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Parametric study of threaded fastener loosening due to cyclic transverse loads
Engineering Failure Analysis 14 (2007) 239–249 www.elsevier.com/locate/engfailanal
Parametric study of threaded fastener loosening due to cyclic transverse loads J.A. Sanclemente, D.P. Hess
*
Department of Mechanical Engineering, University of South Florida, 4202 East Fowler Avenue, ENB 118, Tampa, FL 33620-5350, USA Received 14 October 2005; accepted 17 October 2005 Available online 10 February 2006
Abstract This paper presents results from an experimental investigation of mechanical loosening in bolted joints due to cyclic transverse loads. The influence on the resistance to loosening of basic parameters such as preload, fastener material elastic modulus, nominal diameter, thread pitch, hole fit and lubrication is quantified. Sixty-four tests have been performed as part of a nested-factorial design in which the nominal diameter is the nesting factor of preload, thread pitch and hole fit. A statistical analysis identifies the factors and interactions that significantly affect the resistance to loosening and it is found that the preload and the fastener elasticity are the most influencing parameters. A statistical model is developed that predicts the level of loosening reached by a threaded fastener under defined conditions. The analysis shows that optimum conditions to avoid fastener loosening are high preload, low modulus of elasticity, large diameter, lubrication, tight fit and fine threads. 2005 Elsevier Ltd. All rights reserved. Keywords: Fastener loosening; Transverse loads, Parametric study
1. Introduction and background Traditional methods for designing and selection of the threaded element cover the endurance requirements of the bolt to avoid fatigue or fracture. However, they do not necessarily ensure that the fastener will not fail by loosening when the joint undergoes cyclic loads. This paper presents a set of data and analyses based on formal statistical methods to study the behavior of the joint under dynamic forces, specifically in the transverse direction. The methodology used here involves the statistical quantification of the effect of basic parameters related to the joint on fastener loosening. In the late 1960s, Junker [1] experimentally identified the relationship between the occurrence of slip at the head and thread contacts and the generation of loosening in the joint. Following this work, Finkelston [2] experimentally estimated the effect of individual parameters that significantly affect the vibration life of a joint. However, factor interactions were not studied in this research. In the early 1970s, Walker [3] introduced a *
Corresponding author. Tel.: +1 813 974 5643; fax: +1 813 974 1447. E-mail address: [email protected] (D.P. Hess).
1350-6307/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2005.10.016
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fractional factorial design in a series of experiments. His 251 design allowed quantifying the effect of specific factors and their interactions. A more extensive study was presented by Ramey and Jenkins [4] in which eleven factors and two noise factors were investigated under a fractional factorial design using the Taguchi method. However, due to the high number of factors involved additional tests to estimate the effect of some parameters were required. A parametric study based on a finite element simulation model was also given by Pai [5]. Although the finite element model is in agreement with existing listed experimental results, the findings of the parametric study have not been fully corroborated experimentally. A more detailed description of these works and others in this field is presented by Hess [6]. In this work a balanced number of factors are studied. They correspond to basic factors necessarily defined during the fastener selection process and include preload, fastener material, nominal diameter, thread pitch, hole fit and lubrication. The factorial design used in this experiment is nested since it takes into account that the levels of nominal diameter influence the level values of preload, thread pitch and hole fit, i.e., the nesting effect of the nominal diameter over other factors. This effect has been ignored in other work [4,5]. The related statistical analysis not only identifies and quantifies the contribution of significant parameters, but it provides a model for predicting the experimental variable response or level of loosening over the ranges of factors considered. 2. Test apparatus Fig. 1 is a schematic representation of the transverse test machine utilized in the experiments. The cyclic transverse load is applied to the test bolt through an eccentric. This force is measured with a load cell. The transverse force is transmitted to the bolt primarily by friction between the bolt head and the clamped cone (see Fig. 1). With sufficient bolt deflection, contact between the bolt and the hole wall occurs and a portion of the transverse force is also transmitted through this contact. The clamped cone and the drilled insert locate the test bolt. They are made of hardened steel. The preload is also measured by a load cell. The displacement induced by the eccentric is adjustable from ±0.5 to ±2 mm and is measured with an LVDT. 3. Experimental details Although there are multiple factors affecting the loosening process in a threaded fastener, the six factors studied are considered dominant based on results from previous works and other mechanical considerations. The test matrix in Table 1 summarizes levels of the factors used in the experiment. The fastener material refers to the material of both bolt and nut and it is the interest of this research to evaluate the influence of the modulus of elasticity of the fastener on loosening. The stainless steel alloy 304
Fig. 1. Transverse vibration test apparatus.
