MD1 05 Screw Fasteners PDF

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Summary

Screw Fasteners These are threaded members used for clamping or fastening other members in joints. They include bolts, screws, nuts, etc. Other threaded members used for transmitting power (e. power screws or translation screws are included in the latter part of Combined stresses)where D = nominal s...

Description

Machine Design 1: BASAEN, RV

dr ht β p

5. SCREW FASTENERS Screw Fasteners These are threaded members used for clamping or fastening other members in joints. They include bolts, screws, nuts, etc. Other threaded members used for transmitting power (e.g. power screws or translation screws are included in the latter part of Combined stresses) Crest

p

Root

p

D External thread

where D

=

p

=

= = = =

root or minor diameter thread height thread angle (60° for American V threads) pitch of threads

Thread Specifications 1. American and Unified National Thread Series 1 – 8 UNC – 2 A - RH RH – right hand threaded LH – left hand threaded A – external thread B – internal thread

Crest

D

1 – widest tolerance 2 – normal fit 3 – closest fit

Root Internal thread

UNC – coarse thread UNF – fine thread UNEF – extra fine thread Number of threads per inch (TPI or th/in.); its reciprocal is the pitch of thread in inches, 1 , ฀฀฀฀. ฀฀= ฀฀฀฀฀฀ Nominal size (major diameter)

nominal size of the thread; major diameter; diameter at the crest of an external thread, or at the root of an internal thread pitch of thread

Basic Thread Profile This shows the proportions of the thread. The two thread standards (Unified thread or UN and the metric thread M) have the same profiles. The threads may be coarse (UNC), fine (UNF) or extra fine (UNEF). Flank

Note: For UN threads, sizes may be fractional (greater than ¼” in diameter) or numbered (less than ¼” ). For fastening, both the UN and metric threads have a thread angle of 2฀฀ = 60฀฀ . 2.

Metric Thread Series M – 16x2 – 6g g– external thread Tolerance grade Pitch in mm/thread Nominal size (major diameter; in mm stands for Metric thread series

Terminology of thread profile.

Note: Metric threads can be coarse, fine, or extra fine, and are also specified as right or left hand threaded Example 1: a) Determine the pitch of a 7/8”-9UNC thread. b) Determine the diameter in inches of a 1032UNF thread Solution:

Details of M and UN thread profiles. where dc = dp =

D = diameter at the crest; major diameter pitch diameter 54

Machine Design 1: BASAEN, RV

Tensile stress area, As This represents the equivalent area in determining the tensile stress of a threaded member. It is an area based on a circle whose diameter is the average between the pitch diameter and the minor diameter of the thread. Stress area, As

p

Thread Forms for Screws and Bolts P

Ds

D

60º American V-Threads

P

P

60º

29º

P/8 Seller’s Screw Thread

P 55º

0.3707P

Acme Screw Thread

Whitworth (British) Thread

Note: The following formulas for stress area As, were taken from MED by Mott UN threads

฀฀ ฀฀฀ ฀ = (฀฀ − ฀฀. ฀฀฀฀฀฀ ฀฀฀฀)฀฀ , ฀฀฀฀฀฀ ฀฀ (D and p in inches)

Metric threads

฀฀ ฀฀฀ ฀ = (฀฀ − ฀฀. ฀฀฀฀฀฀ ฀฀฀฀)฀฀ , ฀฀฀฀฀฀ ฀฀ (D and p in mm)

Types of threaded fastener. (a) Bolt and nut; (c) Cap screw; (c) stud.

Empirical Formulas for Bolts from the Textbook Example 2: Determine the stress areas of each of the following threads: a) 1” diameter bolt with fine thread, b) 1.5” diameter screw with coarse thread, and c) M10 x 1.5 bolt.

