Gear Design

[RACK & P INION GEAR DESIGN] DESIGN]

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May 1, 2010

Machine Design & CAD - II POWER TRANSMISSION SYSTEM DESIGN PROJECT Power Transmission System Design Project: P roject: Rack & Pinion Gear Design

Supervisor:

Respected Sir, Prof. Dr. Abdul Hameed Memon Sahab

GROUP MEMBERS:

Khalil Raza Bhatti 07ME40 Waqas Ali Tunio 07ME34 Ayaz Ali Ali Soomro 07M 07M E31 Waqar Wa qar Ahm hmed ed Bhutt Bhutto o 07ME 07M E36 Muhammad Farooque Pirzado 07ME56 Zain-ul-Abideen Qureshi 07ME57

Department of Mechanical Engineering, Quaid-e-Awam University of Engineering, Science & Technology, Nawabshah, Pakistan Machine Design & CAD - II | Power Transmission System Design Project


May 1, 2010

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1 2 3 4 5 6 7

Contents

Page

Introduction Problem Definition Project Objectives Design Methodology Problem Solution Alternatives Working Drawing Conclusion

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Machine Design & CAD - II | Power Transmission System Design Project

4 4 5 20 21 22


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Introduction: Rack and Pinion Gear: Page | 3

A rack and pinion gears system is composed of two gears. The normal round gear is the pinion gear and the straight or flat gear is the rack. The rack has teeth cut into it and they mesh with the teeth of the pinion gear.

Basic Mechanism M echanism Rack and pinion gears provide a greater feedback and steering sensation. A rack and pinion gear gives a positive motion especially compared to the friction drive of a wheel in tarmac. In a rack and pinion railway, a central rack between the two rails engages with a pinion on the engine allowing a train to be pulled up very steep slopes. A well designed mechanism such as the rack and pinion gears save effort and time. The rack and pinion is used to convert between rotary and linear motion. Rack and pinion can convert from rotary to linear of from linear to rotary. The diameter of the gear determines the speed that the rack rack moves as the pinion turns. Rack and pinions are commonly used in the steering steering system of cars to convert the rotary motion of the steering wheel to the side to side motion in the wheels.



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Problem Definition/ Statement Page | 4

Determine the various forces, parameters & Specifications to design the Rack and Pinion Gear mechanism and incorporate those forces to develop a Railway Crossing Sliding Gate. Need is to develop a system for closing and opening of railway crossing gate with rack and pinion mechanism. In order to design that we will have to assume some data as shown: 

Gate is to slide on a rail by rail and wheel mechanism.

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Sliding path is frictionless.

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Two rack and pinion gears are used to slide gate on rail as load will uniformly be distributed mounted on its ends.

Project Objectives 

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Understand rack and pinion gear mechanism. Develop a direct design method for gear design in an efficient way. Come up with an innovative solution for building that design as a standard one. Determine the various forces that are meshed within gears. In context of all the gear parameters referring to right selection of material for rack and as well as for pinion.



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Design Methodology Page | 5

Designing Rack and Pinion



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Spur Gear Design and Selection Objectives Page | 6 • Calculate forces on teeth of spur gears, including impact forces associated with

velocity and clearances. • Determine allowable force on gear teeth, including the factors necessary due to angle of involute of tooth shape and materials selected for gears. • Design actual gear systems, including specifying materials, manufacturing accuracy, and other factors necessary for complete spur gear design. • Understand and determine necessary surface hardness of gears to minimize or prevent surface wear. • Understand how lubrication can cushion the impact on gearing systems and cool them. • Select standard gears available from stocking manufacturers or distributors.

Design Des ign Requir equirement ements s



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Preliminary Design For spur gear design, pinion and rack both have straight teeth or spur geometry of teeth. So for we will first consider the design of pinion as spur s pur gear. Page | 7 Design Process

To select gears from a stock gear catalogue or do a first approximation for a gear design select the gear material and obtain a safe working stress e.g Yield stress / Factor of Safety. /Safe fatigue stress   

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Determine the input speed, output speed, ratio, torque to be transmitted Select materials for the gears (pinion is more highly loaded than gear) Determine safe working stresses (uts /factor of safety or yield stress/factor of safety or Fatigue strength / Factor of safety ) Determine Allowable endurance Stress S e Select a module value and determine the resulting geometry of the gear Use the lewis formula and the endurance formula to establish the resulting face width If the gear proportions are reasonable then - proceed to more detailed evaluations If the resulting face width is excessive - change the module or material or both and start again

The gear face width should be selected in the range 9-15 x module or for straight spur gears-up to 60% of the pinion diameter