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Table 1 Parametric study test matrix Factor
Description
A B C(B) D(B) E(B) F
Fastener material elastic modulus Nominal diameter Thread pitch Preload Hole fit Lubrication
Level Low
High
Aluminum 6.4 mm (1/400 ) UNC 32% Yield Loose Dry
Stainless steel 12.7 mm (1/200 ) UNF 64% Yield Tight SAE 30 Oil
and aluminum alloy 6061T6 have been chosen as the high and low levels for the fastener material factor, respectively. The levels of the nominal diameter are 6.4 mm (1/400 ) and 12.7 mm (1/200 ). The definition of the levels of other factors such as thread pitch, preload and hole fit are dependant on the levels of the nominal diameter. In the case of the thread pitch, the coarse thread series (UNC) are used for the low level while the fine thread series (UNF) for the high level. The preload has been defined as a percentage of the yield strength of the fastener material. In this research the yield strength is approximately the same for both materials (207 MPa) [7]. The high level of the preload is chosen as 64% of yield while the low level as 32% of the yield strength. The hole fit levels are defined by the tight and oversized diameter values for drilled holes [8] and are dependent on the fastener nominal diameter. Tight fit hole sizes are 6.53 for 6.4 mm (1/400 ) bolts and 13.11 for 12.7 mm (1/200 ) bolts, while loose fit hole sizes are 6.75 for 6.4 mm (1/400 ) bolts and 13.49 for 12.7 mm (1/200 ) bolts. For the lubrication factor, the high level corresponds to the presence of SAE 30 lubricant in the contact areas of the fastener, while the low level indicates an absence of lubricant. A few drops of lubricant are applied underneath the head of the bolt, on the bolt threads and on the nut flange. The specified factor levels determine the type of specimens required which include of 1/4-20 UNC, 1/4-28 UNF, 1/2-13 UNC and 1/2-20 UNF hex head bolts and corresponding nuts made from stainless steel 304 and aluminum alloy 6061-T6. The loss of preload is indicative of fastener loosening and is measured throughout the experiment. The initial preload and the residual preload (remaining preload after the test) define the response variable as shown in Eq. (1) Y ¼
F pðt¼0Þ F pðt¼sÞ F pðt¼0Þ
ð1Þ
where y is the dimensionless response variable, Fp(t = 0) is the initial preload, Fp(t = s) the residual preload, s the time at which the residual preload is measured. The response variable is simply a measure or indication of preload loss. It can take a value between 0 and 1. A 0 indicates no loosening and 1 indicates complete loosening. 4. Experiment Sixty-four tests were performed for the 26 nested-factorial design. The order of the runs was random. The machine settings were 15 Hz frequency and ±1.5 mm amplitude of displacement. Each test specimen is subjected to these loading conditions for 1750 cycles. The surfaces of the machine components in contact with the specimen were cleaned with acetone and filter paper before every test. The test results for every treatment combination are summarized in Table 2. In design of experiments, the lower case letters are used to represent the high level for a given factor. The absence of a letter indicates the lower level for a given factor. For example, treatment combination abc indicates high levels for factors A, B and C and low levels for factor D, E and F, Treatment combination (1) indicates low levels for all factors. The best performance (y = 0.01) was obtained with the treatment combination defined by the following conditions: aluminum fastener, 12.7 mm (1/200 ) nominal diameter, UNF threads, high preload, tight fit hole and lubrication. The preload time trace data for this treatment combination are displayed in Fig. 2. The high
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Table 2 Experimental results Run
Treatment combination
Initial preload (N)
Residual preload (N)
Response (y)
57 1 34 64 4 10 19 62 46 42 47 9 5 59 3 29 12 11 16 27 14 50 36 55 35 22 45 24 7 26 21 37
(1) a b ab c ac bc abc d ad bd abd cd acd bcd abcd e ae be abe ce ace bce abce de ade bde abde cde acde bcde abcde
1469 1469 6453 6453 1469 1469 6453 6453 2937 2937 12,905 12,905 2937 2937 12,905 12,905 1469 1469 6453 6453 1469 1469 6453 6453 2937 2937 12,905 12,905 2937 2937 12,905 12,905
399 0 870 0 928 0 4767 4118 2782 0 12,017 0 2700 0 12,239 9398 636 21 2977 0 1331 1063 4932 0 2491 1814 12,248 11,718 2295 1811 12,513 7604
0.73 1.00 0.87 1.00 0.37 1.00 0.26 0.36 0.05 1.00 0.07 1.00 0.08 1.00 0.05 0.27 0.57 0.99 0.54 1.00 0.09 0.28 0.24 1.00 0.15 0.38 0.05 0.09 0.22 0.38 0.03 0.41
13 38 15 17 28 52 6 44 61 51 53 60 2 48 58 49 41 32 33 18 40 54 30 23 31
f af bf abf cf acf bcf abcf df adf bdf abdf cdf acdf bcdf abcdf ef aef bef abef cef acef bcef abcef def
1469 1469 6453 6453 1469 1469 6453 6453 2937 2937 12,905 12,905 2937 2937 12,905 12,905 1469 1469 6453 6453 1469 1469 6453 6453 2937
1229 0 0 0 1301 0 0 164 2559 0 12,315 12,359 2756 0 11,754 12,413 0 92 0 0 1277 68 0 241 2741
0.16 1.00 1.00 1.00 0.11 1.00 1.00 0.98 0.13 1.00 0.05 0.04 0.06 1.00 0.09 0.04 1.00 0.94 1.00 1.00 0.13 0.95 1.00 0.96 0.07
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Table 2 (continued) Run
Treatment combination
Initial preload (N)
Residual preload (N)
Response (y)
63 20 39 43 25 8 56
adef bdef abdef cdef acdef bcdef abcdef
2937 12,905 12,905 2937 2937 12,905 12,905
2375 12,606 12,078 2779 2374 12,725 12,146
0.19 0.02 0.06 0.05 0.19 0.01 0.06
13200
Preload (N)
13000
12800
12600 0
20
40
60
80
100
120
Time (sec)
Fig. 2. Preload versus time plot for best experimental performance.
Table 3 Best eight experimental performances Treatment combination
Elastic modulus
Diameter (mm)
Pitch
Preload (N)
Hole fit
Lubrication
Response
bcdef bdef bcde abcdf abdf bdf bde bcd
AL AL AL SS SS AL AL AL
12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7
UNF UNC UNF UNF UNC UNC UNC UNF
12,905 12,905 12,905 12,905 12,905 12,905 12,905 12,905
Tight Tight Tight Loose Loose Loose Tight Loose
Oil Oil Dry Oil Oil Oil Dry Dry
0.01 0.02 0.03 0.04 0.04 0.05 0.05 0.05
preload and a large diameter are features present in the eight tests with the lowest level of loosening (see Table 3). Aluminum fasteners and oil lubrication are other conditions common in these tests. These results indicate that preload, fastener material, diameter and lubrication are important as individual factors or as part of an interaction. 5. Statistical analysis of data The ANOVA results for this experiment are presented in Table 4. It can be concluded from the low P values, that the factors preload (D(B)) and fastener material elastic modulus (A) have the highest influence in the resistance to loosening. Interactions that provide significant resistance to loosening includes fastener material · diameter interaction (AB), preload · lubrication interaction (D(B)F), fastener material · hole fit interaction (AE(B)), fastener material · diameter · lubrication interaction (ABF).