Bolt head

Fe

D

Solution:

Fe = tensile load of bolt; its safe external load D = nominal size of bolt (major diameter) Sd = design stress of bolt Sy = yield strength of bolt material As = stress area of bolt N = factor of safety

Fe Nut

Connected parts

Cylinder assembly using bolts and nuts.

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Machine Design 1: BASAEN, RV

♦

Strength Consideration

♦

Initial Tightening Torque ฀฀฀ ฀ = ฀฀฀฀ ฀฀฀฀฀฀

Case 1. Design stress is given

where ฀฀฀

฀

฀฀฀฀ ฀฀฀ ฀ = = ฀฀฀฀ : ฀฀฀ ฀ ฀฀ = ฀฀2 : unless specified 4

Note : This is a basic consideration wherein the bolt is treated as an ordinary member of circular section under tension.

Ti Fi D CL

♦

The bolt’s design stress Sd can also be expressed in terms of Sy / N. However, it should have considered the initial stress used during tightening of the bolt prior to the application of the external load Fe. This initial tightening stress is generally high.

tightening torque required in in-lb initial tension desired major diameter, inches friction factor: 0.15 for lubricated bolts; 0.20 for “as received” bolts.

Torque Causing Shear during Tightening ฀฀฀ ฀ = ฀฀. ฀฀฀฀฀฀ Ti = Ts =

tightening torque twisting moment in bolt

Note: This torque causing shear is only present during tightening. It gradually disappears after tightening due to relaxation of the materials, vibration during operation, etc.

Case 2. Only the yield strength is given, factor of safety is not specified. ฀฀฀฀ ฀฀฀ ฀ = (฀฀฀฀ )฀฀.฀฀ ฀฀ (from p. 169, DME Faires) Note: This assumes that the bolt is well-tightened before the external load Fe is applied. Formula applies to D < ¾”.

= = = =

♦

Tightening Stress in Bolts, Si: (p. 169 Faires) Rule of thumb in tightening the bolts ฀฀฀ ฀ ≈ ฀฀. ฀฀฀฀฀฀ : If ฀฀฀฀ is available

where: Sy = bolt material’s yield strength in psi As = stress area in in2 Fe = safe external load in lb.

where ฀฀฀฀

=

Case 3. Bolt material is specified, but no Sy value given

฀฀฀ ฀ ≈ ฀฀. ฀฀฀฀฀฀฀฀ : If ฀฀฀฀ is not available

฀฀฀ ฀ = ฀฀฀฀฀฀ ฀฀.฀฀฀฀฀฀ ฀฀฀฀

(from p. 138, DMM – Doughtie & Vallance) Note: This assumes that the bolt is well-tightened before the external load Fe is applied. Formula applies to D ≥ ¾”. where Ar = stress area, in2 C = material constant: C = 5000 psi for carbon steel bolts; C = up to 15,000 for alloy steels; C = 1000 psi for bronze bolts. For D > 2”, Sd is generally 7,000 to 8,000 psi for carbon steels and up to 20,000 psi for alloy steels.

proof stress of bolts; stress above which permanent deformation of bolt starts to occur

=

yield strength of bolt material

Note: Values of ฀฀฀฀ , ฀฀฀฀ , and ฀฀฀ ฀ for selected bolt materials (฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀) are shown in ฀฀฀฀฀฀฀฀฀ DME Faires. ♦

Threaded Length of Bolts

฀฀฀ ♦

฀

฀฀฀ ฀ = 1.5฀฀: ฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ 1 = 2฀ ฀ +฀฀฀฀. : ฀฀฀฀฀฀ ฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀ 4

Length of Engagement (Cap screws and Stud Bolts) At least ฀ ฀ = 1.5฀฀ : for cast iron and other brittle materials At least ฀ ฀ = ฀฀฀฀฀฀1.25฀฀ : for steel and other ductile materials 56

Machine Design 1: BASAEN, RV

At least ฀ ฀ = 3฀฀ : for aluminum ♦

a. b.

