1 PROBLEM STATEMENT

Carry out a static structural analysis to find out EQUIVALENT STRESS, TOTAL DEFORMATION AND STRESS INTENSITY using CAST IRON (ductile), CAST STEEL, CAST BRONZE.

FIND LOCATION FOR POSSIBLE FRACTURE.

2 INTRODUCTION & THEORY

Spur Gear is a mechanical device used for power transmition from input shaft to output shaft. It connects two shafts rotating in opposite direction. It is a very important to analyse the effect of force on the tooth of gear. As stress concentration is a very important parameter which decide the fatigue life of gear.

With the help of known value of load bearing capacity, the value of maximum moment or torque has been set for operating condition. We can also conclude that with respect to required operating torque the gear is designed so that it can work without any fail during operating conditions.

3 AIM

The aim of this project is to find out equivalent stress, total deformation and stress intensity on gear tooth using 3 different material. We will focus on extreme values of these parameters & compare the results with three different cases.

We will also find a better material for gear design comparing above results.

4 GEOMETRY & MESHING

4.1 GEOMETRY

The following geometry has been used for making 3-d model of gear

4.2 MESHING

Hex dominant meshing method has been adopted using quad/tri type of elements. The element size was 0.7 mm. The total number of nodes & element were 46261 &10996.

Following figure shows the meshed geometry

5 MATTERIALS & PROPERTIES

Following table shows the details of material & its properties

PARAMETERS	CAST STEEL	CAST IRON	CAST BRONZE
YOUNGS MODULOUS (Pa)	2.03E+10	1.71E+11	8E+10
POISSIONS RATIO	0.3	0.275	0.345
BULK MODULOUS (Pa)	1.6917E+11	1.2667E+11	8.6022E+10
SHEAR MODULOUS (Pa)	7.8077E+10	6.7059E+10	2.974E+10
TENSILE YIELD STRENGTH (Pa)	3.49E+08	3.44E+08	1.44E+08
TENSILE SHEAR STRENGTH (Pa)	5.05E+08	5.48E+08	2.67E+08
DENSITY Kg/m3	7820	7130	8810

6 BOUNDARY CONDITION

Joint load has been imposed on both gear component. One component was imposed with joint rotation & other was imposed with joint moment.

Following table shows the details of time step v/s joint rotation

`STEPS	0	1	2	3	4	5	6
TIME in seconds	0	1	2	3	4	5	6
ROTATION in Degree	0	30	60	90	120	150	180

Following table shows the details of time step v/s joint moment

`STEPS	0	1	2	3	4	5	6
TIME in seconds	0	1	2	3	4	5	6
MOMENT in N-m	-10	-10	-10	-10	-10	-10	-10

Revolute joint type was imposed on both gear with frictional contact. The body to ground connection type was also imposed on both gears.

7 RESULT & DISSCUSION

7.1 TOTAL DEFORMATION

Below figure shows the total deformation in cast steel component. The red tag shows the maximum deformation & blue tag shows the minimum deformation

The maximum, average, & minimum value of deformation was 29.995mm, 23.623mm, & 18.496mm. The maximum value occurs on right & minimum value occurs on left components. This value of deformation was recorded at 5.925 second.

Below figure shows the total deformation in cast iron component. The red tag shows the maximum deformation & blue tag shows the minimum deformation

The maximum, average, & minimum value of deformation was 28.827mm, 22.701mm, & 17.772mm. The maximum value occurs on right & minimum value occurs on left components. This value of deformation was recorded at 4.925 second.

Below figure shows the total deformation in cast bronze component. The red tag shows the maximum deformation & blue tag shows the minimum deformation

The maximum, average, & minimum value of deformation was 30mm, 23.627mm, & 18.5mm. The maximum value occurs on left & minimum value occurs on right components. This value of deformation was recorded at 4.925 second.

DEFORMATION-CAST STEEL DEFORMATION-CAST IRON DEFORMATION-CAST BRONZE

7.2 VON MISES STRESS

Below figure shows the von mises stress in cast steel component. The red tag shows the maximum stress & blue tag shows the minimum stress

The maximum, average, & minimum value of von mises stress was 399MPa, 8.4518MPa, & 7.3058e-007MPa. The maximum value occurs on left & minimum value occurs on right components. This value of deformation was recorded at 6 second.

