STATIC ANALYSIS ON BEVEL GEAR USING STRUCTURAL STEEL, GRAY CAST IRON, AND STAINLESS STEEL

Prateek Srivastava1, Rishabh2, Zubair Irshad3, Pankaj Kumar Singh4

1Graduate Student, Mechanical Engineering, Faculty of Engineering and Technology Manav Rachna International Institute of Research and Studies, Faridabad, Haryana, India

2Graduate Student, Mechanical Engineering, Faculty of Engineering and Technology, Manav Rachna International Institute of Research and Studies, Faridabad, Haryana, India

3Graduate Student, Mechanical Engineering, Faculty of Engineering and Technology, Manav Rachna International Institute of Research and Studies, Faridabad, Haryana, India

4Graduate Student, Mechanical Engineering, Faculty of Engineering and Technology, Manav Rachna International Institute of Research and Studies, Faridabad, Haryana, India

Abstract

A Bevel gear is generally used for Shaft. They are at 90o angle with each other, and their teeth which are involved with each other are cut to be straight. There are two types of bevel gear first straight bevel gear and second spiral bevel gear. The use of bevel gear is used to transfer the power from one shaft to another shaft which being perpendicular to each other. The shape of bevel gear is truncated cone. The gear tooth size, thickness and height are to be small or decrease towards the cone apex. In this paper we use to calculate stress, stain and deformation in bevel gear. The design of bevel gear is done in Catia software and the Analysis is done in Ansys 17.2 software

Keywords: Bevel gear, Catia, Ansys, Total deformation, Strain, Stress,

1. Introduction:

A bevel gear is a type of gear which uses to transmit the power from one shaft to another shaft which is perpendicular to each other. In bevel gear the teeth are straight of straight bevel gear, which have a common apex point. And in spinal bevel gear the teeth are spinal curve which also have a common apex point. There is gradual contact in the teeth of spiral gear in which when the tooth of two gear meet with each other there is a smooth and noise less operation is done. Spiral bevel gear have more load capacity as there is simultaneously contact in the teeth and their arc of contact is greater. Bevel gear can be arranged at different pitch angle such that when the pitch angle is less than 90o then external bevel gear, when the pitch angle equal to 90o then crown bevel gear, and when the pitch angle is greater than 90o then internal bevel gear. There are

specific categories of bevel gear which are Miter gear, Crown gear, internal bevel gear, Skew bevel gear, Hypoid gear, Zerol gear, Face gear.

There are some terms which are used in terminology of bevel gear are Pitch cone, Cone center, Cone distance, Pitch angle, Addendum angle, Dedendum angle, Face angle, Root angle, Back cone, Back cone distance. In this paper designing of Bevel gear is done in Catia software and the static analysis on bevel gear is done in Ansys 17.2 software.

Notation

kW- Power

np – No. of rotation per minute

– Pressure angle

Dp- Pitch circle diameter of pinion

Dg – Pitch circle diameter of gear

b – Length of bevel gear

Mt – Torque transmitted by gears

- Pitch angle of pinion (o)

rm- Radius of pinion along face width at midpoint

Pt- Tangential component of force of tooth

Pr – Radial component of force of tooth

Pa- Axial component of force of tooth

2. Analytical Method

In this Analytical Method, we use to give a momentum of the bevel gear which is connected which is connected with each other, while we use to calculate stress, strain and deformation in that gear.

1. To calculate torque transmitted by gear, we use

Mt = 60 X 10 6 (KW) 2np

2. Pitch angle of pinion (o)

tan = Dp Dg

3. Radius of pinion along face width at midpointrm = Dp _ bsin

2 24. Tangential component of force of tooth

Pt = Mt

rm

5. Radial component of force of tooth

Pr = Pt tancos 6. Axial component of force of tooth

Pa = Pt tansin

3. FINITE ELEMENT METHOD

Finite element method is a type of method in which solving problems of mathematical physics with the use of Numerical Method. In this type of finite element method the major problems can solved with the use of structural analysis. In finite element method which is generally consists of different type of heavily meshed geometries along with different materials like structural steel, gray cast iron and stainless steel and with the use of that we use to calculate equivalent stress, equivalent elastic strain, and total deformation, and with the use of mathematical solution it is very complicated solve these types of problems.

4. DESIGN AND DATA

Bevel gear is used to model and design in CATIA V5 R20 software, in this software we use to draw the sketch of bevel gear and then we use to draw the teeth as well. In this paper we also use locate 3D view of teeth and bevel gear as it is design in part design in catia software. Bevel gear have different geometrical data which are Inner radius = 100mm, Outer radius = 120mm, No. of teeth = 17, Diametral pitch = 0.1583, Pitch diameter = 107.391, Whole depth = 13.82386, Addendum = 6.31712, Dedendum = 7.50674, Clearance = 1.18962, Circular tooth thickness = 9.92291, Pitch angle = 90.0004, Pitch cone radius = 53.6955, Face width = 17.89850, Outside diameter = 107.39103, Back cone radius = 8.769 x 1017, Virtual number of teeth = 2.77 x 1017.