Depth of Hole VS. Threaded Length ฀฀฀฀฀฀฀฀ℎ ฀฀฀฀ℎ฀฀฀฀฀฀ = ฀฀฀฀฀฀ + 2

1 c.

♦

Formulas from Machineries Handbook Working Strength of Bolts ฀ ฀ = ฀฀฀฀ (฀฀. ฀฀฀฀฀฀฀ ฀ − ฀฀. ฀฀฀฀฀฀) where W = working strength in lb. St =allowable working stress, psi d = bolt diameter, in.

Specify the standard diameter required for the stud bolts. Compute for the torque required in tightening each bolt if the tightening stress is to be about 70% of the material’s yield strength value. Torsional stress induced at the root diameter of each of the bolts during tightening.

Solution Ten stud bolts: ฀฀฀฀ =10 Pressure:฀ ฀ = 15 ฀฀฀฀/฀฀฀฀ 2 Effective dia,: ฀฀฀ ฀ = 20.32 ฀฀฀฀

Hp rating of a set screw ฀฀฀฀฀฀฀฀.฀฀ ฀฀= ฀฀฀฀ Ref.: Machinery’s Handbook, 23rd ed. p. 1394 d = P = D = N =

set screw diameter required, in. horsepower transmitted by shaft shaft diameter used, in. shaft rpm

♦ Typical Joints using Bolts or Screws

฀฀฀฀ ฀฀

฀฀฀฀

฀฀฀ ฀ ฀฀฀฀฀฀฀฀฀฀

฀฀฀฀ ฀฀

฀฀฀฀

Cylinder assembly using bolts and nuts.

฀฀฀ ฀ ฀฀ = total external load supported by the bolts ฀฀ = pressure inside the vessel ฀฀฀฀ = equivalent diameter at which the pressure is distributed; also the effective vessel diameter Thus, for each bolt the external load is ฀฀ ฀฀ � ฀฀฀฀฀฀� ฀ ฀ ฀฀฀ ฀ = : ฀฀฀ ฀ where nb = number of bolts in the joint Example 1: Ten stud bolts are used to fasten the head of 203.2 ฀฀฀฀ diameter ammonia compressor. The maximum operating pressure inside the cylinder is to be 15 ฀฀฀฀/฀฀฀฀ 2 and the bolts are made of AISI C1020, as rolled steel. 57

Machine Design 1: BASAEN, RV

(b) ฀฀฀ ฀ =?: Circumferential pitch (spacing of the bolts along the circumference of the bolt circle)

Example 2: A steam cylinder, 10 mm thick, is to handle a maximum pressure of 1.25 MPa. The effective cylinder diameter is 350 mm (also the inside diameter, in this case). The cylinder cover is to be held by ฀฀฀฀ machine bolts M24 x 3. (a) Determine the number of bolts required if the design stress of each bolt is about 33 MPa only. (b) What is the circumferential pitch of the bolts? Is this enough for a leak-proof joint? Consider a bolt hole diameter , ฀฀1 = 25฀฀฀฀ and a clearance of 1.5฀฀1 from the center of bolt to the edge of cover and external surface of cylinder. For a leak-proof joint, the circumferential pitch should be about 20�฀฀1 ฀฀฀฀ 30�฀฀1 , where d1 is the bolt hole diameter in mm. Solution: (a) ฀฀฀ ฀ =?: Number of bolts required

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Machine Design 1: BASAEN, RV

Elastic Analysis of Bolted Joints The stiffness of the bolt and that of the connected parts are taken into consideration in the analysis of the joint.