Specifications for standard Gear Teeth



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Standards 

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AGMA 2001-C95 or AGMA-2101-C95 Fundamental Rating factors and Calculation Methods for involute Spur Gear and Helical Gear Teeth BS 436-4:1996, ISO 1328-1:1995..Spur and helical gears. Definitions and allowable values of deviations relevant to corresponding flanks of gear teeth BS 436-5:1997, ISO 1328-2:1997..Spur and helical gears. Definitions and allowable values of deviations relevant to radial composite deviations and runout information BS ISO 6336-1:1996 6336-1:1996 ..Calculation ..Calculation of load capacity of spur and helical gears. Basic principles, introduction and general influence factors BS ISO 6336-2:1996..Calculation of load capacity of spur and helical gears. Calculation of surface durability (pitting) BS ISO 6336-3:1996..Ca 6336-3:1996..Calculation lculation of load capacity of spur spu r and helical gears. Calculation of tooth bending strength BS ISO 6336-5:2003..Calculation of load capacity of spur and helical gears. Strength and quality of materials

If it is necessary to design a gearbox from scratch the design process in selecting the gear size is not complic c omplicated ated - the various design formulea formulea have all been developed developed over time and are available in the the relevant standards. However significant effort, judgement and expertis expertise e is required in designing the whole system including the gears, shafts , bearings, gearbox, lubrication. For the same duty many man y different gear options are available for the type of gear , the materials material s and the the quality. It is always preferable to procure gearboxes gearboxes from specialised gearbox manufacturers

Spur Gear Design The spur gear is is simplest type of gear g ear manufactured manufactured and is generally used for transmission transmissi on of rotary motion between parallel shafts. The spur gear gear is the first choice option for gears except when high speeds, loads, and ratios direct towards other options. Other gear types may also be preferred preferred to provide more silent lowvibration operation. operation. A single spur gear is generally generally selected to have have a ratio range of between 1:1 and 1:6 with a pitch line velocity up to 25 m/s. The spur gear has an operating operating efficiency of 98-99%. 98-99%. The pinion is made from a harder material material than the wheel. A gear pair should be selected to have the highest number of teeth consistent with a suitable safety margin in strength and wear. The minimum number of teeth on a gear with a normal pressure angle of 20 desgrees is 18. The preferred number of teeth are as follows 12 13 14 15 16 18 20 22 24 25 28 30 32 34 38 40 45 50 54 60 64 70 72 75 80 84 90 96 100 120 140 150 180 200 220 250



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Materialsusedforgears

Mildsteelisapoormaterialforgearsasithaspoorresistancetosurfaceloading.The carboncontentforunhardenedgearsisgenerally0.4%(min)with0.55%(min)carbonfor thepinions.Dissimilarmaterialsshouldbeusedforthemeshinggears-thisparticularly Page | 9 appliestoalloysteels.Alloysteelshavesuperiorfatiguepropertiescomparedtocarbon steelsforcomparablestrengths.Forextremelyhighgearloadingcasehardenedsteels areusedthesurfacehardeningmethodemployedshouldbesuchtoprovidesufficient casedepthforthefinalgrindingprocessused. Material

Notes

applications

Ferrousmetals

Cast Iron

Cast Steels Plain-Carbon Steels

Alloy Steels

Stainless Steels (Aust)

Stainless Steels (Mart)

Aluminium alloys

Brass alloys

Low Cost easy to machine with high damping Low cost, reasonable strength Good machining, can be heat treated Heat Treatable to provide highest strength and durability Good corrosion resistance. Nonmagnetic Hardenable, Reasonable corrosion resistance, magnetic Non-Ferrousmetals Light weight, non-corrosive and good machinability Low cost, noncorrosive, excellent

Large moderate power, commercial gears Power gears with medium rating to commercial quality Power gears with medium rating to commercial/medium quality Highest power requirement. requirement. For precision and high precisiont Corrosion resistance resistance with low power ratings. Up to precision quality Low to medium power ratings Up to high precision levels of quality Light duty instrument gears up to high precision quality low cost commercial quality gears. Quality up to medium precision



machinability Excellent machinability, low friction and good compatability with steel Light weight with poor corrosion resistance Low coefficient of thermal expansion. Poor machinability High strength, for low weight, good corrosion resistance Low cost with low precision and strength Low cost, low quality, moderate strength

Bronze alloys

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Magnesium alloys

Nickel alloys

Titanium alloys

Di-cast alloys

Sintered powder alloys

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For use with steel power gears. Quality up to high precision