A) Sketch of bevel gear in catia [12]

Fig 1: Sketch of bevel gear in catia

B) Sketch of bevel gear teeth in catia

Fig 2: Sketch of bevel gear teeth in catia

C) Model of bevel gear teeth in catia

Fig 3: Model of bevel gear teeth in catia

D) Bevel gear final model in catia

Fig 4: Model of bevel gear in catia

5. ANALYTICAL RESULTS

The analyzing of bevel gear is done in Ansys 17.2 software, in this paper the materials which are used are for analyzing of bevel gear are structural steel, gray cast iron, and stainless steel. For calculating maximum and minimum value of Equivalent stress, equivalent elastic strain, and total deformation of bevel gear while applying the moment at 1000N-m and 2000 N-m. [13]

1. Structural steelA) Moment at 1000 N-mi) Equivalent Stress

Fig 5: equivalent stress at 1000N-m for structural steel

ii) Equivalent Elastic Strain

Fig 6: equivalent elastic strain at 1000N-m for structural steel

iii) Total Deformation

Fig 7: total deformation at 1000N-m for structural steel

B) Moment at 2000 N-mi) Equivalent Stress

Fig 8: equivalent stress at 2000N-m for structural steel

ii) Equivalent Elastic Strain

Fig 9: equivalent elastic strain at 2000N-m for structural steel

iii) Total Deformation

Fig 10: total deformation at 2000N-m for structural steel

2. Gray cast ironA) Moment at 1000 N-mi) Equivalent Stress

Fig 11: equivalent stress at 1000N-m for gray cast iron

ii) Equivalent Elastic Strain

Fig 12: equivalent elastic strain at 1000N-m for gray cast iron

iii) Total Deformation

Fig 13: total deformation at 1000N-m for gray cast iron

B) Moment at 2000 N-mi) Equivalent Stress

Fig 14: equivalent stress at 2000N-m for gray cast iron

ii) Equivalent Elastic Strain

Fig 15: equivalent elastic strain at 2000N-m for gray cast iron

iii) Total Deformation

Fig 16: total deformation at 2000N-m for gray cast iron

3. Stainless SteelA) Moment at 1000 N-mi) Equivalent Stress

Fig 17: equivalent stress at 1000N-m for stainless steel

ii) Equivalent Elastic Strain

Fig 18: equivalent elastic strain at 1000N-m for stainless steel

iii) Total Deformation

Fig 19: total deformation at 1000N-m for stainless steel

B) Moment at 2000 N-mi) Equivalent Stress

Fig 20: equivalent stress at 2000N-m for stainless steel

ii) Equivalent Elastic Strain

Fig 21: equivalent elastic strain at 2000N-m for stainless steel

iii) Total Deformation

Fig 22: total deformation at 2000N-m for stainless steel

6. CONCLUSION

A bevel gear is a type of gear which is used in transmitted the power between two perpendicular shafts, bevel gear is modeled in Catia V5 R20 software. While analyzing part is done in Ansys 17.2 software. In which we use to calculate equivalent stress, equivalent elastic strain, total deformation for maximum and minimum value at the moment of 1000N-m and 2000N-m using material structural steel, gray cast iron, and stainless steel.

A) Static structural Analysis for moment at 1000 N-m (Maximum)

Materials Equivalent Stress Equivalent Elastic Strain

Total deformation

Structural steel 6.2672 X 106 3.134 X 10-5 1.4346 X 10-6

Gray cast iron 6.2697 X 106 5.7006 X 10-5 2.573 X 10-6

Stainless steel 6.2658 X 106 3.247 X 10-5 1.4967 X 10-6

B) Static structural Analysis for moment at 1000 N-m (Minimum)

Materials Equivalent Stress Equivalent Elastic Strain

Total deformation

Structural steel 1346.7 9.6099 X 10-9 0

Gray cast iron 1342.7 1.7585 X 10-8 0

Stainless steel 1349.7 9.9249 X 10-9 0

C) Static structural Analysis for moment at 2000 N-m (Maximum)

Materials Equivalent Stress Equivalent Elastic Strain

Total deformation

Structural steel 1.2534 X 107 6.2681 X 10-5 2.8692 X 10-6

Gray cast iron 1.2539 X 107 0.00011401 5.1461 X 10-6

Stainless steel 1.2532 X 107 6.4939 X 10-5 2.9934 X 10-6

D) Static structural Analysis for moment at 2000 N-m (Minimum)

Materials Equivalent Stress Equivalent Elastic Strain

Total deformation

Structural steel 2693.4 1.922 X 10-8 0

Gray cast iron 2685.3 3.5171 X 10-8 0

Stainless steel 2699.3 1.985 X 10-8 0

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