DESIGN AND RELIABILITY INFLUENCES ON SELF-LOOSENING OF MULTI-BOLTED JOINTS

Transcription

1 Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal July 2016 Editors J.F. Silva Gomes and S.A. Meguid Publ. INEGI/FEUP (2016) PAPER REF: 6302 DESIGN AND RELIABILITY INFLUENCES ON SELF-LOOSENING OF MULTI-BOLTED JOINTS Shiva Kumar Manoharan (*), Christoph Friedrich Institute of Engineering Design- MVP, Department of Mechanical Engineering, University of Siegen, Germany. (*) ABSTRACT Research into self-loosening has till date focused on a few of the joint parameters of a onebolt-joint, namely, bolt preload/bolt force, clamp length, friction coefficients at different interfaces, length of thread engagement, diameter of bolt and that of head support. Recent developments have indicated that there is a significant difference in self-loosening behavior between laboratory tests with a single bolt joint without interface friction (Junker s test) and behavior of real component systems. This paper deals with design influences on selfloosening behavior of bolted joints which have so far been neglected, like, different clamped materials, difference between single and multi-bolted joints, influence of distance between the bolts, influence of component stiffness and influence of an offset load. Another part of this paper focuses on the reliability influence on self-loosening behavior. Bolted joints often have deviations between the designed/desired preload level and the actual clamping force due to friction deviations, seating loss, thermal/mechanical (over)loading, creep of materials etc. As a method to develop reliable and robust bolted joints for components, investigations have been performed with not only the maximum design preload but also minimum possible clamping force in application. Keywords: Self-loosening, multi-bolted joints, finite element analysis, design, reliability. INTRODUCTION Self-loosening is a predominant failure mode for bolted joints experiencing dynamic loads. Research into this phenomenon intensified since 1960s with the invention of Junker s test, where a single bolt under tension, with no interface friction, was subjected to transverse vibrations (perpendicular to bolt axis) using an eccentric cam drive that produced a sinusoidal displacement [2]. Such loading led to rotational loosening of the bolt without external aid, hence the term self-loosening. Self-loosening can lead to complete loss of tension in the bolt thereby compromising the joint integrity. The phenomenon is normally not integrated in design process for prediction in applications. Vibration test standard DIN has been created from Junker s test [20]. Research into self-loosening has till date focused mainly on the mechanism leading to rotational self-loosening and few of the joint parameters of a single bolt joint, namely, bolt force, clamp length, friction coefficients at different interfaces, length of thread engagement, diameter of bolt and that of head support [1, 2, 5, 7, 9]. The mechanism for self-loosening that is widely accepted is understood as follows: Due to transverse vibrations in the components that are clamped together, small relative displacements can take place in the components; this leads to bending of the bolt and contact instability (partial slipping of contact surfaces) in the

2 Symposium_17: Mechanical Connections head and thread region. Under the presence of these contact instabilities, the off torque from the pitch of the threads is sufficient to cause small rotations. Details of the mechanism can be found in literature like [1, 2, 6, 8] and published books [5, 18,19]. DIFFERENT METHODS FOR ASSESSMENT OF SELF-LOOSENING IN BOLTED JOINTS Several methods to analyze a joint for self-loosening failure have been presented by researchers in the past. This include analytical method using formulae, laboratory experiments in controlled environment and finite element analysis of a bolted joint. A few interesting analytical formulae and their comparison can be found in [13]. The general form for the analytical formulae that are available in the literature is as follows: s crit = f (bolt preload F P, clamp length l C, friction coefficient at bolt head µ H, stiffness of the bolt, radial clearance between the threads) Eq. 1 Where s crit is the relative transverse displacement of clamped components that leads to complete loosening of bolt preload. Based on their own research different researchers have presented different magnitudes of s crit [2, 3, 5, 7]. From the research findings of Koch, a criterion for analyzing a joint for self-loosening is when the gradient of the rotational loosening curve reaches 0.03 per load cycle in an FE (finite element) simulation within the first 10 load cycles [7]. This had been derived by statistically analyzing experimental work (with Junker s test stand) and simulations. However, for a given design task, it is difficult to assess the relative displacement between components (due to the material stiffness and geometric non-linearities). At best the designer has the knowledge of the forces and moments acting in different locations and directions, based on the preload that prevails in a bolted joint, these forces and moments may or may not cause relative displacements. Another important point worth mentioning is that the analytical formulae generally do not include a function of the pitch angle of threads (off-torque generation comes from threads), which theoretically would be a parameter based on the mechanism of self-loosening. Hence one can conclude that there needs to be further investigation in this regards. From experiments point of view, most popular is Junker s test stand which has also been adopted into standards such as DIN There are several limitations to this test setup, such as friction-less interface of clamped components [2], limited number of parameters that can be varied, influences from real component systems like more than one bolt in a joint and stiffness of clamped materials cannot be assessed directly. Most of all, the loading is a very ideal case of transverse loading whereas other types of loading such as torsional [16] and combination of axial and transverse [17] have also shown to produce rotational selfloosening. Another notable test stand is NAS [25] which produces impact loading on the bolt and nut combination mounted on a vibrating table. The best way to test a joint for self-loosening would be to test it at the component level with the loading from application. Summarizing the introduction, there are no concrete measures that will help a designer to predict the safety of a bolted joint against self-loosening. One useful method is that of simulations, where a complete component system can be analyzed three dimensionally with reduced efforts of analytical design and experiments. In this work several design parameters are assessed with finite element analysis and their influence on self-loosening behavior is discussed. Simulations are often time consuming in nature and several parameters of FEA

