Design and Analysis of Differential Gear Box Used in Heavy Vehicle
Vol.2, No.1 ISSN Number (online): 2454-9614
Proceedings of International Conference on Recent Trends in Mechanical Engineering-2K15(NECICRTME-2K15), 20th – 21st November,2015
DESIGN AND ANALYSIS OF DIFFERENTIAL GEAR BOX USED IN HEAVY VEHICLE
N.Vijayababu#1, Ch.Sekhar#2
Narasaraopeta Engineering College, JNT University, Kakinada.,
Abstract common use is in motor vehicles, where the transmission adapts the output of the internal Differential is used when a vehicle takes a turn, combustion engine to the drive wheels. Such engines the outer wheel on a longer radius than the inner need to operate at a relatively high rotational speed, wheel. The outer wheel turns faster than the inner which is inappropriate for starting, stopping, and wheel that is when there is a relative movement slower travel. The transmission reduces the higher between the two rear wheels. If the two rear engine speed to the slower wheel speed, increasing wheels are rigidly fixed to a rear axle the inner torque in the process. Transmissions are also used on wheel will slip which cause rapid tire wear, pedal bicycles, fixed machines, and anywhere else steering difficulties and poor load holding. rotational speed and torque needs to be adapted. Differential is a part of inner axle 1.1 DIFFERENTIAL GEAR BOX housing assembly, which includes the differential rear axles, wheels and bearings. The differential A differential is a device, usually but not necessarily consists of a system of gears arranged in such a employing gears, capable of transmitting torque and way that connects the propeller shaft with the rear rotation through three shafts, almost always used in axles. one of two ways: in one way, it receives one input and provides two outputs—this is found in most The analysis is conducted to verify the best automobiles—and in the other way, it combines two material for the gears in the gear box at higher inputs to create an output that is the sum, difference, speeds by analyzing stress, displacement and also or average, of the inputs. by considering weight reduction. In automobiles and other wheeled vehicles, the differential allows each of the driving roadwheels to The analysis is done in Cosmos software.Modeling rotate at different speeds, while for most vehicles is done in the Pro/Engineer. supplying equal torque to each of them.
1. INTRODUCTION
A transmission or gearbox provides speed and torque conversions from a rotating power source to another device using gear ratios. In British English the term transmission refers to the whole drive train, including gearbox, clutch, prop shaft (for rear-wheel drive), differential and final drive shafts. In American Fig 1 Differential gear box English, however, the distinction is made that a gearbox is any device which converts speed and torque, whereas a transmission is a type of gearbox that can be "shifted" to dynamically change the 2. AIM OF THE PROJECT speed: torque ratio, such as in a vehicle. The most
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South Asian Journal of Engineering and Technology (SAJET) Vol.2, No.1 ISSN Number (online): 2454-9614
Proceedings of International Conference on Recent Trends in Mechanical Engineering-2K15(NECICRTME-2K15), 20th – 21st November,2015
The main aim of the project is to focus on the TEG=TGsecθp2=50sec81 =319.622 mechanical design and contact analysis on assembly Tooth form factor for the pinion 1 of gears in gear box when they transmit power at y P=0.154-0.912/TEP, for 20° full depth involute different speeds at 2400 rpm, 5000 rpm and 6400 system rpm. Analysis is also conducted by varying the =0.154-0.912/8 materials for gears, Cast Iron, Nickel Chromium =0.04 Alloy Steels and Aluminum Alloy. And tooth form factor for gear 1 The analysis is conducted to verify the best material y G=0.154-0.912/TEG for the gears in the gear box at higher speeds by =0.154-0.912/319.622 analyzing stress, displacement and also by =0.151 considering weight reduction. since the allowable static stresses(σO) for both pinion 1 Design calculations are done on the differential of and gear is same (i.eσO=126.66 Mpa) and y P is less 1 Ashokleyland 2516M by varying materials and than y G, therefore the pinion is weaker. Thus the speeds. Differential gear is modeled in Solid works. design should be based upon the pinion Analysis is done on the differential by applying allowable static stress(σO) =σu/3=380/3=126.66Mpa tangential and static loads.. σu=ultimate tensile strength=380Mpa TANGENTIAL TOOTH LOAD(WT) 1 3. DESIGN CALCULATIONS OF A WT=(σOxCv).b.