Fastener Torque

Fastener Torque

Determining the proper torque for a fastener is the biggest problem in fastener installation. Some of the many variables causing problems are

1. The coefficient of friction between mating threads
2. The coefficient of friction between the bolthead (or nut) and its mating surface
3. The effect of bolt coatings and lubricants on the friction coefficients
4. The percentage of bolt tensile strength to be used for preload
5. Once agreement is reached on item 4, how to accurately determine this value
6. Relative spring rates of the structure and the bolts
7. Interaction formulas to be used for combining simultaneous shear and tension loads on a bolt (Should friction loads due to bolt clamping action be included in the interaction calculations?)
8. Whether "running torque" for a locking device should be added to the normal torque

Development of Torque Tables

The coefficient of friction can vary from 0.04 to 1.10, depending on the materials and the lubricants being used between mating materials. (Table IV from ref. 2 gives a variety of friction coefficients.) Since calculated torque values are a function of the friction coefficients between mating threads and between the bolthead or nut and its mating surface, it is vitally important that the torque table values used are adjusted to reflect any differences in friction coefficients between those used to calculate the table and the user's values. Running torque should be included in the values listed in the tables because any torque puts shear load on the bolt.

The torque values in table V have been calculated as noted in the footnotes, by using formulas from reference 3. (A similar table was published in Product Engineering by Arthur Korn around 1944.)

Higher torques (up to theoretical yield) are sometimes used for bolts that cannot be locked to resist vibration. The higher load will increase the vibration resistance of the bolt, but the bolt will yield and unload if its yield point is inadvertently exceeded. Since the exact yield torque cannot be determined without extensive instrumentation, it is not advisable to torque close to the bolt yield point.

Fastener proof load is sometimes listed in the literature. This value is usually 75 percent of theoretical yield, to prevent inadvertent yielding of the fastener through torque measurement inaccuracies.

Table V -- Bolt Torque

[No lubrication on threads. Torque values are based on friction coefficients of 0.12 between threads and 0.14 between nut and washer or head and washer, as manufactured (no special cleaning).]

Size	Root area, in.2	Torque range (class 8, 150 ksi, bolts (Note 1))
10-24	0.0145	23 to 34 in.-lb
10-32	0.0175	29 to 43 in.-lb
1/4-20	0.0269	54 to 81 in.-lb
1/4-28	0.0326	68 to 102 in.-lb
5/16-18	0.0454	117 to 176 in.-lb
5/16-24	0.0524	139 to 208 in.-lb
3/8-16	0.0678	205 to 308 in.-lb
3/8-24	0.0809	230 to 345 in. -lb
7/16-14	0.0903	28 to 42 ft -lb
7/16-20	0.1090	33 to 50 ft-lb
1/2-13	0.1257	42 to 64 ft-lb
1/2-20	0.1486	52 to 77 ft-lb
9/16-12	0.1620	61 to 91 ft-lb
9/16-18	0.1888	73 to 109 ft-lb
5/8-11	0.2018	84 to 126 ft-lb
5/8-18	0.2400	104 to 156 ft-lb
3/4-10	0.3020	117 to 176 ft-lb (Note 2)
3/4-16	0.3513	139 to 208 ft-lb (Note 2)
7/8-9	0.4193	184 to 276 ft-lb (Note 2)
7/8-14	0.4805	213 to 320 ft-lb (Note 2)
1-8	0.5510	276 to 414 ft-lb (Note 2)
1-14	0.6464	323 to 485 ft-lb (Note 2)
1 1/8-7	0.6931	390 to 585 ft-lb (Note 2)
1 1/8-12	0.8118	465 to 698 ft-lb (Note 2)
1 1/4-7	0.8898	559 to 838 ft-lb (Note 2)
1 1/4-12	1.0238	655 to 982 ft-lb (Note 2)
Note 1:  The values given are 50 and 75 percent of theoretical yield strength of a bolt material with a yield of 120 ksi. Corresponding values for materials with different yield strengths can be obtained by multiplying these table values by the ratio of the respective material yield strengths.
Note 2:  Bolts of 0.75-in. diameter and larger have reduced allowables (75 percent of normal strength) owing to inability to heat treat this large a cross section to an even hardness.

