Slide 1: GEAR DESIGN
Slide 2: GEAR : A gear can be defined as the mechanical element
used for transmitting power and rotary motion from one
shaft to another by means of progressive engagement of
projections called teeth.
Advantages of Gear drives :
a) Compact as compare to belt or chain.
b) Transmit higher power and speed as compare to
belt or chain.
c) Transmit power between shafts which are parallel /
non-parallel, intersecting / non-intersecting.
d ) Used for wide range of speed ratios.
e ) Gear drives are positive drives.
Slide 3: Limitations of gear drives :
a) Gear drives are costlier than belt or chain drives.
b) Require continuous lubrication and precise alignment.
c) Can not be used for transmitting power over very long distance.
Classifications of Gears :
* Parallel Axes - Spur gear / Helical gears /
Herringbone gears/ Internal gear
*Intersecting Axes gears - Bevel gears straight or spiral
bevel
*Non-intersecting and Perpendicular Axes -Worm gear
*Non-intersecting-Non-parallel Axes gear- Crossed
Helical gears
Slide 4: Various factors that needs to be considered while selecting
the type of gear drive for given application are :
1 The relative position of input and output shaft
2 Speed ratio
3 Efficiency
4 Input speed
5 Power to be transmitted
6 Cost
Slide 5: * Helical gears are preferred over spur gear due to
a) Greater tooth strength due to helical wrap around.
b) Increased contact ratio which gives smooth
operational characteristics.
c) Higher load carrying capacity than comparable
spur gear.
Spur and helical gears can be used to transmit large power.
However because of low efficiency ,worm gear drive
is not preferred for high power transmission.
Spur gears are easy to manufacture and cheapest ,followed
by helical and bevel gears . Due to bimetallic construction
of worm wheel and specialized manufacturing method,
worm gears are costlier.
Slide 6: Gear Terminology :
Pitch Circle : It is an imaginary circle which by pure rolling
action would transmit same motion as the actual gear .
Pitch Circle Diameter(d) : It is diameter of pitch circle .
Pressure Angle : It is the angle between the common normal
to the two gear teeth at point of contact and common tangent
to two pitch circles at pitch point.
Circular Pitch : It is the distance measured along the
circumference of the pitch circle ,from point on one tooth to
corresponding point on next tooth.
Slide 7: Module - It is ratio of pitch circle in mm to number of teeth.
Addendum (ha) - It is radial distance between top land of the
teeth and pitch circle. Normally addendum = 1 module.
Dedendum (hf) - It is radial distance between bottom land of
the teeth and pitch circle.
Total depth : It is radial distance between Addendum circle
and dedendum circle. It is sum of Addendum and dedendum.
Base Circle : It is the circle on which the the involute profile
of the gear tooth is generated.
Face width : It is length of gear tooth measured along line
parallel to gear axes.
Slide 8: Backlash -Backlash is thought of as the freedom of one
gear to move while the mating teeth is held stationary.
Backlash allows room for an oil film under all conditions
of thermal expansion or contraction and is influenced by
deviation of center distance ,tooth thickness ,pitch,profile
and lead errors.
Tooth Thickness : It is width of tooth measured along pitch
circle.
Speed ratio : It is ratio of pinion speed to gear speed.
Contact Ratio : Contact ratio can be visualised as the
average number of tooth pairs in contact during mesh . This
means more contact ratio ,smoother will be the operation.
Slide 9: For most of applications it is recommended that contact ratio
should be at least 1.4.
Contact ratio for helical gears is sum of transverse contact
ratio and face contact ratio. The transverse contact ratio is contact ratio in plane of rotation ,whereas face contact ratio is
contact ratio in axial plane . For spur gears ,face contact ratio
is zero.
Root diameter : It is diameter of base of tooth space.
Outside diameter : It is diameter of Addendum circle.
Fillet radius : The curved surface of the tooth flank joining it to
bottom land.
Slide 10: Undercut : A condition in generated gear teeth , when
part of fillet curve lies inside of a line drawn tangent
to true involute form at its lowest point . Undercut may
be deliberately introduced to facilitate finishing operation.