Ligh weight low load gears. Quality up to medium precision Special gears for thermal applications to commercial quality

Special light weight high strength gears to medium precision

High production, low quality gears to commercial quality High production, low quality to moderate commercial quality

Nonmetals

Acetal (Delrin

Phenolic laminates

Nylons

PTFE

Wear resistant, low water absorbtion Low cost, low quality, moderate strength No lubrication, no lubricant, absorbs water Low friction and no lubrication

Long life , low load bearings to commercial quality High production, low quality to moderate commercial quality Long life at low loads to commercial quality

Special low friction gears to commercial quality

Module(m)



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Themoduleistheratioofthepitchdiametertothenumberofteeth.The unitofthemoduleismilli-metres.Belowisadiagramshowingtherelative sizeofteethmachinedinarackwithmodulerangingfrommodulevalues of0,5mmto6mm Page | 11

The preferred module values are 0,5

0,8

1

1,25 1 ,25

1,5

2,5

3

4

5

6 50

8

10 12

16

20

Forces on Spur Gear Teeth

Ft = Transmitted force Fn = Normal force. Fr = Resultant force θ = pressure angle Fn = Ft tan θ Fr = Ft/Cos θ


25 25

32

40


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Surface Speed

Forces on Gear Tooth Forces acting on individual gear tooth.



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Strength of Gear Teeth

Lewis form factor method Lewis equation Fs = Allowable dynamic bending force Page | 13 (lb) Sn = Allowable stress. Use endurance limit and account for the fillet as the stress concentration concentration factor b = Face width (in.) Y = Lewis form factor (From Table) Pd = Diametral pitch 

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Lewis form factors (Y) Tableoflewisformfactorsfordifferenttoothformsandpressureangles No

Load Near Tip of Teeth

Teeth

10 11 12 13 14 15 16 17 18 19 20 21

14 1/2 Y 0,17 6 0,19 2 0,21 0,22 3 0,23 6 0,24 5 0,25 5 0,26 4 0,27 0,27 7 0,28 3 0,28

deg y 0,05 6 0,06 1 0,06 7 0,07 1 0,07 5 0,07 8 0,08 1 0,08 4 0,08 6 0,08 8 0,09 0,09

20 deg Y 0,20 1 0,22 6 0,24 5 0,26 4 0,27 6 0,28 9 0,29 5 0,30 2 0,30 8 0,31 4 0,32 0,32

FD y 0,06 4 0,07 2 0,07 8 0,08 4 0,08 8 0,09 2 0,09 4 0,09 6 0,09 8 0,1 0,10 2 0,10

20 deg Stub Y y 0,26 0,08 1 3 0,28 0,09 9 2 0,31 0,09 1 9 0,32 0,10 4 3 0,33 0,10 9 8 0,34 0,11 9 1 0,36 0,11 5 0,36 0,11 8 7 0,37 0,12 7 0,38 0,12 6 3 0,39 0,12 3 5 0,39 0,12

25 deg Y 0,23 8 0,25 9 0,27 7 0,29 3 0,30 7 0,32 0,33 2 0,34 2 0,35 2 0,36 1 0,36 9 0,37

y 0,07 6 0,08 2 0,08 8 0,09 3 0,09 8 0,10 2 0,10 6 0,10 9 0,11 2 0,11 5 0,11 7 0,12

Load at Near Middle of Teeth 14 1/2 deg 20 deg FD Y y Y y

0,35 5 0,37 7 0,39 9 0,41 5 0,43 0,44 6 0,45 9 0,47 1 0,48 1 0,49

0,11 3 0,12 0,12 7 0,13 2 0,13 7 0,14 2 0,14 6 0,15 0,15 3 0,15


0,41 5 0,44 3 0,46 8 0,49 0,50 3 0,51 2 0,52 2 0,53 4 0,54 4 0,55

0,13 2 0,14 1 0,14 9 0,15 6 0,16 0,16 3 0,16 6 0,17 0,17 3 0,17


22 23 Page | 14 24

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 43 45 50 55

9 0,29 2 0,29 6 0,30 2 0,30 5 0,30 8 0,31 1 0,31 4 0,31 6 0,31 8 0,32 0,32 2 0,32 4 0,32 6 0,32 7 0,32 9 0,33 0,33 3 0,33 5 0,33 6 0,33 9 0,34 0,34 6 0,35 2

2 0,09 3 0,09 4 0,09 6 0,09 7 0,09 8 0,09 9 0,1 0,10 1 0,10 1 0,10 1 0,10 1 0,10 3 0,10 4 0,10 4 0,10 5 0,10 5 0,10 6 0,10 7 0,10 7 0,10 8 0,10 8 0,11 0,11 2

