2.72 Elements Of Mechanical Design Lecture 07: Bolted Joints

2.72 Elements of Mechanical Design Lecture 07: Bolted joints

Bolted joint +’s and –’s Good:    

Low cost? Able to be disassembled Strong Compatible with almost any material

Bad:    

Takes up a lot of space Micro-slip/hysteresis/damping problems Difficult to model and control Can require long fabrication and assembly time

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Bolted joints: Their purpose Bolted joints = connectors, impact many parts: Stiffness

Vibration

Damping

Stability

Load capacity

Bolted joints are semi-permanent!   

Max benefit obtained when it is highly preloaded, i.e. near the yield point Threads can plastically deform/work harden Some elements of bolted joints are not reusable

Bolted joints are used to create assemblies that resist: (i) Tensile loads

(ii) Moments

(iii) Shear loads

Bolts are NOT meant to resist (i) – (iii)

© Martin Culpepper, All rights reserved

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Components

Anatomy of a bolted joint l 

Grip

Ad

At 

Tensile stress area



Major diameter area

Ad L

l

lt 

LT 

Unthreaded length in grip

d 

t1

ld

t2

lt

Threaded length in grip

ld

tw

HBolt

HNut

At

Major diameter (unthreaded)

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tw

Joint components: Clamped member

Things to consider with the clamped member: 2. Stone or lap the surface (increase stiffness) 3. Remove burs (increase joint stiffness) 4. Be sure flange surfaces are flat so bolt does not bend

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Bolted joint components: Bolt Rolled Threads

NEVER in shear or bending 

Head  

Keep threads clean & lubed to minimize losses

Shank



~50% power to bolt head friction



~40% power to thread friction



~10% power to deforming the bolt and flange

Cut Threads

Steel is most common © Martin Culpepper, All rights reserved

Stress concentrations at the root of the teeth Fatigue crack propagation! Exception: Shoulder bolts

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Bolted joint components: Washers Purpose of Washers:

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

Spacer



Distribute load in clamped member



Reduce head-member wear



Lower coefficient of friction/losses



Lock bolt into the joint (lock washer)



Increase preload resolution (wave washer)

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Bolted Joint Components: Nut

Threads do not distribute the load evenly:

What can be done to distribute the load better

2. First thread has the shortest load path (stiffest)

2. Use a softer nut material 3. Use a bolt and nut that have different pitch

plastically used once forwith precision applications 3.Threads The pitch of the boltdeform threads and nutBolts are values to begin threads change as they are loaded © Martin Culpepper, All rights reserved

4. Use a special nut that lengthens the load path of the first thread 9

Stiffness

Preload While preloading joint, are the flange & bolt “springs” in parallel or in series?

Series: • Same Forces • Different Displacements (stretches)

Parallel: • Same Displacements (stretches) • Different Forces

Fpreload = Flange Compression Kflange Fpreload = Bolt Stretch KBolt © Martin Culpepper, All rights reserved

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Preloaded joint modeled as series spring

km

kb

Need to find equivalent bolt and member stiffness © Martin Culpepper, All rights reserved

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Bolt stiffness Shoulder bolt/cap screw consists of two different parts

Ad E kd = ld At E kt = * lt



kd kt



Threaded Unthreaded

Each has different  

Cross sectional area Axial stiffness

The load passes through both

The effective threaded grip length, lt*, used in the stiffness calc is the sum of the threaded grip length plus three threads © Martin Culpepper, All rights reserved

 

They act in series This is a series spring calculation −1

1 1  kt k d kb =  +  = kt + k d  kt k d 

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Member stiffness dw

Pressure cone exists in the member materials and bolt head

z

The clamping area at the member interfaces depends upon α 25o-45o

dh

A z       



Half-apex angle, α Bore clearance, dh

Stiffness calculation by integration through the depth of the member

dw  dh  z tan        2  2 

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Washer diameter, dw



P dz dδ = E A(z ) 