Path of contact :The curve on either tooth surface along
which contact occurs in gears which normally engage
with only single point contact.
Interference :The contact between mating teeth at some
other point than along line of action .
Slide 13: GEAR TERMINOLOGY:
M Module
a Center distance
Z Number of teeth
u Gear Ratio
Beta Helix Angle
Beta (b) Base helix angle
Alpha Pressure Angle
Alpha (t) Transverse Pressure Angle
x Addendum modification coefficient
k No. of teeth spanned for base tangent length
P Normal pitch
d Reference Diameter
Mt Transverse Module
Pt Transverse Pitch
Pb Base Pitch
Slide 14: GEAR TERMINOLOGY Cont..
Pb Base Pitch
db Base Diameter
df Root Diameter
da Tip Diameter
g alpha Length of path of contact
hfp Dedendum of basic rack profile * Module
Cp Bottom clearance of basic rack profile
Slide 15: Gear Materials : Desirable properties for gear material are as follows:
a) Endurance strength in bending to avoid bending failure.
b) Surface endurance strength to avoid destructive pitting.
c) Low coefficient of friction to avoid scoring.
d) Low and consistent thermal distorsion during Heat
treatment.
A) Ferrous Metals :
Cast Iron : Gears of large and complicated shapes are made from Cast Iron .
Advantages :Cheap , good damping hence damp out noise and vibration, graphite present acts as lubricant thus reducing possibility of scoring , can be cast in complicated shapes , excellent machinability.
Slide 16: Cast Iron ..
Disadvantages : Low bending strength , brittle hence can
not be used for shock loading.
Material : FG 260 of IS 210 , SG 400/12 of IS -1865:1991
Steels :
1) Case Hardening steel :
Advantages :
a) High bending and surface endurance strength.
b) Can absorb shocks hence can be used for shock loading.
Disadvantages : a) They are expensive .
b) They have poor damping properties.
Example- 17CrNiMo6 of DIN 17210 or En 36 B or C
of BS 970 or 15Ni2Cr1Mo15 of IS 4432 or equivalent
Slide 17: 2) Plain carbon steel : Used for medium duty application. These steel contains alloying elements such as nickel ,
chromium ,manganese ,molybdenum in controlled quantity.
These are rarely used in non-heat-treated condition .
Different alloying elements impart different properties :e.g.
Nickel & chromium - increase hardness and strength
Manganese- Increase hardness and strength
Examples - En 24 or En 19 of BS 970, 45C8 ,
40Ni2Cr1Mo28 of IS 5517-1978 or 42Cr Mo4 of DIN etc.
Nitriding Steel : Nitriding is process of casehardening alloy
steel gears .The nitriding is done by ammonia gas which breaks down in to nitrogen and hydrogen at the surface of steel . The atomic nitrogen slowly penetrates the steel
surface and combines with element like aluminium , chromium, molybdenum ,tungsten etc. to form hard nitrates.
Slide 18: Thus useful case can be formed by nitrogen and alloying
elements present in a gear .A straight -carbon steel gear
can not be successfully nitrided.
Nitrided steels give higher surface hardness and reduced
distorsion. Nitriding process takes long time and case depth
is small .
Examples of Nitriding steels are :En40C ,En41A,En41B
of BS 970 ,34CrAlMo5 as per DIN ,40Cr2Al1Mo18 of
IS 1570 etc.
B) Non Ferrous Metals : The non ferrous metals like
Copper,Zinc ,Aluminium etc. are used in various
combinations as gear material . The most common material
is bronze which is used for its ability to withstand heavy
sliding in worm application.
Slide 19: Main advantages are :
* Low coefficient of friction
*Excellent conformability
*Good castiability
*Good corrosion resistance
*High toughness
Sintered metals : Recently sintered iron gears made from
powder metallurgy are used for low cost /strength
requirements in applications such as washing machine,
mixtures ,toys etc..
Non metallic gears : Normally Nylon or bakelite gears
are also used for low strength and light duty applications .
