosening in bolted joints” – Fernando 3 the de cit between tightening and loosening torque T = Fb .D.K (7) is independent of the fastener diameter, it is better where the geometry of the joint is as shown in Figure to use a larger diameter fastener for an application 1. subject to signi cant vibration. Similarly, increasing thread angle (α) will increase both break-loose and installation torque if all the other parameters are kept constant. Therefore a “buttress” thread (α=0°) will loosen easily compared to a metric thread (α=30°). The break-loose torque (Tp) increases linearly with the pre-tension load at a rate lower than the increase of the tightening torque. Once the possible magnitude of the loosening torque anticipated during the life- span of the bolted joint is estimated, a minimum pre-tension load can be determined to prevent vibration loosening without using any additional locking devices. The above analysis does not take into account any break-loose torque component due to thread damage or plastic/elastic deformation of thread. The analysis is only a first order (linear) analysis. When the Figure 1: Geometry of a typical bolted joint fastener is tightened closer to the yield load, local (left hand thread). plastic deformation occurring at the threads will incorporate further break-loose torque. When an installation torque (initial tightening torque) Now that we have some understanding of the break- of T is applied on the bolted joint the resulting bolt i loose torque or the torque preventing loosening, it pre-tension force F will produce a clamping force i is opportune to investigate the mechanisms of F between the joint members when the joint is free i loosening. from external loads. For a non-locking fastener, this pre-tension force Fi will produce a break-loose torque T given by; p 3 LOOSENING MECHANISMS ⎡ − p r μ r μ ⎤ = + t t + b b Tp Fi .D.⎢ ⎥ There are several theories on the mechanisms of ⎣2π D D cosα D ⎦ (8) loosening in a vibratory environment.1 Tp = Fi .D.(−K1 + K2 + K 3 ) (9) 3.1 Mechanism of a vibratory conveyor This Tp will be the initial torque required to loosen the joint. The above break-loose torque (Tp) will be One theory proposes that the bolt loosening smaller than the installation torque (Ti) by amount: mechanism is similar to the mechanism of a vibratory ⎡ p ⎤ conveyor transporting a particle up a ramp. The − = static friction associated between the particle and Ti Tp Fi .⎢ ⎥ ⎣π ⎦ (10) the ramp surface and the inertia forces developed by particular vibration mechanism will drive the This indicates that the break-loose torque for a particle up the ramp. The vibration mechanism coarse threaded fastener will be smaller than that causes an overall upward (along the ramp) inertial for a ne threaded fastener if everything else remains force larger than the downward force on the particle. the same. In fact, the break-loose torque (T ) will p When the upward inertial force is larger than the p decrease linearly with the pitch ( ) of the fastener. resultant of gravitational force and the static friction As is well known in the industry, fine threaded the particle will travel upwards.