6 0,33 0,33 3 0,33 7 0,34 0,34 4 0,34 8 0,35 2 0,35 5 0,35 8 0,36 1 0,36 4 0,36 7 0,37 1 0,37 3 0,37 7 0,38 0,38 4 0,38 6 0,38 9 0,39 7 0,39 9 0,40 8 0,41 5

4 0,10 5 0,10 6 0,10 7 0,10 8 0,10 9 0,11 1 0,11 2 0,11 3 0,11 4 0,11 5 0,11 6 0,11 7 0,11 8 0,11 9 0,12 0,12 1 0,12 2 0,12 3 0,12 4 0,12 6 0,12 7 0,13 0,13 2

9 0,40 4 0,40 8 0,41 1 0,41 6 0,42 1 0,42 6 0,43 0,43 4 0,43 7 0,44 0,44 3 0,44 5 0,44 7 0,44 9 0,45 1 0,45 4 0,45 5 0,45 7 0,45 9 0,46 7 0,46 8 0,47 4 0,48

7 0,12 9 0,13 0,13 1 0,13 2 0,13 4 0,13 6 0,13 7 0,13 8 0,13 9 0,14 0,14 1 0,14 2 0,14 2 0,14 3 0,14 4 0,14 5 0,14 5 0,14 5 0,14 6 0,14 9 0,14 9 0,15 1 0,15 3

7 0,38 4 0,39 0 0,39 6 0,40 2 0,40 7 0,41 2 0,41 7 0,42 1 0,42 5 0,42 9 0,43 3 0,43 6 0,44

0,13 1 0,13 3 0,13 4 0,13 5 0,13 7 0,13 8 0,13 9 0,14

0,44 3 0,44 6 0,44 9 0,45 2 0,45 4 0,45 7 0,46 4 0,46 8 0,47 7 0,48 4

0,14 1 0,14 2 0,14 3 0,14 4 0,14 5 0,14 5 0,14 8 0,14 9 0,15 2 0,15 4

0,12 2 0,12 4 0,12 6 0,12 8 0,13

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0,49 6 0,50 2 0,50 9 0,51 5 0,52 2 0,52 8 0,53 4 0,53 7 0,54 0,55 4 0,54 7 0,55 0,55 3 0,55 6 0,55 9 0,56 3 0,56 5 0,56 8 0,57 0,57 4 0,57 9 0,58 8 0,59 6

6 0,15 8 0,16 0,16 2 0,16 4 0,16 6 0,16 8 0,17 0,17 1 0,17 2 0,17 6 0,17 4 0,17 5 0,17 6 0,17 7 0,17 8 0,17 9 0,18 0,18 1 0,18 1 0,18 3 0,18 4 0,18 7 0,19


3 0,55 9 0,56 5 0,57 2 0,58 0,58 4 0,58 8 0,59 2 0,59 9 0,60 6 0,61 1 0,61 7 0,62 3 0,62 8 0,63 3 0,63 9 0,64 5 0,65 0,65 5 0,65 9 0,66 8 0,67 8 0,69 4 0,70 4

6 0,17 8 0,18 0,18 2 0,18 5 0,18 6 0,18 7 0,18 8 0,19 1 0,19 3 0,19 4 0,19 6 0,19 8 0,2 0,20 1 0,20 3 0,20 5 0,20 7 0,20 8 0,21 0,21 3 0,21 6 0,22 1 0,22 4


60 65 70

0,35 5 0,35 8 0,36

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75 80 90 100 150 200 300 Rac k

0,36 1 0,36 3 0,36 6 0,36 8 0,37 5 0,37 8 0,38 0,39

0,11 3 0,11 4 0,11 5 0,11 5 0,11 6 0,11 7 0,11 7 0,11 9 0,12 0,12 2 0,12 4

0,42 1 0,42 5 0,42 9 0,43 3 0,43 6 0,44 2 0,44 6 0,45 8 0,46 3 0,47 1 0,48 4

0,13 4 0,13 5 0,13 7 0,13 8 0,13 9 0,14 1 0,14 2 0,14 6 0,14 7 0,15 0,15 4

0,48 4 0,48 8 0,49 3 0,49 6 0,49 9 0,50 3 0,50 6 0,51 8 0,52 4 0,53 4 0,55

0,15 4 0,15 5 0,15 7 0,15 8 0,15 9 0,16 0,16 1 0,16 5 0,16 7 0,17 0,17 5

0,49 1 0,49 6 0,50 1 0,50 6 0,50 9 0,51 6 0,52 1 0,53 7 0,54 5 0,55 4 0,56 6

0,15 6 0,15 8 0,15 9 0,16 1 0,16 2 0,16 4 0,16 6 0,17 1 0,17 3 0,17 6 0,18

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0,60 3 0,60 7 0,61 0,61 3 0,61 5 0,61 9 0,62 2 0,63 5 0,64 0,65 0,66