Below figure shows the von mises stress in cast iron component. The red tag shows the maximum stress & blue tag shows the minimum stress

The maximum, average, & minimum value of von mises stress was 399.18MPa, 8.4193MPa, & 5.7416e-007MPa. The maximum value occurs on left & minimum value occurs on right components. This value of deformation was recorded at 6 second.

Below figure shows the von mises stress in cast bronze component. The red tag shows the maximum stress & blue tag shows the minimum stress

The maximum, average, & minimum value of von mises stress was 398.71MPa, 8.458MPa, & 3.7299e-007MPa. The maximum value occurs on left & minimum value occurs on right components. This value of deformation was recorded at 6 second.

7.3 STRESS INTENSITY

Below figure shows the stress intensity in cast steel component. The red tag shows the maximum stress intensity & blue tag shows the minimum stress intensity

The maximum, average, & minimum value of von mises stress was 442.32MPa, 9.182MPa, & 8.4264e-007MPa. The maximum value occurs on left & minimum value occurs on right components. This value of deformation was recorded at 6 second.

Below figure shows the stress intensity in cast iron component. The red tag shows the maximum stress intensity & blue tag shows the minimum stress intensity

The maximum, average, & minimum value of von mises stress was 439.61MPa, 9.1366MPa, & 6.6299e-007MPa. The maximum value occurs on left & minimum value occurs on right components. This value of deformation was recorded at 6 second.

Below figure shows the stress intensity in cast bronze component. The red tag shows the maximum stress intensity & blue tag shows the minimum stress intensity

The maximum, average, & minimum value of von mises stress was 439.95 MPa, 9.2115 MPa, 4.2325e-007MPa. The maximum value occurs on left & minimum value occurs on right components. This value of deformation was recorded at 6 second.

8 CONCLUSION

8.1 TOTAL DEFORMATION

Following table shows the comparison of above 3 material for total deformation

PARAMETER	DEFORMATION MINIMUM In mm	DEFORMATION AVERAGE In mm	DEFORMATION MAXIMUM In mm
CAST STEEL	18.496	23.623	29.995
CAST IRON	17.772	22.701	28.827
CAST BRONZE	18.5	23.627	30

From above table we can conclude that the maximum deformation occurs in CAST BRONZE, & minimum deformation occurs in CAST IRON. The magnitude of maximum deformation is 30 mm.

8.2 VON MISES STRESS

Following table shows the comparison of above 3 material for von mises stress

PARAMETER	VON MISES STRESS MINIMUM In MPa	VON MISES STRESS AVERAGE In MPa	VON MISES STRESS MAXIMUM In MPa
CAST STEEL	7.3058e-007	8.4518	399
CAST IRON	5.7416e-007	8.4193	399.18
CAST BRONZE	3.7299e-007	8.458	398.71

From above table we can conclude that the maximum stress occurs in CAST IRON, & minimum stress occurs in CAST BRONZE. The magnitude of maximum stress is 399.18MPa.

8.3 STRESS INTENSITY

Following table shows the comparison of above 3 material for stress intensity

PARAMETER	STRESS INTENSITTY MINIMUM In MPa	STRESS INTENSITTY AVERAGE In MPa	STRESS INTENSITTY MAXIMUM In MPa
CAST STEEL	8.4264e-007	9.182	442.32
CAST IRON	6.6299e-007	9.1366	439.61
CAST BRONZE	4.2325e-007	9.2115	439.95

From above table we can conclude that the maximum stress intensity occurs in CAST STEEL, & minimum stress intensity occurs in CAST BRONZE. The magnitude of maximum stress intensity is 442.32MPa.

We can conclude that cast steel is having maximum yield stress is magnitude is 3.49E+08 Pa. At the same time cast bronze is having maximum deformation & deformation in cast steel is greater than cast iron by 1.1 mm only. If we compare stress variation in all 3 components there is difference of only 1 MPa from each other.

HENCE, WE CAN PROCEED WITH CAST STEEL.

we can also conclude that the fracture will occur at the tooth having maximum stress genrated.