3 Proceedings of the 5th International Conference on Integrity-Reliability-Failure (finite element analysis) and numerical methods themselves can become influencing factors. A good solution to the self-loosening problem would be in the direction of analytical calculation such that designers have the chance to predict the phenomena in advance. Combination of experimental results and simulation results to bring up a modified analytical formula is a future need. SIMULATION OF ROTATIONAL SELF-LOOSENING IN BOLTED JOINTS In the last two decades, simulation of self-loosening behavior can be found in the literature. Most researchers have proposed simulations as an alternative to Junker s test and as a means to study the mechanism which normally cannot be realized from experiments without much efforts. For the simulation of rotational self-loosening, three dimensional helical threads must be modelled [4, 7, 8, 16]. Apart from this, the influence of various contact interfaces must be taken into account e.g. bolt head bearing surface, interface between clamped components, nut bearing surface and mating threads. A simple check of the joint model can be performed with comparing the bolt stiffness from the FE model to analytical calculation (e.g. from [19]). The behavior, in simulation, is found to be quite sensitive to the stiffness of bolt and to that of the clamped components [9]. In this work results are presented by using Abaqus 6.9 a commercial FE solver. For the right influence of stiffness, elastic-plastic material data is used. For realistic simulation, modelling the bolt head with the respective inclination of the bearing surface is important as it would determine the level of resistance against loosening moment at head. Fig. 1 - A FE model for simulation of self-loosening, here example of a single bolt joint. In Fig. 1 above, a cut section of a meshed model used to study the characteristics of selfloosening is shown. Some simplifications are made by neglecting the radius at head-shank transition region, neglecting the thread root radius and modelling a separate thread part which is attached with tie function to the bolt shank. This is done because the focus of the investigation is on the loosening behavior and not the stress distribution. In this work an M10 bolt is modelled according to DIN EN 1665 [21] with a pitch of 1.5 mm and 60 thread angle and 0.75 head bearing surface inclination angle. The threads are modelled as per DIN ISO 965 [22] with average values of tolerance combination 6g, 6H from DIN [23]. Clearance at the bore of clamped parts is set to 1 mm as per DIN EN [24]. Selective usage of reduced and fully integrated elements provides an optimal computation time. Mesh

