Design and Analysis of Gear Pinion

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Design and Analysis of Gear Pinion

(For Spur, Helical and Bevel pinions)

E. Shiva Shanker Kumar

Automobile Engineering Department.

Maturi Venkata Subba Rao (MVSR) Engineering College.

Hyderabad, Telangana, India.

AbstractA Pinion is a ger usually meshed with a driven gear is used for power transmission. The power from the source is directly transmitted to pinion by means of shafts, belts or chains etc.. A pinion is the live gear in the drive train. It is therefore very Important to design a pinion in such a way that it withstands all the designed loads on the transmission system. There are several parameters which influence the design of a pinion gear. In this paper we deal with design and analysis of all the gear pinions like spur, helical and bevel pinions.

KeywordsPinion, spur, bevel, helical and transmission.

  1. INTRODUCTION

    The pinion gear is the driving force for the entire transmission system. In this paper we discuss the parameters that affect the design of a gear pinion and the analysis of the gear. We take an example of a gear train and calculate all the parameters of the gear. We check the designed for maximum load conditions.

    • The diameter of pinion links all the parameters required for designing a drive train.

    • The diameter of pinion depends on the availability of space for the drive train and the selection of material.

    • As we all know diameter of driven gear is directly proportional to dia. Of pinion.

    • In case of high gear ratio applications, the size of gearbox is huge, in such cases multiple reduction geartrain is used.

    • Selection of material plays a very important role in compatibility of geartrain.

      Properties of gear materials

      Material

      Condition

      B.H.N.

      Minimum tensile strength(N/ mm2)

      Malleable cast iron (a)White heart castings,

      Grade B

      (b)Black heart castings, Grade B

      217 max

      149 max

      280

      320

      Cast iron

      As cast As cast As cast

      Heat treated

      179 min

      197 min

      207 min

      300 min

      200

      250

      250

      350

      Cast steel

      145

      550

      Carbon steel (a)0.3%carbon (b)0.3%carbon

      Normalised Hardened and

      tempered

      143

      152

      500

      600

      (c)0.4%carbon (d)0.4%carbon

      (e)0.35%carbon (f)0.55%carbon

      Normalised Hardened and tempered

      Normalised Hardened and tempered

      152

      179

      201

      223

      580

      600

      720

      700

      Carbon manganese steel (a)0.27%carbon (b)0.37%carbon

      Hardened and tempered

      170

      201

      600

      700

      Manganese molybdenum steel (a)35 Mn 2 Mo 28

      (b)35 Mn 2 Mo 45

      Hardened and tempered

      201

      229

      700

      800

      1. Grade 20

      2. Grade 25

      3. Grade 35

      4. Grade 35

      Properties of gear materials

      Material

      Condition

      B.H.N.

      Minimum tensile strength(N/ mm2)

      Malleable cast iron (a)White heart castings,

      Grade B

      (b)Black heart castings, Grade B

      217 max

      149 max

      280

      320

      Cast iron

      As cast As cast As cast

      Heat treated

      179 min

      197 min

      207 min

      300 min

      200

      250

      250

      350

      Cast steel

      145

      550

      Carbon steel (a)0.3%carbon (b)0.3%carbon

      Normalised Hardened and

      tempered

      143

      152

      500

      600

      (c)0.4%carbon (d)0.4%carbon

      (e)0.35%carbon (f)0.55%carbon

      Normalised Hardened and tempered

      Normalised Hardened and tempered

      152

      179

      201

      223

      580

      600

      720

      700

      Carbon manganese steel (a)0.27%carbon (b)0.37%carbon

      Hardened and tempered

      170

      201

      600

      700

      Manganese molybdenum steel (a)35 Mn 2 Mo 28

      (b)35 Mn 2 Mo 45

      Hardened and tempered

      201

      229

      700

      800

      1. Grade 20

      2. Grade 25

      3. Grade 35

      4. Grade 35

  2. TERMS USED IN GEARS.

    S.No.

    Terms used in Gears.

    Terms.

    Definition.

    1.

    Pitch circle.

    Imaginary circle which would give same motion as actual gears.

    2.

    Pitch circle diameter.

    Diameter of pitch circle.

    3.

    Pitch point.

    Point of contact between two pitch circles.

    4.

