Transmissions
2
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
3
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
4
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
5
Comparison of performance of varioustransmission types
6
Types of belt transmissionsMain types:•Flat belt•Round belt
•V-belt
multiple V-belt, micro-V®
7
•Timing belt – widelyused, various teethprofiles, double sidedteeth
Types of belt transmissions
8
Timing belt transmissions•Belt structure
Main feature:Positive engagement (no slip)
•Belt selection
9
Chain transmissions.... not only in bicycles
.... but also in IC engines
10
Variable speed transmissionsgear chain
belt friction
Prz_Wariat.exe
11
Comparison of performance
12
10
100
1000
10000
100000
1000 10000 100000 1000000
prędkość obrotowa [m/s]
moc
[kW
]
zebatehydrostciernepasy plaskiepasy klinpasy wieloklinpasy zebatełańcuchowe
Comparison of performance
13
Types of gear transmissionsMain types of gear transmissions:•gear transmissions with spur gears, helical gears and herringbone gears
14
Types of gear transmissionsBevel gears with straight teeth and spiral teeth (hypoid gears sometimes)
15
Types of gear transmissionsInternal gear
Planetary
Worm gears
16
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)
17
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.
?
18
Spur gearsIn most cases teeth have a profile of an involute
Aplikacja
19
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
20
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
21
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.)
22
Standarization of gear profiles-tooth system
23
Two gears in operation
Aplikacja
24
Manufacturing techniquesMachining Formed disc
cutter (frez kształtowy)
Hobbing (za pomocą frezaślimakowego)
25
Manufacturing techniquesWith rack shapedcutter (za pomocą zębatki)
Reciprocating gearshaper (za pomocą dłutaka)
26
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
27
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!!!!
28
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
29
Gears – contact length and contact ratioHow many teeth are in mesh?
Aplikacja
30
Contact ratio:
bpAE
=ε
Gears – contact length and contact ratioHow many teeth are in mesh?
31
Teeth correction
Google result for „teeth correction”
32
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
33
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”
34
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”
35
Correction coefficient should be selected from the range betweenxxgrgr’’ (coeff. to avoid cutout) and
value that will cause„sharpening” of the addendum
Gear- „correction”
36
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?
37
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
38
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 (+)
39
Profits of correction
Transmissions – helical and bevelgears
41
Helical gears Herringbone gears (zęby daszkowe)
42
Helical gears
Schematic view of involutecreation
Manufactiring with theuse of rack
43
Helical gears
In transverse plane profile is different: Transverse pitch (podziałka czołowa)..............Transverse module (Moduł czołowy).............Pitch dia (Średnica podziałowa).....................Transverse pressure angle...................
44
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:...................
45
Helical gearsCutout limit – number of teeth:
46
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
47
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
48
Bevel gears
Straight teeth Spiral teeth
49
Schematic view of creation ofinvolute surface
Bevel gears
50
Equivalent spur gears
Bevel gears
Gear ratio....................
Transmissions – evaluation ofstrength, failures
52
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.
53
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
54
Transmissions – limits of operation
For heat treated steel - pitting is the most important limiting factor
55
For hardened gears tooth breakage limit is the most important limiting factor
Transmissions – limits of operation
56
Gears - calculationsTooth break:Bending stress(sometimes alsocompression andshear stress are considered)
57
Pitting –Surface stress in pitch center –Hertzian stresses. Two cylinders of relevant radi –such as involute radius
Gears - calculations
58
Influence of maufacturing/material/heat treatmenton performance
Transmission M1=21kNm, i=3, n1=500 rpm (power ca. 100 kW)
59
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)
60
Spray lubrication
Transmissions - lubrication
61
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