2

2

 Ed tan   

km 

  d w  d h  2t tan      d w  d h  

ln 



  d w  d h  2t tan      d w  d h   14

Loading

Tensile loads in bolted joints Fi 

Preload



External tensile load



Portion of P taken by bolt

P Pb L

l

Pm 

LT 

Fraction of P carried by bolt



Fraction of P carried by members

t1

ld

t2

lt

Portion of P taken by members

C

tw

HBolt

HNut

1-C © Martin Culpepper, All rights reserved

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tw

Forces in the bolt and the members When loaded with a tensile force   

Most of the force is taken by the members Very little (<15%) of the force is taken by the bolt For most, this is counter intuitive….

P

P

P

P

© Martin Culpepper, All rights reserved

km

kb

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Forces in the bolt and the members So how much does each see? 

Pm = Portion of P taken by members



Pb = Portion of P taken by bolt

km

kb

kb Pb  PPC k m  kb

P = Pm + Pb

Pm = P (1 − C )

Pb Pm δ= = kb k m

Fb  Pb  Fi Fm  Pm  Fi

High preload = High load capacity

P,δ

Fb  CP  Fi

What happens when joint separates? © Martin Culpepper, All rights reserved

Fm = (1 − C ) P − Fi 18

Static load capacity CP Fi σb = + At At

Typically the bolt fails first, why?  

It is the least expensive It is the most easily replaced

Proof load and stress 

Sp = proof stress = Limiting value of σb (~ 0.85 σy)

n=

Load factor (like a factor of safety) 

n > 1 ensures σb < Sp

How high should the pre-load be? 

Non-permanent: Some suggest 0.75 Fp



Permanent:

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Some suggest 0.90 Fp

C n P Fi + = Sp At At S p At − Fi CP

P

P

P

P

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Shear resistance When joint is in shear   

Friction between the members takes the load, not the bolt Coefficient of friction and preload are the important properties Dowel pins or shoulder bolts should be used to resist shear

P

P

P

P

© Martin Culpepper, All rights reserved

P   s Fi

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Torque, friction, preload

Bolt torque and preload How to measure   

Via stretch = but impractical Via strain = expensive built-in bolt sensor Via torque = not “ultra-repeatable” but easy and most often used

Relationship between Torque and Stretch?

ETorque = E friction + Estretch

How much do you torque the bolt when tightening?   

Too little = weak, compliant joint Too much = bolt may break or the joint may bulge Usually torque the bolt until Proof Load is reached

Continuous tightening is important: © Martin Culpepper, All rights reserved

μs > μ k

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Best practices

Best practices D

H >2D

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Threads should be at least 1.5 D deep for bolt to reliably hold a load

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Applications: Gasket / roller bearings Gasket

Roller Bearings

Wave washers can reduce tightening sensitivity to achieve desired preload. © Martin Culpepper, All rights reserved

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Exercise

Group exercise The tool holder stiffness is critical to lathe accuracy.

Calculate the stiffness of the bolted joint between your tool holder and cross slide bearing.

How does the relative stiffness of this compare with the stiffness of other parts in the load path?    

Structure Bearings Rails Etc…

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Preventing Bolts from Coming Loose How do you prevent bolts from coming loose? 2. Use the joint in a low vibration environment 3. Use bolts with fine threads (small pitch) 4. Use a large preload 5. Use materials with high coefficients of friction 6. Use Loctite on the threads 7. Use an adhesive between the bolt head and flange 8. Use lock washers

N F F = μ s*N

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Applications: Bearing Rails

Rails

Carriage

Tighten bolts sequentially

1.5 L © Martin Culpepper, All rights reserved

L 29

Applications: Bearing Rails Objectives: • Maximize stiffness • Decrease manufacturing cost • Maximize accuracy

Accuracy is maximized by overlapping strain cones. Therefore, the thicker the rail, the few bolts are necessary. But the rail becomes less stiff.

Same stiffness Beware of bulging

High manufacturing cost Bolt spacing should be about 4x the bolt diameter

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