Transmissions

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Purposes for which transmissions are usedWhy do we use transmissions? a) Usually torque of the motor/engine is different from the torque required to

drive the machine

Examples.... Winch: electric motor power 2.2 kW n=1450 rpmTorque = ?Steel wire rope 8 mm + rope drum 200 mmWeight to carry = force in rope = ?Speed of the load = ?

Car: torque of the engineWheel radiusForce on wheel circumeference (if no gear)Speed at 4000 rpmForce required to accelerate to 100 km/h (30 m/s) in 11 s

b) Sometimes direction of rotation has to be changedc) Soemtimes rotational speed has to be changedd) Location of the engine/motor with respect to the machine

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Purposes for which transmissions are usedUsually it is convenient to produce mechanical energy in high speed motors, on the other hand in the drive systems a lower speed is required.Therefore most often we use transmissions which reduce rotational speed -reducers

In case of cage AC motors (induction motors) there is a problem of changing itsrotational speed – then the driving systems may require transmissions withvariaable ratio.Nowadays also FREQUENCY CONVERTERS are being used

For H=100 mmAvailable rated powers are:3 kW if 2850 rpm2.2 kW if 1450 rpm1.5 kW if 940 rpm0.75 kW if 705 rpm

If we need a 3 kW AC motor we will have to pay 77 EUR, 81, 112 or 160 EUR

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TransmissionsBasic parameters are:Gear /transmission ratio – ratio of input rot. speed to output rot. speedefficiency - ratio of output power to input power (always <1)

3 lectures on this!!!!

Mechanical transmissions are the most important in machine. Most commontypes are:•Gear transmissions•Belt transmissions•Chain transmissions•Friction transmissions

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Comparison of performance of varioustransmission types

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Types of belt transmissionsMain types:•Flat belt•Round belt

•V-belt

multiple V-belt, micro-V®

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•Timing belt – widelyused, various teethprofiles, double sidedteeth

Types of belt transmissions

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Timing belt transmissions•Belt structure

Main feature:Positive engagement (no slip)

•Belt selection

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Chain transmissions.... not only in bicycles

.... but also in IC engines

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Variable speed transmissionsgear chain

belt friction

Prz_Wariat.exe

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Comparison of performance

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10

100

1000

10000

100000

1000 10000 100000 1000000

prędkość obrotowa [m/s]

moc

[kW

]

zebatehydrostciernepasy plaskiepasy klinpasy wieloklinpasy zebatełańcuchowe

Comparison of performance

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Types of gear transmissionsMain types of gear transmissions:•gear transmissions with spur gears, helical gears and herringbone gears

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Types of gear transmissionsBevel gears with straight teeth and spiral teeth (hypoid gears sometimes)

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Types of gear transmissionsInternal gear

Planetary

Worm gears

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Gear transmissions in practical designGear transmissions are usually selected from a manufacturers’ catalogue on the basisof:•configuration – input shaft with respect to the output shaft, distance between the axes•Required transmission ratio•Required power

Sometimes whole drive systems are selected composed of a motor, coupling andtransmission MOTOREDUKTOR = Silnik (elektryczny) + sprzęgło+ reduktor (przekładnia zwalniająca)

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Gear transmissions

Within the housing there are:Gears mounted on shafts and supported in the bearings.Bearings and gears need lubrication – usually with oil splashed by the gears.

?

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Spur gearsIn most cases teeth have a profile of an involute

Aplikacja

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Properties of involute profile

Adavantages:•Constant ratio•No problem with small errors in center distance (distance between the axes)•Constant direction of force acting between the teeth•Various gears can work in pairs (the same pitch!!!!, the same angle)•Gear can operate with internal, external gear, and rack (toothed bar)•Manufacturing techniques are relatively simple and efficient•One tool can be used to cut many different wheels (e.g. various number of teeth, various teeth correction coefficients, helical teeth gears)

Drawbacks: Convex surface against a convex surface – high surface pressureIntense sliding – energy losses due to friction

