Factors Affecting the Tightening Characteristics of Bolts A factorial experiment was performed to analyze the tightening characteristics of bolt-nut-washer assemblies. Results were obtained by a testing machine designed for the purpose by A. Bray and R. Levi

ABSTRAcT--A study on the tightening characteristics of bolt-nut-washer assemblies was undertaken after a preliminary literature survey showed different opinions to exist on the effect of several commonly encountered factors on the torque-tension relationship. The test program included tightening bolts up to the yield point under a planned series of combination of factors, and recording nut-tightening torque, bolt torque and tension. The main factors tested were: (a) Plating of the mating surfaces of bolt, nut and washer (b) Lubrication of the interfaces. Among the subsidiary factors considered were the hardness and yield stress of the materials and the class of fit of the threads. The tests were planned and analyzed with statistical techniques in order to obtain estimates of the effects of each factor and the more i m p o r t a n t interactions (singled out of the total number in a series of pilot tests) as well as of the errors to be considered for the tests of significance. The analysis was carried out with mathematical and graphical methods giving accurate results in an easily understandable form from a reasonably small number of experimental data. The isolation of the main effects and interactions was achieved with no loss of general applicability of the results, taking advantage of the peculiar properties of the factorial experimental design adopted. A comparison between the torque wrench and the turnof-nut method of bolt tightening is made in terms of closeness of bolt tension control. A simple bolt-testing machine was built for the tests. A motor-driven wrench with a strain-gage bridge measuring the input torque tightened the nut a t low speed while a two-component strain-gage transducer measured bolt torque and tension. Provision was also made for measuring the angle of rotation of the nut and the torsion of the bolt's shank.

Introduction T h e p r o p e r t i g h t e n i n g o f t h r e a d e d f a s t e n e r s is k n o w n t o p l a y a n i m p o r t a n t p a r t in t h e i r p e r f o r m ance under both static and fatigue conditions. In the friction-grip-bolted structural joints, the l o a d b e t w e e n a s s e m b l y m e m b e r s is t r a n s m i t t e d A. Bray and R. Levi are associated with Istitnto Dinamometrico Italiano, Torino, Italy. Paper was presented at Second S E S A International Congress on Experimental Mechanics held in Washing~n, D. C. on September 28-October 1, 1965.

by the friction produced by the bolt-clamping a c t i o n . A s n o s h e a r o r b e a r i n g o f t h e b o l t s is u s u a l l y r e l i e d u p o n for t r a n s m i t t i n g t h e l o a d , 1 bolt tension controls directly the maximum service l o a d . I t h a s b e e n p r o v e d 2 t h a t , if f a i l u r e in t h e b o l t h a s n o t o c c u r r e d d u r i n g t i g h t e n i n g , i t will n o t o c c u r in service; t h e r e f o r e , t h e b e s t p e r f o r m a n c e s a r e t o b e o b t a i n e d f r o m b o l t s s t r e s s e d as close a s p o s s i b l e to the condition of failure. T h e m a i n p r o b l e m in b o l t t i g h t e n i n g , h o w e v e r , is n o t o n l y t o i n d u c e a h i g h t e n s i o n , b u t also t o d o so c o n s i s t e n t l y . W i t h a t i g h t e n i n g t e c h n i q u e w h i c h l e a d s t o h i g h l y s c a t t e r e d r e s u l t s , no full u s e o f t h e c l a m p i n g c a p a b i l i t y o f t h e b o l t s c a n b e m a d e if t h e n u m b e r o f f a i l u r e s is t o b e k e p t low. T h e p o t e n t i a l efficiency o f t h e b o l t e d c o n n e c t i o n is t h u s l o w e r e d . T h e c o n t r o l o f b o l t t e n s i o n calls f o r a k n o w l e d g e o f w h i c h f a c t o r s , i f a n y , e x e r t a s i z e a b l e influence o n bolt performance during tightening. The literature a v a i l a b l e in t h i s field s h o w s t h a t no g e n e r a l a g r e e ment has yet been reached about the importance of the most commonly encountered factors. L u b r i c a t i o n is c o n s i d e r e d b y s o m e a u t h o r s 3 as h a v i n g a l m o s t no effect on t h e u l t i m a t e l o a d , w h i l e a m a r k e d i n f l u e n c e h a s b e e n r e p o r t e d elsewhere. 4 I n d u c e d t e n s i o n s l a r g e r b y s o m e 60 p e r c e n t t h a n those predicted by the relevant specifications have been caused by lubrication, 1while a (dimensionless) coefficient, l a r g e l y d e t e r m i n i n g t h e t o r q u e - l o a d r e l a t i o n s h i p a n d r e l a t e d t o t h e f r i c t i o n , is i n d i c a t e d a s h a v i n g t h e v a l u e o f 0.2 in o n e s p e c i f i c a t i o n , 5 0.16 in a n o t h e r , 6 w h e r e a s v a I u e s a s h i g h a s 0.29 h a v e b e e n measured. 7 S u r f a c e t r e a t m e n t s , s u c h as c o r r o s i o n - p r o t e c t i n g p l a t i n g s , a r e also r e p o r t e d t o h a v e effects n o t t o o c l e a r l y defined. In one instance, the scatter of experimental results w a s so l a r g e . . . " t h a t c o n f i d e n c e in t h e t e s t i n g w a s l o s t . ''4 I n a n o t h e r p a p e r , t h e u t m o s t c a u t i o n is a d v i s e d t o p l a t e d - b o l t users; 8 a n d excessive s c a t t e r h a s also b e e n t r a c e d t o t h e p l a t i n g o f b o t h n u t a n d stud threads. 9 These indications, however scanty, seemed to p o i n t t o a s i t u a t i o n in w h i c h t h e effects a r e so m i x e d

