Modelling and Analysis of a Leaf Spring

Chapter 4

Modeling and Analysis

In engineering the stress and strain concentration at any point has been eliminated by trial and error method. This trial and error method requires high investment cost and large material wastage, enormous time. Hence software package such as ANSYS are used to reduce the investment cost and large material wastage, etc. the finite element analysis involves number of iterations to determine the stress concentration of the various parts. The stress concentrations are directly proportional to the design, material, and mechanical properties. Hence it is of significance to compare the outcome of input material such as aluminum, brass, mild steel, etc. Moreover the above said process can be incorporated to validate the strength of the model.

4.1 Modeling of the problem

Pro/ENGINEER is a feature- based, parametric solid modeling system with many extended design and manufacturing applications which is developed by PARAMETRIC TECHNOLOGY CORPORATION, As a comprehensive CAD/CAE/CAM system, covering many aspects of mechanical design, analysis and manufacturing, Pro/ ENGINEER represent the leading CAD/CAM/CAE technology.

The solid model of the laminated leaf spring component part can be created through the following steps

Create the parts of the laminated leaf spring with a coordinate system. Datum Planes are chosen as reference planes for constructing and dimensioning solid models. Commands like, sketch, extrude, line,

circle, arc are used for creating the leafs for the spring. Since Pro engineer is feature based design software, it is very simple to create solid parts in it

Assemble the created parts. Proper constraints like, mate, align, move, rotate, spin etc., are given while assembling the parts to form the final component for the analysis. The final component is converted into an iges file to export into Ansys for analysis. The iges file is created as solid part.

Figure shows the main leaf spring created in Pro Engineer software. It has two eye ends for arresting the leaf spring.

Fig 4.1Main leaf of the laminated leaf spring

4.2 Model Generation

In ANSYS terminology, model generation usually takes on the narrower meaning of generating the nodes and elements that represent the spatial volume and connectivity of the actual system. Thus, model generation in this discussion means the process of defining the geometric configurations of the model’s nodes and elements. The ANSYS program offers the following approaches of model generation.

Creating a solid model within ANSYS using direct generation of the component within the software itself or importing model created in any other computer aided design software which is compatible with Ansys software. Direct generation of solid in Ansys software is somewhat tedious because the person who knows completely about Ansys software can create few parts in software. Some parts with complicated structure and dimensions cannot be created by this software. In these cases, it is better to model the problem in any other computer aided design software and import the component for analysis into this Ansys software, because created a complete component in Ansys software is somewhat time consuming processes.

4.3 Importing the Model

As an alternative to creating the solid models within ANSYS, we can create them in favorite CAD system and then import them into ANSYS for analysis, by saving them in the IGES file format or in a file format supported by an ANSYS connection product. Creating a model using a cad package has the following advantages:

We avoid a duplication of effort by using existing cad models to generate solid models for analysis. We use more familiar tools to create models. However, models imported from cad systems may require extensive repair if they are not of suitable quality for meshing.

While building the Model in the CAD systems we to observe Ansys solid modeling procedures with regard to planning, symmetry and the amount of detail needed for a finite element analysis. For example, for axis symmetric models, the Ansys program requires that the global Y axis be the axis of rotation. Avoid creating closed curves (that is, a line that starts and ends at the same point) and closed surfaces (such s a surface that starts and ends at the same edge). Ansys can’t store closed curves or closed surfaces (it

requires at least two key points). If a closed curve, closed surface, or “trimmed” closed surface defined by IGES entities, Ansys will attempt to split it into two or more entities As much as possible, write to the iges file by data that the Ansys program supports.

4.4 Analysis of the Leaf Spring

Structural analysis is the most common application of the finite element engineering structures such as bridges and buildings, but also naval, aeronautical, and mechanical structures such as ship hulls, aircraft bodies, and machine housings, as well as mechanical components such as pistons, machine parts, and tools.

The seven types of structural analyses available in the ANSYS family of products are explained below. The primary unknowns (nodal degrees of freedom) calculated in a structural analysis are displacements. Other quantities, such as strains, stresses, and reaction forces, are then derived from the nodal displacements.

Structural analyses are available in the ANSYS Multiphysics, ANSYS Mechanical, ANSYS Structural, and ANSYS Professional programs only.

You can perform the following types of structural analyses. Each of these analysis types are discussed in detail in this manual.

Static Analysis--Used to determine displacements, stresses, etc. under static loading conditions both linear and nonlinear static analyses. Nonlinearities can include plasticity, stress stiffening, large deflection, large strain, hyper elasticity, contact surfaces, and creep.

Modal Analysis--Used to calculate the natural frequencies and mode shapes of a structure. Different mode extraction methods are available.

Harmonic Analysis--Used to determine the response of a structure to harmonically time-varying loads.

Transient Dynamic Analysis--Used to determine the response of a structure to arbitrarily time-varying loads. All nonlinearities mentioned under Static Analysis above are allowed.

Spectrum Analysis--An extension of the modal analysis, used to calculate stresses and strains due to a response spectrum or a PSD input (random vibrations).

Buckling Analysis--Used to calculate the buckling loads and determine the buckling mode shape. Both linear (eigenvalue) buckling and nonlinear buckling analyses are possible.

Explicit Dynamic Analysis--This type of structural analysis is only available in the ANSYS LS-DYNA program. ANSYS LS-DYNA provides an interface to the LS-DYNA explicit finite element program. Explicit dynamic analysis is used to calculate fast solutions for large deformation dynamics and complex contact problems.

In addition to the above analysis types, several special-purpose features are available:

• Fracture mechanics
• Composites
• Fatigue
• p-Method
• Beam Analyses

4.5 Element Type

Symmetry is considered and only one half is taken into consideration for analysis. The middle portion is arrested and the load is applied at the end of the leaf spring. Solid 45 8-noded elements are chosen for analysis. Solid 45 is used for the 3-D modeling of solid structures.

