A Thesis Entitled Design, Analysis and Optimization of Rear Sub-Frame Using Finite Element Modeling and Modal Analysis by Gaurav

Home , Chassis, Subframe, Vehicle frame

A Thesis

entitled

Design, Analysis and Optimization of Rear Sub-frame using Finite Element Modeling

and Modal Analysis

Gaurav Kesireddy

Submitted to the Graduate Faculty as partial fulfillment of the requirements for the

Master of Science Degree in

Mechanical Engineering

______Dr. Hongyan Zhang, Committee Chair

______Dr. Sarit Bhaduri, Committee Member

______Dr. Matthew Franchetti, Committee Member

______

Dr. Amanda Bryant-Friedrich, Dean College of Graduate Studies

The University of Toledo

May 2017

This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author.

An Abstract of

Design, Analysis and Optimization of Rear Sub-frame using Finite Element Modeling

and Modal Analysis

Gaurav Kesireddy

Submitted to the Graduate Faculty as partial fulfillment of the requirements for the

Master of Science Degree in

Mechanical Engineering

The University of Toledo

May 2017

A sub-frame is a structural component of an automobile that carries suspension, exhaust, engine room, etc. The sub-frame is generally bolted to Body in White(BIW). It is sometimes equipped with springs and bushes to dampen vibration. The principal purposes of using a sub-frame are, to spread high chassis loads over a wide area of relatively thin sheet metal of a monocoque body shell, and to isolate vibration and harshness from the rest of the body. As a natural development from a car with a full chassis, separate front and rear sub-frames are used in modern vehicles to reduce the overall weight and cost. In addition, a sub-frame yields benefits to production in that subassemblies can be made which can be introduced to the main body shell when required on an automated line. The objective of the project is the design, analysis and optimization of Rear Sub-frame considering the modal analysis and natural frequency of the system using Altair

Hypermesh®, Optistruct®, RADIOSS® and Altair HyperView®.

iii

Acknowledgements

I would like to thank Dr. Hongyan Zhang and Dr. Wang Bin for their guidance and patience during my time at The University of Toledo. Their support and encouragement has helped me in addition to countless other students at aspiring highest goals in the field of mechanical engineering.

Special thanks to Dr. Sarit Bhaduri and Dr. Mathew Franchetti for evaluating my work and being a member of my thesis defense committee.

Lastly, I would like to thank my friends and family for their patience, support and all the encouragement they have provided during this stressful period of my life.