Stiffness, k: • For the bolt:

• Fe = tensile load of bolt; its safe external load D = nominal size of bolt (major diameter) Sd = design stress of bolt Sy = yield strength of bolt material As = stress area of bolt N = factor of safety

Fi D

Bolt (b) Fi Fe

Nut

where, ฀฀฀฀ ฀฀฀฀

For the parts:

Fe

Bolt head

Connected parts (c)

=

initial tension; serves as the initial tensile load of the bolt or the initial clamping force of the parts = external load of joint; (a fraction of this load becomes the additional tensile load of the bolt and the remaining fraction serves as a reduction in the clamping force of the parts

฀฀฀฀฀฀฀฀฀฀,฀฀

Stiffness line of bolts (b) : ฀฀฀ ฀ = ฀฀฀฀ ฀฀฀฀

฀฀฀฀

∆฀฀฀฀

฀฀฀฀

฀฀

Δ฀฀

฀฀฀฀

∆฀฀฀฀

฀฀฀ ฀

Final loads after Fe is applied: For the bolts: ฀฀฀ ฀ = ฀฀฀ ฀ + ∆฀฀฀฀ For the connected parts: ฀฀฀ ฀ = ฀฀฀ ฀ − ∆฀฀฀฀ where ฀฀฀ ฀ = ∆฀฀฀ ฀ + ∆฀฀฀฀ Reduction in the clamping force of parts

฀฀฀฀ ฀฀฀฀ Stiffness line of connected parts (c): ฀฀฀ ฀ = ฀฀฀ ฀ ฀฀฀฀

฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀,

Thus, Δ฀฀ =

฀฀฀฀ Δ฀฀฀฀ ฀฀฀ ฀ = = ฀฀฀ ฀ Δ฀฀ ฀฀฀฀ Δ฀฀฀฀ ฀฀฀ ฀ = = ฀฀฀ ฀ Δ฀฀

Δ฀฀฀฀ Δ฀฀฀฀ ฀฀฀฀ = : Δ฀฀฀ ฀ = (Δ฀฀฀฀ ) ฀฀฀ ฀ ฀฀฀ ฀ ฀฀฀ ฀

Derivations for ฀฀฀฀฀฀ ฀฀฀฀฀฀ ฀฀฀฀฀฀, etc.: From ฀฀฀ ฀ = ∆฀฀฀ ฀ + ∆฀฀฀฀ ฀฀฀฀ ฀฀฀฀ ฀฀฀ ฀ = ∆฀฀฀ ฀ + (Δ฀฀฀฀ ) = ∆฀฀฀ ฀ �1 + �: ฀฀ ฀฀฀ ฀ ฀฀ ฀฀฀฀ � ∆฀฀฀ ฀ = ฀฀฀ ฀ � ฀฀฀ ฀ + ฀฀฀฀ Similarly, for Δ฀฀฀฀

฀฀฀฀ ฀฀฀ ฀ = ∆฀฀฀ ฀ + ∆฀฀฀ ฀ = (Δ฀฀฀ ฀ ) + Δ฀฀฀฀ ฀฀฀ ฀ ฀฀฀฀ ฀฀฀ ฀ = ∆฀฀฀ ฀ �1 + �: ฀฀฀ ฀ ฀฀฀฀ � ∆฀฀฀ ฀ = ฀฀฀ ฀ � ฀฀฀ ฀ + ฀฀฀฀

