Based on physical and thermal properties graphite cast iron has got more strength than sand cast Mg alloy and it is clear from the results that the load carrying capacity of former is larger than the later. Hence Graphite cast iron is preferred for the manufacture of rack and pinion. In static structural analysis the total deformation and von - mises stresses are more in sand cast Mg alloy than graphite cast iron. Hence graphite cast iron has better strength than Sand cast Mg alloy. In modal analysis the number mode shapes are higher for graphite cast iron than sand cast Mg alloy. Under transient conditions the total deformation of Graphite CI is less than that of Sand cast mg alloy. Hence former is preferred under Transient conditions. Under fatigue loads the damage is more in sand cast Mg alloy. Hence graphite CI is preferred for manufacturing of Rack and pinion. Hence Keeping all the analysis in view the graphite cast iron is preferred over sand cast Mg alloy.

1. Kondrasi Nagaraju ( Mechanical 4th year)
kondrasinag123@gmail.com
ph. No. 8008244575/ 9052832464
SNIST, Yamnapet, Ghatkesar

2. Problem statement
• RACK AND PINION : Rack and pinion is an assembly which converts the
rotational motion of steering in Linear motion of the wheels.
• Therefore in order to simulate it, Static analysis of the gears and Transient
analysis should be performed.
• ANALYSIS OF RACK AND PINION using ANSYS:
• Perform Static Structural and Transient Structural Analysis on Rack and
Pinion
• Input : Mesh the Geometry using HEX elements.
• (Note : This can be achieved by using different options under Mesh and
the Element size can be selected as per the requirement in order to
achieve HEX elements)
• Material Properties : Graphite Cast Iron
• Density: 7.91g/cc
• Young’s Modulus: 99GPa
• Poisson’s Ratio: 0.21
• Thermal Conductivity: 46 W/mK
• Specific Heat: 490 J/kg
• Sand Cast Magnesium Alloy
• Density: 1.81g/cc
• Young’s Modulus: 45GPa
• Poisson’s Ratio: 0.35
• Thermal Conductivity: 62 W/m.K
• Composition:
• Aluminium 10.7%
• Magnesium 90%
• Zinc 0.3%
ANALYSIS :
(Note: All the analysis are to be performed for all the materials specified above)
Case 1:
Static Analysis (for all the types of materials):
1. Apply Force of 1000N on one teeth.
Output :
1. Von- Misses stress
2. Deformation
3. Pressure generated at the contact region.
Case 2:
1. Perform modal analysis to find the mode shapes under 1000Hz.
Output :
1. Deformation of all Mode shapes under 1000Hz.
Case 3:
1. Apply transient load when vehicle is steering on zig-zag road i.e Left - Right - Left.
2. The pressure acting on single teeth during mesh is 1000N when steering towards
Left from 0 - 0.5 seconds i.e on 5 teeths.
3. One teeth will be in contact with the other at a time for 0.1 seconds.
4. Step 3 and 4 will be repeated when the vehicle steers towards right side from 0.6 –
1 Second
Load during Left Turn at 0.1 sec Eg: Load during Right Turn at 0.6 sec
Output :
1. Von- Misses stress
2. 2. Deformation
3. Pressure generated at the contact region.
Case 4:
1. Fatigue analysis using Transient Condition.
Output :
1. Fatigue Life
2. Damage
3. Safety Factor

3. Details of mesh REASON:
• As per the problem statement the same mesh has
been generated for all the cases for comparison of the
results.
• The zone at which the results are prominent , at that
zones smaller mesh has been generated with max
layers to support Hex elements generation.
• All quad mesh has been chosen to get better results as
triangular elements (stiffer) do not give better results.
Method : Hex Dominant
Order: Linear order elements
Mesh type: All quad
Mesh size : 3mm, 12mm at contact
zones and other zones respectively.
Inflation: 10 layers at the meshed zone
No. of Nodes: 15107
No. of Elements: 18826

4. CASE 1: STATIC STRUCTARAL
Input:
• Output:
Graphite cast iron:
Vonmises stressTotal deformation
Sand cast Mg Alloy
Total deformation Vonmises stress

