07 power screws and threaded fasteners [handout]

Design of Machine ElementsPower Screws and Threaded Fasteners

Dr. R. Prasanth KumarAssistant Professor

Department of Mechanical EngineeringIndian Institute of Technology Hyderabad

Course: ME3130Aug-Dec 2013

R. P. Kumar (IITH) Design of Machine Elements Power Screws and Threaded Fasteners 1 / 32

Introduction

Fastening – process of joining two parts together temporarilyFastener – the part which is used for fasteningThreaded fastener – machine element which has helicalthreads on it which is used for fastening two parts

I helical threads are also called screw threads which are ridgesformed on a cylindrical or conical surface

Power screw - mechanical device used for converting rotarymotion to linear motion and transmitting power.

I lead screw in lathes, screw-jacks, vices


Forms of Screw Threads

Right-handed threads are always used unless there is a special requirement for left-handedthreads.Right-handed helix will advance when it is turned clock-wise, irrespective of the directionof viewing.Three major types of screw threads: ISO metric vee threads, square threads, ISO metrictrapezoidal threads

I Vee threads are used for fastening; not suitable for power transmission (Threaded fasteners)I Square and trapezoidal threads for power transmission (Power screws)


Power Screws

Applications:raise loads (ex: screw jack)obtain accurate motion in machiningoperations (ex: lead-screw of lathe)clamp a work piece or specimen (ex: vice)

Advantages:Compact with large load carrying capacitySimple to design, easy to manufactureLarge mechanical advantage hencemanually operatedCan be designed with self-locking property

Limitations:Poor efficiency, as low as 40%High friction causes rapid wear; usuallynut is made of soft material so that it canbe replaced.

Exception: Recirculating ball screw


Power ScrewsSquare Threads Vs Trapezoidal Threads

Square threads are more efficient thantrapezoidal threadsThere is no radial (bursting) pressure onthe nut, life of nut is increasedDifficult to manufacture; machining withsingle point cutting tool is expensiveWeak at the core compared to trapezoidalthreadWear cannot be compensated;replacement required

Tapezoidal threads are less efficientThere is radial (bursting) pressure on thenut, life of nut is decreased.Easier to manufacture; multipoint cuttingtool (thread milling machine)Strong at the core compared to squarethreadWear can be compensated using split-typenut.


Terminology of Power Screw Threads

Major diameter(Nominal diameter) dMinor diameter(Core diameter)dc = d − pMean diameter dm = d − 0.5p

Pitch pI distance measured parallel to the axis from

one point on one thread to the correspondingpoint on adjascent thread

Lead lI distance measured parallel to the axis which

the nut will advance in one revolution of screwThread angle 2θ

I angle included between thread surfacesmeasured in an axial plane

Helix angle or lead angle αI angle made by the helix of the screw with the

plane perpendicular to the axis of the screw


Power ScrewsTorque Requirement for Lifting Load

Effort P should act towards right to lift theload W .Considering equilibrium of horizontal forces,

P = µN cosα+ N sinα.

Considering equilibrium of vertical forces,

W = N cosα− µN sinα.

P = W (µ cosα+ sinα)(cosα− µ sinα)

Coefficient of friction µ can be expressed asµ = tanφ, where φ is the friction angle.

P = W tan(φ+ α).

Torque Mt required to raise the load is

Mt = Pdm2 = Wdm

2 tan(φ+ α).


Power ScrewsTorque Requirement for Lowering Load

Effort P should act towards left to lower theload W .Considering equilibrium of horizontal forces,

P = µN cosα−N sinα.

Considering equilibrium of vertical forces,

W = N cosα+ µN sinα.

P = W (µ cosα− sinα)(cosα+ µ sinα)

Coefficient of friction µ can be expressed asµ = tanφ, where φ is the friction angle.

P = W tan(φ− α).

Torque Mt required to raise the load is

Mt = Pdm2 = Wdm

2 tan(φ− α).