4 Symposium_17: Mechanical Connections match technique was used in order to facilitate initial contact between the various contact regions. Surface-to-surface contact formulation with finite sliding and penalty algorithm for both normal and tangential contacts are used. When using penalty algorithm, care must be taken to define a small elastic slip factor in order to achieve exact stick-slip effects. Penalty algorithm is preferred here for its speed. Boundary conditions for the investigations are inspired from Junker s test. Preload is introduced in the form of a pretension section which is a built-in function of the FE package. Sensitivity analysis can be performed with varying amplitudes of transverse displacements in sinusoidal form to replicate the effects of vibration. An important assumption is that the process of self-loosening is quasi-static based on Junker s work from 1969 wherein the state of stick-slip and the number of transverse load cycles are the main influencing factors [2]. The critical output parameters monitored in this analysis are the preload F P, rotation at head of the bolt ϑ Lh and transverse force F Q causing the sinusoidal displacement. The major advantage of this method is that critical force levels can be established for different preload levels, hence providing an input for the designer to check his joint against the possibility of self-loosening. The term s crit has been defined as the minimum relative slip between the clamped components that sets up a constant loosening gradient of 0.03 per load cycle in the first ten cycles of simulation [7], the same is used in this work. This generally leads only to partial slip in the bolt head bearing surface [4, 6, 7, 8, 9]. Static friction coefficients are defined as 0.15 at head bearing surface, 0.07 at component interface and 0.2 at threads. Clamp length of the joint is 15 mm. RESULTS AND DISCUSSION In the last years, efforts have been redirected towards the design stage assessment of selfloosening [11, 12, 13]. Simulation method involving finite element analysis have been improved to predict and avoid self-loosening in the design phase of real components. The principle is to apply a displacement load (sinusoidal) to the structure and evaluating the resulting behavior of the bolts. Displacement load is preferred because from the mechanism, a relative movement of the clamped components is essential in causing self-loosening. In this work a comprehensive study is performed with single bolted joints and multi-bolted joints (with two bolts) to assess the parameters that are additionally important from design perspective for components. Self-loosening behavior of multi-bolted joints The prediction for self-loosening with FEA involves conducting sensitivity analysis of a single bolt joint in order to determine the smallest (critical) amplitude of transverse vibration that may cause complete loosening of the joint. However significant difference is observed in the behavior of a single bolt joint and a multi-bolted joint as shown in Fig. 2. The source for the difference in behavior for the same amplitude of relative transverse displacement comes from the combined preload of two bolts, the deformation behavior of the clamped parts and the stiffness of the clamped parts in the transverse direction under the influence of bolts clamping the plates. Due to this the transverse load is unable to produce the required shear under the bolt head that corresponds to the single bolt model as shown in Fig. 3. There also exists a difference in the maximum transverse force (F Qmax ) that is required to create the displacement of 0.2 mm due to the fact that the force only needs to be high enough to cause the deformation at the point of loading and not till the other end of the joint

5 Proceedings of the 5th International Conference on Integrity-Reliability-Failure Fig. 2 - Difference in self-loosening behavior of a single bolt joint (a) and a multi-bolted joint (b1, b2) with aluminum clamped part (red) and steel nut component (green) subjected to same amplitude of transverse vibration S Qmax = 0.2 mm (in the form of load cycles with sinusoidal displacement) here the clamp length is 10 mm [13]. Fig. 3 - Shear force under bolt head for a single bolt joint (a), multi bolted joint (b1) and (b2) corresponding to Fig. 2 above. Influence of clamped material on self-loosening behavior Light weight components are often vibration critical in application. In this section a comparison is made between the self-loosening behavior of bolted joint with steel and aluminum clamped part during the search for the critical relative displacement of component from simulation, s crit. As discussed earlier, the search for the critical relative displacement involves varying the amplitude of displacement such that the resulting gradient of selfloosening achieves or crosses 0.03 /load cycle. Regarding this criterion, when the clamped part is made of steel, s crit = 0.18 mm and when it is made of aluminum it is s crit = mm. However, the transverse force value that causes the critical self-loosening gradient are similar

6 Symposium_17: Mechanical Connections This means that that a value of critical displacement calculated by analytical formulae does not hold true for different clamped materials. The comparison can be seen in Fig 4. The reason for the difference could be associated to the elastic strain energy that is absorbed by aluminum to deform due to the presence of the bolt force, hence a greater relative displacement is required in order to produce sufficient shear force under the bolt head. Moreover, for aluminum clamped part with lower strength and modulus of elasticity, there can been seen a greater embedment of the bolt head into the clamped part (Fig. 5), this gives a small resistance to self-loosening. Fig. 4 - Evaluation to determine s crit for a single bolt joint, with change in material of the clamped part. M10 bolt according to dimensions from DIN 1665 with 25 kn preload via a pretension section and clamp length of 15 mm. Fig. 5 - Embedment of bolt head (modelled with bearing angle of 0.75 ) into clamped part (modelled flat) with aluminum and steel material under a preload of F P = 25 kn