Experimental Mechanics I 409

Fig. l(b)--Bolt-tightening system and transducers

Fig. l(a)--General view of the testing machine

RECORDING OSCILLOGRAPH 7

VARIABLE RELUCTANCE

CARRIER AMPLIFIER

TRANSDUCER 8

REDUCTO IN

I TORQUE I ~

410 I August 1966

9

6

[----~,_._A~ :FZ

JWRENCHA N D ~ j

Fig. 2--Block diagram of testing machine and instrumentation

AMPLIFIER

I

~

TRANS4DUCER

I FORCE TRANSsDUCER

k

I I

Fig. 3--Section view of bolt-tightening system

to be almost hopelessly inextricable unless a syst e m a t i c procedure of analysis is used. T h e recent advances in experimental statistics will here be shown to provide a simple and useful procedure of planning and analyzing multi-factor experiments a d e q u a t e for dealing with this kind of problem. T h e trend toward the turn-of-the-nut m e t h o d of tightening suggested to us t h a t a comparison m i g h t profitably be made, with these statistical techniques, between the a b o v e - m e n t i o n e d m e t h o d and the older one based on the use of the torque wrench. T h e comparison will be m a d e in t e r m s of closeness of control of induced bolt tension and safety against failure during tightening. A graphical m e t h o d will be used, based upon the cumulative-distribution function approach.

Experimental Equipment A testing machine was designed for the purpose of measuring the torque applied to the nut, the absorbed torque, induced bolt tension and angle of rotation of nut. A sensitivity as high as possible and a reasonable accuracy had to be obtained b y m e a s u r e m e n t s in order to separate small effects of the p a r a m e t e r s under investigation. Since an experimental re-

search p r o g r a m on bolts usually entails quite a large n u m b e r of tests, the testing machine m u s t be simple and the d a t a collected in an easy m a n n e r so t h a t their interpretation can be immediate. W i t h such aims in mind, we concluded t h a t the mentioned mechanical quantities had to be transformed into electrical signals and t h e n recorded, being sure t h a t each signal is not influenced b y quantities other t h a n t h a t to be measured. T h e pictures of a general view of the testing machine and a detail of the bolt-tightening s y s t e m and transducers are given in Fig. 1 (a and b) and the block d i a g r a m in Fig. 2. T h e operation conditions are the following: a torque wrench(3, Fig. 3) is powered b y a m o t o r (1, Fig. 2) through a speed reducer (2) (two worm-gear drives in series, the first having a ratio 10 : 1 and the second one 70 : 1). T h e wrench is connected to the driving shaft b y m e a n s of a universal joint and a splined shaft which allows the wrench to m o v e along the longitudinal axis. T h e wrench screws the n u t of the bolt which is m o u n t e d between two parallel plates, one of which (10, Fig. 3) is screwed to a cylindrical b a r (12), where the head of the bolt is located, and the other (11) is fixed to a f r a m e (13) connected to the machine bench (Fig. 3). I n order to avoid a n y friction to the shank, a ball bearing (14) is m o u n t e d on the

Experimental Mechanics [ 411

+

Fig. 4 (a)--Bridge circuit of absorbed torque. (b)-Bridge circuit of induced tension

sl

$2

(a)

SI

$2

(b)

Fig. 5--Recorded curves showing: angle of rotation (1), applied torque (2), absorbed torque (3) and induced tension (4)

Fig. 6--Recorded curves showing bolt chatter

f r a m e on the underside of the p l a t e ( l l ) . During tightening, the cylindrical bar (12) reacts to applied torque and tension; b y measuring such reactions, it is possible to obtain the absorbed torque (4, Fig. 2) and tensile load (5) applied to the bolt. T h e machine c o m p o n e n t s were dimensioned for testing bolts of 10-mm nominal diameter. B y changing some of such components, bolts up to 24m m nominal d i a m e t e r can be tested.

