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- 1. INTERNATIONALMechanical Engineering and Technology (IJMET), ISSN 0976 – International Journal of JOURNAL OF MECHANICAL ENGINEERING 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME AND TECHNOLOGY (IJMET)ISSN 0976 – 6340 (Print)ISSN 0976 – 6359 (Online) IJMETVolume 4, Issue 2, March - April (2013), pp. 141-151© IAEME: www.iaeme.com/ijmet.aspJournal Impact Factor (2013): 5.7731 (Calculated by GISI) ©IAEMEwww.jifactor.com NOMINAL DIAMETER, CLAMP LENGTH AND THREAD PITCH ANALYSIS FOR BOLT PRELOAD AUGMENTATION Satish S. Kadam1, S. G. Joshi2 1 (Associate Professor, Mechanical Engineering Department, BharatiVidyapeeth Deemed University College of Engineering, Pune 411043, Maharashtra (India) 2 (formerly Professor in Department of Mechanical Engineering, Walchand College of Engineering, Sangli, Maharashtra, India) ABSTRACT Threaded fastening is used mainly for fastening together mechanical parts. Compared to other types of jointing methods such as adhesion, welding, brazing and pressure insertion, threaded fastening has a unique characteristic that elastic energy is built up inside the joint members. Tension in the bolt and compression in the fastened parts are created as a product of action and reaction. These forces can make the joint less susceptible to fatigue and loosening when external load is applied or internal pressure is increased. Since the torque applied to a fastener must overcome all friction before any loading takes place, the amount of friction present is important. It is seen that approximately 50% of the torque applied will be used to overcome bolt head-bearing friction and another 35% to overcome the thread friction and approximately 5% is consumed by prevailing torque. Thus only 10% torque is available to produce clamping force. In this paper, an analysis is presented to study the effect of various parameters such as clamp length, nominal diameter and thread pitch on the preload required for maintaining joint integrity. The suggested design guidelines are useful for proper selection of threaded fasteners used in different assemblies of structures, machine elements etc. Keywords : Bolted Joints, Preload Augmentation 141
- 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEMEI. INTRODUCTION A screw thread is an extension of one of the basic machines, the inclined plane,that has been wrapped around a shaft. When the thread is turned, it moves the mating partor nut up the inclined plane. When increased turning force or torque is applied to theshaft, the force exerted on the nut is increased. This force creates a tension in the bolt,which clamps the mating parts together. Preload is the technical term for the tensioncaused by tightening the fastener that holds the assembled parts together. Generatingsufficient preload force is the key to strong and reliable bolted joints that will not loosenor break under load. Figure 1 shows the forces that act on a bolted joint. Bolted joint design is an iterative process. To make some design decisions thedesigner relies mostly on trial and error, past experience and personal judgment. Thedesigner is able to make better judgments regarding the effect of certain designparameters and decisions with the increase in his experience and knowledge. However, regardless of the size, application or operating parameters of a joint,following some steps which are commonly followed in practice are:1. Define the purpose of the joint: Define what the joint is designed to do, environmentalconditions, cost targets, size and operating parameters, desired life, critical nature,potential failure modes etc. involved in the purpose of the joint.2. Design the joint: Determine the layout of the joint, including joint members, size, shapeand material(s).3. Estimate service loads: The static and dynamic loads to be considered include weight,pressure, shock, inertial effects, thermal effects, etc.4. Define bolts to be used: With the joint geometry and service loads established, the boltsize, number and strength can be determined. Bolt selection should include material,diameter, thread pitch, length, tensile strength, head style, drive style, thread style,hardness and plating.5. Determine required bolt preload and clamping force: The minimum clamping forceshould