0,19 2 0,19 3 0,19 4 0,19 5 0,19 6 0,19 7 0,19 8 0,20 2 0,20 4 0,20 7 0,21

Classes of Gears • Transmitted

load depends on the accuracy of the gears • Gear Manufacture – Casting – Machining • Forming • Hobbing • Shaping and Planing

Forc orce e Tra rans nsmit mittted

Transmitted load depends on the accuracy acc uracy of the gears. A dynamic load factor is added to take care of this. Machine Design & CAD - II | Power Transmission System Design Project

0,71 3 0,72 1 0,72 8 0,73 5 0,73 9 0,74 7 0,75 5 0,77 8 0,78 7 0,80 1 0,82 3

0,22 7 0,23 0,23 2 0,23 4 0,23 5 0,23 8 0,24 0,24 8 0,25 1 0,25 5 0,26 2


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• Ft = Transmitted force • Fd = Dynamic force • Commercial Page | 16

Classes of Gears

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Carefully cut

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Precision

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Hobbed or shaved

Expected Error in Tooth Profiles



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Design Methods Page | 17

• Strength of gear tooth should be greater than the dynamic force; Fs • You should also include the factor of safety, Nsf.

Service Factors

Face width of Gears Relation between the width of gears and the diametral pitch.

Dynamic Beam Strength of the Gear Machine Design & CAD - II | Power Transmission System Design Project

≥ Fd


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To increase the dynamic beam strength str ength of the gear – Increase tooth size by decreasing the diametral pitch – Increase face width upto the pitch diameter of the pinion Page | 18

– Select material of greater endurance limit – Machine tooth profiles pr ofiles more precisely – Mount gears more precisely – Use proper lubricant and a nd reduce contamination

Buckingham Method of Gear Design • It offers greater flexibility. • Expected error is based on different-pitch teeth. • More conservative design.

Wear strength (Buckingham)

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Fw = tooth wear strength.

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Dp = diametral pitch of pinion. Machine Design & CAD - II | Power Transmission System Design Project


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Dg = diametral pitch of gear.

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b = face width.

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Kg = load stress factor.

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Rack and Spur Gear Calculation

The following table presents the method for calculating the mesh of a rack and spur gear.

Table presents the calculation calculation of a meshed profile shifted shifted spur gear and rack. rack. If the correction factor x1 is 0, then it is the case of a standard gear meshed with the rack.



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The rack displacement, l, is not changed in any way by the profile shifting. Equation remains applicable for any amount of profile pr ofile shift. Page | 20

Problem Solution Alternatives Our basic purpose of the project is to slide the railway crossing gate by a mechanism that is much mechanical convenient to translate that load uniformly. So for we have been able to do that by using rack and pinion gear mechanism. Since the rack and pinion gear transmit the rotary power into linear and linear into rotary one that is the reason that we have incorporated the pinion and rack gear g ear mechanism for opening and closing of the railway crossing gate.



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Working Drawing Page | 21

This shows the pitch circle of a standard gear and the pitch line of the rack. One rotation of the spur gear will displace the rack l one circumferential length of the gear's pitch circle, per the formula: l = πmz

This shows a profile shifted spur gear, with positive correction xm, meshed with a rack. The spur gear has a larger pitch radius than standard, by the amount xm. Also, the pitch line of the rack has shifted outward by the amount xm.



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Conclusion Page | 22

We the whole group involved in it can conclude the whole project as a thought processing one. First of all as an engineering student we wanted to design such a thing that has not been commonly considered before. So for this reason we wanted the railway crossing gate to be opened and closed by some electric motor power. But in order to do that we required a mechanism that could be used in it and it could work efficiently. In search of those parameters regarding the power transmission devices that could work feasible in this manner we found the one mechanism that has been discussed in detail above that is rack and pinion gear which is used to transmit power linear to rotary and vice versa. To make this project much practical we went to railway station to sort out all sorts of elements that are covered in driving the railway gate horizontally out and in. Meanwhile we got know how about the safe design of the gears and examined that steps that are taken in the real design of any machine element. It has been a practical approach designing a railway gate on rack and pinion gear. Moreover It has nice task to carry out and we the whole group learnt a lot of things regarding Machine Design.


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