412 ] August 1966

T h e applied torque is measured b y strain gages (Tepic B L 1-120 Huggenberger, Switzerland) cemented to the shaft of the tightening wrench at 45 deg with respect to its axis. T h e absorbed torque and induced tension are also measured b y strain gages cemented to the cylindrical bar. Strain gages of each transducer are connected in a W h e a t s t o n e bridge circuit. Besides 4 equal wire gages (PS-5, 120 Tokio Sokki K e n k y u t o , J a p a n ) , applied at 45

deg, some a r m s of the bridge circuit for the absorbed torque contain parallel and series resistors [Fig. 4 (a) ] b y which misalignment of opposite gages and variations of gage factor of each gage are corrected when bending and tension are acting on the transducer. Besides 4 equal wire gages (Tepic B L 1120), applied along the longitudinal axis of the transducer, some a r m s of the bridge circuit measuring t h e induced tension contains also one series and one parallel resistor to correct for the variation of gage factor of each gage. T w o other wire gages (PS-5, 120) [Fig. 4 (b)], applied along an almost longitudinal axis, introduce on one a r m the necessary correction due to misalignment of gages when torque is acting on the transducer. B y m a k i n g these corrections, the absorbed torque and induced tension are measured within a n accuracy of 1 percent. T h e bridges are connected to a carrier amplifier (C.E.C. t y p e 1-1271, USA), including a regulated power supply, and t h e n to a recording oscillograph (O.T.E. Galileo, I t a l y ) . T h e angle of r o t a t i o n of the torque wrench is measured b y a contactless variable-reluctance t r a n s d u c e r (8, Fig. 2) (Philips, Holland), utilizing 3 ferromagnetic elements which are m o u n t e d on the shaft a t the o u t p u t of the first w o r m - g e a r drive. T h e o u t p u t signal is fed to a channel of the oscillog r a p h (7) t h r o u g h an amplifier (9). T h e calibration of the torque wrench and absorbed-torque transducers is m a d e b y a dead-load and lever s y s t e m and the calibration of the tension t r a n s d u c e r is m a d e b y loading the cylindrical b a r in compression and measuring the load b y a loop elastic device (Amsler, Switzerland). T h e load is t r a n s m i t t e d to the transducer t h r o u g h the elastic device b y a screw-pushing system, m o u n t e d on the f r a m e (13, Fig. 3). T h e m a i n characteristics of the testing machine and oscillograph are the following: Angular speed of torque 1.42 rpm wrench Output of torque-wrench 0.146 m v / v kgm (0.194 kgm/mm) * transducer Output of absorbed torque 0.162 m v / v kgm (0.092 kgm/mm) transducer Output of induced-tension 0.362 mv/v 1000 kg (48 transducer kg/mm) 14,300 k g / m m Stiffness of frame (13, Fig. 3) Speed of oscillograph paper 5 mm/sec Number of pulses of trans- 210/rev. ducer (8, Fig. 2) Time base of the paper 1 sec/div. I n Fig. 5, representative results f r o m one bolt are given. This figure shows the b e h a v i o r of the wrench torque (curve 2), absorbed torque (curve 3), induced tension (curve 4) and angle of r o t a t i o n (curve 1) during bolt tightening. While the wrench screws the nut, the applied torque increases and, in the m e a n t i m e , the absorbed torque and induced tension increase. D u e to a c c o m m o d a t i o n of the mechanical components, the initial p a r t of the cycle is not linear as the r o t a t i o n angle increases;

later, torques and tension increase linearly u p to the porportional limit, t h e n the yielding condition starts. At the beginning of such condition, the cycle is interrupted, and the m o t o r driving the wrench is reversed in order to unscrew the nut, causing the two torques to fall. After the backlash is recovered, t h e y change their sign in order to overcome the reaction torques and t h e n fall again until the unloaded conditions are reached. T h e induced tension starts to decrease when tol~que reaches the m i n i m u m value, t h e n it decreases proportionally with the angle of rotation. After the first cycle, the bolt is reloaded up to rupture. All the bolts failed b y r u p t u r e in the t h r e a d e d p a r t of the shank, a b o u t half w a y between the n u t and the solid p a r t of the shank. F o r the elaboration of the results, the yield conditions corresponding to a n angle of r o t a t i o n of 25 deg 42 rain were chosen, corresponding a p e r m a n e n t bolt elongation of 0.107 ram. W h e n the q u a n t i t a t i v e values change f r o m bolt to bolt, the general b e h a v i o r of the curves is the s a m e for all the bolts with two m a r k e d exceptions, represented b y bolts exhibiting the c h a t t e r phen o m e n o n 9 which originates f r o m the m a t i n g surfaces. T h e stud and the n u t of the two bolts are the same material, and the washers are hardened. T h e y are b o t h oil lubricated. W i t h conditions of the thread surfaces and m a t e rials of the rubbing surfaces t other t h a n the tests under investigation, c h a t t e r was m o r e frequent b u t always of the same shape. I n fact, the p h e n o m e n o n is similar to a stick-slip process of the irregular t y p e 1~ because the fluctuations of friction forces are v e r y severe, as shown in Fig. 6, which refers to a blued oillubricated bolt. Such fluctuations let the force decrease during the slipping phase whether the p h e n o m e n o n occurs during tightening or untightening. T h e i r a m p l i t u d e increases a s l o n g as the torque increases. Because of the origin of friction a n d torsional stiffness of the system, the highest amplit u d e is measured b y the a b s o r b e d - t o r q u e transducer.

* The values between brackets correspond to the ordinates of the diagram scales (Fig. 5).