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Alternative Torque Formula

A popular formula for quick bolt torque calculations is T = KFd, where T denotes torque, F denotes axial load, d denotes bolt diameter, and K (torque coefficient) is a calculated value from the formula:

$$ K = \left({ d_m \over 2d }\right) { \tan{\psi} + \mu \sec{\alpha} \over 1 - \mu \tan{\psi} \sec{\alpha} } + 0.625 \mu_c $$

as given in reference 4 (p. 378) where

dm	thread mean diameter
ψ	thread helix angle
μ	friction coefficient between threads
α	thread angle
μc	friction coefficient between bolthead (or nut) and clamping surface

The commonly assumed value for K is 0.2, but this value should not be used blindly. Table VI gives some calculated values of K for various friction coefficients. A more realistic "typical" value for K would be 0.15 for steel on steel. Note that μ and μ_c are not necessarily equal, although equal values were used for the calculated values in table VI.

Table VI -- Torque Coefficients

Friction coefficient		Torque Coefficient, K
Between threads, μ	Between bolthead (or nut) and clamping surface, μc
0.05	0.05	0.074
0.10	0.10	0.133
0.15	0.15	0.189
0.20	0.20	0.250

Torque-Measuring Methods

A number of torque-measuring methods exist, starting with the mechanic's "feel" and ending with installing strain gages on the bolt. The accuracy in determining the applied torque values is cost dependent. Tables VII and VIII are by two different "experts," and their numbers vary. However, they both show the same trends of cost versus torque accuracy.

Table VII -- Industrial Fasteners Institute's Torque-Measuring Method

[From ref. 1.]

Preload measuring method	Accuracy, percent	Relative cost
Feel (operator's judgment)	±35	1
Torque wrench	±25	1.5
Turn of the nut	±15	3
Load-indicating washers	±10	7
Fastener elongation	±3 to 5	15
Strain gages	±1	20

Table VIII -- Machine Design's Torque-Measuring Method

[From ref. 5.]

(a) Typical tool accuracies

Type of tool	Element controlled	Typical accuracy range, percent of full scale
Slug wrench	Turn	1 Flat
Bar torque wrench	Torque	±3 to 15
	Turn	1/4 Flat
Impact wrench	Torque	±10 to 30
	Turn	±10 to 20°
Hydraulic wrench	Torque	±3 to ±10
	Turn	±5 to 10°
Gearhead air-powered wrench	Torque	±10 to ±20
	Turn	±5 to 10°
Mechanical multiplier	Torque	±5 to 20
	Turn	±2 to 10°
Worm-gear torque wrench	Torque	±0.25 to 5
	Turn	±1 to 5°
Digital torque wrench	Torque	±1/4 to 1
	Turn	1/4 Flat
Ultrasonically controlled wrench	Bolt elongation	±1 to 10
Hydraulic tensioner	Initial bolt stretch	±1 to 5
Computer-controlled tensioning	Simultaneous torque and turn	±0.5 to 2

(b) Control accuracies

Element controlled	Preload accuracy, percent	To maximize accuracy
Torque	±15 to ±30	Control bolt, nut, and washer hardness, dimensions, and finish. Have consistent lubricant conditions, quantities, application, and types.
Turn	±15 to ±30	Use consistent snug torque. Control part geometry and finish. Use new sockets and fresh lubes.
Torque and turn	±10 to ±25	Plot torque vs turn and compare to previously derived set of curves. Control bolt hardness, finish, and geometry.
Torque past yield	±3 to ±l0	Use "soft" bolts and tighten well past yield point. Use consistent snugging torque. Control bolt hardness and dimensons.
Bolt stretch	±1 to ±8	Use bolts with flat, parallel ends. Leave transducer engaged during tightening operation. Mount transducer on bolt centerline.

References

1. Fastener Standards. 5th ed., Industrial Fasteners Institute, Cleveland, OH, 1970.
2. Baumeister, et al.: Mark's Standard Handbook for Mechanical Engineers. 8th ed., McGraw-Hill, 1978.
3. Seely, F.B.: Resistance of Materials. 3rd ed., Wiley & Sons, 1947.
4. Shigley, J.E.; and Mitchell, L.D.: Mechanical Engineering Design. 4th ed., McGraw-Hill, 1983.
5. Machine Design, Nov. 19, 1981.

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