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Table 4 ANOVA results for parametric study Factor
SS
DF
MS
F
P
Model D(B) A AB DðBÞF AE(B) ABF E(B) C(B) F B Residual Total
8.534 4.270 2.004 0.442 0.594 0.578 0.232 0.314 0.313 0.010 0.008 2.451 10.984
15 2 1 1 2 2 1 2 2 1 1 48 63
0.569 2.135 2.004 0.442 0.297 0.289 0.232 0.157 0.157 0.010 0.008 0.051
11.142 41.816 39.255 8.665 5.819 5.657 4.548 3.074 3.066 0.186 0.163
<0.0001 <0.0001 <0.0001 0.0050 0.0055 0.0062 0.0381 0.0554 0.0558 0.6681 0.6886
Diameter (B) and lubrication (F) have been included in the ANOVA table for the hierarchical model, which takes into account not only the effect of the significant factors and interactions but the effect of non-significant factors included in the analysis of variance. Eq. (2) provides the general form for this model. Y ijklmn ¼ l þ Ai þ Bj þ ðABÞij þ C kðjÞ þ DlðjÞ þ EmðjÞ þ ðAEÞimðjÞ þ F n þ ðDF ÞlðjÞn þ ðABF Þijn þ eðijklmnÞ
ð2Þ
where Yijklmn is the variable response, l is the overall mean, Ai is the effect of the ith level of factor A, Bj the effect of the jth level of factor B, (AB)ij the AB interaction effect at levels ith and jth, respectively, Ck(j) the effect of the kth level of the factor C(B) within the jth level of factor B, Dl(j) the effect of the lth level of the factor D(B) within the jth level of factor B, Em(j) the effect of the mth level of the factor E(B) within the jth level of factor B, (AE)im(j) the AE(B) interaction effect at the ith level of factor A and the mth level of factor E(B) within the jth level of factor B, Fn the effect of the nth level of the factor F, (DF)l(j)n the D(B)F interaction effect at the nth level of factor F and the lth level of factor D(B) within the jth level of factor B, (ABF)ijn the ABF interaction effect at the ith level of factor A, the jth level of factor B and the nth level of the factor F, and eijklmn the residual error term. The subscripts i, j, k, l, m, n can take a value of 1 or 1 representing the low (1) or the high (1) level of each factor. The estimates of each effect term in the model are given in Table 5. The fitted values are calculated based on these estimated values. Fig. 3 compares these fitted values against the response variable defined in Eq. (1). The fitted response closely follows the trend of the response in most cases. The model has an R2 factor of 0.78 (R2 = 0.78). 6. Interpretation of results The analysis shows that preload and fastener material are the most significant parameters influencing the loosening. These factors are involved in significant interactions and therefore their overall effects are influenced by the factors in these interactions. In the case of the preload, the overall effect has to be estimated from the preload itself, the preload · lubrication interaction and the lubrication. The overall effect of fastener material with other factors leads to a more complex situation. To simplify its interpretation the effect of the less significant interaction (fastener material · diameter · lubrication) is excluded. In addition, since lubrication is not a significant parameter (even though it is included in the preload overall effect), it is not considered in the fastener material overall effect. The effect of thread pitch is studied separately since non-significant interactions are related to this parameter. The overall effects are estimated by adding the individual effects of the related factors and interactions. The resulting fitted response will increase or reduce from the mean l according to the levels of the factors involved. The flow charts in Figs. 4 and 5 map the overall effects of the preload and fastener material. From these figures, one sees that the overall effects for high preload and aluminum bolts are negative while the overall effects for low preload and stainless steel bolts are positive. Similarly, the effect of the fine thread is negative and the effect of the coarse thread is positive. Resistance to loosening increases as the overall effect decreases. There-
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Table 5 Estimates for model parameters Factor description
Estimator
Overall mean
^ l
Estimate 0.497
Level
Fastener material
b A
0.177 0.177
i = 1 i=1
Diameter
b B
0.011 0.011
j = 1 j=1
Fastener material · diameter
c AB
0.083 0.083
i · j = 1 i·j=1
Thread pitch
b C
0.076 0.076 0.063 0.063
k = 1 at j = 1 k = 1 at j = 1 k = 1 at j = 1 k = 1 at j = 1
Preload
b D
0.136 0.136 0.339 0.339
l = 1 at j = 1 l = 1 at j = 1 l = 1 at j = 1 l = 1 at j = 1
Hole fit
b E
0.097 0.097 0.018 0.018
m = 1 at j = 1 m = 1 at j = 1 m = 1 at j = 1 m = 1 at j = 1
Fastener material · hole fit
^ AE
0.134 0.134 0.012 0.012
i · m = 1 at j = 1 i · m = 1 at j = 1 i · m = 1 at j = 1 i · m = 1 at j = 1
Lubrication
Fb
0.012 0.012
n = 1 n=1
Preload · lubrication
c DF
0.027 0.027 0.134 0.134
l · n = 1 at j = 1 l · n = 1 at j = 1 l · n = 1 at j = 1 l · n = 1 at j = 1
Fastener material · diameter · lubrication
d ABF
0.060 0.060
i · j · n = 1 i·j·n=1
Response Fitted Response 1.20 1.00 0.80 0.60 0.40 0.20 0.00 1
10
19
28
37
46
55
64
Observations
Fig. 3. Response and range corrected fitted response comparison (—, response; - - - -, fitted response).
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High Preload
Large Dia.?
Yes
Overall Effect: -0.339
Yes
Oil ?
No
No
Overall Effect: -0.136
Oil ?
Overall Effect: -0.460
Overall Effect: -0.218
Yes
Overall Effect: -0.151
No
Note: Resistance to loosening increases as the overall effect decreases.
Overall Effect: -0.122
Fig. 4a. Overall effect of high preload.
Low Preload
Large Dia.?
Yes
Overall Effect: 0.339
Yes
Oil ?
No
No
Overall Effect: 0.136
Overall Effect: 0.193
Yes Oil ?
Overall Effect: 0.485
Overall Effect: 0.175
No
Overall Effect: 0.097
Note: Resistance to loosening increases as the overall effect decreases.
Fig. 4b. Overall effect of low preload.
fore, the results show high preload and low elasticity modulus fasteners with fine threads increase resistance to loosening. The benefits of a higher preload were expected based on the results obtained by other researchers [2,4,5,9]. At higher preloads the friction force is increased and the transverse force required to overcome the friction is higher and the occurrence of slippage is reduced leading to reduced or no loosening. The low modulus of elasticity of the aluminum mitigates loosening because: (a) it reduces the bending moment at the threads and thereby reduces localized slip since the reaction force distribution at the threads during the loading cycle is more even and, (b) it leads to contact between the fastener rod and the wall of the hole. This is consistent with Pai [5], who found when lateral contact occurs the applied transverse force is transmitted mostly through this contact point inhibiting slip at the bolt head.