Power ScrewsSelf-Locking Screw

If friction angle is less than helix angle (φ < α), then the torque required to lower the load

Mt = Wdm2 tan(φ− α) < 0.

Mt < 0 indicates that no torque is required to lower the load; the load itself will turn thescrew and descend down (assuming no restraining torque).

I This condition is called overhauling of the screw or back driving of the screw.When φ ≥ α, positive torque is required to lower the load.

I If no torque is applied, the load will stay in its place – self-lockingI Required property for screw-jack application

For a self-locking screw, φ ≥ α, or

tanφ ≥ tanα, or, µ ≥ lπdm

.

High coefficient of friction and/or low lead help achieve self-locking.R. P. Kumar (IITH) Design of Machine Elements Power Screws and Threaded Fasteners 9 / 32

Power ScrewsEfficiency of Square Threaded Screw

Efficiency is the ratio of the work outputto the work input.Assuming friction loss is only betweenscrew and nut, efficiency is

η = WlPπdm

= WP tanα = tanα

tan(φ+ α) .

Efficiency can also be written as

η = sin(2α+ φ)− sinφsin(2α+ φ) + sinφ.

Efficiency is maximum when sin(2α+ φ) ismaximum or

α = 45◦ − φ

2 .

Maximum efficiency of a square threadedpower screw is

ηmax = 1− sinφ1 + sinφ.


Power ScrewsTrapezoidal and Acme Threads

Trapezoidal and acme threads look alike except for thread angle: 2θ = 30◦ fortrapezoidal, and 2θ = 29◦ for acmeExpressions for effort P and efficiency η are similar to those of square threads, except forthe friction coefficient µ which is replaced by µ sec θ.

I This is done to compensate the effect of inclined thread profile in axial plane.


Power ScrewsCollar Friction Torque

When load being raised is supported on acollar, collar friction has to be considered.Torque required to overcome collar frictioncan be determined by using:

I uniform pressure theory,

(Mt)c = µcW3

D3o −D3

iD2

o −D2i

I uniform wear theory.

(Mt)c = µcW4 (Do + Di)

I Uniform pressure theory is used for newsurfaces, whereas uniform wear theory forsurfaces after initial wear.


Power ScrewsOverall Efficiency

Total external torque required to raise the load is

(Mt)t = Mt + (Mt)c,

where (Mt)t is the external torque required to raise the load, Mt is the torque required toovercome friction at the thread surface, and (Mt)c is the collar friction torque.Overall efficiency is given by

ηo = Wl2π(Mt)t

.


Power ScrewsExercises

1) The nominal diameter of a triple theraded square screw is 50 mm, while the pitch is 8 mm.It is used with a collar having an outer diameter of 100 mm and inner diameter of 65 mm.The coefficient of friction at the thread surface as well as at the collar surface can be taken as0.15. The screw is used to raise a load of 15 kN. Using uniform wear theory for collar friction,calculate:(i) torque required to raise the load; (ii) torque required to lower the load; and (iii) the forcerequired to raise the load, if applied at a radius of 500 mm.Answers: (i) 204.64 N-m, (ii) 87.4 N-m, (iii) 409.3 N2) Lead screw of a lathe has single-start ISO metric trapezoidal threads of 52 mm nominaldiameter and 8 mm pitch. The screw is required to exert an axial force of 2 kN to drive thecarriage. Collar has outer and inner diameters as 100 mm and 60 mm respectively. Coefficientof friction for threads is 0.15 and collar is 0.12. The lead screw rotates at 30 rpm. Calculate(i) power required to drive the lead screw, (ii) efficiency of the screw.Answers: (i) 61.8 W, (ii) 12.94%


Threaded Fasteners

Threaded joint is a separable joint of two or more machine parts that are held together bymeans of a threaded fastening such as a bolt and a nut.Extensively used in mechanical assemblies – over 60% of all parts have threadsAssembled by means of a spanner – mechanical advantageSelf-locking – can be placed in any position, vertical, horizontal or inclined

Limitations of Threaded Joints:Requires holes in machine parts – results in stress concentrationLoosen when subjected to vibrationMajor obstacle for efficient assembly - “cost of tightening a screw can be six to ten timesthe cost of the screw itself”.