The advantages of non metallic gears are : low cost ,
easy to manufacture ,light weight ,absorbs shocks and
operate with marginal lubrication .
Slide 20: Basic Design Considerations :
In order to drive in a given direction and to transmit
power smoothly and without loss of energy , gears
should have following properties
1) Before one pair of teeth goes out of contact during
mesh , second pair will have to pick up its share of load.
This is called ‘continuity of action’
2) The angular velocity of driving member is smoothly
imparted to the driven member and transmission ratio
should be constant at every instant of engagement.
Gears which meet this requirement are called conjugate
gears.
Slide 21: Condition 2 is confirmed by basic law of gearing
which states that ‘Normals to the profiles of mating
teeth must , at all points of contact , pass through a
fixed point located on the line of centers called pitch
point.
Pitch point is on the line joining the centers of two gears and divides it in the proportion of number of teeth on the
gears.
Tooth profile which meet this conjugacy requirement are
* Involute profile
*Cycloidal profile
*Novikov Profile
Slide 22: Involute Profile- This is most commonly used profile .
Involute is path traced by end of inextensible cord as
unwound over base circle.
Cycloidal profile - Cyclodal is profile traced by a point
on the circumference of a circle as it rolls on a line
without slipping.
Novikov Profile - It is profile of circular arc. Gear are very
sensitive to center distance variation .
Slide 23: Steps for Gear Design
a) Inputs for gear design are ratio, input speed , torque to be
transmitted , duty cycle ,type of loading ,ambient condition
etc..
b) Decide center distance and gear geometric parameters
based on above parameters.
c) Based on installation requirements ,decide gearing
arrangement required i.e spur/helical or bevel
d)Depending upon pitch line velocity and application
decide class of accuracy.
DIN 3962 - Class from 1 to 12 ,Class 1- Most accurate gear
AGMA - Class 1 to 15 , Class 15 -Most accurate gear
BS 436 and IS 3681 - Class 1 to 12 ,
Class 1 gear is most accurate gear.
Slide 24: e)Check for gear rating in pitting & bending
f)If gear rating in bending is not sufficient increase
module and adjust number of teeth accordingly.
g) Achieve desired safety factors(S.F.) in pitting and bending rating. Guide lines are available in AGMA for S.F.
h) Freeze all gear geometric parameters so as to achieve
desired gear ratings.
i) Check gear parameters for undercutting and
minimum top land .
j) Depending upon class of accuracy specify inspection
parameters like profile , pitch or lead error as per standard.
k)Specify heat treatment parameters like case depth, core hardness etc. Case depth depends on module and to be specified from standard charts.
Slide 25: l)Specify tooth thinning on drawing in terms of span
measurement. The span measurement decides backlash of
gears. Backlash is necessary for several reasons and is
influenced by various factors like :
* Operating Temperature
*Thermal expansion
*Tooth size and class of accuracy.
*Shaft run outs
*Gear loads ,speeds and running conditions.
*Mounting tolerance
Over pin measurement is also used as alternative to span.
m) Specify heat treatment details like case depth & core
hardness , K charts to specify tip and root relief,tooth finish and material details on drawing.
Slide 26: Addendum modification : When gears are produced
by generation process ,the datum line of basic rack
profile ,need not necessarily form a tangent to reference
circle . The tooth form can be altered by shifting the
datum line from tangential position. This shift is known
as Addendum Modification.
Reasons for Addendum modified gears
1. To obtain a given gear ratio maintaining same center
distance.
2 To cut smaller number of teeth .
3 Possible to design gears to suit given loads in a given
drive.
4. Load capacity and sliding conditions can be improved
without altering dimensions in a major way.
Slide 27: Following information should be available on gear drawing
1) Tooth shape details
2) Number of teeth
3) Module
4)Normal pressure angle
5)Pitch circle diameter
6)Base circle diameter
7)Addendum modification
8)Span measurement
9)Tooth depth
10)Center distance
11)Weight of gears
12)Surface finish at various locations
13)Tooth errors as per standard
14)Heat treatment details
15)Material specification
Slide 28: Heat treatment of gears: Gears can be through hardened
or surface Hardened .