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Low Elasticity Modulus
Large Dia.?
Yes
Overall Effect: -0.105
No
Overall Effect: -0.136
No
Overall Effect: -0.249
Tight Fit ?
Yes
Tight Fit ?
247
Overall Effect: -0.075
Yes
Overall Effect: -0.212
No
Note: Resistance to loosening increases as the overall effect decreases.
Overall Effect: -0.285
Fig. 5a. Overall effect of low elasticity modulus without interaction ABF.
High Elasticity Modulus
Large Dia.?
Yes
Overall Effect: 0.083
No
No
Overall Effect: 0.503
Overall Effect: 0.076
No
Overall Effect: 0.272
Tight Fit ?
Yes
Tight Fit ?
Overall Effect: 0.089
Yes
Overall Effect: 0.043
Note: Resistance to loosening increases as the overall effect decreases.
Fig. 5b. Overall effect of high elasticity modulus without interaction ABF.
The effect of the fine thread on the loosening is attributed to the lower off-torque obtained with a smaller thread pitch. Fig. 4a shows that the effect of high preload is higher in 12.7 mm (1/200 ) bolts than in 6.4 mm (1/400 ) bolts. The normal stress generated by the preload has the same value for large or small bolts. However, the preload magnitude is different depending on the cross sectioned area of the fastener. Since larger bolts require a higher preload than smaller size fasteners in order to attain the same normal stress level, the tangential force necessary to overcome the friction force is higher in large size bolts. The coefficient of friction decreases with the application of lubricant. Low coefficients of friction promote slippage and thereby loosening. This is the behavior observed in Fig. 4b. However when higher preloads are applied in combination with lubrication, the resulting effect is beneficial for vibration resistance (see Fig. 4a).
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To obtain the same level of preload it is necessary to apply a much higher tightening torque in a joint without lubrication than in an oiled joint. In addition, a larger amount of torsional energy is stored in bolts under higher preloads with no lubrication. During the loading cycle this energy is released aiding the turning of fastener loosening. Fig. 5a reveals that the smaller diameter 6.4 mm (1/400 ) aluminum bolts have a more positive effect reducing loosening than the 12.7 mm (1/200 ) bolts. The effect of an aluminum fastener is expected to be more positive when combined with a smaller diameter since the low modulus of elasticity and the low moment of inertia (produced by the small diameter) reduce the bending moment and facilitate the lateral contact occurrence. In general, a tight fit is a condition that helps prevent loosening since it promotes lateral contact. However, when tight fit is used in combination with small diameter and low elastic modulus bolts an opposite effect may be obtained (see Fig. 5b). Tight fit holes induce higher deformation of the bolt and slender, flexible bolts may experience plastic deformation that manifest as loss of preload. 7. Application to bolted joint design Standard procedures in the design of bolted joints, e.g., VDI 2230 [10], recommend the use of as high preloads as possible without causing damage to the fastener, to avoid joint separation. The results obtained experimentally indicate that this recommendation is valid for the load conditions studied in this paper. At higher preloads the friction moments are higher reducing the possibility of slip and loosening. The range of applications for fasteners made of materials with low elastic modulus is typically limited to requirements with respect to corrosion, weight and thermo-conductivity or electrical conductivity. The results presented in this study reveal an advantage with respect to vibration resistance for this type of fastener. Disadvantages include higher cost and lower mechanical capacity for a given size. The use of fasteners with large diameters is desirable to ensure joint integrity under both static and dynamic loads. The experimental results show that when vibrations are present, large diameter fasteners are preferred because they allow the application of higher preloads and reduce the variability in the level of loosening. The resistance to loosening becomes more dependent on preload and less dependent of other parameters as diameter increases. Thus, the utilization of generous safety factors in the design process in specifying fastener size is recommended when the load conditions are of a dynamic nature, especially in the transverse direction. Regarding the selection of thread series for fasteners, fine thread fasteners are preferred in applications containing cyclic loads because their smaller helix angle reduces the off-torque. A lower tightening torque reduces the stored torsional energy which can aid loosening. In addition, they possess a larger tension area than coarse thread fasteners, which allows the application of higher preloads. The tight hole fit is preferred in joints under transverse vibration because it minimizes slip between the contact surfaces in the joint. Although lubrication reduces the coefficient of friction, when the preload is high, lubrication becomes beneficial for loosening resistance. This results from lower torsional energy stored during installation and released during use. 8. Conclusions A parametric study of the basic factors affecting threaded fastener loosening has been developed. The results of the study identified fundamental factors related to the fastener loosening phenomena. Their contributions to the level of loosening experienced by the joint have been quantified and assembled into a statistical model. The model is at least useful for comparing relative percentage of loss of preload for different combinations and levels of the factors studied. This has been presented graphically in flow charts to aid the joint design process. References [1] Junker GH. New criteria for self-loosening of fasteners under vibration. SAE Transactions 1969;78:314–35. [2] Finkelston RJ. How much shake can bolted joints take. Mach Des 1972;44:122–5.
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[3] Walker RA. The factors which influence the vibration resistance of fasteners. Jenkintown (PA): Standard Pressed Steel Co.; 1973. [4] Ramey GE, Jenkins RC. Experimental analysis of thread movement in bolted connections due to vibrations, NASA Research Project NAS8-39131. AL: Marshall Space Flight Center; 1995. [5] Pai NG. Vibration induced loosening of threaded fasteners: mechanisms, modeling and design guidelines, Ph.D. Dissertation. Tampa: University of South Florida; 2002. [6] Hess DP. Vibration- and shock-induced loosening. In: Bickford JH, Nasser S, editors. Handbook of bolts and bolted joints. New York: Marcel Dekker, Inc.; 1998. p. 757–824. [7] Blake A. What every engineer should know about threaded fasteners: materials and design. New York: Marcel Dekker, Inc.; 1986. [8] Oberg E, Jones FD, Horton HL, Ryffel HH. Machinery’s handbook. New York: Industrial Press; 2000. [9] Hess DP. Counter-threaded spring-actuated lock-fasteners. J Mech Des 2002;124:582–5. [10] Bickford JH. An introduction to the design and behavior of bolted joints. New York: Marcel Dekker; 1995.