be great enough to overcome vibration loosening, joint separation, slippage,fatigue, leakage and other similar type failures. Maximum clamp force should not begreat enough to cause bolt yielding, joint crushing, stress cracking, fatigue failure, tensilefailure or other similar failures in service.6. Determine tightening methods and assembly line accuracy: During assembly, there aredifferent fastener assembly methods and tightening strategies which must be considered.Among the potential tightening strategies and their preload accuracy are: Torque: ± 35 %,Torque-Angle: ± 15 %, Torque - to -Yield: ± 7 %7. Finalize joint design: At this point, it may be necessary to make changes in jointmaterial, bolt preload range, bolt selection, tightening methods, etc. depending upon whatwas determined during the other steps of the joint design process. 142
- 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Figure 1 Bolted jointII. TORQUE-TENSION RELATIONSHIP The torque required to turn the nut can be related to the axial load in the bolt by thefollowing formula: [1] T = Fi × d × K (1)Where,T = Torque required to develop desired bolt preloadFi = Bolt preload (Equivalent to clamping force FC)d = Bolt nominal diameter mmK = Nut Factorand, K = K 1 + K 2 + K 3 p rt × µ t rb × µ bK1 = ; K2 = ; K3 = 2× πd d cosα dK1 = Factor for torque contribution towards Joint compression and Bolt elongation (alsotermed as geometric factor)K2 = Factor for torque contribution for overcoming thread frictionK3 = Factor for torque contribution for overcoming bolt / nut under-head bearing friction under head 143
- 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME p r ×µ r ×µ ∴ T = Fi × d + t t + b b (2) 2 × π d d cosα d p = Thread pitchα = Half thread flank angle (π/6 for ISO thread)rt = Thread root radiusrb = Effective bearing radiusµt = Coefficient of friction between male and female threadsµb = Coefficient of friction between the bearing surfaces under the turning fastener head ornutAs we know; T = T1 + T2 + T3 (100% Torque)Where,T1 = Torque contribution towards Joint compression and Bolt elongationT2 = Torque contribution for overcoming thread friction N-mT3 = Torque contribution for overcoming bolt / nut under-head bearing friction p T1 = Fi × d × K 1 = Fi × d (3) 2× πd rt × µ t T2 = Fi × d × K 2 = Fi × d (4) d cosα rb × µ b T3 = Fi × d × K 3 = Fi × d (5) d To get the values of rt and rb it is necessary to calculate thread stress area (AS) and Bearingarea (AC) under nut or bolt head respectively. πAS = (d − 0.9382 × p )2 (6) 4 2 π d3 + d2 2 AC = − d1 (7) 4 2 d1 = Bolt hole diameter = d (for small clearance)d2 = Nut head diameter = 1.5 d (for standard hexagonal headed bolts)d3 = Fastener head outer bearing or bearing cone diameter = d2 + L tan 300 = 1.5 d + L tan 300Where, L = Clamp length 144
- 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME π∴ AC = 16 [5d 2 0 2 + 6 d L tan 30 + L tan 30 2 0 ] 2 2∴ A C ≈ d + 0.68 d L + 0.065 L (8)For comparing the performance of different bolted joints, the analysis of the effect of variousparameters such as coefficient of friction, clamp length, nominal bolt diameter, pitch etc. isimportant. So the calculations are made for M12×1.25 size bolts which are commonly used innumber of engineering applications. On the basis of such an analysis the joint parameterswere suggested to obtain desired preload.For M12×1.25 bolts, d = 12 mm; p = 1.25 mm; α = 300Assuming, Clamping length, L = 30 mmPutting above values in equations (6) and (8) one can get, πAS = [d − 0.9382 × p ]2 = π × rt2 4 π = [12 − 0.9382 × 1.25]2 = 92.0717 mm 2 4from which rt = 5.4136 mm 2 2A C ≈ d + 0.68 d L + 0.065 L = π × rb2 = 12 + (0.68 × 12 × 30 ) + 0.065 × 30 2 ( 2 ) = 447.3 mm 2from which rb = 11.9323 mmThe most important parameter is preload (Fi) produced by tightening torque (T). Thetightening torque (T) depends mainly upon thread friction and bearing friction. In thefollowing sections, the bolt preload influencing factors such as friction, diameter, pitch andclamp length are discussed and analyzed in detail.III. FRICTION Lambert [6] states that the coefficient of friction depends on a number of factors suchas the method of manufacture and surface finish of the threads, the degree of lubrication andnature of the lubricant and the number of times the bolt