"~ These cases correspond to another series of tests whose results will be published in a coming paper, where chatter is examined.

Experimental Material T h e bolts used were 10-ram nominal diameter, 10 M A U N I 185 t y p e ; the t h r e a d s were cold rolled. S h a n k length was 150 m m , t h r e a d e d length 35 ram. Steel U N I C40 was used, with a nominal yield stress of 80 k g / m m 2 ; the actual yield-stress range was f r o m 98 to 102 k g / m m ~ (in eight tensile tests), hardness range f r o m 83 to 104 Rockwell B (50 tests). T h e bolts were used zinc plated or c a d m i u m plated. T h e same surface t r e a t m e n t s were applied to the nuts. T w o grades of steel were used, n a m e l y U N I C20 and U N I C40, with corresponding nominal yield stresses of 50 and 80 k g / m m 2. H a r d n e s s ranges were 77-79 and 102-104 Rockwell B.

Experimental Mechanics [ 413

TABLE 1--FACTORS AND LEVELS Levels Factors

0

A. Bolt-surfacetreatment Cadmium Zinc plating plating B. Nut-surface treatment Cadmium Zinc plating C. Nut-material nominal yield strength, kg/mm 2 50 8O D. Washer treatment None Case hardening E. Lubrication Light motor oil Molykote G F. Fit between mating Loose Tight threads

T w o types of washers were used, plain (92-93 Rockwell B) and case hardened (72-75 Rockwell

A). The combinations tested are indicated in Table 2, coded according to Table 1. The class of fit between mating threads, as m e a s ured b y the difference between bolt and n u t effective diameters, was also considered as a factor. Bolt-thread effective diameter was measured with well known three-wire technique. As no corresponding simple measurement m e t h o d was found to be available for internal screw threads, a special technique was developed, based on the use of bore micrometers with steel balls contacting the threads. 11 Bolts and nuts were grouped in two classes of fit, with an average difference between the effective diameters of m a t i n g threads of 0.19 m m

(tight fit) and 0.29 m m (loose fit). Two t y p e s of lubricants were used, light engine oil and molybd e n u m disulfide (Molykote G). B o t h were applied sparingly to the threads of the bolt and on the face of the nut.

Design of Experiment W h e n u n d e r t a k i n g t h e p ] a n n i n g o f the experiment, it was realized t h a t a sizeable n u m b e r of

factors could exert rather i m p o r t a n t effects on the variables under investigation, and it was b y no means clear whether these effects would be applied independently or not. Furthermore, the large n u m b e r of t r e a t m e n t s (e.g., surface treatments) usually given to the bolts made it desirable to broaden the inductive basis from which the conclusions were to be drawn 12 b y also including in the experiment some subsidiary factors even t h o u g h their influence could be assumed to be small. A factorial design was accordingly selected. I t proved to be a convenient way of testing the effects of the six factors, each chosen at two levels. T h e factors and levels are listed in Table 1. Briefly, the plan of a complete factorial experim e n t consists in taking an observation at each one of all the possible combinations t h a t can be formed with the different levels of the factors. The whole experiment m a y then be repeated,

TABLE 2--PLAN OF THE EXPERIMENT, WITH CODING OF THE TREATMENT COMBINATIONS

~ 414 ] August1966

Block1

~

Block2

TABLE 3--EXPERIMENTAL RESULTS 9 Test

Load, t Raw

-Yield p o i n t v a l u e s . ~Torque, Adj. Raw

(1) af bf ab cf ac bc a bcf df ad bd a bdf cd acdf bc df abcd ef ae be a bef ce acef bcef abce de adef bdef a bd e cd ef ac be dcde abcdef

4.72 4.64 3.03 3.56 3.41 3.70 4.28 3.46 4.37 3.86 2.79 3.30 3.61 3.82 3.84 3.60 4.24 4.18 3,06 4,25 4.70 4.56 4.71 4.70 4.28 4.56 4.50 3.59 3.30 4.15 3.56 4~29

4.54 4.62 2.85 3.46 3.15 3.84 4.26 3.76 4.35 4.16 3.09 3.28 3.51 3.64 3.66 3.42 4,30 4.48 3.28 4.23 4.52 4.46 4.45 4.44 4.34 4.46 4.32 3.41 4.01 4.21 3.78 4.35

Average

3.957

3.957

460 427 1078 1020 1089 840 970 812 745 372 800 1015 990 982 1078 970 624 445 630 655 830 629 691 670 700 826 825 800 674 740 480 714 779.3

Kg-cm~ Adj.