Table of Contents

Abstract ...... iii

Acknowledgements ...... iv

Table of Contents ...... v

List of Tables ...... viii

List of Figures ...... ix

List of Abbreviations ...... xii

List of Symbols ...... xiii

1 Introduction ...... 1

1.1 Introduction to Design ...... 1

1.2 Noise, Vibration and Harshness ...... 2

1.2.1 Normal Mode Analysis ...... 3

1.2.2 Degrees of Freedom ...... 5

1.2.2.1 Single Degree of Freedom ...... 5

1.2.2.2 Multiple Degree of Freedom ...... 6

2 Literature Review and Background ...... 8

2.1 Literature Review...... 8

2.2 Manufacturability ...... 10

2.3 Design Considerations ...... 11

3 Tools and Resources ...... 12

3.1 FEM & FEA ...... 12

3.1.1 FEA Process Introduction ...... 13

3.1.2 Pre-Analysis Processing...... 14

3.2 Mesh Generation ...... 14

3.2.1 Mesh Setup...... 14

3.3 Converting Solid Bodies to Surface Bodies...... 17

3.4 Creating New Simulation and Finite Element Model ...... 20

3.4.1 Element Simulated Physical and Material Properties ...... 24

3.4.2 1D,2D & 3D Mesh ...... 26

3.4.3 Simulation Constraints and Loading Applications ...... 27

3.4.3.1 Constraints ...... 27

3.4.3.2 Load & Other Factors ...... 28

3.5 Solving Simulations ...... 29

3.6 Post-Processing Results ...... 30

4 Simulation Loading Scenarios ...... 33

4.1 Loading Conditions ...... 33

4.1.1 Two-Wheel Bump ...... 34

4.1.2 Forward Braking ...... 34

4.1.3 Reverse Braking ...... 35

4.1.4 Cornering ...... 35

4.1.5 Forward Acceleration...... 35

4.1.6 Reverse Acceleration ...... 35

4.1.7 Max Torque ...... 35

5 Sub-frame Modified Design ...... 36

5.1 Design Space ...... 36

5.2 Optimization and Results ...... 38

6 Conclusions ...... 54

6.1 Conclusions ...... 54

References ...... 56

Appendix A: Types of Load Cases and Results...... 58

Appendix B: Original and New sub-frame FEA Results ...... 60

vii

List of Tables

3.1 Physical properties of steel ...... 25

3.2 Frequency and Mode shape of original sub-frame ...... 31

5.1 Frequency and Mode shape of optimized result ...... 42

5.2 Frequency and Mode shape of Final sub-frame ...... 44

5.3 Comparison between original and optimized model ...... 45

5.4 Von-Mises Maximum Stress Comparison of Optimized and Original model ...... 46

5.5 Component Mass and Name ...... 47

5.6 Summary Table of new and original sub-frames ...... 52

viii

List of Figures

1-1 Original Sub-frame CAD model ...... 1

1-2 Modal analysis of a car body ...... 4

1-3 Single DOF System...... 6

1-4 2-DOF System ...... 7

2-1 BMW 5 series model with front and rear axle subframes ...... 10

3-1 Graphic window of Altair Hypermesh® ...... 13

3-2 Graphic window for preference options ...... 15

3-3 Graphic window for mesh settings ...... 15

3-4 Graphic window for Check element window ...... 16

3-5 Graphic window for Check element settings ...... 16

3-6 Graphic window for solid geometry ...... 17

3-7 Delete option in tool bar ...... 17

3-8 Delete panel for solid geometry ...... 18

3-9 Graphic window for Solid geometry deletion ...... 18

3-10 Components of the sub-frame ...... 19

3-11 Midsurface extraction ...... 19

3-12 Midsurfaces of Sub-frame ...... 20

3-13 2D panel ...... 21

3-14 Automesh options ...... 21 ix

3-15 Midsurface component with 2D mesh ...... 22

3-16 Component with 3D mesh ...... 22

3-17 1D panel ...... 23

3-18 Connectors Tab ...... 23

3-19 Seam weld Tab ...... 24

3-20 Seam weld visual representation ...... 24

3-21 Physical Properties of components ...... 25

3-22 1D, 2D & 3D Element types ...... 26

3-23 SPC Constraint ...... 27

3-24 Load Collector Tab ...... 28

3-25 Constraint panel in Analysis Tab ...... 28

3-26 Load Collector create panel ...... 29

3-27 Frequency Range setup ...... 29

3-28 Analysis Panel ...... 29

3-29 Normal Mode of original sub-frame ...... 31

4-1 Z-direction for car ...... 34

5-1 Design space for sub-frame ...... 36

5-2 3D Tetra Mesh cross-section view ...... 37

5-3 Physical Property Creation for design & non-design space...... 38

5-4 Optistruct solver panel ...... 39

5-5 Optistruct solver run time visualization ...... 39

5-6 Optimization result from Altair Hyperview® ...... 40

5-7 Sheet metal design of optimization result ...... 41

5-8 Normal mode analysis result of Optimization result ...... 41

5-7 Final sub-frame design ...... 43

List of Abbreviations

CAD ...... Computer Aided Design

FEM ...... Finite Element Method FEA ...... Finite Element Analysis

NVH ...... Noise, Vibration and Harshness SAE ...... Society of Automotive Engineers

xii

List of Symbols

x...... Variable of interest

xiii

Chapter 1

Introduction

1.1 Introduction to Design

This study examines the design, analysis, optimization and validation of rear sub- frame of an automotive (i.e. Sedan Car) to be used in a car of same segment. The new design was created without changing the mounting locations of the suspension from base design with a goal to substantially minimize the mass of the sub-frame without reducing the performance and structural integrity.