1) Methods of surface hardening :
* Case Hardening
* Nitriding
* Flame Hardening
*Induction Hardening
* Carbo nitriding
Case hardening - Consists of two steps
- Enriching the outer case to about 0.85 % C - This is called
carburising.
- Hardening
Slide 29: Carburising can be done by any of following processes :
-Solid carburising
-Liquid carburising
-Gas carburising
Solid carburising : Parts are packed in boxes surrounded by
carbonaceous material. Ingress of air is prevented and boxes
are heated to 900 to 950 deg C. Carbon from carbonaceous
material combines with oxygen of the energiser to form
carbon monoxide (CO) . This CO is decomposed in to
carbon at the surface of the part and diffuses in steel . The
carbonaceous material used are charcoal, charred leather
and energiser is barium carbonate ,soda or ash etc.
Slide 30: Liquid Carburising :Parts are immersed in bath of sodium
cynide and sodium carbonate maintained at 900 to 950
deg C. Since sodium cynide is very poisonous , this
method is discontinued.
Gas carburising :Parts are heated to 900 to 950 deg.C in
suitable gaseous atmosphere so that carbon from gas
penetrates in surface layer . Normally gas used is butane,
propane or natural gas.
After case carburising hardening is carried out. Hardening
consists of heating to a temperature 30 to 50 deg.
above upper critical point and then cooling it at faster
rate to obtain Martensitic structure by transformation of
Austenite.
Slide 31: Normal range of case hardness is 58 to 62 HRC.
Tempering is followed by hardening .After hardening
steel is hard and brittle , so to reduce internal stresses
produced by quenching and to increase the toughness,
tempering is done.
It is essential to obtain desired core hardness after heat treatment.
Slide 32: Case hardening alloy steel have a tough core and highly
hardened case. The hardened case gives high resistance
to wear.
Through hardening steel have a high strength ,toughness
and resistance to shock.
Nitrided steels gives higher surface hardness and reduced
distorsion . Nitriding process takes longer time and case
depth is small . Nitried gears are normally used for
precision motion transmission and not for heavy torque
transmission.
Slide 33: Gear rating - Normally three types of gear ratings are
calculated i.e pitting ,bending and scoring.
There are major differences between pitting resistance ,
bending and scoring rating.
Pitting is a function of Hertzian contact (compressive )
stress between two curved surfaces of tooth , which is
proportional to the square root of applied load.
As pure rolling normally occurs at pitch circle , pitting
occurs at or slightly below pitch line.
Bending strength is measured in terms of bending stress
in a cantilever plate and is directly proportional to this
same load. Bending failure normally occurs with a fatigue
fracture initiated at or near the root fillet .
Slide 34: If scoring rating is exceeded ,oil film between surfaces
breaks ,allows the contacting surfaces to weld together and
abrade .
The induced stresses should be lower than allowable stress
limits which is function of material hardness , tensile
strength and microstructure with reasonable material
cleanliness .
Nowadays ,the calculations of pitting and bending
strength are based on AGMA 2001 or DIN 3990 or
ISO 6336. The calculated gear ratings as per DIN and as
per AGMA for the same gear pair are normally different
and there is no constant or conversion factor exists for
AGMA rating to DIN rating and vice versa.
Slide 35: The DIN 3990 is in full accordance with ISO 6336.
The use of standard depends upon design approval
agency , type of machinery or availability of software .
e.g. in Europe DIN or ISO is popular while in USA
AGMA is normally preferred.
Various gear rating software are available in market for
finding out gear geometrical parameters and bending ,
pitting or scoring rating . Most popular are UTS software ,
AGMA etc.