Π.m.y P((L-b)/L) DIFFERENTIAL CROWN WHEEL Cv=velocity factor =3/3+v, for teeth cut by form cutters Specifications of heavy vehicle v=peripheral speed in m/s Maximum power= 162 bhp at 2400 rpm b=face width Bevel gearing arrangement =90° m=module=10 1 Diameter of crown wheel =DG= 475mm y p=tooth form factor Number of teeth on gear = TG=50 L=slant height of pitch cone √( ) ( ) Number of teeth on pinion= TP = 8 Module = m=DG/TG=475/50=9.5=10 (according to DG= pitch diameter of gear =475 stds) Dp= pitch diameter of gear =80
Diameter of pinion =m x TP=10x8=80mm V=
Module = m=DG/TG=475/50=9.5=10 (according to stds) =10.048m/s Material used for both pinion and gear is nicr Cv==3/3+10.048=0.229 steel=30ni4cr1 L=√( ) ( ) Brinell hardness number (BHN)=444 Pressure angle of teeth is 20° involute system Ø=20° =240.844 P=162BHP = 162x745.7w=120803.4 The factor (L-b/L) may be called as bevel factor We know that velocity ratio For satisfactory operation of the bevel gears the face width should be from 6.3m to 9.5m V.R=TG/TP= DG/DP=NP/NG So b is taken as 9.5m V.R=TG/TP=50/8=6.25 b= 9.5x10=95 V.R=NP/NG
6.25=2400/N W =(126.66x0.229)x95xΠx10x0.04( ) G T NG=384rpm =2093.840N For satisfactory operation of bevel gears the number odf teeth in the pinion must not be DESIGN CALCULATION OF SUN GEAR Less than where v.r=velocity ratio √ ( )
= =7.5 Diameter of sungear =DG=150mm √ ( ) Diameter of pinion =DP=70mm Since the shafts are at right angles therefore pitch Number of teeth on gear = T =18 angle for the pinion G -1 Number of teeth on pinion = TP = 15 θp1=tan (1/v.r) D=D +D =220 =tan-1(1/6.25) G P T=TG+TP = 33 =9.0 Module = m=D/T=220/33=6.66=7(according to stds) Pitch angle of gear θp2=90°-9=81 Brinell hardness number(BHN)=444 We know that formative number of teeth for pinion Pressure angle of teeth is 20° involute system Ø=20° TEP=TPsecθp1=8sec9 =8 P=162BHP = 162x745.7w=120803.4w And formative number of teeth for gear
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South Asian Journal of Engineering and Technology (SAJET) Vol.2, No.1 ISSN Number (online): 2454-9614
Proceedings of International Conference on Recent Trends in Mechanical Engineering-2K15(NECICRTME-2K15), 20th – 21st November,2015
We know that velocity ratio V.R=TG/TP= DG/DP=NP/NG V.R=DG/DP =150/70=2.142 V.R=NP/NG 2.142=2400/NG NG=1120.448rpm Since the shafts are at right angles therefore pitch Fig 4: PLANET angle for the pinion . -1 θp1=tan (1/v.r) =tan-1(1/2.142) =25.025 Pitch angle of gear θp2=90°-25.025=64.974 We know that formative number of teeth for pinion TEP=TPsecθp1=15sec25.025 =16.554 And formative number of teeth for gear TEG=TGsecθp2=18sec64.974 =42.55 Fig 5: SUNGEAR Tooth form factor for the pinion 1 y P=0.154-0.912/TEP, for 20° full depth involute system 4.1STRUCTURAL ANALYSIS OF =0.154-0.912/16.554 DIFFERENTIAL GEAR =0.099 And tooth form factor for gear 1 y G=0.154-0.912/TEG =0.154-0.912/42.55 =0.132 since the allowable static stresses(σO) for both pinion 1 and gear is same (i.eσO=126.66 Mpa) and y P is less 1 than y G, therefore the pinion is weaker. Thus the design should be based upon the pinion allowable static stress(σO) =σu/3=380/3=126.66Mpa σu=ultimate tensile strength=380Mpa Fig 6: ASSEMBLY OF DIFFERENTIAL 4 MODEL OF DIFFERENTIAL GEAR GEAR BOX
Fig 2:CROWN Table 1 Material Properties Model Properties Reference
Fig 3:PINION
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South Asian Journal of Engineering and Technology (SAJET) Vol.2, No.1 ISSN Number (online): 2454-9614
Proceedings of International Conference on Recent Trends in Mechanical Engineering-2K15(NECICRTME-2K15), 20th – 21st November,2015
Name: Nickel Chrome Model Properties Steel Reference Model Linear Elastic type: Isotropic Name: al_alloy7 Default Max von Mises 475-t761 failure Stress Model type: Linear criterion: Elastic Yield 1.72339e+008 Isotropic strength: N/m^2 Default Max von Tensile 4.13613e+008 failure Mises strength: N/m^2 criterion: Stress Elastic 2e+011 N/m^2 Yield 1.65e+00 modulus: strength: 8 N/m^2 Poisson's 0.28 Tensile 3e+007 ratio: strength: N/m^2 Mass 7800 kg/m^3 Elastic 7e+010 density: modulus: N/m^2 Shear 7.7e+010 Poisson's 0.33 modulus: N/m^2 ratio: Thermal 1.1e-005 Mass 2600 expansion /Kelvin density: kg/m^3 coefficient: Shear 3.189e+0 modulus: 08 N/m^2