Parametric study of threaded fastener loosening due to cyclic transverse loads J.A. Sanclemente, D.P. Hess
*
Department of Mechanical Engineering, University of South Florida, 4202 East Fowler Avenue, ENB 118, Tampa, FL 33620-5350, USA Received 14 October 2005; accepted 17 October 2005 Available online 10 February 2006
Abstract This paper presents results from an experimental investigation of mechanical loosening in bolted joints due to cyclic transverse loads. The influence on the resistance to loosening of basic parameters such as preload, fastener material elastic modulus, nominal diameter, thread pitch, hole fit and lubrication is quantified. Sixty-four tests have been performed as part of a nested-factorial design in which the nominal diameter is the nesting factor of preload, thread pitch and hole fit. A statistical analysis identifies the factors and interactions that significantly affect the resistance to loosening and it is found that the preload and the fastener elasticity are the most influencing parameters. A statistical model is developed that predicts the level of loosening reached by a threaded fastener under defined conditions. The analysis shows that optimum conditions to avoid fastener loosening are high preload, low modulus of elasticity, large diameter, lubrication, tight fit and fine threads. 2005 Elsevier Ltd. All rights reserved. Keywords: Fastener loosening; Transverse loads, Parametric study
1. Introduction and background Traditional methods for designing and selection of the threaded element cover the endurance requirements of the bolt to avoid fatigue or fracture. However, they do not necessarily ensure that the fastener will not fail by loosening when the joint undergoes cyclic loads. This paper presents a set of data and analyses based on formal statistical methods to study the behavior of the joint under dynamic forces, specifically in the transverse direction. The methodology used here involves the statistical quantification of the effect of basic parameters related to the joint on fastener loosening. In the late 1960s, Junker [1] experimentally identified the relationship between the occurrence of slip at the head and thread contacts and the generation of loosening in the joint. Following this work, Finkelston [2] experimentally estimated the effect of individual parameters that significantly affect the vibration life of a joint. However, factor interactions were not studied in this research. In the early 1970s, Walker [3] introduced a *
Corresponding author. Tel.: +1 813 974 5643; fax: +1 813 974 1447. E-mail address: [email protected] (D.P. Hess).
1350-6307/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2005.10.016
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fractional factorial design in a series of experiments. His 251 design allowed quantifying the effect of specific factors and their interactions. A more extensive study was presented by Ramey and Jenkins [4] in which eleven factors and two noise factors were investigated under a fractional factorial design using the Taguchi method. However, due to the high number of factors involved additional tests to estimate the effect of some parameters were required. A parametric study based on a finite element simulation model was also given by Pai [5]. Although the finite element model is in agreement with existing listed experimental results, the findings of the parametric study have not been fully corroborated experimentally. A more detailed description of these works and others in this field is presented by Hess [6]. In this work a balanced number of factors are studied. They correspond to basic factors necessarily defined during the fastener selection process and include preload, fastener material, nominal diameter, thread pitch, hole fit and lubrication. The factorial design used in this experiment is nested since it takes into account that the levels of nominal diameter influence the level values of preload, thread pitch and hole fit, i.e., the nesting effect of the nominal diameter over other factors. This effect has been ignored in other work [4,5]. The related statistical analysis not only identifies and quantifies the contribution of significant parameters, but it provides a model for predicting the experimental variable response or level of loosening over the ranges of factors considered. 2. Test apparatus Fig. 1 is a schematic representation of the transverse test machine utilized in the experiments. The cyclic transverse load is applied to the test bolt through an eccentric. This force is measured with a load cell. The transverse force is transmitted to the bolt primarily by friction between the bolt head and the clamped cone (see Fig. 1). With sufficient bolt deflection, contact between the bolt and the hole wall occurs and a portion of the transverse force is also transmitted through this contact. The clamped cone and the drilled insert locate the test bolt. They are made of hardened steel. The preload is also measured by a load cell. The displacement induced by the eccentric is adjustable from ±0.5 to ±2 mm and is measured with an LVDT. 3. Experimental details Although there are multiple factors affecting the loosening process in a threaded fastener, the six factors studied are considered dominant based on results from previous works and other mechanical considerations. The test matrix in Table 1 summarizes levels of the factors used in the experiment. The fastener material refers to the material of both bolt and nut and it is the interest of this research to evaluate the influence of the modulus of elasticity of the fastener on loosening. The stainless steel alloy 304
Fig. 1. Transverse vibration test apparatus.