401 420 1019 987 1004 886 963 910 738 830 898 1008 957 923 1019 911 644 543 702 648 771 596 606 585 720 793 766 741 904 760 552 734 779,3

or replicated, in order to provide d a t a for the estimation of the error. Replication is not, however, the only available w a y for m a k i n g an estimate of the experimental error f r o m which the significance os the results is to be judged. W h e n several factors are introduced, it is often likely 13 t h a t thirdand higher-order interactions m a y be assumed to h a v e little, if any, statistically significant effect, and thus m a y be available to supply the required estim a t e of error. T h e analysis of the available experimental results confirmed the a d e q u a c y of such a hypothesis for the case in hand. E v e n a single complete replication m a y comprise a n u m b e r of tests larger t h a n required for the particular purposes of the experiment. I t is t h e n possible to test b u t a given subset of the t o t a l n u m b e r of combinations, selected in order to satisfy the requirements set forth. Such a p l a n is called a fractional factorial. T h e particular one a d o p t e d is a one-half replicate os a 26 factorial, comprising 32 of the 64 possible combinations of six factors a t two levels each. I4 T h e plan is shown in T a b l e 2, with the coding adopted for the designation of factors and levels. T h e efficiency of the plan m a y be appreciated f r o m the fact t h a t t h i r t y - t w o tests are used to evaluate no less t h a n six m a i n effects and fifteen two-factor interactions, still leaving ten higher-order interactions available to provide an internal estimate of

N u t revs.

.Ultimate v a l u e s Torque, Load, t Kg-m

0.87 0.66 0.67 0.72 0.76 0.70 0.70 0,76 0.88 0.75 0.58 0.67 O.64 O.79 O.79 O.79 0.86 0.65 0.70 0.78 0.79 0.89 0.93 0.89 0.81 0.83 0.89 0.76 0.78 0.74 0.69 0.86

5.20 5.06 3.44 3.60 3.58 3.64 3.58 3.44 4.52 4.21 2.97 3.51 3.56 3.67 3.80 3.79 4.69 4.52 3.84 4.77 5.30 4.96 5.20 5.24 4.64 5.09 5.11 4.65 4.00 4.53 4.03 4.70

0.768

4.276

5.72 5.72 11.50 10.21 11.40 9.04 10.05 9.53 9.76 8.60 9.57 11.17 11.20 13.25 11.50 10.35 7.71 5.00 6.85 8.20 8.19 7.81 8.30 7.25 7.55 9,43 9.15 10.15 8.02 8.06 7.84 8.30 8.949

N u t revs.

3.41 3.55 1.46 1.63 1.73 1.79 1.45 2.20 2.92 2.93 1.68 1.50 I. 52 I . 73 1.74 I. 75 3.11 3.66 3.19 2.70 3.32 3.52 3.81 3.32 3.32 3.33 3.43 2.91 4.59 3.14 3.93 3.51 2.743

error. M a i n effects and two-factor interactions are confounded only with fifth- and fourth-order interactions, whose effect is p r o v e d to be small c o m p a r e d with the precision of the experiment. T h e heterogeneity os the experimental m a t e r i a l m a d e it desirable to arrange the plan in blocks. T h e b e t t e r u n i f o r m i t y obtainable within each block would lead to a higher precision, without increasing the size of the experiment. While this simple i m p r o v e m e n t was found to be a d e q u a t e for a first appraisal of the effects, the analysis of bolt-tension d a t a showed t h a t a f u r t h e r i m p r o v e m e n t m i g h t be obtained using the conc o m i t a n t m e a s u r e m e n t of hardness, performed on each bolt, for m a k i n g a n allowance for differences of tensile s t r e n g t h between bolts. T h e a d j u s t m e n t was calculated f r o m the experim e n t a l results, 15 a n d the variance estimated f r o m the adjusted d a t a was reduced b y one third as compared with t h a t obtained f r o m the r a w data. I t is not u n c o m m o n to obtain even larger increases in precision t h r o u g h the use of simple analysis os covariance techniques. 16

Analysis of Experimental Data T h e main results of the tests are shown in Table 3. I n a factorial experiment, the m a i n factors are evaluated b y the difference obtained between the

Experimental Mechanics I 415

the a b o v e - m e n t i o n e d exception) to provide the e s t i m a t e of error, since a t e s t based on B a r t l e t t ' s criterion 18 showed t h a t there was no reason for rejecting the hypothesis t h a t the m e a n squares were in fact estimates of the same variance, in spite of w h a t could be hinted b y the large value of the B C interactions. T h e m a i n effects and interactions shown to be significant at the 5 and i percent levels are indicated in T a b l e 6. I t should be remarked, however, that, when several tests of significance are performed in an experiment, the p r o b a b i l i t y for a nonsignificant effect of appearing significant b y chance is greater t h a n the level of significance chosen, and possibly relied upon, b y the experimenter. No completely satisfactory m e t h o d for dealing with this p r o b l e m has been published u p to date; 19 therefore, an appraisal of the physical meaning of the effects indicated as significant is needed before drawing a n y conclusions.

