MODELING AND ANALYSIS OF CONSTANT MESH ......So in constant mesh gear box we can change the gear...

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International Journal of Mechanical Engineering and Technology (IJMET)

Volume 9, Issue 3, March 2018, pp. 991–1006, Article ID: IJMET_09_03_102

Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=9&IType=3

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Scopus Indexed

MODELING AND ANALYSIS OF CONSTANT

MESH TRANSMISSION SYSTEM ALONG WITH

CASING

Dasari Ajay

Associate Professor, CMR College of Engineering & Technology,

Hyderabad, Telangana, India

A Vishnu Naga Kumar

Student, CMR College of Engineering & Technology, Hyderabad, Telangana, India

ABSTRACT

Transmission System is used to transmit power from engine to axles. Constant

Mesh Transmission System is one of the famous types of Transmission System where

all gears are constantly mesh with each other at all the times. .Transmission is a

mechanism in a power transmission system, which provides controlled application of

the power. Often the term transmission refers simply to the gearbox that uses gears

and gear trains to provide speed and torque conversions from a rotating power source

to another device .For modelling of the component a CAD software known as CREO

3.0 is used. In CREO 3.0. some of the basic operations like revolve, extrude, helical

sweep etc are used. Generally, FEA analysis is used to identify the nature and

characteristics of stresses acting on the assembly and evaluating the influence of

load/mass/geometry/boundary conditions over the Constant Mesh Transmission

System. For FEA analysis, software named ANSYS Work Bench 18.0 is used

Keywords: constant mesh transmission system, gear box, Creo-3, FEA, ANSYS

Cite this Article: Dasari Ajay and A Vishnu Naga Kumar, Modeling and Analysis of

Constant Mesh Transmission System Along With Casing, International Journal of

Mechanical Engineering and Technology, 9(3), 2018, pp. 991–1006.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=3

1. INTRODUCTION

This is one of the famous type used in twenty centuries. It this gearbox, all the gears are in

constant mesh with each other all the time. The gears on the main shaft rotate freely without

rotating the main shaft. Constant mesh gear box consists two dog clutches. These clutches are

provided on the main shaft, one between the clutch gear and the second gear and the other

between the first gear and reverse gear. When the left side dog clutch is made to slide left by

means of gearshift lever, it meshes with the clutch gear and the vehicle runs on top speed. If

this clutch slide right and mesh with second gear, than the vehicle runs on second gear speed.

Modeling and Analysis of Constant Mesh Transmission System Along With Casing


So in constant mesh gear box we can change the gear ratio by shifting the dog clutch. This

type of gear box is more popular than sliding mesh because it creates low noise and less wear

of gears.

Figure 1 Constant Mesh Gear Box

A gear or cogwheel is a rotating machine part having cut teeth or cogs which mesh with

another toothed part to transmit torque. The use of gear is to increase speed, increase torque

and change direction

2. MODELING

The modeling of Constant mesh gear box along with spur, helical and zero bevel gear will be

considered.

2.1. Basic Formulae for designing of Spur Gear

Diametral Pitch = Number of Teeth / Pitch Diameter

Base Diameter = Pitch Diameter * cos(Pressure Angle)

Whole Depth = (2.2 / Diametral Pitch) + 0.002

Root Diameter = Outer Diameter - (2 * Whole Depth)

Addendum = 1 / Diametral Pitch

Dedendum = Whole Depth -Addendum

Circular Tooth Thickness = Pi / (2 * Diametral Pitch)

For generation of involute curve

BaseRadius = BaseDiameter / 2

Angle = t*90

Cirlen = (PI * BaseRadius * t ) / 2

X_PNT = BaseRadius * cos(Angle)

Y_PNT = BaseRadius * sin(Angle)

x = X_PNT + ( Cirlen * sin(Angle))

y = Y_PNT - ( Cirlen * cos(Angle))