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Table 1 Parametric study test matrix Factor
Description
A B C(B) D(B) E(B) F
Fastener material elastic modulus Nominal diameter Thread pitch Preload Hole fit Lubrication
Level Low
High
Aluminum 6.4 mm (1/400 ) UNC 32% Yield Loose Dry
Stainless steel 12.7 mm (1/200 ) UNF 64% Yield Tight SAE 30 Oil
and aluminum alloy 6061T6 have been chosen as the high and low levels for the fastener material factor, respectively. The levels of the nominal diameter are 6.4 mm (1/400 ) and 12.7 mm (1/200 ). The definition of the levels of other factors such as thread pitch, preload and hole fit are dependant on the levels of the nominal diameter. In the case of the thread pitch, the coarse thread series (UNC) are used for the low level while the fine thread series (UNF) for the high level. The preload has been defined as a percentage of the yield strength of the fastener material. In this research the yield strength is approximately the same for both materials (207 MPa) [7]. The high level of the preload is chosen as 64% of yield while the low level as 32% of the yield strength. The hole fit levels are defined by the tight and oversized diameter values for drilled holes [8] and are dependent on the fastener nominal diameter. Tight fit hole sizes are 6.53 for 6.4 mm (1/400 ) bolts and 13.11 for 12.7 mm (1/200 ) bolts, while loose fit hole sizes are 6.75 for 6.4 mm (1/400 ) bolts and 13.49 for 12.7 mm (1/200 ) bolts. For the lubrication factor, the high level corresponds to the presence of SAE 30 lubricant in the contact areas of the fastener, while the low level indicates an absence of lubricant. A few drops of lubricant are applied underneath the head of the bolt, on the bolt threads and on the nut flange. The specified factor levels determine the type of specimens required which include of 1/4-20 UNC, 1/4-28 UNF, 1/2-13 UNC and 1/2-20 UNF hex head bolts and corresponding nuts made from stainless steel 304 and aluminum alloy 6061-T6. The loss of preload is indicative of fastener loosening and is measured throughout the experiment. The initial preload and the residual preload (remaining preload after the test) define the response variable as shown in Eq. (1) Y ¼
F pðt¼0Þ F pðt¼sÞ F pðt¼0Þ
ð1Þ
where y is the dimensionless response variable, Fp(t = 0) is the initial preload, Fp(t = s) the residual preload, s the time at which the residual preload is measured. The response variable is simply a measure or indication of preload loss. It can take a value between 0 and 1. A 0 indicates no loosening and 1 indicates complete loosening. 4. Experiment Sixty-four tests were performed for the 26 nested-factorial design. The order of the runs was random. The machine settings were 15 Hz frequency and ±1.5 mm amplitude of displacement. Each test specimen is subjected to these loading conditions for 1750 cycles. The surfaces of the machine components in contact with the specimen were cleaned with acetone and filter paper before every test. The test results for every treatment combination are summarized in Table 2. In design of experiments, the lower case letters are used to represent the high level for a given factor. The absence of a letter indicates the lower level for a given factor. For example, treatment combination abc indicates high levels for factors A, B and C and low levels for factor D, E and F, Treatment combination (1) indicates low levels for all factors. The best performance (y = 0.01) was obtained with the treatment combination defined by the following conditions: aluminum fastener, 12.7 mm (1/200 ) nominal diameter, UNF threads, high preload, tight fit hole and lubrication. The preload time trace data for this treatment combination are displayed in Fig. 2. The high
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Table 2 Experimental results Run
Treatment combination
Initial preload (N)
Residual preload (N)
Response (y)
57 1 34 64 4 10 19 62 46 42 47 9 5 59 3 29 12 11 16 27 14 50 36 55 35 22 45 24 7 26 21 37
(1) a b ab c ac bc abc d ad bd abd cd acd bcd abcd e ae be abe ce ace bce abce de ade bde abde cde acde bcde abcde
1469 1469 6453 6453 1469 1469 6453 6453 2937 2937 12,905 12,905 2937 2937 12,905 12,905 1469 1469 6453 6453 1469 1469 6453 6453 2937 2937 12,905 12,905 2937 2937 12,905 12,905
399 0 870 0 928 0 4767 4118 2782 0 12,017 0 2700 0 12,239 9398 636 21 2977 0 1331 1063 4932 0 2491 1814 12,248 11,718 2295 1811 12,513 7604
0.73 1.00 0.87 1.00 0.37 1.00 0.26 0.36 0.05 1.00 0.07 1.00 0.08 1.00 0.05 0.27 0.57 0.99 0.54 1.00 0.09 0.28 0.24 1.00 0.15 0.38 0.05 0.09 0.22 0.38 0.03 0.41
13 38 15 17 28 52 6 44 61 51 53 60 2 48 58 49 41 32 33 18 40 54 30 23 31
f af bf abf cf acf bcf abcf df adf bdf abdf cdf acdf bcdf abcdf ef aef bef abef cef acef bcef abcef def
1469 1469 6453 6453 1469 1469 6453 6453 2937 2937 12,905 12,905 2937 2937 12,905 12,905 1469 1469 6453 6453 1469 1469 6453 6453 2937
1229 0 0 0 1301 0 0 164 2559 0 12,315 12,359 2756 0 11,754 12,413 0 92 0 0 1277 68 0 241 2741
0.16 1.00 1.00 1.00 0.11 1.00 1.00 0.98 0.13 1.00 0.05 0.04 0.06 1.00 0.09 0.04 1.00 0.94 1.00 1.00 0.13 0.95 1.00 0.96 0.07
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Table 2 (continued) Run
Treatment combination
Initial preload (N)
Residual preload (N)
Response (y)
63 20 39 43 25 8 56
adef bdef abdef cdef acdef bcdef abcdef
2937 12,905 12,905 2937 2937 12,905 12,905
2375 12,606 12,078 2779 2374 12,725 12,146
0.19 0.02 0.06 0.05 0.19 0.01 0.06
13200
Preload (N)
13000
12800
12600 0
20
40
60
80
100
120
Time (sec)
Fig. 2. Preload versus time plot for best experimental performance.
Table 3 Best eight experimental performances Treatment combination
Elastic modulus
Diameter (mm)
Pitch
Preload (N)
Hole fit
Lubrication
Response
bcdef bdef bcde abcdf abdf bdf bde bcd
AL AL AL SS SS AL AL AL
12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7
UNF UNC UNF UNF UNC UNC UNC UNF
12,905 12,905 12,905 12,905 12,905 12,905 12,905 12,905
Tight Tight Tight Loose Loose Loose Tight Loose
Oil Oil Dry Oil Oil Oil Dry Dry
0.01 0.02 0.03 0.04 0.04 0.05 0.05 0.05
preload and a large diameter are features present in the eight tests with the lowest level of loosening (see Table 3). Aluminum fasteners and oil lubrication are other conditions common in these tests. These results indicate that preload, fastener material, diameter and lubrication are important as individual factors or as part of an interaction. 5. Statistical analysis of data The ANOVA results for this experiment are presented in Table 4. It can be concluded from the low P values, that the factors preload (D(B)) and fastener material elastic modulus (A) have the highest influence in the resistance to loosening. Interactions that provide significant resistance to loosening includes fastener material · diameter interaction (AB), preload · lubrication interaction (D(B)F), fastener material · hole fit interaction (AE(B)), fastener material · diameter · lubrication interaction (ABF).
