Design and Analysis of Gear Pinion

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.

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.