    Pitch surface.

    Surface of two rolling discs which the gears have replaced.

    5.

    Pressure angle.

    Angle between normal and tangent at the point of contact ().

    6.

    Addendeum.

    Distance between pitch circle and top of gear.

    7.

    Dedendum.

    Distance between pitch circle and bottom of gear tooth.

    8.

    Circular pitch.

    Distance between two corresponding points on gear tooth when measured wrt circumference.

    9.

    Diametral pitch.

    Ratio of no.of teeth to pitch circle diameter.

    10.

    Module.

    Ratio of pitch circle diameter to no of teeth.

  3. FACTORS AFFECTING THE DIAMETER OF PINION.

      • A common question arises in designing a gear or a drive train is what should be the diameter of the pinion?.

        Properties of gear materials

        Material

        Condition

        B.H.N.

        Minimum tensile strength(N/ mm2)

        Chromium molybdenum steel (a)40 Cr 1 Mo 28

        (b)40 Cr 1 Mo 60

        Hardened and tempered

        201

        248

        700

        900

        Nickel steel 40 Ni 3

        Hardened and tempered

        229

        800

        Nickel chromium steel 30 Ni 4 Cr 1

        Hardened and tempered

        444

        1540

        Nickel chromium molybdenum steel 40 Ni 2 Cr 1 Mo 28

        Hardened and tempered

        255

        900

        Surface hardened steel

        (a)0.4% carbon steel

        (b)0.55% carbon steel

        (c)0.55% carbon chromium steel

        145(core 460(case)

        200(core) 520(case)

        250(core) 500(case)

        500(case)

        200(core) 300(case)

        551

        708

        866

        708

        708

        Case hardened steel (a)0.12 to 0.22%

        carbon (b)3% nickel

        (c)5% nickel steel

        650(case)

        200(core) 600(case) 250(core) 600(case)

        504

        708

        866

        Phosphorus bronze castings

        Sand casting Chill cast Centrifugal cast

        60min 70min 90 min

        160

        240

        260

        1. 1% chromium steel

        2. 3% nickel steel

        Fig.1. Spur gear terminology.

        Design considerations for a gear.

        In designing and analyzing a gear the following data is required:

        • The power to be transmitted.

        • The maximum torque on the system.

        • The speed of pinion (or driving gear) usually given in RPM.

        • The speed of driven gear.

        • The Centre distance between gears. (The Centre distance depends on the orientation, availability of space and mounting feasibility of the gearbox).

    1. The following requirements must be met in the design of gear:

      1. The gear teeth should have sufficient strength so that they will not fail under static or dynamic loading during normal running conditions.

      2. The gear teeth should have wear characteristics so that their life is satisfactory.

      3. The use of space and material should be economical.

    Fig.2. bevel gear nomenclature

    V. DESIGN PROCEDURE OF GEAR.

    S.No.

    Input parameters

    values

    1.

    Power

    10 hp

    2.

    Torque

    150 n-m

    3.

    Pinion RPM

    3400

    4.

    Driven gear RPM

    1500

    5.

    Gear ratio

    2.27:1

    6.

    Center distance

    50 mm

    7.

    Material

    Alloy steel

    1. Calculating the no. of teeth:

      The minimum no. of teeth required to avoid interference of gears:

      2Aw

      Tp =

      G[(1+1/G{1/G+2}sin2)-1]

      Tp = teeth on pinion G = gear ratio.

      = pressure angle

      2(1)

      Tp = 2.26[(1+1/2.26{1/2.26+2}sin2200)-1]

      Tp = 14.4 (lets say 15)

      Tg = 34

    2. Calculating module:

      w = 450 × 0.42 = 192.85 N/mm2

      b) Lewis form factor (y): y = 0.154 0.912

      T

      y = 0.083

      Tangential tooth load:

      WT = 192.85 × 15 × × 1.5 × 0.083 WT = 1142.97 N

      Therefore, the gear can transmit 1147.97 N

      We know that

      Now,

      L=DP/2 + DG/2 = 50mm 2.26 DG/2 +DG/2 = 50

      DG = 30.67mm ; DP = 19.32mm

      Module m = DP = 19.32 = 1.28

      TP 15

      The nearest standard module is 1.5

      TP = 19.32 = 13 teeth

      1.5

      TP = 30.67 = 20 teeth

      1.5

    3. Beam strength of gear:

      WT = w × b × × m × y

      Standard proportions of gear systems

      S.No.

