The Augustus Group Products Projects and Engineering Consulting

TORQUE PRELOAD CONTROL Jesse Meisterling

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BOLT PRELOAD Definition: • Initial Preload: the tensile stress created in an individual fastener when first tightened. • Residual Preload: the tensile stress in an individual fastener when the joint tightening process is completed. • Operational Bolt Load or In Service Tension: resultant bolt load under operating conditions; temperature, pressure, external loads, etc. 3/1/2006

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BOLT BASICS A bolt is a spring.

Angle Torque

∂F≅ ∂ The elastic behavior of our bolting materials keeps everything together.

Load

Stretch has been used for many years to control preload. As long as the initial ‘loading’ of the fastener is below the yield point, the ∂ from“zero load” to the target will be proportional to the tension force in the fastener.

Stretch

Load

If the fastener is taken beyond the yield point it is still the elastic “stretch” that produces the residual bolt load. An “unload” stretch measurement will produce an accurate load measurement in the fastener. 3/1/2006

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TORQUE PRELOAD RELATIONSHIP T = Fp(P/2π + μtRt/cosΒ+ μnRn) Where: T=torque Fp=Preload P= Thread Pitch μt=Friction on thread flank Rt=Radius of thread flank Β=Flank angle/2 μn=Friction under head or nut Rn =Radius of nut bearing surface

3/1/2006

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TORQUE PRELOAD RELATIONSHIP What are the forces?

μ

•Fp(P / 2π) - creates load in the fastener - lead screw •Fp(μtRt/cosΒ) - reaction torque in threads •Fp(μnRn) - reaction torque under nut

Lube Graphite, mineral oil Graphite, machine oil Molykote-G Fel-Pro C5A Crane 425A Grafo 360 Neolube

min 0.035 0.035 0.03 0.045 0.07 0.1 0.03

max 0.06 0.055 0.075 0.08 0.09 0.115 0.09

avg 0.048 0.045 0.053 0.063 0.08 0.108 0.06

The reaction forces work against us tightening the bolt and keep the screw together when installed

3/1/2006

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TORQUE PRELOAD RELATIONSHIP Bolt Tension using Torque In the ideal world there would be a linear repeatable correlation.

B o l t P r e l o a d

Torque applied

3/1/2006

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But:

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TORQUE PRELOAD RELATIONSHIP Variables Affecting Bolt Torque/Tension VDI analysis UASF study came up w/ 71

3/1/2006

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TORQUE PRELOAD RELATIONSHIP From our first equation we see the friction dependence. •Fp(P / 2π) •Fp(μtRt/cosΒ) •Fp(μnRn)

3/1/2006

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TORQUE PRELOAD RELATIONSHIP 160

120000

Load as k changes (2% of base) 120

% Change in Load

100000

% K 2% 80000

%

100 80

60000

60

Load lbs

140

40000

40 20000

20 0 0.35

0 0.3

0.25

0.2

0.15

0.1

k

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TORQUE PRELOAD UNCERTAINTY Experiments show that the torque/preload relationship is uncertain. There is a family of torque/preload lines. The Air Force study identified 74 factors. Some are: •Lube and application method •Hardness •Surface finish •Plating •Material •Angularity of parts •Thread fit •Combination of above... 3/1/2006

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MATERIAL HARDNESS AND TORQUE 50 each - 1.25” axle flange bolts, 4 strength grades, tightened to 2000 ft-lbs. Data taken after assembly and after 24 hrs. 4000XXX Engineering Test Report Ultrasonic Clamp Load M easurement In Axle Assembly - 13 Bolts per Sample Group Installed to 2,000 ft-lb 140,000 180 ksi Proof Load - 139,500 lbs

130,000 170 ksi Proof Load - 131,700 lbs 2nd Tightening On Right Side Of Axle 150 ksi

120,000

Ultrasonic Clamp Load (lbs)

110,000 100,000 90,000 80,000 70,000

1st Tightening On Left Side Of Axle 180 ksi

60,000 1st Tightening On Right Side Of Axle 170 ksi

50,000

2nd Tightening On Left Side Of Axle 170 ksi

40,000 30,000 20,000

Average + 3 Sigma Average - 3 Sigma Average 180 ksi - 10 min

180 ksi - 24 hrs

170 ks i - 10 min

170 ksi - 24 hr

170 ksi - 10 min

170 ksi - 24 hr

Gr 8 - 10 min

Gr 8 - 24 hr

Bolt Strength - M easurement Period

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SHORT FORM TORQUE TO PRELOAD T= kDFp Where: T = Torque k = Nut factor D = Nominal diameter Fp = Preload