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Ząb )tooth) deddendum (stopa zęba)Addendum (głowa zęba (wierzchołek))Module (moduł)Circular pitch (podziałka)Whole depth (wysokość zęba), grubość zęba (tooth thickness)Szerokość wieńca (gear width)Pitch circle (koło podziałowe)Pitch dia Średnica (walec) podziałowa(y)Base wheel (koło zasadnicze)

d=mz πd= tz

Gear nomenclature

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Standarization of gear teeth profiles

Pressure angle - kąt przyporu α=20°Addendum - wys. głowy zęba ha=mDeddendum - wys. stopy zęba hf=m+cmClearance - luz c=0.25Tooth (whole) depth wys. zęba h=ha+hf=2.25 mRoot diameter - średnica stópAddendum diameter - średnica głów (wierzch.)

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Standarization of gear profiles-tooth system

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Two gears in operation

Aplikacja

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Manufacturing techniquesMachining Formed disc

cutter (frez kształtowy)

Hobbing (za pomocą frezaślimakowego)

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Manufacturing techniquesWith rack shapedcutter (za pomocą zębatki)

Reciprocating gearshaper (za pomocą dłutaka)

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Center distance (odległość osi)aw= 0.5m(z1+ z2 )

Two gears in mesh - nomenclature

Line of action – contact length

Koła tocznert1+rt2 = awrt1/rt2 = i

Gear ratioi=z1/ z2

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Gears – tooth loads

In reality there are no forces but surface pressure actingbetween teeth and friction(because of sliding)

Aplikacja

We neglect friction (it isconsidered in worm gears only)Surface pressure is replacedwith a force Fn perpendicular to contact surface

direction!!!!

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It is convenient to resolve it into twocomponenets

tangential (circumeferential): P= 2M/dt

and radial:Pr= P tgαt

Normal force (perpendicular to the teeth)

Pn= P/cosαt

22rn PPP +=

αt – real pressure angle (standard for uncorrected teeth or teeth corrected with P-0 method) and different for P method of correction

dt – diameter (equal to pitchdia for uncorrected gears but different for gears withcorrection

Gears – tooth loads

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Gears – contact length and contact ratioHow many teeth are in mesh?

Aplikacja

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Contact ratio:

bpAE

=ε

Gears – contact length and contact ratioHow many teeth are in mesh?

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Teeth correction

Google result for „teeth correction”

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Gear- „correction”Involute gears - problem of cutout of teeth

z=12

z=50

Why do we want to have gears with a small number teeth?

It is a problem for gears with a smallnumber of teeth

For normal height (y=1) and pressure angle α=20°zgr=17 In practical applications often a small cutout does not havea great influence and zgr’=14

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In order to avoid cutout a different part of involute curve can be used

The effects of such correction are following:Thicker root of the toothIncrease of diameters (addendum and deddendum circle)Decrease of the addendum thickness („acute”)Increase of profile radiusIncrease of pressure angle (only in contact with another

corrected gear (+))

In manufacturing use of different partof the involute curve is achieved by moving the rack (tool) away from thecentre

Aplikacja

Gear- „correction”

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Next problem – adjustment of center distance

Standards of center distance !!!

In transmissions with varaiableratio (car transmission)In multiple stage transmissions –

manufacturing, design, costreasons

According to Polish standard centerdistances are standarized [mm]:40; 50; 63; 80; 100; 125; 160; 200; 250; 315; 400; 500; 630; 800; 1000

Gear- „correction”

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Correction coefficient should be selected from the range betweenxxgrgr’’ (coeff. to avoid cutout) and

value that will cause„sharpening” of the addendum

Gear- „correction”

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Correction – used methodscorrection (with no change in center distance) P-0 One gear (which????) is corrected with the use of x coefficient (value????)

The other one –x Then no change in: center distance, pressure angleThere are changes in gears diameters (addendum and deddendum))When such method is used?

Correction P Both gears are corrcted x1 i x2

Changes in center distance, pressure angle and in gears diameters(addendum and deddendum) occurWhen such a method is used?

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How x should be selected?

Sometimes there are constraints (e. g. specified center distance) And (x1 + x2) is fixed because of centerdistanceHow (x1 + x2) should be distributed to both gears?

