GEAR DESIGN

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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.

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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

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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

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* 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.

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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.

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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.

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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.

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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.

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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 .

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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

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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

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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.

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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

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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 .

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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.

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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

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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 .

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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.

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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.

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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.

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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

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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.

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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

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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.

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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.

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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 .

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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.

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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.

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THANK YOU.