z = 0

Dasari Ajay and A Vishnu Naga Kumar


Table 1 Calculation of Spur Gear

Main Gear Counter Gear

1 2 3 4 1 2 3 4

Outer

Diameter 117 105 90 77 30 42 57 70

Number of

Teeth 46 41 35 29 10 15 21 27

Pitch

Diameter 115 102.5 87.5 72.5 25 37.5 52.5 67.5

Pressure

Angle 20 20 20 20 20 20 20 20

Width 14 12 11 11 14 12 11 11

Diametral

Pitch 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

Base

Diameter 108.6 96.31

82.2

3 68.12

23.4

9

35.2

3 49.33 63.42

Whole

Depth 5.502 5.502

5.50

2 5.502

5.50

2

5.50

2 5.502 5.502

Root

Diameter 105.9 93.99

78.6

9 65.99

18.9

9

30.9

9 45.99 58.99

Addendum 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5

Dedendum 3.002 3.002 3.00

2 3.002

3.00

2

3.00

2 3.002 3.002

Circular

Tooth

Thickness

3.926 3.926 3.92

6 3.926

3.92

6

3.92

6 3.926 3.926

Module 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5

Table 2 Calculations of Spur Gear

Idle Gear Differential

Spur Gear

Reverse

Gear Big Small

Outer Diameter 64 54 148 79

Number Of Teeth 24 21 59 30

Pitch Diameter 60 52.5 147.5 75

Pressure Angle 20 20 20 20

Width 10 21.5 18 20

Diametral Pitch 0.4 0.4 0.4 0.4

Base Diameter 56.38 49.33 138.604 70.476

Whole Depth 5.502 5.502 5.502 5.502

Root Diameter 52.996 42.996 136.996 67.996

Addendum 2.5 2.5 2.5 2.5

Dedendum 3.002 3.002 3.002 3.002

Circular Tooth

Thickness 3.926 3.926 3.926 3.926

Module 2.5 2.5 2.5 2.52



3. PROCEDURE FOR HELICAL GEAR

3.1. Basic Formulae for Helix Gear

Transverse module = normal module / cos (helix angle)

Normal circular pitch = pi * normal module

Transverse circular pitch = pi * transverse module

Transverse pressure angle = atan ((tan (normal pressure angle))/(cos (helix angle)))

Outer diameter = pitch diameter + (2 * normal module)

Root diameter = pitch diameter - (2 * 1.25 * normal module)

Base diameter = pitch diameter * cos (transverse pressure angle)

Normal tooth thickness = (pi * normal module) / 2

Transverse tooth thickness = (pi * transverse module) / 2

Lead = pi * Pitch diameter / tan (Helix angle)

Addendum = normal module

Dedendum = 1.25 * normal module

Tooth depth = 2.25 * normal module

3.2. For generation of curve

BaseRadius = BaseDiameter / 2

Angle = t*90

Cirlen = (PI * BaseRadius * t ) / 2

X_PNT = BaseRadius * cos(Angle)

Y_PNT = BaseRadius * sin(Angle)

x = X_PNT + ( Cirlen * sin(Angle))

y = Y_PNT - ( Cirlen * cos(Angle))

z = 0

3.3. Calculation of Helical Gear

Number of Teeth = 65

Normal Module = 1.5

Pitch Diameter = 111

Normal Pressure Angle = 20

Helix Angle = 25

Width = 13.5

Side = Right Hand

Transverse Module = 1.655

Normal Circular Pitch = 4.712

Transverse Circular Pitch = 5.199

Transverse Pressure Angle = 21.880203

Outer Diameter = 114

Root Diameter = 106.5

Base Diameter = 103.004



Normal Tooth Thickness = 23.5619

Transverse Tooth Thickness = 2.5999

Lead = 747.8255

Addendum = 1.5

Dedendum = 1.875

Tooth Depth = 3.375

4. PROCEDURE FOR BEVEL GEAR

Table 3 Calculations of Bevel Gear

Symbol Formula Bevel Gear

Pinion (1)

Bevel Gear

(2)

Shaft Angle 900

900

Module m 4.73 4.73

Pressure Angle A 200

200

Number of Teeth Z 22 26

Pitch Diameter d Z*m 104.06 122.98

Pitch Circle Cone Angle δ1

δ2

atan(z1/z2)

90 - δ1 40.237 49.763

Cone Diameter R d2/2*Sin(δ2) 80.55 80.55

Face Width B < R/3 24 24

Addendum ha 1*m 4.73 4.73

Dedendum hf 1.25 * m 5.1925 5.1925

Dedendum Angle θf aTan(hf/R) 3.688 3.688

Addendum Angle θa aTan(ha/R) 3.3606 3.3606

Tip Angle δa δ + θa 43.5976 52.879

Root Angle δf δ - θf 35.0445 46.075

Outer Diameter Da d+2*hacos(δ) 111.22 129.09

Base Diameter B d * Cos(δ) 79.43722 79.49302

Root Diameter Rd d – 2 * hf 93.675 112.595

Diametral Pitch P z/d 0.2114 0.2114

Whole Depth h (2.2/P) + 0.002 10.4088 10.4088

Circular Tooth Thickness t 1.5708 /P 7.43046 7.43046

Parts List

Gears of 4 main shaft

Main shaft

Reverse shaft with reverse shaft

Counter Gear of 4 spur and one helical gear

Idle Gears of big and small

Differential of 2 sun gears and 2 star gears with a pin and spur gear

Cross gear, Cross bolt, Cross bolt bush

Gear Shifter

Casing of 4 parts



Figure 2 Four Gear Shaft Assembly

Figure 3 Countershaft assembly

Gear Ratio

The Gear Ratio is defined as the input speed relative to the output speed.