If no other conditions (constraints) thencoefficient to avoid cutout and„sharpening” is appliedOften x=0.5 (DIN)

Correction – used methods

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Profits of correctionImplications of profile modification:Ad 1. effect?Increase of toothstrength (bendingsection modulus)

Ad 4. effect?Decrease of surfacepressureAd 5. effect?Increase of radial force(bearings load)

Geometry (profile) modification:1. Thicker root of the tooth2. Increase in diameters3. Decrease of adendum thickness

(sharpening)4. Increase of profile radius5. Increase of pressure angle (only

in contact with another corrected gear (+)

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Profits of correction

Transmissions – helical and bevelgears

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Helical gears Herringbone gears (zęby daszkowe)

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Helical gears

Schematic view of involutecreation

Manufactiring with theuse of rack

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Helical gears

In transverse plane profile is different: Transverse pitch (podziałka czołowa)..............Transverse module (Moduł czołowy).............Pitch dia (Średnica podziałowa).....................Transverse pressure angle...................

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Helical gearsEquivalent spur gear

On such a circle teeth of thesame module are distributed

Circle of a radius equal to theradius of an ellipse at pitch point

Equivalent number of teeth:...................

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Helical gearsCutout limit – number of teeth:

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Helical gears - loads

tangential: P= 2M/dt

radial:Pr= P tgαt= P tgαn/ cosβ

Resultant force (normal):222wrn PPPP ++=

αt – transverse pressure angle

dt – pitch diameter

Aplikacja

Axial (thrust): Pw= P tgβ= P tgαn/ cosβ

It is convenient to resolve itinto three componenets

Surface pressure is substituted with a forcenormal to the teeth surface in contact point

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Helical gears – profits and problems

Profits of using halical gears:•Quiet running, Płynność zazębienia, cichobieżność,•Compact design due to better load sharingbetween teeth (lower dynamic load coefficients incalculations)•Possibility to change center distance withoutcorrection•Possibility to machine gears with smaller numberof teeth without cutoutProblems:•More difficult standarization (helix angles)•Axial forces – more complex bearing systems

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Bevel gears

Straight teeth Spiral teeth

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Schematic view of creation ofinvolute surface

Bevel gears

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Equivalent spur gears

Bevel gears

Gear ratio....................

Transmissions – evaluation ofstrength, failures

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Transmissions

?

Within the housing there are:Gears mounted on shafts and supported in the bearings.Bearings and gears need lubrication – usually with oil splashed by the gears.

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Gears – forms of failure

Other forms – abrasive wear (slow running wear)

Break of the tooth - overload Pitting- small cavities under pitch circledue to fatigue

Scuffing – welding – close to addendumBreak of the tooth - fatigue

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Transmissions – limits of operation

For heat treated steel - pitting is the most important limiting factor

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For hardened gears tooth breakage limit is the most important limiting factor

Transmissions – limits of operation

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Gears - calculationsTooth break:Bending stress(sometimes alsocompression andshear stress are considered)

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Pitting –Surface stress in pitch center –Hertzian stresses. Two cylinders of relevant radi –such as involute radius

Gears - calculations

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Influence of maufacturing/material/heat treatmenton performance

Transmission M1=21kNm, i=3, n1=500 rpm (power ca. 100 kW)

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Transmissions - lubricationFailure caused by inadequate lubrication comprises :ScuffingOverheatingAbrasive wear

Conditions in gears in mesh relevant to EHL – characteristic features: •Substantial increase of viscosity at high pressure•Elastic deformations modify film profile

Oil functions?

Methods of lubrication –bath (1-6 modules)

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Spray lubrication

Transmissions - lubrication

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Ankieta

Proszę Państwa o uwagi i rady dla wykładowcy na następujące tematy:Wykład: • sposób prowadzenia i tłumaczenia, • tempo, • materiały ilustracyjne, • przydatność wykładu do rozwiązywania zadań na ćwiczeniachĆwiczenia rachunkowe: • dobór tematów zadań, poziom ich trudności i złożoności, • związek ćwiczeń z wykładem• sposób prowadzenia ćwiczeń: przystępność tłumaczenia, sposób

oceniania, podejście do studenta Projektowanie (jak wyżej)Inne uwagi