Slide 37: The rated power to resist PITTING of gear teeth Pac-
as per AGMA
np F . I.Cv d . Sac CL C H
Pac= ------------- {----------------- } ^2
1.91x 10^7 Cs Cm Cf Ca Cp CT CR
Where np- Pinion speed
F - Face width of narrowest member
I- Gear geometry factor ,Cp-Elastic coefficient
Cv-Dynamic factor , Cs-size factor
d - Pinion Pitch circle diameter ,CR- Reliability factor
Sac- Allowable contact stress number
CL - Life factor ;CH -Hardness factor,
Ca-Application factor ,CT -Temperature factor
Cm-load distribution factor,Cf- Surface condition factor
Slide 38: The rated power to resist BENDING of gear teeth Pac as per AGMA-
np d Kv F m J Sat KL
Pat= ----------------------------------
1.91x 10^7 Ka Km Ks KR KT
Where np- Pinion speed
F - Face width of narrowest member
J- Gear geometry factor , m-module
Kv-Dynamic factor , Ks-size factor
d - Pinion Pitch circle diameter ,KR- Reliability factor
Sac- Allowable bending stress number
KL - Life factor ;KH -Hardness factor,
Ka-Application factor ,KT -Temperature factor
Km-load distribution factor,Kf- Surface condition factor
Slide 39: Size factor- The size factor accounts for increased
likelyhood of encountering fatigue initiating defects due to
non-uniformity of material properties. It depends upon:
Tooth size,diameter of shaft,face width etc.
Load distribution factor - This factor accounts for non
uniform distribution of load across face width. The amount
of non-uniformity of the load distribution is influenced by
gear alignment, elastic deflection of shaft/gears,bearing
clearances , deflections due to centrifugal force etc.
Surface condition factor : Surface condition factor in pitting
considers effects of surface finish of tooth ,residual stress ,
work hardening effect etc .
Slide 40: Application factor (Ka /Ca) : This factor make allowance
for any externally applied load in excess of nominal
tangential load . The factors which influence application
factor are system vibration, over speeds , braking ,
accelerating torque etc.
Life factors (CL/KL)- These factors adjust allowable stress
numbers for required number of cycles of operation
Allowable stress numbers : (Sac and Sat) : These are
defined in AGMA standard and depend on material
composition, material cleanliness ,material properties ,
hardness ,residual stress etc.
Slide 41: Hardness ratio factor (CH) -This factor accounts for
variation in hardness between gear and pinion.
Dynamic Factors (Kv/Cv) -This accounts for internally
generated gear tooth loads which are induced by non
conjugate action of gear tooth. Dynamic loads are normally
generated by
a) Inaccuracy in tooth profile
b)Gear run out
c)Gear mesh stiffness variation as gear teeth pass through
meshing cycle
Geometry factors (I and J) : These factors evaluate the
effects of gear geometry on gear tooth stresses.
Slide 42: Reliability factor (CR & KR ) : These factors accounts
for the effect normal statistical distribution of failures
found in material testing.
Elastic Coefficient Cp- The elastic coefficient of gear
depends upon Young’s modulus of elasticity and
Poission’s ratio.
Slide 43: Scoring rating : Scoring rating is a measure of surface
capacity and depends on the oil film strength to prevent
metal to metal contact. If scoring occurs ,welding and
tearing apart action results in profile surface deterioration.
As per MAAG ,the scoring safety is verified by following
equation-
F load < = F geom
F load- Load function=w (v’)^1/4 (46/υ40 ) ^1/6
F geom- Geometric function = (50+z1+z2) (a)^1/2 Cu / 350
where , υ40- Viscisity at 40 deg
w -Specific load
v’-Pitch line velocity ,z- no. of teeth
a - Center distance ,Cu-constant
Slide 44: Gear tooth modifications :
Tip relief : It is an arbitrary modification of tooth profile
whereby a small amount of material near tip is removed.
Root relief : It is modifications of tooth profile whereby
small amount of material is removed near tooth root.
The main purpose of applying tip and root relief is to
compensate for elastic deflection of tooth.
These corrections improve the performance not only in
the sense of smoother transmission , but also in sense
of load carrying capacity.
Root relief helps to reduce the stress at root caused by
binding when teeth are actually going out of mesh .
Slide 45: Gear Lubrication : Lubrication is essential when two tooth slide over each other .
In gear tooth , normally pure rolling exists at pitch point while sliding exists above and below pitch point which
generates heat .