Thus, the final loads after Fe is applied are: ฀฀฀ ฀ = ฀฀฀ ฀ + ∆฀฀฀฀ ฀฀฀฀ ฀฀฀ ฀ = ฀฀฀ ฀ + ฀฀฀ ฀ � � (฀฀฀฀฀฀฀฀฀฀฀฀฀฀) ฀฀฀ ฀ + ฀฀฀฀ ฀฀฀ ฀ = ฀฀฀ ฀ − ∆฀฀฀฀ ฀฀฀฀ � (฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀) ฀฀฀ ฀ = ฀฀฀ ฀ − ฀฀฀ ฀ � ฀฀฀ ฀ + ฀฀฀฀ Note: ฀฀฀ ฀ > 0; to ensure that a clamping force still exists in the parts ฀฀฀฀ should not exceed the bolt’s safe stress External load that opens the joint, ฀฀฀฀ : If the external load ฀฀฀฀ is too high, ฀฀฀ ฀ approaches ฀฀฀฀ and the joint starts to open (i.e. ฀฀฀ ฀ = 0). From the chart, by similar triangles ฀฀฀฀ ฀฀฀฀ = ฀฀฀ ฀ ฀฀฀ ฀ + ฀฀฀฀ But, ฀฀฀฀ ฀฀฀฀ ฀฀฀ ฀ = : ฀฀฀฀฀฀ ฀฀฀ ฀ = ฀฀฀ ฀ ฀฀฀฀ ฀฀฀฀ ฀฀฀฀ ฀฀ + ฀฀฀฀ : ฀฀฀฀ , ฀฀฀ ฀ = ฀฀฀ ฀ � ฀ ฀ = � ฀฀฀฀ ฀฀฀฀ ฀฀฀฀ ฀฀฀ ฀ + ฀฀฀฀ ฀฀฀ ฀ ฀฀฀฀

Additional tensile load of bolts External load applied

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Machine Design 1: BASAEN, RV

Final Stress in the Bolt after External Load ฀฀฀฀ is applied: For the Bolt

Note:

Solution:

฀฀฀฀ ฀฀฀ ฀ = ฀฀฀฀

Bolts (b): ฀฀฀ ฀ = 4 D=?

Final tensile stress in bolt, ฀฀฀฀ this should not exceed the proof strength of the bolt material. For the Connected Parts ฀฀฀ Note:

฀

฀฀฀฀ = ฀฀฀฀

฀฀฀฀ ฀

Connected parts (c)

If ฀฀฀ ฀ ≤ 0 the joint opens, i.e. no more clamping force is left in the connected parts.

Example 3: A set four bolts in a joint provides a clamping force of 16000 ฀฀฀฀, which is equally shared among the bolts. a. Specify the bolt size required if they are to be designed based on an initial stress of 75% of their proof stress/strength. (This is not a standard procedure in selecting the bolts since the basis is not the external load ฀฀฀฀ that they are supposed to handle). The bolts are to be made of SAE Gr. 5 or ASTM A325 (Table 5.2 of DME by Faires) Also compute for the torque necessary in tightening each lubricated bolt. b. Assume that the above joint is subjected to a total external lead of 12,000 lb after the bolts have been tightened, and that the stiffness of the connected parts is three times that of the bolts. Compute for the final stress in each bolt. Are the bolts still safe? c. What total external land may open the joint? d. The same as (b) and (c) except that the stiffness of the parts is only one-tenth that of the bolt: ฀฀฀ ฀ = 1 ฀฀ . 10 ฀฀ e. Redesign the bolts (i.e. Solve for the required bolt size in (d) if they are to be based on the external load that they are supposed to handle. f. Estimate the factor of safety (based on the Soderberg criterion) of the bolts in (฀฀ ) if they are to be made of SAE Gr. 5, with seller’s threads that are cut & hardened (฀฀฀฀12), use the same load values in (฀฀) & (฀฀) with ฀฀฀ ฀ = 3฀฀฀฀ . Consider the loads to vary indefinitely. g. Redesign the bolts in (f) based on a Soderberg’s factor of safety of N = 2.0 only.

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Machine Design 1: BASAEN, RV

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Machine Design 1: BASAEN, RV

Calculation of Stiffness, ฀ ฀

&฀ ฀

฀ ฀

Bolt (b)

฀฀฀฀

฀฀1

D

฀฀2

฀฀฀฀

฀฀3

ℎ

ℎ = bolt grip ฀฀฀ ฀ = unthreaded length of bolt ฀฀฀฀ = threaded length of bolt ฀฀1 , ฀฀2 , ฀฀3 = thickness of parts ฀฀ = bolt diameter ฀฀ℎ = bolt hole diameter

Dh Connected parts (c)