has been previously tightened. Thechange in the coefficient of friction, under different conditions, can have a very significanteffect on the slope of the torque preload curve. Better the lubrication on the fastener the moreof the torque energy will be converted into actual clamping force. The type of lubricant usedhas a definite effect on how much of the torque is needed to overcome friction. As such inthis section, the effects of variation in coefficient of friction µtand µbare discussed.The values of T1, T2 and T3 based respectively on equations (3), (4) and (5) are obtained forM12×1.25 sizes as;T1 ≈ 0.2 × Fi (9)T2 = 6.2511 × Fi × µ t (10) 145
- 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEMET3 = 11 .9323 × Fi × µ b (11)∴ T = Fi (0.2 + 6.2511 µ t + 11.9323 µ b ) (12)The equation (12) shows that to develop the desired bolt preload (Fi), torque (T) is required,which is taken as 100%. As per VDI 2230, the values for µtand µbrange between 0.1 and 0.18. s To calculate the individual contributions of T1, T2 and T3 to give total torque T, putting theaverage value of µt= 0.14 and µb= 0.14 in equation (12) one obtains;T = Fi (0.2 + 0.8752 + 1.67 ) (13) The individual contributions of T1, T2 and T3 in the total torque T are 7.28418%,31.8739% and 60.8419% respectively. This shows that the bolt / nut under- under-head bearingfriction has the significant share in the total torque T (Fig.2 shows the distribution of T3 forall the cases). Similarly for different combinations of µtand µbthe percentage contribution ofT1, T2 and T3 in the total torque T have been calculated. Figure 2 Torque distribution against bearing friction and thread friction coefficientFor the case of minimum value of friction, i.e. µt= 0.1 and µb= 0.1;T = 2.01834 Fi (14)and for the maximum friction value, i.e. µt=0.18 and µb= 0.18,T = 3.473012 Fi (15) From the catalogue of standard fasteners, the recommended torque (T) is 88 N for Grade N-m8.8-M12×1.25. By putting these value in equations (14) and (15) respectively one can get the .extreme values of preload Fi, as 43600 N and 25360 N respectively, which shows the 146
- 7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEMEvariation of 18240 N (approximately 42%).The individual contributions of T1, T2 and T3 in the total torque T, for all the values of µt andµb in the range of 0.1 to 0.18 have been calculatedand its distributions are shown in Fig. 3. Figure 3 Individual torque distribution ureFigure 3 exhibits the scatter of torque values required to overcome the friction and developthe desired clamping force in the joint.IV. NOMINAL DIAMETER To ensure a Tensile strength of a bolt is represented by the material and size. T load Thecarrying capacity of a bolt is proportional to the square of the bolt diameter.The individual diameter.Thecontributions of T1, T2 and T3in the total torque T, for different values of nominal diameterare calculatedusing equations (3), (4) and (5), and the results are presented in Table 1 and usingFigure 4. Table 1 Torque Contribution for Bolt Diameters Bolt Diameter (%) Torque Contribution % Change % Change (d) mm in Bolt in T1, T2 and T3 T1 T2 T3 Diameter T1 T2 T3 8 9.5376 26.46 64.01 33.33 24 17.02 4.90 10 8.2333 29.53 62.24 16.66 11.96 7.39 2.20 12 7.2484 31.88 60.86 0 0 0 0 147
- 8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Figure 4 Torque contribution against bolt nominal diameterFigure 4 shows that, for smaller size bolts, increased capacity of torque T1 is available.Torque T1 is required to develop desired preload.V. CLAMP LENGTH From equation (8), it is seen that the clamp length ‘L’ has the significant effect on thebearing radius ‘rb’, which ultimately affects the value of T3, i.e. Torque contribution forovercoming bolt / nut under-head bearing friction. For analyzing the role of clamp length inthe tightening process, it has been varied from 20 to 50 mm in the step of 5 mm. Putting thesevalues in equation (8), bearing radius ‘rb’ is calculated. With the help of equations (3), (4) and(5), for µt= 0.14 and µb= 0.14; the torque contribution data of T1, T2 and T3 are calculated andthe results are presented in Table 2 and displayed in Figure 5. Table 2 Torque Contribution for Clamp Length Clamp (%) Torque Contribution % Change % Change Length in Clamp Length in T1, T2 and T3 (L) mm T1 T2 T3 T1 T2 T3 20 7.9461 34.77 57.28 0 0 0 0 25 7.5980 33.25 59.15 20 4.58 4.58 3.163 30 7.2842 31.87 60.84 33.33 9.08 9.08 5.8484 35 6.9989 30.63 62.37 42.85 13.53 13.53 8.16 40 6.7381 29.48 63.77 50 17.93 17.93 10.1821 45 6.4982 28.43 65.07 55.55 22.28 22.28 11.96 50 6.2765 27.46 66.26 60 26.6 26.6 13.55 148
