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Abstract

Finite element method is an ideal method for component design assessment and optimization. In the present study, a slotted link has been modelled and analysed for in-service loads on its connecting location through pins. The contact between the pin and upper inner quadrant surface of the slotted link also causes the temperature to locally rise to 80ºC. For this, thermal analysis has been carried out in ANSYS APDL at 2 different convection condition which is 10 and 100 W/m2.K. Coupled analysis results of thermal and structural loads are reported.

1. Introduction

Finite element methods are a widely used approach to digitally study performance of a designed component for service loads and optimization of the same. In the current work, a study is performed using numerical method in ANSYS on a slotted link for both thermal as well structural loads. The design, material and applied load together decide overall performance of the slotted link in terms of displacements & stresses. It has been demonstrated in current study.

1.1 Objectives

Objective of current study is numerical studies on a modeled slotted link geometry with following objective.

1. Effect of different heat transfer conditions which are natural convection (h=10 W/m².K) and forced convection (h=100 W/m².K)
2. Coupled analysis taking thermal profiles from thermal analysis and applying structural loads

1.2. Problem description

Current analysis aims to study the effect of different thermal conditions on the deformation and stresses of slotted link using finite element methods.

2. Numerical Model

The steps used to prepare the model are described in the current section.

2.1 Geometry modelling

A slotted link has been modeled in ANSYS Design modeler for which provided dimensional sketch is shown in figure 1. It is sketched in ANSYS with provided dimensions which is shown in figure 2. Since the thickness of the slotted link is 4mm, it has been extruded and a 3D geometry is created as shown in figure 3.

Figure 1. Dimensional sketch of slotted link

 

Figure 2. Prepared sketch of slotted link in ANSYS with dimensions

 

Figure 3. Prepared 3D CAD of slotted link with 4mm thickness

2.2. Meshing & Element types

Prepared 3D geometry of slotted link is meshed in ANSYS APDL. For the results of structural results to be meaningful and independent of meshing density, a mesh convergence study is performed. For the current case, a mesh size of 2 mm, 1 mm, 0.7 mm and 0.5 mm are selected. Analysis with applied loads and boundary conditions are performed for all the load cases. It was observed that the maximum von-mises stress for 2 mm mesh is 172 MPa, 1 mm mesh is 162 MPa, 0.7 mm mesh is 153 MPa, and 0.5 mm mesh is 152 MPa. Since with 0.7 mm mesh, after further refinement, there is less than 2% change in stress results, mesh is decided to be converged and used for analysis results. The final mesh used in the analysis with 0.7 mm size is shown in figure 4.

Figure 4. Converged mesh with 0.7 mm element size as used for analysis in ANSYS

The type of element used for pure structural analysis is SOLID186 which is non-linear element. This is only used for the analysis where temperature is not used in the analysis.

2.3. Loads and Boundary conditions for thermal analysis

The loads and boundary condition used in the structural analysis is shown in figure 6. Internal quadrant surface is applied with a temperature of 80ºC. A convection boundary condition is applied on the front and back surface as well as outside surface of slotted link. For the natural convection case, heat transfer coefficient applied is 10 W/m2.K and for the case when fan is used, heat transfer coefficient is 100 W/m2.K.

Figure 5. Loads and boundary conditions applied for thermal analysis

2.4. Loads and boundary conditions for structural analysis

The loads and boundary condition used in the structural analysis is shown in figure 5. The first slot (marked as A) is applied with fixed displacement boundary condition since it is mounted on a shaft. The load is applied at the quadrant at location B. A total load of 190 N is applied at the quadrant surface. The surface area is 50.2 mm2, hence calculated pressure applied on the surface is 3.7849 MPa.

Figure 6. Loads and boundary conditions applied for structural analysis

2.5. Material data used in analysis

The material used for current analysis is structural steel. The data used for thermal as well as structural analysis is shown in Table 1.

Table 1. Material data used in current analysis

Rate of thermal expansion	1.2 × 10-5 / ⁰C
Modulus of elasticity	203 GPa
Poisson’s ratio	0.29
Thermal conductivity	48 W/mk
Convective heat transfer coefficient, HTC	10 and 110 W/m2.K
Ambient temperature	25 ⁰C

 

2.6. Assumptions

Following are the assumptions used in current analysis:

1. The material is assumed to be homogeneous
2. The pressure load is assumed to act only on 1 quadrant of the pin contact at slot B and uniformly distributed
3. The initial effect of temperature rise is neglected and steady-state is considered

3. Analysis Results

Analysis results for different cases are shown in this section.

