mechanical engineer's data handbook - gear

7/28/2019 Mechanical Engineer's Data Handbook - Gear

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APPLIED MECHANICS 95

2.9.1 Service factor fo r ro lli ng bearingsThe bearing load should be m ultiplied by the followingfactor when selecting a bearing.

Uneven Mo derate Heavy Very heavyType of load Even light shock shock shock shockService factor 1o 1.2-1.5 1.7-2.0 2.2-2.5 2.7-3.0

2.9.8 Coefficient of fr ic tion for bearingsPlain bearings - boundary lubrication Rolling bearings

P

Mixed film (boundary plushydrodynamic) 0.024.08Thin film 0.084.14Dry (metal to m etal) 0.2M.40Plain journal bearings- il bath lubrication

P

Velocity Pressure PressureLubr icant (ms- ) 7 b ar 30 barMineral grease 1.0 0.0076 0.00016Mineral grease 2.5 0.0151 0.0027Mineral oil 1o 0.0040 0.0012Mineral oil 2.5 0.007 0.0020

P

Self-aligning ball 0.001&0.0066Rollers 0.00124.0060Thrust ball 0.001 4 . 0 0 6 0Deep groove ball 0.0015-0.0050Taper roller 0.00254.0083Spherical roller 0.00294.0071Angular contact 0.00184.00 19

2.10 GearsGears are toothed wheels which transmit motion andpower between rotating shafts by means of success-ively engaging teeth. They give a constant velocityratio a nd different types are av ailable to suit different

relative positions of the axes of the shafts (see table).Most teeth are of the involute type. The nomen-clature for spur gears is given in the figures.


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96 MECHANICAL ENGINEERS DATA HANDBOOKI_ entredistance

s

/2. IO . I Classificationof gears

Type of gear Relation of axes Pitch surfaces Eleme nts of teethSpu r Parallel Cylinder Straight, parallel toaxisParallel helical Parallel Cylinder HelicalHerringbo ne Parallel Cylinder Dou ble helicalStraight bevel Intersecting Cone StraightSpiral bevel Intersecting Co ne SpiralCrossed helical Crossed but not Cylinder Helicalworm Right angle but Cylinder Helicalintersectingnot intersecting

2.10.2 Metri c gear teethDTMetric module m = - (in millimetres)

where: D=pitch circle diameter, T=number of teeth.The preferred values of mod ule are: 1, 1.25, 1.5,2,2.5,3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40 an d 50.

ItDTCircular pitch p=- m

Addendum =mDedendum =1.25m

0.39mDatum

2.25m

Height of tooth =2.25mThe figure show s the metric tooth form for a rack(Le.a gear with infinite diameter).


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Design of gearsThe design of gears is complex and it is recommendedthat British Standards (or other similar sources) beconsulted.See BS 436 for the design of gears and BS 1949 for

permissible stresses.2.10.3 Spur gearsSymbols used:F=ooth forceF,= angential component of tooth forceF ,= eparating component of tooth forcer#J =pressure angle of teeth

D , =pitch circle diameter of driver gearD, =pitch circle diameter of driven gearN , =speed of driver gearN , =speed of driven gearn, =number of teeth in driver gearn2 =number of teeth in driven gearP=powerT = torque9=efficiency

Tangential force on gears F,=F cos #JSeparating force on gears F,=F , tan q5Torque on driver gear T I=-FIDI2

FID,Torque on driven gear T , =- 2. N , D , nSpeed ratio ---=A

N 2 D , n,D2Input power P i=271N, ,

D2Output power P , = 2 n N 2 F , ~ q

PoEfficiency q=-piRack and pinion driveFor a pinion, pitch circle diameter D speed N andtorque T :Rack velocity V = n D N

2TForce on rack F=- DRack power P=FVq= nN Tqwhere: 9 =efficiency.2.10.4 Helical spur gearsIn this case there is an additional component of forceFa in the axial direction.


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98 MECHANICAL ENGINEER'S DATA HANDBOOK

Let:&= pressure angle normal to the tootha= helix angle

Separating force F ,=F, tan-6"cos a

Axial force Fa=F, ta n aDouble helical gearsT o eliminate the axial thrust, gears have two sectionswith helices of opposite hand. These are also called'herringbone gears'.

- @- 1 -Single helical gear. .

Double helical gear

2.10.5 Bevel gearsStraight bevel gearsLet:4 =pressure angle of teethB=pinion pitch cone angleTangential force on gears=F,Separating forceF,=F, ta n (bPinion thrust F,=F, sin BGear thrust F,=F, cos f l

Spiral bevel gearLet:a=spiral angle of pinion

c$, =normal pressure angle

1an 6, in k an a cosg[ cosaForce on pinion F , =F, 1an cosB -+ t a n a sin[ cosaForce on gear F, = F,

For the diagram shown the signs are '+' for F, an d'-' for F,. The signs are reversed if the hand of thehelix is reversed or the speed is reversed; they rem ainthe same if both are reversed.

r i g h t evel gear

I '~,,'p,

Spiral bevel gear


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2.10.6 Wor m gearsThe worm gear is basically a screw (the worm)engaging with a nut (the gear). The gear is, in effect, apartial nut whose length is wrapped ar ou nd in a circle.Let :b,,=normal pressure angle

u =worm helix anglen, =number of threads or starts on wormn, =number of teeth in gearD, =worm pitch circle diameterD,= ear pitch circle diameterL= ead of wormp=pitch of worm threads and gear teethp =coefficient of frictionq =efficiencyu=velocity of gear teeth

T , =worm torqueN, =peed of wormN , = peed of gear

Worm\

Tangen tial force on worm ,F ,=axial force on gear$,=- 2TWDWcos 4,, - p ta n ucos 4" an u+pTangential force on gear ,F, =axial force on worm =F,

sin 4"co s4, sin u+ cos uSeparating force on each component F,= ,F,

Ltanu=-; L=pn,; D,=pn,JnEfficiency q =Input power P, =2nN,T,Gear tooth velocity u=nD, N,

nDW 1os b,,-/* an LY( os 4"+ co t a


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100 MECHANICAL ENGINEERS ATA HANDBOOK

Coefficient of friction for worm gearsVelocity (m s - *)

0.5 1o 2.0 5.0 10.0 20.0Hard steel worm/phosphor bronze wheel 0.06 0.05 0.035 0.023 0.017 0.014Cast iron worm/cast iron wheel 0.08 0.067 0.050 0.037 0.022 0.018

2.10.7 Epicyclic gearsThe m ain adv antage of an epicyclic gear train is tha tthe input a nd o utp ut shafts are coaxial. The basic typeconsists of a sun gear several planet gears and a ringgear which has internal teeth. Various ratios can beobtained, depending o n which member is held station-ary.

Let :N=speedn=number of teethN ote th at a negative result indicates rotation reversal.

Ratio of output to input speed for various types

mechanical engineer's data handbook - gear

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