•

฀ ฀

ℎ = ฀฀฀ ฀ + ฀฀฀฀ ℎ = ฀฀1 + ฀฀2 + ฀฀3 + ⋯

Stiffness of the Bolt, ฀฀฀฀ Two sections of the bolt connected in series: ฀฀ ฀฀ ฀฀ = + ฀฀฀ ฀ ฀฀฀ ฀ ฀฀฀฀ where,

฀฀฀฀฀฀ ฀฀ ∶ ฀ ฀ =฀฀2 4 ฀฀฀ ฀ ฀฀฀฀ ฀฀฀฀ : ฀฀฀ ฀ = stress area of bolt = ฀฀฀ ฀

฀฀฀ ฀ = ฀฀฀

•

฀

Stiffness of the Connected Parts For the ‘n’ clamped members that are connected

in series,

Or,

฀฀ ฀฀ ฀฀ ฀฀ ฀฀ + ⋯+ + + = ฀฀฀ ฀ ฀฀฀ ฀ ฀฀฀ ฀ ฀฀฀ ฀ ฀฀฀฀ ฀฀

฀฀฀฀ ฀฀฀฀ ฀฀฀฀ +⋯ + + = ฀฀ ฀฀฀ ฀ ฀฀฀฀ ฀฀฀ ฀ ฀฀฀฀ ฀฀฀ ฀ ฀฀ ฀฀฀ ฀

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Machine Design 1: BASAEN, RV

where, ฀฀฀฀ = ฀฀฀฀

equivalent compressed area of the connected parts ฀฀ ฀฀฀ ฀ = [฀฀฀ ฀฀฀ − ฀฀ ฀฀ ] ฀฀ = equivalent outside diameter of parts being clamped

Note: If the area being clamped is too large, an estimation formula for ฀฀฀฀ may be used (page 169, DME Faires) ℎ ฀฀฀ ฀ = (Dimension ฀฀ from ฀฀฀฀฀฀฀฀) + 2

•

Stiffness of the connected parts, ฀฀฀฀ For the 3 parts

where Dimension A = width of nut across flats as given by AT14 h

=

bolt grip

฀฀ ฀฀

Note: If the compress area is clear (i.e. solvable and not too large), don’t use the above estimation formulas.

฀฀฀ ฀

฀฀

Example 4 Determine ฀฀฀฀ /฀฀฀฀ from the given bolted joint by considering the following dimensions. The bolt has coarse threads. Bolt : AISI C 1020, rolled steel Gasket, Eg = 19ksi ฀฀฀฀

฀฀1

D

฀฀฀฀

฀฀3

ℎ

Other Data: ฀฀฀ ฀ = 2.25” ฀฀฀฀ = 0.75” ฀฀1 = 1.45” ฀฀2 = 0.05 ฀฀3 = 1.5” ฀฀ = 1” ฀฀ℎ = 1.125”

D Cast iron ASTM 40 blocks

Solution: • Stiffness of the bolt ฀฀฀฀ :

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Machine Design 1: BASAEN, RV

Table 5.2 of DME Faires MINIMUM STRENGTHS OF BOLTS (ksi) (SELECTED STANDARD SPECIFICATIONS) SIZES, ฀฀฀฀, ฀฀฀฀฀฀ ฀฀฀฀, ฀฀฀฀฀฀ ฀฀฀฀, ฀฀฀฀฀฀ GRADE

SAE Grade 2

SAE Grade 5, ASTM A325

BB ASTM 354

BC BD

INCL. (in.) 1 3 − 4 4 7 −1 8 1 1 1 −1 8 2 1 3 − 4 4 7 −1 8 1 1 1 −1 8 2 1 1 −2 4 2 1 2 −4 2 1 1 −2 4 2 1 2 −4 2 1 1 −1 4 2

55

69

52

64

28

55

85

120

88

78

115

81

74

105

77

80

105

83

75

100

78

105

125

109

95

115

99

120

150

125

64...