5. CASE 2: Modal Analysis
Sand cast Mg alloy:
No.of mode shapes: 5
Frequency: 0 to 1000Hz
Graphite cast iron:
No. of mode shapes : 7
Frequency : 0 to 1000HZ

6. CASE 3: TRANSIENT STRUCTURAL
Time step min. stress Max. Stress
0.1 1.9971e-003 153.08
0.2 2.009e-003 153.64
0.3 2.006e-003 153.55
0.4 2.0231e-003 154.1
0.5 2.0064e-003 153.71
0.6 2.0067e-003 153.76
0.7 2.0015e-003 153.14
0.8 2.001e-003 153.15
0.9 2.033e-003 154.58
1. 1.9949e-003 153.07
Time step min. stress Max. Stress
0.1 4.4492e-002 0.33471
0.2 4.4638e-002 0.33584
0.3 4.4649e-002 0.3359
0.4 4.4752e-002 0.33671
0.5 4.4809e-002 0.33708
0.6 4.4728e-002 0.33649
0.7 4.4719e-002 0.33635
0.8 4.4659e-002 0.33599
0.9 4.462e-002 0.33575
1. 4.4557e-002 0.33514
Time step min. stress Max. Stress
0.1 3.0264e-003 152.26
0.2 3.0227e-003 152.74
0.3 3.0324e-003 152.78
0.4 3.0427e-003 153.13
0.5 3.042e-003 153.33
0.6 3.0398e-003 153.04
0.7 3.0382e-003 153.03
0.8 3.0301e-003 152.8
0.9 3.0238e-003 152.68
1. 3.0287e-003 152.48
Sand cast Mg alloy
Graphite cast iron
Time step min. stress Max. Stress
0.1 2.0691e-002 0.15593
0.2 2.0767e-002 0.15652
0.3 2.0769e-002 0.15637
0.4 2.0833e-002 0.15697
0.5 2.0784e-002 0.15656
0.6 2.0793e-002 0.1566
0.7 2.0703e-002 0.15599
0.8 2.0701e-002 0.156
0.9 2.088e-002 0.1575
1. 2.0704e-002 0.15588
Total deformation
Vonmises stress
Input

7. CASE 4: FATIGUE ANALYSIS
INPUT:
Damage
Life
Safety factor
Life
Damage
Safety factor
Graphite cast iron
Sand cast Mg Alloy
loading
loading

8. Type of Analysis Graphite cast
iron
Sand cast Mg
Alloy
Static structural Total deformation(mm) .1572 .3381
Von-mises stress ( Mpa) 150.25 152.32
Modal Analysis
Frequency range : 0 to
1000 Hz
No. of mode shapes 7 5
Last mode frequency (Hz) 895.97 717.43
Transient structural Total deformation(mm) .155 .3351
Von-mises stress (Mpa) 153.07 152.48
Fatigue Analysis Life 1e6 1e6
No. of cycles 70933 70255
Damage 14098 14234
Safety factor 15 15
Comparative study of results:
Conclusion:
1. Based on physical and thermal properties graphite cast
iron has got more strength than sand cast Mg alloy
and it is clear from the results that the load carrying
capacity of former is larger than the later. Hence
Graphite cast iron is preferred for the manufacture of
rack and pinion.
2. In static structural analysis the total deformation and
von - mises stresses are more in sand cast Mg alloy
than graphite cast iron. Hence graphite cast iron has
better strength than Sand cast Mg alloy.
3. In modal analysis the number mode shapes are higher
for graphite cast iron than sand cast Mg alloy.
4. Under transient conditions the total deformation of
Graphite CI is less than that of Sand cast mg alloy.
Hence former is preferred under Transient conditions.
5. Under fatigue loads the damage is more in sand cast
Mg alloy. Hence graphite CI is preferred for
manufacturing of Rack and pinion.
6. Hence Keeping all the analysis in view the graphite
cast iron is preferred over sand cast Mg alloy.