Threaded FastenersBasic Types of Screw Fastening

Through boltsI Also called machine bolts, automobile

bolts, eyebolts or carriage boltsI Shank (cylindrical portion between head

and threads) does not require a finishedsurface

Tap bolts and cap screwsI Cap screws are smaller sized tap bolts (5

to 30 mm)I One of the parts is thick enough to

accommodate a threaded holeI No place to accommodate the nut

StudsI Cylindrical rod threaded at both endsI Parts that require frequent dismantling and reassembly


Threaded FastenersCap Screws

Cap screws are of two categoriesI engaged externally by a spannerI engaged internally from end face

Internally engaged cap screws:I Useful in confined spaces and counter

bored holesI Result in better appearance of the

product


Threaded FastenersSet Screws

Used to prevent relative motion betweentwo parts by frictionThreaded portion passes through one part,end portion presses against another partDiffer from cap screws

I subjected to compressive forces onlyI short and threaded over full length


Threaded FastenersBolt of Uniform Strength

Energy absorbed during shockand imact loading depends onresilence of the material

Energy absorbed is directly proportional to thestress in the materialStress is more in the threaded portion because

I core diameter is less than shank diameterI stress concentration

Bolt of uniform strength absorbs energy uniformlyand releases when unloadedThere are two ways of achieving this:

I Reduce the shank diameter to less than the corediameter

I Drill a hole in the shank reduce the cross-sectionalarea


Threaded FastenersLocking Devices

Static working conditionsI self-locking (α < φ), does not

loosenDynamic working conditions

I loosens due to vibrationI locking can be achieved by

creating additional friction,split pin, elastic deformation


Threaded FastenersTerminology of Screw Threads

For ISO metric screw threads,dc = d − 1.22687p.Approximate relationship: dc = 0.8d


Threaded FastenersMaterials and Manufacture

Free cutting steels for lightly loaded smallbolts, studs, and nutsPlain carbon and alloy steels for highstrength boltsStainless steel where corrosion resistancerequired

Two methods for making threads:I Thread cutting – automatic machines

that cut threadsI Thread rolling (cold forming) – threads

are rolled from bar stock between dies;induces residual compressive stresseswhich improves fatigue strength; reducedstress concentration due to radii at crestand root; less wastage of material


Threaded FastenersSimple Analysis of Bolted Joint

Maximum tensile stress in the bolt at the weakest cross-section:

σt = 4Pπd2

c= Syt

fs

For threads of the bolt to be equally strong in tension and shear

τ = Pπdch = Ssy

fs = Syt2 fs = 2P

πd2c

which gives height of the nut h = 0.5dc.Standard proportion has h = 0.4d (since dc = 0.8d)


Threaded FastenersSimple Analysis of Bolted Joint: Exercise1) An electric motor weighing 10 kN is lifted by means of an eyebolt. The eye bolt is screwed into the frame of the motor. Theeye bolt has coarse threads. It is made of plain carbon steel 30C8(Syt = 400 N/mm2) and the factor of safety is 6. Determine thesize of the bolt.

Answer: d = 17.27 mm; M20

2) Two plates are fastened by means of two bolts asshown in figure. The bolts are made of plain carbonsteel 30C8 (Syt = 400 N/mm2) and the factor of safetyis 5. Determine the size of the bolts if P = 5 kN.

Answer: d = 8.92 mm; M10


Threaded FastenersEccentrically Loaded Bolted Joints in Shear

Ai is cross-sectional area of bolt i.

x =∑

Aixi∑Ai

, y =∑

Aiyi∑Ai

Primary shear, P ′i = Pno. of blots

P × e =∑

P ′′i ri

Secondary shear is produced by moment due to eccentricity.