      Particulars

      14 ½ composite or full depth involute system

      20 full depth involute system

      Values (mm)

      1.

      Addendum

      1m

      1m

      1.5

      2.

      Dedendum

      1.25m

      1.25m

      1.875

      3.

      Working depth

      2m

      2m

      3

      4.

      Minimum total depth

      2.25m

      2.25m

      3.375

      5.

      Tooth thickness

      1.5708m

      1.5708m

      2.35

      6.

      Minimum clearance

      0.25m

      0.25m

      0.375

      7.

      Fillet radius at root

      0.4m

      0.4m

      0.6

      Standard proportions of gear systems

      S.No.

      Particulars

      14 ½ composite or full depth involute system

      20 full depth involute system

      Values (mm)

      1.

      Addendum

      1m

      1m

      1.5

      2.

      Dedendum

      1.25m

      1.25m

      1.875

      3.

      Working depth

      2m

      2m

      3

      4.

      Minimum total depth

      2.25m

      2.25m

      3.375

      5.

      Tooth thickness

      1.5708m

      1.5708m

      2.35

      6.

      Minimum clearance

      0.25m

      0.25m

      0.375

      7.

      Fillet radius at root

      0.4m

      0.4m

      0.6

      Abbreviations:

      P

      Power

      T

      Torque

      TP

      Teeth on pinion

      TG

      Teeth on gear

      G

      Gear ratio

      N

      Rpm

      V

      Pitch line velocity

      W

      Permissible working stress

      o

      Allowable working stress

      EV

      Velocity factor

      WT

      Tangential load

      m

      Module

      b

      Width of gear

      y

      Lewis form factor

      Q

      Pressure angle

      DP

      Diameter of pinion

      DG

      Diameter of gear

      L

      Centre distance

      P

      Power

      T

      Torque

      TP

      Teeth on pinion

      TG

      Teeth on gear

      G

      Gear ratio

      N

      Rpm

      V

      Pitch line velocity

      W

      Permissible working stress

      o

      Allowable working stress

      EV

      Velocity factor

      WT

      Tangential load

      m

      Module

      b

      Width of gear

      y

      Lewis form factor

      Q

      Pressure angle

      DP

      Diameter of pinion

      DG

      Diameter of gear

      L

      Centre distance

      1. permissible working stress for gear teeth:

w = o × CV w = 450 × CV

CV = 3 = 3 = 0.42

3+V 3+4

Simulation of spur pinion.

Model Reference

Properties

Name: Alloy Steel (SS)

Model type: Linear Elastic

Isotropic

Default failure Unknown

criterion:

Yield strength: 620.422

N/mm^2

Tensile 723.826

strength: N/mm^2

Elastic 210,000

modulus: N/mm^2

Poisson's ratio: 0.28

Mass density: 7.7 g/cm^3

Shear 79,000

modulus: N/mm^2

Thermal 1.3e-05

expansion /Kelvin

coefficient:

STUDY RESULTS

Fig.3. von mises stress result.

Fig.4. Resultant displacement result.

Fig.5. equivalent strain result.

Fig.6. FOS result.

CONCLUSION.

The gear is designed and simulated the maximum displacement was found 2.028e-03mm. The above calculations are applicable for helical and Bevel gears as well.

REFERENCES.

  1. Budynas-Nisbett Shigleys Mechanical Engineering Design,

    Eighth Edition, 2008; Pg. 746-47

  2. Gitin M. Maitra: Handbook of gear design, 1994 Stephen, P. Radzevich; Dudleys Handbook of Practical Gear Design and Manufacture,Second Edition, 2012.

  3. Kapelevich, A. and McNamara, T., Direct Gear Design for Automotive Applications, 2013

  4. Milosav Ognjanovicl Miroslav Milutinovic2, Design for Reliability Based

    Methodology For Automotive Gearbox Load Capacity Identification, 2012

  5. R.S. Kurmi, Theory of Machines, 14th Revised Edition, 2004.

  6. R.S. Kurmi, J.K.Gupta Machine Design,Eurasia Publication House, 2005.

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