7 Proceedings of the 5th International Conference on Integrity-Reliability-Failure Influence of component stiffness/geometry on self-loosening behavior of multibolted joints From the previous section, a significant influence of the stiffness of the clamped part can be seen on self-loosening behavior of bolted joints based on material of clamped part. With this motivation, an extended evaluation with a multi-bolted joint was conducted. Two bolts of M10 according to DIN EN 1665, separated by a distance of seven times the nominal diameter (7D) was modelled to simulate self-loosening behavior for assessment of geometrical stiffness. Two geometries of the clamped part are assessed, one with rectangular plates (stiff component) and another with a small portion of the clamped parts cut away resulting in C like plates (reduced stiffness). For comparison, both geometries are loaded with the same amplitude of relative transverse displacement between components, s Q = 0.2 mm (which is greater than s crit from previous section). The same test is performed for steel clamped part and aluminum clamped part. The results are shown in Fig. 6 and 7. For both materials, sum of the rotational loosening for two bolts increases when the stiffness of the component in between the bolts reduces. On the other hand, for the aluminum clamped part, the s crit from previous section was = mm, even though the s Qmax in this section is greater than s crit, only bolt 1 (B1) reaches the critical gradient but not bolt 2 (B2). This is due to the stiffness of the clamped part and the energy absorbed for elastic strain between the two bolts in the rectangular plates. Hence when reducing this cross section, the C plates show increased loosening in both B1 and B2 for the aluminum plates. However, for steel plates with reduced cross section, the stiffness goes down and the force absorbed for deformation is higher hence B1 rotates more and B2 rotates less than the rectangular plates. Fig. 6 - Influence of geometrical stiffness on self-loosening behavior of a multi-bolted joint with two M10 bolts according to DIN EN 1665 and aluminum clamped part. Clamp length here is 15 mm

8 Symposium_17: Mechanical Connections Fig. 7 - Influence of geometrical stiffness on self-loosening behavior of multi-bolted joint with two M10 bolts according to DIN EN 1665 and steel clamped part. Clamp length here is 15 mm. Influence of distance between the bolts on self-loosening behavior of multi-bolted joints Taking the investigation with multi-bolted joints further, another variation is made with distance between the bolts. For the C-plates, two distances were evaluated, four times the nominal diameter (4D) and seven times the nominal diameter (7D). From Fig. 8 and Fig. 9, it can be seen that reducing the distance between the bolts, increases the rotational loosening of bolt 2 (B2), whereas the rotational loosening of bolt 1 (B1) remains almost the same. This means that the influence of the stiffness reduces with decreasing distance between the bolts in a multi bolted joint. As a result, the force absorbed for elastic strain is less, the transmission to second bolt is higher. This behavior can be better understood with example of an imaginary spring with length l, thickness t and a very low stiffness, connecting the two bolts B1 and B2. When l =, all the force pushing B1 towards B2 will be utilized for deflection of the spring, no force will be transferred to B2. At l = 0, force on B1 = force on B2. When > l > 0, some amount of energy is absorbed for elastic strain of the spring before part of the force is transferred to B2. This behavior leads to an increase in the deflection of bolt head about the bolt axis in the 4D model as compared to the 7D model as shown in Fig. 10. The reason for increase in bolt head rotation of B2 in the 4D model is the presence of a torsional moment in addition to the transverse load due to the geometry of the clamped part

9 Proceedings of the 5th International Conference on Integrity-Reliability-Failure Fig. 8 - Influence of distance between the bolts on self-loosening behavior of the multibolted joint with C-plates from previous section and aluminum clamped part Fig. 9 - Influence of distance between the bolts on self-loosening behavior of the multibolted joint with C-plates from previous section and steel clamped part