The nut factor is an empirical factor that is obtained by tests. It is developed with the target lubricant. The “short form” k factor is not one number, it has a range and mean for each lubricant used. 3/1/2006

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COMMON k FACTORS Nut Factors (K)

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Lube

Min. Reported

Mean

Max. Reported

As-Received

0.158

0.2

0.267

Alloy or Mild Steel Fasteners As-Received Stainless Steel Fasteners Cadmium Plate (Dry) Copper Based Anti-Seize Cadmium Plate (Waxed) Fel-Pro CS4 Fel-Pro C70 Fel-Pro N 5000 (paste) Machine Oil Moly Plate or Grease Never-Seeze (Paste) Neolube Phos-Oil Solid Film PTFE Zinc Plate (Waxed) Zinc PIate (Dry)

-

0.3

0.106 0.08 0.17 0.08 0.08 0.13 0.10 0.10 0.11 0.14 0.15 0.09 0.071 0.075

0.2 0.132 0.187 0.132 0.095 0.15 0.21 0.13 0.17 0.18 0.19 0.12 0.288 0.295

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0.328 0.23 0.198 0.23 0.15 0.27 0.225 0.18 0.21 0.20 0.23 0.16 0.52 0.53

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NON-PARAMETRIC k STUDY Fel Pro to N5000 Fel-Pro N5000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Fel Pro N5000

Molycote G 0.1113 0.1113 0.123 0.1346 0.1352 0.1352 0.1371 0.1397 0.1412 0.1447 0.1452

0.1463 0.1523 0.1533 0.1551 0.1577 0.1598 0.1605 0.1621 0.1631 0.1696 0.172 0.1757 0.1768 0.1852 0.189 0.1954 0.2043 0.2061 0.2267 0.2703 0.2703

Num ber of runs - 8 Rank sum of Y's - 23 Num ber of X's above m edian 13 Num ber of Y's above m edian -3 Median of com bined set - 16.5

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Fel Pro to Molycote G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Never Seeze 0.1183 0.1183 0.1452

0.1463 0.1523 0.1537 0.1537 0.1551 0.1577 0.1577 0.1598 0.1604 0.1605 0.1621 0.172 0.1752 0.1768 0.178 0.1852 0.189 0.1892 0.1936 0.1954 0.1968 0.2013 0.2043 0.2061 0.2102 0.2267 0.2365 0.2703 0.2703

Number of runs - 18 Rank sum of Y's - 58 Number of X's above median - 9 Number of Y's above median - 7 Median of combined set - 16.5

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K FACTOR: MULTIPLE TIGHTENINGS 2 1/4 - 8 x 12 B16 Studs A - Mo2 Grease b - Clean and Dry

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HIGH-SPEED TIGHTENING

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ASSEMBLY BOLT STRESS - Txx Tensile Stress (Txx) Txx = Fp/A = Fp/(π D2/4) Since we are applying torque (T) T = kD Fp Then: Fp = T/kD and Txx = 4T/(π D3)

3/1/2006

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TORSIONAL STRESS - TXY Assume only 50% of the applied torque twists the bolt, the other 50% is lost in overcoming the friction at the bearing surface of the head and into loading the bolt.

TXY = (0.5T)C/J Where: J = Polar moment of inertia = π D2 /32 C = Max radius = D/2

TXY = (0.5T) 16/ π D3) 3/1/2006

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COMBINED STRESS Calculate the maximum stress from the combined tensile and shear stress Txx max = Txx/2 + [Txy2 + (Txx/2)2] 1/2 Form a ratio Txy/Txx Txy/Txx = (0.5(16)T/ (n D3) )/ 4T / (n (k) D3) Txy/Txx = 2 (k)

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COMBINED STRESS Now pick a nut factor (k) and go back to Equation 1 Txx max = 1/2 + [(0.3)2 + (1.0/2)2] 1/2 Txx max = 1/2 + 0.58 Txx max = 1.08 The torsional stress increases the maximum stress by 8%. This is crude; haven't worried much about the diameter. The VDI calculation is a little more detailed. 3/1/2006

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DISTORTION ENERGY THEORY PER ANSI B 1.1 Syp = [St2 + 3Ss2]1/2 Where: Syp = Yield stress St = Tensile stress Ss = Shear stress Ss = 0.3 St for k = 0.15

Syp = = [St2 + 3(0.3 St 2]1/2 St = 0.89 Syp 3/1/2006

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