3.1. Thermal model with 10 W/m2.K heat transfer coefficient

A steady-state thermal analysis has been performed for natural convection (heat transfer coefficient = 10 W/m2.K). A temperature of 80ºC is applied on the inner quadrant of the pin surface. The resultant contour is shown in figure 7 where maximum temperature is 80ºC and minimum temperature is 50.3ºC.

Figure 7. Temperature contour of the slotted link with 10 W/m².K heat transfer coefficient

3.2. Thermal model with 100 W/m2.K heat transfer coefficient

4. A steady-state thermal analysis has been performed for natural convection (heat transfer coefficient = 100 W/m2.K). A temperature of 80ºC is applied on the inner quadrant of the pin surface. The resultant contour is shown in figure 8 where maximum temperature is 80ºC and minimum temperature is 26.3ºC which is very close to applied ambient temperature of 25ºC.

Figure 8. Temperature contour of the slotted link with 100 W/m².K heat transfer coefficient

4.1. Stand-alone static structural analysis

In the current analysis, loads and boundary conditions are applied for purely structural analysis. The left slot A is applied with fixed displacement in all X, Y and Z directions. The quadrant at slot B is applied with a pressure load to take effect of contact. Maximum deformation from the static structural analysis is 0.337 mm as shown in figure 9. Maximum von-mises’ stress from the analysis is 153.3 MPa as shown in figure 10.

Figure 9. Deformation plot from standalone static structural analysis

Figure 10. von-Mises’ plot from standalone static structural analysis

4.2. Structural analysis with results from thermal model with 10 W/m2.K heat transfer coefficient

A structural analysis is performed using temperature profile solved with natural convection (10 W/m2.K heat transfer coefficient). This analysis is solved in two load steps. In the first step, the temperature profile from thermal analysis is imported and applied on respective nodes. First step solves for thermal expansion and thermal stresses. In the second step, the pressure load due to pin contact is applied. The results from step 1 of thermal expansion is shown in figure 11. Maximum deformation corresponding to thermal expansion is 0.046 mm. The results from step 2 of thermal expansion is shown in figure 12. Maximum deformation after pin load application is 0.337 mm and maximum von-mises’ stress is 164.1 MPa.

Figure 11. Deformation plot corresponding to step 1 of thermal expansion

 

Figure 12. Deformation plot and stress plot for step 2 of pressure load application

4.3. Structural analysis with results from thermal model with 100 W/m2.K heat transfer coefficient

Same structural analysis is repeated with temperature profile from second thermal analysis with natural convection (100 W/m2.K heat transfer coefficient). The results from step 1 of thermal expansion is shown in figure 13. Maximum deformation corresponding to thermal expansion is 0.028 mm. The results from step 2 of thermal expansion is shown in figure 14. Maximum deformation after pin load application is 0.325 mm and maximum von-mises’ stress is 153.22 MPa.

Figure 13. Deformation plot corresponding to step 1 of thermal expansion

 

Figure 14. Deformation plot and stress plot for step 2 of pressure load application

4.4. Analytical calculations

For convective heat transfer, rate of heat flux (per unit time) can be calculated per following equation:

Q = h.A.(T – T_A)

 

Where h is convective heat transfer coefficient, A is total area loosing heat and TA is the ambient temperature.

For the case of natural convection, rate of heat flux is:

Q = 10 x 0.0042026 x (80 – 25) = 2.31143 Watt

For the case of forced convection, rate of heat flux is:

Q = 100 x 0.0042026 x (80 – 25) = 23.1143 Watt

The slotted link can be seen as an equivalent to a cantilever beam with length of 95 mm and applied vertical load of 190N at one end. For this cantilever, the deformation can be calculated as follows.

Deformation = F.L³/ (3.E.I)

Where F is the applied load, L is the length, E is the elastic modulus and I is the second moment of inertia.

Moment of inertia = b.h³/12 = 26 x (4)³/32 = 52 mm⁴

Deformation = 190 x (95³) / 3 x (203000) x (52) = 5.14 mm

The maximum deformation is calculated to higher because of approximations with solid cantilever beam.

5. Conclusions

The analysis results of temperature from 2 different convection conditions reveal that the minimum temperature corresponding to 10 W/m2.K and 100 W/m2.K is 50ºC and 26ºC respectively. Hence with forced convection condition, the temperature drops and hence the thermal expansion reduces. The maximum deformation and stress from standalone static structural analysis is 0.337 mm and 153 MPa respectively. When a coupled analysis is performed where temperature profile of natural convection is taken as input, the deformation almost remains same at 0.337 mm while stress slightly increase to 164 MPa. Compared to this, when temperature profile from forced convection analysis is taken, the deformation reduces slightly to 0.325 mm while stress remains constant at 153 MPa. Present analysis proves that the forced convection condition is better for reduced deformation and stress of slotted link.

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