The next step is to solve the loaded finite element model for given boundary conditions using a suitable solver. The solver forms a mathematical model from the given geometry and boundary conditions. The equations in the mathematical model are solved by the solver with very fast calculation speed. The required results are interpreted from the solution values obtained by solving the mathematical equations formed in the mathematical model. The results obtained from the mathematical model are applied back to the geometry to be represented as contour plots. The following Fig. 12 shows the total deformation of the assembly under the action of the load applied. The deformation ranges from 0.0 mm (min) to 0.86166 mm (max). The deformation in our area of interest is found in safe limits ranging from 0.1566 mm to 0.3133 mm.

The equivalent stress induced in the assembly according to von- mises stress theory ranges from 0 MPa to 136.37 MPa as shown in Fig. 13. The stresses induced towards the support sides are towards the higher side but are within the permissible limits. The stress concentration mainly occurs near the welded parts in the connecting link.

The safety margin for yoke is presented in Fig. 14 followed by maximum shear stress as given in Fig. 15.

## 4.1 VALIDATION

The validation of the yoke analysis is carried out considering analytical calculations.

Area calculations are as follows

$${a}_{1}=17\times 50=850 m{m}^{2}$$

$${a}_{2}=\frac{1}{2}\times 40\times 160=3200 m{m}^{2} {x}_{2}=\frac{2}{3}\times 40=26.67 mm$$

$${a}_{3}=160\times 10=1600 m{m}^{2}$$

$${a}_{4}=242.72\times 8=1941.76 m{m}^{2}$$

$${a}_{5}=28.63\times 50=1431.5 m{m}^{2}$$

$${a}_{6}=179\times 15=2835 m{m}^{2}$$

$${a}_{7}=\frac{1}{2}\times 198\times 35=3307.5 m{m}^{2}$$

Total area of the body is given by,

$$A={a}_{1}+{a}_{2}+{a}_{3}+{a}_{4}+{a}_{5}+{a}_{6}+{a}_{7}=15165.76 m{m}^{2}$$

Now,

$$\stackrel{-}{y}=\frac{{a}_{1}{x}_{1}+{a}_{2}{x}_{2}+{a}_{3}{x}_{3}+{a}_{4}{x}_{4}+{a}_{5}{x}_{5}+{a}_{6}{x}_{6}+{a}_{7}{x}_{7}}{A}$$

$$\therefore \stackrel{-}{y}=\frac{21250+85344+72000+104855.04+11881.5+185692.5+280349.7}{15165.76}$$

$$\therefore \stackrel{-}{y}=52.98 mm$$

Moment of inertia calculations for the bodies,

$${I}_{x{x}_{1}}=\frac{b{d}^{3}}{12}+A{h}^{2}=\frac{17\times {50}^{3}}{12}+850\times {\left(27.98\right)}^{2}=842531.67 m{m}^{4}$$

$${I}_{x{x}_{2}}=\frac{160\times {40}^{3}}{36}+3200\times {26.31}^{2}=2499535.96 m{m}^{4}$$

$${I}_{x{x}_{3}}=\frac{160\times {10}^{3}}{12}+1600\times {7.98}^{2}=115221.97 m{m}^{4}$$

$${I}_{x{x}_{4}}=\frac{242.92\times {8}^{3}}{12}+1941.76\times {1.02}^{2}=12376.26 m{m}^{4}$$

$${I}_{x{x}_{5}}=\frac{28.63\times {50}^{3}}{12}+1431.5\times {30.46}^{2}=1626391.47 m{m}^{4}$$

$${I}_{x{x}_{6}}=\frac{189\times {50}^{3}}{12}+2835\times {11.96}^{2}=458979.186 m{m}^{4}$$

$${I}_{x{x}_{7}}=\frac{189\times {35}^{3}}{12}+3307.5\times {31.130}^{2}=3430315.97 m{m}^{4}$$

Thus total moment of inertia

$$I=8.8816\times {10}^{6} m{m}^{4}$$

Now, deflection

$$\delta =\frac{P{l}^{3}}{3EI}=\frac{735.75\times {242.172}^{3}}{3\times 2\times {10}^{5}\times 8.8816\times {10}^{6}}$$

$$\therefore \delta =1.07 mm$$

Modification Suggested

## 5.1 Modification 1

The first modification suggested is to reduce the thickness of the fouling block. The block is 43 mm initially. This thickness of the block is reduced to 33 mm in order to safely accommodate the fouling part during the assembly. The existing part in the assembly is replaced with the part with the reduced dimensions and the new assembly is reanalysed for the new deformation and stresses induced.

The analysis procedure remains same as described in the previous section. The procedure consists of importing the assembly, selectively meshing it. The meshed body is applied with the loads and the model is solved as shown in Fig. 16. The results for these modifications are shown in the Figs. 17, Fig. 18 and Fig. 19 below.

## 5.2 Modification 2

The second modification suggested is making the groove on the block as shown in Fig. 20. The profile of the groove is that of the profile of the pipe which fouls the assembly. The semicircular profile is drawn on the face and it is extruded along the profile of the pipe shape. This block is replaced in the existing assembly. The main aim behind the grooving of the block is to accommodate the pipe in least possible material reductions. The making of groove permits the modification in least possible material reductions which improves the load carrying capacity of the assembly. Meshing for modified model 2 is given in Fig. 21 followed by results of total deformation is mentioned in Fig. 22.

Figure 23 highlights the Stress distribution for modification 2. It was found that it is safe for the present working conditions.

## 5.3 Comparative Results

The results obtained after analyzing the above mentioned cases are tabulated as follows

Table 2

Sr. No. | Parameters | Without any Modification | Modification No.1 |
---|

1 | Total Deformation | 0.8616 mm | 0.94225 mm |

2 | Equivalent Stress | 136.37 MPa | 152.97 MPa |

3 | Max. Shear stress | 75 MPa | 84.2 MPa |

4 | Equivalent Strain | 0.00068 | 0.0007645 |

5 | Strain Energy | 1.37 mJ | 1.65 mJ |

6 | Safety factor | 8.33 | 10 |

7 | Safety Margin | 9 | 6.5 |