Table 4 Gear Ratio

Gear Ratio

values

Gear

Ratio

1st Gear 46/10 4.6

2nd Gear 41/15 2.733

3rd Gear 35/21 1.667

4th Gear 29/27 1.074

Reverse Gear: Idle

Gear 30/24 1.25

Idle Gear:

Differential Spur

Gear

21/59 0.3559

Bevel Gear Pinion:

Bevel Gear 22/26 0.8461



Lesser the Gear Ratio, Higher the speed and lesser, the torque needed and vice-versa

One of the main benefits of a gear box is it allows you to make adjustments to the speed

and torque of a motor

Figure 4 Main shaft and Countershaft assembly

Figure 5 Assembly of Gears

Figure 6 Main Assembly Isometric View



5. MATERIAL PROPERTIES

Table 5 Material Properties

Properties High Carbon

Steel

Medium Carbon Steel

SAE 1055

Aluminum

Alloy

Yield strength (MPa) 350-550 355 280

Tensile strength (MPa) 650-880 650 310

Poisons ratio 0.27-0.30 0.27-0.30 0.33

Density (kg/m3) 7700 7800 2770

Shear modulus (GPa) 80 80 26.692

Thermal expansion coefficient (/k) 10 11 8

Thermal Conductivity (W/m.K) 26 51.9 41.9

High Carbon Steel for Gears

Medium Carbon Steel for Shafts

Aluminum alloy for Casing

SOLID185 is used for 3-D modeling of solid structures. It is defined by eight nodes

having three degrees of freedom at each node: translations in the nodal x, y, and z directions.

The element has plasticity, hyperelasticity, stress stiffening, creep, large deflection, and large

strain capabilities. It also has mixed formulation capability for simulating deformations of

nearly incompressible elastoplastic materials, and fully incompressible hyperelastic materials.

Two Gear Assembly of Main Gear 1 and Counter Gear 1

Figure 7 Total Deformation

Table 6 Equivalent Stress

Time [s] Minimum [MPa] Maximum [MPa]

1. 2.9576e-003 314.21

Figure 8 Equivalent Stress



Table 7 Safety factor

Time [s] Minimum Maximum

1. 2.0687 15.

Figure 9 Safety Factor Figure 10 status

Table 7 Pressure


1. -7215. 73362

Figure 11 Pressure

Transient Structural Analysis

Figure 12 No separation Connection



Figure 13 Total Deformation Graph


Four Gear Pair Assembly

Figure 15 Four Gear Pair Assembly



Element: Solid 185

Materials used for:

Shaft: Medium Carbon Steel

Gears: High Carbon Steel

6. MODAL ANALYSIS

Table 8 Modal Frequency

Mode Frequency [Hz]

1. 719.17

2. 747.93

3. 1131.8

4. 1908.7

5. 2017.6

6. 2424.4

7. 2538.

8. 2896.4

9. 3152.5

10. 3202.7

11. 3537.

12. 4078.9


Transient Structural Analysis

Figure 17 Total Deformation Graph




MAIN ASSEMBLY

Figure 19 Main Assembly

Element: Solid 185

Materials used:

High Carbon Steel: Gears

Medium Carbon Steel: Shafts

Aluminum Alloy: Casing

Figure 20 Moment and Fixed Supports



Table 9 Total Deformation

Time [s] Minimum [mm] Maximum [mm]

1. 0. 1.1479e-002


Table 10 Equivalent Stress


1. 0. 29.664

Figure 22 Equivalent Stress

Modal Analysis

Table 11 Modal Frequencies

Mode Frequency [Hz]

1. 527.47

2. 531.21

3. 897.

4. 898.7

5. 1428.2

6. 1582.6

7. 2023.5

8. 2885.8

9. 3029.9

10. 3186.9



11. 3847.7

12. 3974.5

Figure 23 Total Deformation in Modal

7. CASING

Figure 24 Casing

Element: Solid 18

Material used is Aluminum Alloy for Casing

STATIC ANALYSIS

Figure 25 Bonded Connections



Figure 26 Bonded Connections Figure 27 Total Deformation

8. CONCLUSION

Reference value of an existing manufactured product is taken and rest is calculated with the

available formulae. Designing of the model is done in CREO 3.0. Modeling is done using

some operations like sketching, extrude, swept blend, round, etc., Spur gear is designed using

involute curve method along with using some operations like angled datum plane and pattern

commands. Helical gear is designed using involute curve method along with using some

operations like angled datum plane, helical sweep, swept blend and pattern commands. Bevel

gear is designed using some operations like revolve, helical sweep and pattern commands.

The designed model is analyzed in Static, Dynamic and Kinematic modes using ANSYS 18.0.

The obtained values were below the working limits ensuring a safe design.

Static and Transient Analysis of two gear assembly

Static, Modal and Transient Analysis of four gear assembly

Static and Modal Analysis of main assembly

Static Analysis of Casing

Yield strength of the material in static structural is 350MPa.

Obtained values for two gears is 314MPa

Obtained values for four gear pair assembly is 236.8MPa

Obtained values for main assembly is 29.664MPa

From the above values we can conclude the designed model is safe

FUTURE SCOPE OF THE RESEARCH

The future scope of this research is by replacing the material of the components with

extremely low weight and high strength materials. The dog clutch can be engaged or

disengage by hydraulic or pneumatic systems with help of sensors. There can also be a

provision to reduce the number of gears and obtain the same number of speeds. The type of

engagement between the dog clutch and the gear can also be enhanced by some other means.

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MODELING AND ANALYSIS OF CONSTANT MESH ......So in constant mesh gear box we can change the gear...

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