results of tests with the given factor at its higher level and those a t the lower level. Similarly, the interaction between two factors is evaluated b y t h e difference obtained between the results of tests with b o t h factors either a t their higher or lower level and those in which the two factors enter at different levels. T h e s y s t e m a t i c use of the whole b o d y of experimental results to estimate each m a i n effect and interaction explains the high efficiency of the factorial design. T h e analysis is m a d e c o m p a r a t i v e l y simple and straight-forward b y using the convenient t a b u l a r f o r m introduced b y Yates. 17 T a b l e 4 shows the analysis according to this technique of bolt-tension data; other results such as nut-tightening torque and angle of r o t a t i o n of n u t were treated in a similar way. T h e significance of m a i n effects and interactions, such as those listed in the last column of T a b l e 4, has been tested with " S t u d e n t ' s t"; using the estim a t e of error supplied b y the third-order interactions (excluding the one confounded with block effects). T h e a d e q u a c y of the internal estimate of error for significance tests can be judged f r o m the d a t a shown in T a b l e 5, where the ratio of s t a n d a r d deviation to sample m e a n is indicated for r a w and adjusted results, and also for another experiment with three replications. All the third-order interactions were used (with

Comparison between Two Current Methods of Bolt Tightening T h e results obtained f r o m the tests p e r m i t a comparison to be established between two m e t h o d s of tightening the bolts, based respectively on the a m o u n t of applied torque and on the a m o u n t of n u t turning. T h e results were arranged in order to get

TABLE 4--ANALYSIS OF ADJUSTED BOLT-TENSION DATA WITH YATES' METHOD Treatment combination

Response kg X 10

(1)

(2)

(3)

(4)

(5)

(1) af bf ab cf ac bc abcf df ad bd abdf cd acdf bcdf abcd ef ae be abef ce acef bcef abce de adef bdef abde cdef acde bcde abcdef

454 462 285 346 315 384 426 376 435 416 309 328 351 364 366 342 430 448 328 423 452 446 445 444 434 446 432 341 401 421 378 435

916 631 699 802 851 637 715 708 878 751 898 889 880 773 822 813 8 61 69 --50 --19 19 13 --24 18 95 --6 --1 12 --91 20 57

1547 1501 1488 1423 1629 1787 1653 1635 69 19 0 --11 113 --7 --79 77 --285 103 --214 --7 --127 --9 --107 --9 53 --119 38 --37 77 5 --103 37

4308 2911 3416 3288 88 --11 106 --2 --182 --221 --136 --116 --66 --1 82 --66 --46 --65 158 --18 --50 --11 --120 156 388 --207 118 98 --172 --75 --72 140

5959 6704 77 104 --403 --252 --65 16 --111 140 --61 36 595 216 --247 68 --137 --128 --99 --108 --39 20 67 --148 --19 --176 39 276 --181 --20 97 212

12663 181 --655 49 29 --25 811 --179 --265 --207 --19 --81 --195 315 --201 309 745 27 151 81 251 97 --379 315 9 --9 59 --215 --157 237 161 115

* Used for estimation o f error. t C o n f o u n d e d with block effects.

416 I August 1966

Factor

G

A

B AB O AC BC ABC* D AD BD AnD CD ACD* BCD* EF E AE BE ABE* CE ACE* BCE* DF DE ADE* BDE* CF CDEt BF AF F

Effect, kg

" i3 --409 --31 18 --16 507 ..,

--166 --129 --12 --51 --122 ... 193 465 17 94 157 ... ,..

197 6 ... --135

... 148 101 72

~y

90~ BAND

98

Ty

Iu

Fig. 7--Cumulative-distribution functions for the ultimate and yield angles of rotation of the nut (~u, ~y) and the ultimate and yield tightening torques (Tu, Ty). (The average ultimate values are chosen as unit for the abscissas. 90-percent confidence bands are shown for the ~y and Ty lines)

0[. u

95" .

90" 80p

7060 50 4 I q

4O

P

30 2O

10 7u=I /

qs 0

~5 TABLE 5--COMPARISON BETWEEN SEVERAL ESTIMATES OF STANDARD DEVIATIONS

TABLE 6--SIGNIFICANT MAIN EFFECTS AND INTERACTIONS

Ratios of standard deviations to sample means estimated from: Earlier Data experiadjusted ments for (repliRaw data hardness cared)

Bolt tension at yield point Torque applied to nut at bolt yield point

2

0.104

0.087

0.051

0.135

0.116

0.136

f r o m a graphical representation some i m m e d i a t e conclusions on which one of the m e t h o d s give m o r e uniformity of results as far as tension induced in the bolts and safety against failure during tightening are concerned. F o r this purpose, the following quantities were determined f r o m the records: 1. T h e bolt loads induced b y the tightening angle and torque corresponding to an average tension of 75 and 90 percent of the p r o o f load (determined according to A S T M A 325); b o t h of t h e m were related to 90 percent of the a v e r a g e p r o o f load, in order to present the results in a dimensionless form; 2. T h e values of yielding and u l t i m a t e angles and torques, related to the average of the u l t i m a t e values respectively. T h e angles were measured f r o m the records, starting f r o m an origin determined as shown in Fig. 5. T h e experimental d a t a were used to construct

Factor

B C BC D BD E BE CE

~ - B o l t toad a t ~ yield point SignifEffect, icant at kg level

--409 ...... 507 ...... ...... 466 ...... ......