Secondary shear, P ′′i = Cri C = Pe∑r2

iPi = P ′i + P ′′i (vector sum)


Threaded FastenersEccentrically Loaded Bolted Joints in Shear

Exercise1) The structural connection shown in previous slide is subjected to an eccentric force P of 10kN with an eccentricity of 500 mm from the CG of the bolts. The center distance betweenbolts 1 and 2 is 200 mm, and the center distance between bolts 1 and 3 is 150 mm. All thebolts are identical. The bolts are made from plain carbon steel 30C8 (Syt = 400 N/mm2) andthe factor of safety is 2.5. Determine the size of the bolts. (Assume tap bolts)Answer: d = 17.34 mm, M20


Threaded FastenersEccentric Load Perpendicular to Axis of Bolt Assumptions :

1 Bracket and the steel structure are rigid.2 Bolts are fitted in reamed and ground holes.3 Bolts are not preloaded (no initial tension).

Upper and lower bolts denoted by 1 and 2respectively. Moment tends to tilt the bracketabout C .

Direct shear, P ′i = Pno. of blots Stretch, δi ∝ li Resisting force, P ′′i = Cli

External force, Pe = 2P ′′1 l1 + 2P ′′2 l2 C = Pe2(l2

1 + l2)Farthest bolt is subjected to maximum tension. Shear stress P ′1/A. Tensile stress σt = P ′′1 /A.

σ1 = Sut(fs) τmax = Ssy

(fs) Ssy = 0.5Syt


Threaded FastenersEccentric Load Perpendicular to Axis of Bolt

Exercise1) The following data are given for the bracket shown in the previous slide. P = 25 kN, e =100 mm, l1 = 150 mm, l2 = 25 mm. There is no preload in the bolts. The bolts are made ofplain carbon steel 45C8 (Syt = 380 N/mm2) and the factor of safety is 2.5. Using maximumshear stress theory, specify the size of the bolts.Answer: M16


Threaded FastenersEccentric Load on Circular Base

Assumptions:Bolts are identicalBearing and structure are rigid, nopre-load and stress concentration in boltsShear stresses relieved through dowel pins

Pl =∑

Pi li =∑

Cl2i , C = Pl∑

l2i


Threaded FastenersEccentric Load on Circular BaseSuppose, a is radius of the flange, b is radiusof pitch circle of the bolts. From Fig. (b)

l1 = a − b cosα, l2 = a + b sinαl3 = a + b cosα, l4 = a − b sinαl21 + l2

2 + l23 + l2

4 = 4a2 + 2b2

The resisting force

P1 = Pl(a − b cosα)2(2a2 + b2) = 2Pl(a − b cosα)

4(2a2 + b2)

For n (even number of) bolts,

P1 = 2Pl(a − b cosα)n(2a2 + b2) .

For α = 180◦, bolt 1 will occupy the top mostposition and will be subjected to highest load.

Pmax = 2Pl(a + b)n(2a2 + b2) .

In case of pillar crane, direction of P changes.Design each bolt for highest load Pmax .In case where direction of P is fixed, designsuch that two bolts are equally far from C .

α = π − β, β = 12

2πn cosα = − cos

(π

n

)P1 =

2Pl(a + b cos(

πn))

n(2a2 + b2) .


Threaded FastenersEccentric Load on Circular Base

1) A pillar crane shown in figure is fastened to the foundation bymeans of 16 identical bolts spaced equally on 2 m pitch circlediameter. The diameter of the pillar flange is 2.25 m. Determinethe size of the bolts if a load of 50 kN acts at a radius of 7.5 mfrom the axis of the crane. The maximum permissible tensilestress in the bolt is limited to 75 N/mm2.

Answer: M24


ReferencesDesign of Machine Elements, 3e, V. B. BhandariMachine Design: An Integrated Approach, 3e, Robert L. Norton


07 power screws and threaded fasteners [handout]

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