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Table 4 ANOVA results for parametric study Factor
SS
DF
MS
F
P
Model D(B) A AB DðBÞF AE(B) ABF E(B) C(B) F B Residual Total
8.534 4.270 2.004 0.442 0.594 0.578 0.232 0.314 0.313 0.010 0.008 2.451 10.984
15 2 1 1 2 2 1 2 2 1 1 48 63
0.569 2.135 2.004 0.442 0.297 0.289 0.232 0.157 0.157 0.010 0.008 0.051
11.142 41.816 39.255 8.665 5.819 5.657 4.548 3.074 3.066 0.186 0.163
<0.0001 <0.0001 <0.0001 0.0050 0.0055 0.0062 0.0381 0.0554 0.0558 0.6681 0.6886
Diameter (B) and lubrication (F) have been included in the ANOVA table for the hierarchical model, which takes into account not only the effect of the significant factors and interactions but the effect of non-significant factors included in the analysis of variance. Eq. (2) provides the general form for this model. Y ijklmn ¼ l þ Ai þ Bj þ ðABÞij þ C kðjÞ þ DlðjÞ þ EmðjÞ þ ðAEÞimðjÞ þ F n þ ðDF ÞlðjÞn þ ðABF Þijn þ eðijklmnÞ
ð2Þ
where Yijklmn is the variable response, l is the overall mean, Ai is the effect of the ith level of factor A, Bj the effect of the jth level of factor B, (AB)ij the AB interaction effect at levels ith and jth, respectively, Ck(j) the effect of the kth level of the factor C(B) within the jth level of factor B, Dl(j) the effect of the lth level of the factor D(B) within the jth level of factor B, Em(j) the effect of the mth level of the factor E(B) within the jth level of factor B, (AE)im(j) the AE(B) interaction effect at the ith level of factor A and the mth level of factor E(B) within the jth level of factor B, Fn the effect of the nth level of the factor F, (DF)l(j)n the D(B)F interaction effect at the nth level of factor F and the lth level of factor D(B) within the jth level of factor B, (ABF)ijn the ABF interaction effect at the ith level of factor A, the jth level of factor B and the nth level of the factor F, and eijklmn the residual error term. The subscripts i, j, k, l, m, n can take a value of 1 or 1 representing the low (1) or the high (1) level of each factor. The estimates of each effect term in the model are given in Table 5. The fitted values are calculated based on these estimated values. Fig. 3 compares these fitted values against the response variable defined in Eq. (1). The fitted response closely follows the trend of the response in most cases. The model has an R2 factor of 0.78 (R2 = 0.78). 6. Interpretation of results The analysis shows that preload and fastener material are the most significant parameters influencing the loosening. These factors are involved in significant interactions and therefore their overall effects are influenced by the factors in these interactions. In the case of the preload, the overall effect has to be estimated from the preload itself, the preload · lubrication interaction and the lubrication. The overall effect of fastener material with other factors leads to a more complex situation. To simplify its interpretation the effect of the less significant interaction (fastener material · diameter · lubrication) is excluded. In addition, since lubrication is not a significant parameter (even though it is included in the preload overall effect), it is not considered in the fastener material overall effect. The effect of thread pitch is studied separately since non-significant interactions are related to this parameter. The overall effects are estimated by adding the individual effects of the related factors and interactions. The resulting fitted response will increase or reduce from the mean l according to the levels of the factors involved. The flow charts in Figs. 4 and 5 map the overall effects of the preload and fastener material. From these figures, one sees that the overall effects for high preload and aluminum bolts are negative while the overall effects for low preload and stainless steel bolts are positive. Similarly, the effect of the fine thread is negative and the effect of the coarse thread is positive. Resistance to loosening increases as the overall effect decreases. There-
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Table 5 Estimates for model parameters Factor description
Estimator
Overall mean
^ l
Estimate 0.497
Level
Fastener material
b A
0.177 0.177
i = 1 i=1
Diameter
b B
0.011 0.011
j = 1 j=1
Fastener material · diameter
c AB
0.083 0.083
i · j = 1 i·j=1
Thread pitch
b C
0.076 0.076 0.063 0.063
k = 1 at j = 1 k = 1 at j = 1 k = 1 at j = 1 k = 1 at j = 1
Preload
b D
0.136 0.136 0.339 0.339
l = 1 at j = 1 l = 1 at j = 1 l = 1 at j = 1 l = 1 at j = 1
Hole fit
b E
0.097 0.097 0.018 0.018
m = 1 at j = 1 m = 1 at j = 1 m = 1 at j = 1 m = 1 at j = 1
Fastener material · hole fit
^ AE
0.134 0.134 0.012 0.012
i · m = 1 at j = 1 i · m = 1 at j = 1 i · m = 1 at j = 1 i · m = 1 at j = 1
Lubrication
Fb
0.012 0.012
n = 1 n=1
Preload · lubrication
c DF
0.027 0.027 0.134 0.134
l · n = 1 at j = 1 l · n = 1 at j = 1 l · n = 1 at j = 1 l · n = 1 at j = 1
Fastener material · diameter · lubrication
d ABF
0.060 0.060
i · j · n = 1 i·j·n=1
Response Fitted Response 1.20 1.00 0.80 0.60 0.40 0.20 0.00 1
10
19
28
37
46
55
64
Observations
Fig. 3. Response and range corrected fitted response comparison (—, response; - - - -, fitted response).
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High Preload
Large Dia.?
Yes
Overall Effect: -0.339
Yes
Oil ?
No
No
Overall Effect: -0.136
Oil ?
Overall Effect: -0.460
Overall Effect: -0.218
Yes
Overall Effect: -0.151
No
Note: Resistance to loosening increases as the overall effect decreases.
Overall Effect: -0.122
Fig. 4a. Overall effect of high preload.
Low Preload
Large Dia.?
Yes
Overall Effect: 0.339
Yes
Oil ?
No
No
Overall Effect: 0.136
Overall Effect: 0.193
Yes Oil ?
Overall Effect: 0.485
Overall Effect: 0.175
No
Overall Effect: 0.097
Note: Resistance to loosening increases as the overall effect decreases.
Fig. 4b. Overall effect of low preload.
fore, the results show high preload and low elasticity modulus fasteners with fine threads increase resistance to loosening. The benefits of a higher preload were expected based on the results obtained by other researchers [2,4,5,9]. At higher preloads the friction force is increased and the transverse force required to overcome the friction is higher and the occurrence of slippage is reduced leading to reduced or no loosening. The low modulus of elasticity of the aluminum mitigates loosening because: (a) it reduces the bending moment at the threads and thereby reduces localized slip since the reaction force distribution at the threads during the loading cycle is more even and, (b) it leads to contact between the fastener rod and the wall of the hole. This is consistent with Pai [5], who found when lateral contact occurs the applied transverse force is transmitted mostly through this contact point inhibiting slip at the bolt head.