Fig7:2part_assm-2400_nicrsteel_tangential_load- Strain-Strain1
Fig9:2part_assm- 2400_aluminiumally_tangential_load-Strain- Strain1
Fig 8 2part_assm-2400_nicrsteel_static_load- Stress-Stress1
Fig10:2part_assm- 2400_aluminiumally_static_load-Strain-Strain1
4.5 ALUMINUM ALLOY
Table 2 Material Properties
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South Asian Journal of Engineering and Technology (SAJET) Vol.2, No.1 ISSN Number (online): 2454-9614
Proceedings of International Conference on Recent Trends in Mechanical Engineering-2K15(NECICRTME-2K15), 20th – 21st November,2015
4.7 CAST IRON
Table 3 Material Properties
Model Properties Reference Name: Malleable Cast Iron Model Linear Elastic type: Isotropic Default Max von Mises failure Stress Fig 12: 2part_assm-2400_castiron_static_load- criterion: Strain-Strain1 Yield 2.75742e+008 strength: N/m^2 5. RESULTS TABLE : Tensile 4.13613e+008 strength: N/m^2 ANALYSIS OF THREE DIFFERENT Elastic 1.9e+011 MATERIALS BY modulus: N/m^2 USING ON DIFFERENT SPEEDS Poisson's 0.27 ratio: Mass 7300 kg/m^3 density: Table 4: ANALYSIS OF 2400 RPM Shear 8.6e+010 modulus: N/m^2 TANGENT Aluminum Cast Cast Steel Thermal 1.2e-005 IAL Alloy Iron expansion /Kelvin coefficient: LOAD (N) 2093.8 2922.51 3243.08 DISPLACE 0.0061541 0.01005 MENT 0.0241696 3 66 (mm)
STRESS 2.29414 3.19018 3.57544 (N/mm2) 1.69558 STRAIN 1.0400e-5 4.1593e-5 e-5 STATIC 56141.9 18143.3 37933.7 LOAD (N) DISPLACE MENT 0.164988 0.150063 0.11763 (mm) STRESS 63.5052 19.8068 41.8212 (N/mm2) 0.0002808 0.0002582 0.00019 STRAIN 82 39 8329
Fig11:2part_assm-2400_castiron_tangential_load-
Strain-Strain1
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South Asian Journal of Engineering and Technology (SAJET) Vol.2, No.1 ISSN Number (online): 2454-9614
Proceedings of International Conference on Recent Trends in Mechanical Engineering-2K15(NECICRTME-2K15), 20th – 21st November,2015
Table 5:ANALYSIS OF 5000RPM of a spur gear, “Journal of Engineering and Applied Sciences 2 (12); pp 17431747. 2. Zeping Wei., 2004”Stresses and Deformations in Involute spur gears by Finite Element TANGEN Cast Aluminu method,” M.S, Thesis, College of Graduate Studies Cast Iron TIAL Steel m Alloy and research, University of Saskatchewan, Saskatchewan. 3. DarleW.Dudley, 1954, Hand book of practical gear LOAD (N) 1818.54 1595.22 1770.24 design DISPLAC 4. Alec strokes, 1970, High performance of gear 0.005411 0.013194 0.005488 EMENT design 8 4 66 (mm) 5. Maitra, G.M, 2004, Hand Book of Gear Design, TataMcGrawHill, STRESS 2 2.584 1.70369 2.01579 New Delhi.. (N/mm ) 6. S.Md.Jalaluddin., 2006, “Machine Design, 1.04958e- 9.32532 STRAIN 2.2558e-5 “Anuradha publications, Chennai. 5 e-6 7. ThirupathiChandrupatla, Ashok D.Belegundu, STATIC “Introduction to finite element in Engineering” , 2003 LOAD (N) 56141.9 18143.3 37933.7 8. PSG, 2008.”Design data,” KalaikathirAchchagam publishers, Coimbatore, India. DISPLAC 9. S.Mahalingam, R.E.D Bishop, 1974, “Dynamic EMENT 0.164853 0.150036 0.117614 loading of Gear tooth”, Journal of sound and (mm) vibration, 36(2), pp179189 STRESS 2 74.4963 22.6949 43.1949 (N/mm ) 0.000309 0.000274 0.000199 STRAIN 415 774 826
6. CONCLUSION
In our project we have designed a differential gear box for Ashok Leyland 2516M. Loads are calculated when the gears are transmitting different speeds 2400rpm, 5000rpm Structural analyses are done on the differential gear box to verify the best material by taking in to account stresses, displacements, weight etc.
By observing the structural analysis results using Aluminum alloy the stress values are within the permissible stress value. So using Aluminum Alloy is safe for differential gear. When comparing the stress values of the three materials for all speeds 2400rpm, 5000rpm the values are less for Aluminum alloy than Alloy Steel and Cast Iron.
By observing analysis results, Aluminum Alloy is best material for Differential.
REFERENCES
1. J.O.Nordiana, S.O.Ogbeide, N.N.Ehigiamusoe and F.I.Anyasi., 2007,”Computer aided design
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