- 9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Figure 5 Torque contribution against clamp lengthVI. PITCH The thread pitch is linked with the stress induced in the bolt. The cross-sectional areaused for stress calculations is the thread tensile stress area which is different for coarse andfine threads. The torque recommendations, therefore, are slightly higher for fine threads thanfor coarse threads to induce the same stress. Choice between coarse or fine screw threadsrequires a compromise or balancing of the advantages and disadvantages of each thread seriesfor the specific application.M12×1.25, 1.5 and 1.75 bolt sizes are taken for calculation. Corresponding values of pitch pare used in equations (3), (4) and (5), and with µt= 0.14 and µb= 0.14; the torque contributionsT1, T2 and T3 are obtained. The results are given in Table 3 and displayed in Figure.6. Table 3 Torque Contribution for Thread Pitch Pitch (%) Torque Contribution % Change % Change in T1, T2 and T3 (p) mm in Pitch T1 T2 T3 T1 T2 T3 1.25 7.2484 31.88 60.86 0 0 0 0 1.5 8.6326 30.96 60.41 16.66 16.03 2.90 0.75 1.75 9.9961 30.05 59.95 28.57 27.48 5.76 1.49 149
- 10. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Figure 6 Torque contribution against pitchVII. CONCLUSIONS(i) Controlling the friction between the mating surfaces must be the highest priority whileassembling the joint. Section III of the paper highlights the scattered nature of the torque-tension relationship arrived due to variation in the values of coefficient of friction.(ii) Bolt nominal diameter plays an important role in the strength consideration of thethreaded fastener, for a given joint. More number of slender (small diameter) bolts arepreferred, instead of a small number of large size bolts.(iii) With the increase in the joint length, the value of torque T1 (required for developingpreload) increases and potential loss of preload is decreased.(iv) The proper selection of bolt diameter and grip length (d/L = aspect ratio) is desired toachieve the required preload.(v) It is seen that large pitch values help to achieve more clamping force due to lesserfrictional resistance. However, the larger the pitch value, smaller is the effective tensile stressarea. In general, both coarse and fine threads are capable of providing sufficient strength formost applications.REFERENCES[1] J. H. Bickford, Design and analysis of bolted joints (Marcel and Dekker, 1995).[2] E. Dragoni, “Effect of thread pitch and frictional coefficient on the stress concentration in metric nut bolt connections,” Transactions ASME Journal OMAE, 116(1), 1994, 21-27.[3] J. F. Ferrero et. al. “Analysis of a dry friction under small displacements: applications to a bolted joint,” Wear, 256, 2004, 1135-1143. 150
- 11. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME[4] T. H. Lambert, “Effect of variation in the screw thread coefficient of friction on the clamping force of bolted connections,” Journal Mechanical Engineering Science, 4(4), 1962, 401-403.[5] A. F. Luscheret. al., “Increasing abutment friction at bolted joint interfaces through particle enhanced sealants,” International Journal of Vehicle Design, 29(3), 2002, 288- 306.[6] S. A. Nassaret. al., “Bearing friction torque in bolted joints,” STLE Tribology Transactions, 48, 2005, 69-75.[7] S. A. Nassaret. al., “Thread friction torque in bolted joints,” ASME Journal of Pressure Vessel Technology, 127, 2005, 387-393.[8] M. P. Oliver. (2003). Thread and under head friction. Fastener Technology. Available: http://www.delphi.com[9] W. G. Waltermire, “Coarse or fine threads,” Machine Design, 32(6), 1960, 134-140.[10] A. I. Yakushev, Effect of manufacturing technology and basic thread parameters on the strength of threaded connections (Pergamon Press, 1964).[11] Modelling design and control of flexible manipulator arms: A tutorial review, Proc.29th IEEE Conf. on Decision and Control, San Francisco, CA, 1990, 500-506. 151

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