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Low Elasticity Modulus
Large Dia.?
Yes
Overall Effect: -0.105
No
Overall Effect: -0.136
No
Overall Effect: -0.249
Tight Fit ?
Yes
Tight Fit ?
247
Overall Effect: -0.075
Yes
Overall Effect: -0.212
No
Note: Resistance to loosening increases as the overall effect decreases.
Overall Effect: -0.285
Fig. 5a. Overall effect of low elasticity modulus without interaction ABF.
High Elasticity Modulus
Large Dia.?
Yes
Overall Effect: 0.083
No
No
Overall Effect: 0.503
Overall Effect: 0.076
No
Overall Effect: 0.272
Tight Fit ?
Yes
Tight Fit ?
Overall Effect: 0.089
Yes
Overall Effect: 0.043
Note: Resistance to loosening increases as the overall effect decreases.
Fig. 5b. Overall effect of high elasticity modulus without interaction ABF.
The effect of the fine thread on the loosening is attributed to the lower off-torque obtained with a smaller thread pitch. Fig. 4a shows that the effect of high preload is higher in 12.7 mm (1/200 ) bolts than in 6.4 mm (1/400 ) bolts. The normal stress generated by the preload has the same value for large or small bolts. However, the preload magnitude is different depending on the cross sectioned area of the fastener. Since larger bolts require a higher preload than smaller size fasteners in order to attain the same normal stress level, the tangential force necessary to overcome the friction force is higher in large size bolts. The coefficient of friction decreases with the application of lubricant. Low coefficients of friction promote slippage and thereby loosening. This is the behavior observed in Fig. 4b. However when higher preloads are applied in combination with lubrication, the resulting effect is beneficial for vibration resistance (see Fig. 4a).
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To obtain the same level of preload it is necessary to apply a much higher tightening torque in a joint without lubrication than in an oiled joint. In addition, a larger amount of torsional energy is stored in bolts under higher preloads with no lubrication. During the loading cycle this energy is released aiding the turning of fastener loosening. Fig. 5a reveals that the smaller diameter 6.4 mm (1/400 ) aluminum bolts have a more positive effect reducing loosening than the 12.7 mm (1/200 ) bolts. The effect of an aluminum fastener is expected to be more positive when combined with a smaller diameter since the low modulus of elasticity and the low moment of inertia (produced by the small diameter) reduce the bending moment and facilitate the lateral contact occurrence. In general, a tight fit is a condition that helps prevent loosening since it promotes lateral contact. However, when tight fit is used in combination with small diameter and low elastic modulus bolts an opposite effect may be obtained (see Fig. 5b). Tight fit holes induce higher deformation of the bolt and slender, flexible bolts may experience plastic deformation that manifest as loss of preload. 7. Application to bolted joint design Standard procedures in the design of bolted joints, e.g., VDI 2230 [10], recommend the use of as high preloads as possible without causing damage to the fastener, to avoid joint separation. The results obtained experimentally indicate that this recommendation is valid for the load conditions studied in this paper. At higher preloads the friction moments are higher reducing the possibility of slip and loosening. The range of applications for fasteners made of materials with low elastic modulus is typically limited to requirements with respect to corrosion, weight and thermo-conductivity or electrical conductivity. The results presented in this study reveal an advantage with respect to vibration resistance for this type of fastener. Disadvantages include higher cost and lower mechanical capacity for a given size. The use of fasteners with large diameters is desirable to ensure joint integrity under both static and dynamic loads. The experimental results show that when vibrations are present, large diameter fasteners are preferred because they allow the application of higher preloads and reduce the variability in the level of loosening. The resistance to loosening becomes more dependent on preload and less dependent of other parameters as diameter increases. Thus, the utilization of generous safety factors in the design process in specifying fastener size is recommended when the load conditions are of a dynamic nature, especially in the transverse direction. Regarding the selection of thread series for fasteners, fine thread fasteners are preferred in applications containing cyclic loads because their smaller helix angle reduces the off-torque. A lower tightening torque reduces the stored torsional energy which can aid loosening. In addition, they possess a larger tension area than coarse thread fasteners, which allows the application of higher preloads. The tight hole fit is preferred in joints under transverse vibration because it minimizes slip between the contact surfaces in the joint. Although lubrication reduces the coefficient of friction, when the preload is high, lubrication becomes beneficial for loosening resistance. This results from lower torsional energy stored during installation and released during use. 8. Conclusions A parametric study of the basic factors affecting threaded fastener loosening has been developed. The results of the study identified fundamental factors related to the fastener loosening phenomena. Their contributions to the level of loosening experienced by the joint have been quantified and assembled into a statistical model. The model is at least useful for comparing relative percentage of loss of preload for different combinations and levels of the factors studied. This has been presented graphically in flow charts to aid the joint design process. References [1] Junker GH. New criteria for self-loosening of fasteners under vibration. SAE Transactions 1969;78:314–35. [2] Finkelston RJ. How much shake can bolted joints take. Mach Des 1972;44:122–5.
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[3] Walker RA. The factors which influence the vibration resistance of fasteners. Jenkintown (PA): Standard Pressed Steel Co.; 1973. [4] Ramey GE, Jenkins RC. Experimental analysis of thread movement in bolted connections due to vibrations, NASA Research Project NAS8-39131. AL: Marshall Space Flight Center; 1995. [5] Pai NG. Vibration induced loosening of threaded fasteners: mechanisms, modeling and design guidelines, Ph.D. Dissertation. Tampa: University of South Florida; 2002. [6] Hess DP. Vibration- and shock-induced loosening. In: Bickford JH, Nasser S, editors. Handbook of bolts and bolted joints. New York: Marcel Dekker, Inc.; 1998. p. 757–824. [7] Blake A. What every engineer should know about threaded fasteners: materials and design. New York: Marcel Dekker, Inc.; 1986. [8] Oberg E, Jones FD, Horton HL, Ryffel HH. Machinery’s handbook. New York: Industrial Press; 2000. [9] Hess DP. Counter-threaded spring-actuated lock-fasteners. J Mech Des 2002;124:582–5. [10] Bickford JH. An introduction to the design and behavior of bolted joints. New York: Marcel Dekker; 1995.