10 Symposium_17: Mechanical Connections Fig Deflection of bolt head about the bolt axis for the two distance variations between the bolts with aluminum clamped part. Influence of offset load on self-loosening behavior of multi-bolted joints In this section another experiment is performed by considering an offset loading to the C- plates via a small lever arm at 20 mm above the plane of bolt head bearing surface. Aluminum has been defined as the material for the clamped component. Loading is the same displacement based loading of s Qmax = 0.2 mm. The results are shown in Fig. 11. It can be seen that no self-loosening has occurred in the joint. The reason can be associated with the strain energy absorbed by the by the lever arm itself to deform, hence there is no significant slipping of the components that takes place. Additionally, when the clamped part deforms, the transverse load generates a bending moment which leads to higher pressure in the component contact; therefore, more component deformation and less relative movements of surfaces in contact. This can be seen in the global deformation behavior in Fig

11 Proceedings of the 5th International Conference on Integrity-Reliability-Failure Fig Comparison of self-loosening angles when loading is in plane of the bolt head contact surface and when loading is at an offset of 20 mm, both variation with aluminum clamped part. Fig Global deformation behavior of the clamped parts for studying the influence of load offset on self-loosening behavior of the multi bolted joint with C-plates

12 Symposium_17: Mechanical Connections Reliability influence on self-loosening behavior of multi-bolted joints Bolted joints often have deviations in assembly preload due to frictional stability, tightening torque and other deviations in assembly. Once assembled, further deviations can come from effects like seating of roughness, thermal and mechanical (over-)loading. A detailed view of different reliability aspects can be found in [10, 15]. A typical range of deviation of preload resulting from relaxation of bolted joints is 15% to 40% of the design preload for light weight components tightened close to the yield point [10]. Hence it is essential to perform the investigation with not only the maximum assembly preload but also the worst case of minimum clamping force in application. To illustrate the influence of these reliability issues on self-loosening behavior, a simple test is carried out by taking a multi-bolted joint with dissimilar preload levels in the bolts. For the C-plates, two simulations are compared in Fig. 13, one with preload F P1 = F P2 = 25 kn and another with F P1 = 25 kn and F P2 = 15 kn. The results show that for a multi-bolted joint, reduction in preload of even one bolt can lead to greater self-loosening in both the bolts. This could be attributed directly to the decrease of total preload in the joint which thereby makes self-loosening to proceed at a higher rate as preload determines the main resisting torque at bolt head that needs to be overcome by thread off-torque for self-loosening. Fig Influence of reliability of preload on the self-loosening behavior in the multi-bolted joint with C-plates and two M10 bolts according to DIN EN CONCLUSION AND OUTLOOK Self-loosening behavior of multi-bolted joints show significant differences from that of a single bolt joint. Additionally, factors like material of clamped part, geometry of clamped part (stiffness and load offset), distance between the bolts and deviations in bolt preload can lead to difference in the self-loosening behavior of the joint. Following points can be concluded from above: Assessment of self-loosening for a single bolt joint is not transferrable directly to multi-bolted joints

13 Proceedings of the 5th International Conference on Integrity-Reliability-Failure Lightweight materials like aluminum can give a better resistance to self-loosening than stiff materials like steel due to their ability to store higher strain energy. Distance between the bolts must be assessed for obtaining the right combination of material and resistance to self-loosening based on geometry of clamped parts. Geometric shapes of the clamped components and load offsets can be crucial in determining the self-loosening behavior of a multi bolted joint. Deviations of preload in application must be assessed beforehand in order to guarantee a joint safe against self-loosening. Integrity of a multi-bolted joint, against self-loosening failure, is subject to design and reliability influences. It is also quite clear that analytical formulae are not sufficient to encompass the vast influences of design. For component systems with particular load cases, a simple laboratory test with one bolt, does not necessarily guarantee the safety against selfloosening. The method of simulation with finite element analysis is robust enough to assess components for individual load cases, design and reliability influences. For the future, a need exists for enhancement of analytical methods for prediction of self-loosening which could result from combination of assessments from FE simulation and laboratory experiments. REFERENCES [1]-Goodier, J. N., Sweeney, R. J., Loosening by vibration of threaded fastenings, New York, American Society of Mechanical Engineers, pp , [2]-Junker, G.H., New criteria for self-loosening of fasteners under vibration, Society of Automotive Engineers, pp , [3]-Blume, D., Wann müssen Schraubenverbindungen gesichert werden? From: Verbindungstechnik, Vol. 1, pp , Ingenieur Digest Verlag, [4]-Pai, N. G., and Hess, D.P., Three dimensional finite element analysis of threaded fastener loosening due to dynamic shear load, Engineering Failure Analysis, vol. 9, pp , [5]-Sakai, T., Bolted Joint engineering: Fundamentals and applications, Berlin, Beuth Verlag GmbH, [6]-Koch, D., Friedrich, C., and Dinger, G., Simulation of rotational self-loosening of bolted joints, Proceedings of NAFEMS Seminar, April [7]-Koch, D., Beitrag zur numerischen Simulation des selbsttätigen Losdrehverhaltens von Schrauben-verbindungen. Dissertation, Shaker Verlag, Aachen, [8]-Dinger, G., Friedrich, C., Avoiding self-loosening failure of bolted joints with numeric assessment of local contact state, in Engineering Failure Analysis, vol. 18, pp , [9]-Dinger, G., Ermittlung des selbsttätigen Losdrehens bei Mehrschraubenverbindungen. Dissertation, Shaker Verlag, Aachen, [10]-Friedrich, C., Hubbertz, H., Engineering calculation of threaded fastening systems considering deviations in advanced design, Proceedings of IMECE 2012, paper no , ASME, Houston,