0.01 0.01

0.01

Torque applied to nut SignifEffect, icant at kg cm level

Ultimate angle of rotation of nut SignifEffect, icant at rev. level

72 76 --138 98 --72 --176 --122 --83

--0.46 ...... 0.51 ...... ...... 1.36 ...... 0.54

0.05 0.05 0.01 0.05 0.05 0.01 0.01 0.05

0.05 0.05

0.01 0.05

cumulative-distribution functions, which were plotted on p r o b a b i l i t y paper. T h e percentage accounted for b y the populations of bolts, whose properties are estimated f r o m the sample formed b y the t h i r t y - t w o units tested, is plotted on the ordinate of the diagrams. Figure 7 shows the cumulative-distribution functions for the u l t i m a t e and yield angles of r o t a t i o n of the n u t (au, ay) and the u l t i m a t e and yield tightening torques (T~, Tv), the average u l t i m a t e values being chosen as unit for the abscissas. T h e 90-percent confidence b a n d s are d r a w n for a~, T~ functions. Tables of median-, 95-percent and 5-percent r a n k s ~~ were used for preparing these figures.

Experimental Mechanics I 417

99,5

Fig. 8--Cumulative-distribution functions of bolt loads induced by applying to nut two torques (Lt.9, L~.vs) and two angles of rotation (Lozt.9 Lczt.75)corresponding on the average to 90 percent and 75 percent of the bolt proof load

i

L CZo~o

98. 95. 90 80 70 60 50.

40. 30. 20. 10. 5

0,5 0,5

1,25

q75

Figure 8 shows the cumulative-distribution functions of the bolt loads induced b y applying to the nuts the two torques corresponding to an average induced load of 75 and 90 percent, respectively, of the proof load (Lt0.9, Lt0.w), and the two angles of rotation of the n u t corresponding to the above mentioned fractions of the proof load (L~0.9, L~0.~5).

1,5

Conclusions F r o m the experimental results, the following conclusions can be drawn. Higher loads can be induced in the bolt b y tightening the n u t before reaching the yield point with the nuts cadmium plated, Molykote G lubrication and soft nuts cadmium plated or hard nuts zinc plated.

99.5 M

98

0

/

95 90

/

80

70 60

50 40 90 ~ BAND

30 20 Fig. 9--Cumulative-distribution functions with 90percent confidence bands for nut-rotation angles at bolt yield point for oil (0) and molybdenum-disulfide (M) lubricated bolts. (The abscissa unit is the average angle of rotation of the nut at bolt yield point)

418 I August 1966

10

J

5 2 0;5 0

O.5

0.75

~

~25

1.5

An axial load up to one eighth larger t h a n the average value m a y be induced in the bolt before causing it to yield b y tightening the n u t under a given favorable condition. T h e range of axial loads at yield point is f r o m 0.8 to 1.2 the average value. T h e torque applied to the n u t required for reaching a given axial load in the bolt is v e r y sensitive to changes in the conditions of the m a t i n g surfaces. This is easily explained considering t h a t a b o u t nine tenths of the applied torque is required to overcome friction between the m a t i n g threads and between n u t and washer. 2~ T h e distribdtion of load on the threads has also been shown 22 to be affected b y friction. I t follows t h a t the higher the friction, the higher the torque is a t bolt yield point. T h e torque is thus significantly increased using n u t s h a r d a n d / o r zinc plated, hardened washers, also in combination with zinc platings, and soft washers with c a d m i u m - p l a t e d nuts. T h e effect of lubricant and its interaction with n u t plating are shown to be highly significant. T h e presence of three two-factor interactions, all exceeding in m a g n i t u d e the significant m a i n effects, explains the i n a d e q u a c y of the one-fac~or-at-a-~ime a p p r o a c h for the purpose of examining the effects of several factors on the torque applied to the nut. T h e range of torques applied to the nuts at bolt yield point is f r o m 0.5 to 1.3 times the average value. Bolt plating and the class of fit of m a t i n g threads did not show a n y significant effect. T h e precision of the e x p e r i m e n t is large enough to allow detection of effects as small as one f o u r t e e n t h of the m e a n value of the yield load a t a 0.05 significance level. T h e results point out t h a t the precision should a t least be doubled in order to m a k e the experim e n t sensitive enough to measure those effects at the a b o v e - m e n t i o n e d level, b u t t h e n it m i g h t be questioned whether an i m p r o v e m e n t of the order of m a g n i t u d e of three percent in bolt p e r f o r m a n c e could justify such an increase in the cost of the experiment. T h e angle of r o t a t i o n of the n u t required for tightening the bolt to the yield point is significantly affected b y lubrication. T h e cumulative-distribution functions for oil and molybdenum-disulfide lubricated bolts are plotted with their 90-percent confidence b a n d s in Fig. 9. This graphic p o r t r a y a l of the effect of the lubricant shows t h a t , when the n u t is turned an angle corresponding to the average yield (selected as unit for the abscissa), o v e r 70 percent of the oil-lubricated bolt has already yielded against less t h a n 19 percent for the M o l y k o t e lubricated. T h e induced load a t yield point was, on the average, over 90 percent of the p r o o f load for the m o l y b denum-disulfide lubricated bolts against 80 percent for the oil-lubricated ones. F u r t h e r m o r e , no m e a s u r a b l e increase of load could be obtained b y tightening the n u t a f t e r the yield point in fourteen of the sixteen oil-lubricated