Thus presence of lubrication is essential for
A) Eliminate possibility of scoring
B) To reduce wear of the teeth.
C) To reduce power loss.
D) To act as coolant by dissipating the heat.
E) To carry away the worn out particles.
F) To minimise the noise and shocks
G)To prevent corrosion.
Slide 46: Lubricating media can be grease or oil . However use of
grease is limited only to low pitch line velocities . Normally
open type gearing is lubricated by grease.
Gear oil- The heavy duty gears are lubricated by gear oil.
Oil is normally blended with additives like antifoaming ,
anti-oxidant , extreme pressure additives .
Gear oils can be hydrocarbon based or synthetic . Synthetic
oils are preferred for better performance and long life
however they are costly .
Oils for IGB -ISO VG SP320 or ISO VG SP460
Slide 47: Methods of Lubrication-
* Splash Lubrication
* Spray Lubrication
*Mist lubrication
Quantity of Lubrication Q= 30 * Nloss / (DEL THETA)
Where Q-Oil quantity in liters/min
Nloss- Frictional loss in HP in gear pair.
DEL THETA - Temperature rise of oil between inlet
and outlet
Slide 48: Design of QUITE gears:
Since transmission error is major source of gear noise
following actions to reduce transmission errors will reduce
gear noise.
1) Use high quality number gears.
2) Better surface finish.
3)Balance gear properly and reduce shaft deflections.
4)Introduce proper tooth modifications like tip /root relief
etc. and use proper backlash.
5)Ensure that critical speeds are 20 % apart from operating
speed.
6) Use finest pitch allowable for that rating.
7) If pinion is hard and gear soft ,during running, cold
working of gear occurs and it conforms to pinion
thereby promoting quite operation.
Slide 49: Gear failures :
By modifying certain design parameters , gear failures can be eliminated. Following are major type of gear failures :
a) Bending failure : Gear tooth may break due to repetitive bending stress. The continuous repetition of bending stress plus its varying magnitude leads to fatigue which may result in crack that widens till a portion or whole of tooth break away. Tooth breakage also occurs when the bending stress exceeds bending endurance limit of gear tooth .
Gear tooth breakage can be avoided by adjusting the parameters such as module and face width in a gear design.
b) Wear failure : Wear is a phenomenon which removes
the complete layer of surface or makes scratches on surface.
Slide 50: Pitting is one of the wear failure.
Pitting- It is fatigue failure . It is due to surface fatigue
failure due to repetitive contact stresses .Pitting is a surface
fatigue failure which starts when maximum Hertz contact
stress induced on the gear tooth surface exceeds the
surface endurance strength of the tooth . Thus design
gears in such a way that induced Hertz stresses are lesser
than permissible material contact stress.
C)Scoring - Scoring is essentially a lubrication failure.
Inadequate lubrication along with high tooth load and
pure surface finish results in breakdown of the oil film
and causes metal to metal contact .
Slide 51: The coefficient of sliding friction resulting from
inadequate lubrication and poor surface finish ,together
with high tooth load and high sliding velocity results in
high rate of heat generation in localized region of metal
to metal contact . This causes rapid welding and tearing
at high spots which is known as stick-slip phenomenon.
Scoring can be avoided by
* providing adequate lubrication - Adequate quantity ,
proper quality,and proper method of lubrication.
* Providing proper surface finish.
* Maintaining sliding velocity within limits.
*Keeping tooth pressure within limits.
Scoring is also termed as scuffing or galling.
Slide 52: D)Abrasive wear : Abrasive wear is surface damage caused
by particles trapped between mating teeth surfaces .These
particles may be present in lubricant as impurity or dirt
entering in gearbox from outside.
Use of proper filter and high viscosity oil will reduce
abrasive wear
e)Corrosive Wear : The corrosive wear is due to chemical
action by improper lubricant or sometimes due to
surrounding atmosphere which may be corrosive in nature.
Remedies are, use proper lubricants with proper additives
and provide complete enclosure to gears.
Slide 53: THANK YOU.