14 Symposium_17: Mechanical Connections [11]-Manoharan, S.K., Friedrich, C., Self-loosening of three similar bolted joint designs using finite element analysis, Proceedings of International Conference on Automotive Materials & Manufacturing, SAE International, paper no , Pune, [12]-Manoharan, S.K., Friedrich, C., Self-loosening behaviour of multi-bolted joints requirements for engineering design in real applications, Proceedings of the 6 th International Conference on Manufacturing, Machine Design and Tribology, paper no. TH-A-1-4, Okinawa, [13]-Guggolz, D., Manoharan, S.K., Friedrich, C., Avoiding of self-loosening in components with multiple screw joints, Proceedings of IMECE 2015, paper no , ASME, Houston, [14]-Hareyama, S., Manabe, K., Nakashima, M., The absolute evaluation and loosening life prediction method on self-loosening of bolted joints during actual machine operation, Proceedings of the IMECE 2012, ASME, paper number 86415, Houston, [15]-Hareyama, S., Manabe, K., Nakashima, M., Advantage of elliptical confidence limit method for bolted joint tightening reliability, Proceedings of the IMECE 2015, ASME, paper number 50729, Houston, [16]-Takashi Yokoyama, Marten Olsson, Satoshi Izumi, Shinsuke Sakai, Investigation into the self-loosening behavior of bolted joint subjected to rotational loading, Engineering Failure Analysis, vol. 23, pp 35-43, [17]-Eccles, W., Sherrington, I., Arnell, R.D., Towards an understanding of the loosening characteristics of prevailing torque nuts, Proceedings of the Institution of Mechanical Engineers, Journal of Mechanical Engineering Science, 224 (C2), pp , [18]-Friedrich, C., Designing fastening systems, in - Modelling and simulation for material selection and mechanical design, 1st ed., Marcel Dekker, pp , New York, [19]-Bickford, J.H., An introduction to design and behaviour of bolted joints. 4th ed., Marcel Dekker, [20]-DIN 65151: Aerospace series - Dynamic testing of the locking characteristics of fasteners under transverse loading conditions (vibration test). Beuth Verlag, Berlin, [21]-DIN EN 1665, Hexagon bolts with flange, heavy series, Beuth Verlag, Berlin, [22]-DIN ISO 965, ISO general purpose metric screw threads - Tolerances - Part 1: Principles and basic data, Beuth Verlag, Berlin, [23]-DIN 13-20: ISO general purpose metric screw threads - Part 20: Limits of sizes for coarse pitch threads with the prefered tolerance classes; nominal sizes from 1 mm to 68 mm. Published by Beuth Verlag, Berlin, [24]-DIN EN 20273, Fasteners, clearance holes for screws and bolts, Beuth Verlag, Berlin, [25]-MIL-STD-1312B, Military Standard Fastener Test Methods, Department of Defense, Washington,