bolts, while all those lubricated with M o l y k o t e showed an u l t i m a t e load exceeding t h a t corresponding to the yield point b y 5 percent on the average (range 0.5 to 9 percent). T h e u l t i m a t e angle of r o t a t i o n of the n u t is affected at a highly significant level b y lubrication; the effect of this factor is a b o u t 50 percent of the average u l t i m a t e angle of r o t a t i o n of the nut. T h e nut-surface t r e a t m e n t , and the interactions of n u t material with nut-surface t r e a t m e n t and lubrication are also significant. I t follows t h a t an i m p o r t a n t p a r t in bolt performance is played b y lubrication, whose effects can be precisely assessed using a d e q u a t e experimental methods. T h e turn-of-the-nut m e t h o d of bolt tightening affords a far b e t t e r control of the induced bolt load t h a n is obtainable with the torque wrench. T h e s c a t t e r in bolt loads induced b y a given tightening torque is shown (from slopes of the curves) in Fig. 8 to be more t h a n four times larger t h a n when a given angle of r o t a t i o n is applied to the n u t u n d e r comparable conditions. Such a large difference, even if p a r t l y traceable to the purposely large inhomogeneity of the experim e n t a l material, can justify the trend toward b e t t e r m e t h o d s of controlling bolt performance, such as those recently investigated. 23

References 1. Adler, J . F., "'Exploratory Tests on Friction Grip Bolted Joints," Inst. Structural Engrs., Proc. Syrup. H. S. Bolts, 37, London (1959). 2. Drew, F. P., "Tightening High-Strength Bolts," Proc. paper No. 786, A S C E , 81 (August 1955). 3. Pauw, A., and Howard, L. I., "Tension Control for High Strength Structural Bolts," Proc. 1955 A I S C National Engrg. Conf. (1956). 4, Hanneman, W . M., " H o w Plated Finishes Affect Bolt Tightening," Fasteners, 16 (1-2), 7 (1961). 5. Specification for Assembly of Structural Joints using High Strength Bolts, Rsch Council Riveted and Bolted Structural Joints, Cleveland (1954). 6. Preliminary Directives for the Calculation, Design and Assembly ol Non-Slip Bolted Connexions for Steel Structures, Bridges and Cranes, Stahlbau-Verlags G.m.b.H., K6ln (1956). 7. Munse, W. H., Wright, D. T., and Nemark, N . M., "Laboratory Tests of Bolted Joints," Trans. A S C E , 120, 1296 (1955). 8. Martin, H., "' The Properties of High Strength Bolts," Inst. Structural Engrs., Proc. Symp. on H . S. Bolts, 96, London (1959). 9. Pickel, W. F., "'Tightening Characteristics of N u t and Stud Assemblies," Product Engrg., 98, (January 1949). 10. Rabinowicz, E., "'A Study on the Stick-Slip Process," Proc. 1957 Symposium on Fr&thm and Wear (R. Davies ed.), Elsevier (1959). 11. Levi, R., "'Mieura rapida del diametro medio di filettature interne," Ingegneria Meccanica (Novembre 1965). 12. Fisher, R. A., The Design of Experiments, Sec. 39-40, 7th ed. Oliver and Boyd, Edinburgh (1960). 13. Natrella, M . G., Experimental Statistics, Sec. 12-4, N . B . S . Handbook 91, Washington (1963). 14. Statistical Engineering Lab., Fractional Factorial Experiment Designs for Factors at Two Levels, Sec. 5, 2.6.16, N . B . S . Applied Mathematics Series 48, 2nd ed., Washington (1962). 15. Fisher, R. A., Statistical Methods for Research Workers, Sec. 26, 13th ed., Oliver and Boyd, Edinburgh (1958). 16. Cochran, W. G., and Cox, G. M., Experimental Designs, Sec. 3.87, 2nd ed., g. Wiley, N e w York (1957). 17. Yates, F., The Design and Analysis of Factorial Experiments, Tech. Comm. No. 35, Imp. Bur. of Soil Science, Harpenden (1937). 18. Bartlett, M . S., "Properties of Sufficiency and Statistical Tests," Prac. Royal Soc. A., 160~ 268 (1937). 19. Davies, O. Y. (ed.), Design and Analysis of Industrial Experiments A p p . 7e, 2nd e d , Oliver and Boyd, Edinburgh (1963). 20. Johnson, L. G., Theory and Technique of Variation Research, Elsevier, Amsterdam (1964). 21. Maney, G. A., Predicting Bolt Tension, Fasteners, 3 (5) (1947). 22. Goodier, g. N . , "Distribution of Load on the Threads of Screws," Trans. A S M E , Jnl. Appl. Mech. 7 (1) 10 (1940). 23. Discussion of Session Two, Bolts and Wrenches, Inst. of Structural E~grs., Proc. Syrup. on H. S. Bolts, 131, London (1959).

Experimental Mechanics [ 419