Fig 4.2 Solid 45 Element type used for analysis

4.6 Material Properties

The material selection depends upon the energy that is to be stored by the leaf spring. The amount of elastic energy that can be stored by a leaf spring volume is given by

where s is the maximum allowable stress and E is the young’s modulus of the material to be selected. Considering the vertical force that is to be applied over the leaf spring, the material has to be selected. Composite material has excellent characteristics of withstanding high loads. In this paper, a four-leaf

steel spring used in passenger cars is taken into consideration and is replaced with composite spring made of titanium alloy. The ultimate aim of the study is to reduce the weight of the leaf spring.

Uniquely among engineering alloys, titanium possesses the strength, density and modulus to make the component for almost every application. The key to successful design is to optimize the saving of weight and space. Titanium leaf springs are smaller and typically 60-70% lighter than equivalent steels. Spring weight for a given load and deflection rate is proportional to the product of shear modulus and density of the alloy divided by the square of the allowable stress.

Weight is minimized when titanium is used because of its low shear modulus and density combined with high allowable stress. At the same time, spring deflection is inversely proportional to the shear modulus and is therefore high for titanium, so fewer leafs are needed, with further weight reduction and a higher natural frequency.

A wide range of titanium alloys are suitable for making leaf spring. Of these Ti-4.5Fe-6.8Mo-1.5Al alloy (Timetal LCB) offers the best combination of desirable properties at an economical price. Table shows the properties of timetal LCB

Table 4.1 Properties of Titanium alloy and Timetal LCB

The strength, density, shear modulus and relative weight of this alloy are compared with those of steel of similar tensile strength in the table.

Table 4.2 Comparison of Properties of Steel and Timetal LCB

Table 4.3 Properties of various Timetal LCB grade

4.7 Design considerations

The following details are calculated and taken for analysis.

Type of leaf: Flat leaf

Total span length = 1000 mm

Number of leaf = 8

Length of main leaf = 1000 mm

Length of the second leaf = 1000 mm

Length of the third leaf = 812 mm

Length of the fourth leaf = 721 mm

Length of the fifth leaf = 588 mm

Length of the sixth leaf = 451 mm

Length of the seventh leaf = 314 mm

Length of the eighth leaf = 177 mm

Maximum load = 5000 N

Thickness of the leaf = 8 mm

Width of the leaf = 55 mm

Radius of curvature = 1633 mm

Figure shows the model of the complete laminated spring with assembly which is designed using Pro Engineer and converted into iges file which is imported into Ansys for analysis

Fig 4.3 Assembly of laminated leaf spring

4.8 Meshing

Figure shows the meshed model of the main leaf spring with eye end. Tetrahedral elements are used for meshing the leaf spring which provides much better structural results when analyzed.

Fig 4.4 Meshed model of the main leaf spring

Fig 4.5 Meshed model of the whole assembled leaf spring

Fig 4.6 Side view of the meshed model

4.9 Applying Boundary Conditions

The element 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, creep, swelling, stress stiffening, large deflection and large strain capabilities.

For various loading conditions the displacement and von-misses stress is obtained. The results are obtained and tabulated.

Fig 4.7 Pressure applied at the eye end of the leaf spring

Since the model is symmetry about y axis only one half of the model is considered for analysis. The mid part of the assembled model is arrested by applying the boundary condition that all the degrees of freedom is arrested. The pressure is applied at the eye end such that when analyzed it gets deflected in the y direction.

Initially for main leaf the analysis is done, after that the leaf numbers are increased and the analysis is continued.

Fig 4.8 Stress distribution over the main leaf spring

Fig 4.9 Stress distribution over the eye end

The stress value that are obtained are tabulated and analyzed.

Chapter 5

Result and Discussion

The results obtained are tabulated and compared. The result shows that leaf spring with steel as material shows minimum deflection when compared to that titanium alloys as material for leaf spring. When compared with the stress developed in the leaf spring, titanium alloy has less stress to that of steel as the materials for the leaf spring. This result gives more suspension for titanium alloy when compared to that of steel. But as far titanium alloy is considered the cost of metal and manufacturing is 25% high when compared to that of steel. Mostly titanium alloys as a metal is mainly used as internal components where it is subject to thermal stresses.

Fig 5.1 Comparison of Displacement for Single Leaf

Figure shows the comparison of displacement of single under load. The graph is plotted with load vs displacement. With the increase in load the titanium alloy has much displacement when compared to that of steel as material of the laminated leaf spring.

Fig 5.2 Comparison of Von-Misses Stress for Single Leaf

But if the stress developed in the laminated leaf spring is considered, the leaf spring made of titanium develops less stress to that of the steel as material.

Fig 5.3 Comparison of Displacement for Double Leaf

Fig 5.4 Comparison of Von-Misses Stress for Double Leaf

So selection of titanium alloy for automotive parts depends upon the designer’s choice and also the necessity of the material.

References

1. A.M. Wahl, Mechanical Springs, Mc Graw-Hill, 1984
2. Masayoshi Simozeki, FEM on springs, Japan Society of Spring Engineers, 1997
3. Y.Prawoto, the effects of residual stress on Fatigue Crack Propagation, Journal of Practical Failure Analysis, ASM International, 2002
4. ANSYS User Manual V10.0, Ansys Inc
5. W.D. Callister Jr., Materials Science and Engineering, John Willey and Sons Inc, 2003.
6. SAE Internationals, Vehicle Dynamics Terminology, SAE 2002
7. Gillespie T., Fundamentals of Vehicle Dynamics, SAE 1992.