The motivating factor for minimizing the mass is to improve the overall efficiency of the vehicle. Vehicular mass is one of the significant factors which contribute to vehicular efficiency. Figure 1 shows the CAD model present to generate the design space which is currently used in the rear suspension of the vehicle.

Figure 1-1 Original Sub-frame CAD model 1

1.2 Noise, Vibration and Harshness:

NVH have become increasingly key factors in vehicle design because of the quest for increased refinement. Vibration has always been a prominent issue closely related to reliability and quality, while noise is of increasing importance to vehicle users and environmentalists. Harshness, which is related to the quality and transient nature of vibration and noise, is also strongly linked to vehicle refinement.

The trend has been towards lighter vehicle constructions and higher engine speeds to meet the requirements for improved fuel consumption and engine performance. This has tended to increase the potential for noise and vibration, posing many new problems for automotive engineers. These developments have also coincided with a reduction in the time to market for new vehicles and created an increased dependency on computer-aided design and analysis with less time spent on prototype testing. While NVH analysis has in recent years been aided by developments in finite element and multi-body systems analysis software, there is still an underlying need to apply basic vibration and noise principles in vehicle design.

Vibration arises from a disturbance applied to a flexible structure or component.

Common sources of vibration in vehicles are road and off-road inputs to suspensions, rotating and reciprocating unbalance in engines, fluctuating gas loads on crankshafts, gear manufacturing errors and tooth loading effects in transmissions, generation of fluctuating dynamic forces in constant velocity joints and inertia and elasto-dynamic effects in engine valve trains.

Vibration sources are characterized by their time and frequency domain characteristics. In automotive engineering, most vibration sources produce continuous disturbances as 2

distinct from shocks and short duration transients encountered in some machine systems.

They can therefore be categorized principally as either periodic or random disturbances.

The former are the easiest to define and originate from the power unit, ancillaries or transmission, while random disturbances arise from terrain inputs to wheels.

From the vibration point of view, the frequency content of a random signal is very important. For example, the frequency spectrum of a road input to a vehicle is a function of the spatial random profile of the road and the speed of the vehicle. All mass-elastic systems have natural frequencies, i.e. frequencies at which the system naturally wants to vibrate. For a given (linear) system these frequencies are constant and are related only to the mass and stiffness distribution. They are not dependent on excitation applied to the system provided that the system can be classified as linear.

An arbitrary short duration disturbance applied to the system tends to excite all the system’s natural frequencies simultaneously. Most systems have a very large number of natural frequencies, but normally only a few of the lower order ones are of interest because the higher ones are more highly damped. At each natural frequency, a system vibrates in a particular way, depicted by the relative amplitude and phase at various locations. This is called the mode of vibration.

1.2.1 Normal Mode Analysis

A normal mode is a motion where all parts of the system are vibrating in sinusoidal motion with the same frequency and in phase. All observed configurations of a system may be generated from its normal modes. Each normal mode has a characteristic frequency, its eigenvalue. The majority of structures can be made to resonate, i.e. to 3

vibrate with excessive oscillatory motion. Resonant vibration is mainly caused by an interaction between the inertial and elastic properties of the materials within a structure.

Resonance is often the cause of, or at least a contributing factor to many of the vibration and noise related problems that occur in structures and operating machinery. To better understand any structural vibration problem, the resonant frequencies of a structure need to be identified and quantified. Today, modal analysis has become a widespread means of finding the modes of vibration of a machine or structure (Figure 2). In every development of a new or improved mechanical product, structural dynamics testing on product prototypes is used to assess its real dynamic behavior.

Figure 1-2 Modal analysis of a car body

1.2.2 Degrees of Freedom

Modes are inherent properties of a structure, and are determined by the material properties (mass, damping, and stiffness), and boundary conditions of the structure. Each mode is defined by a natural (modal or resonant) frequency, modal damping, and a mode shape (i.e. the so-called “modal parameters”). If either the material properties or the boundary conditions of a structure change, its modes will change. For instance, if mass is added to a structure, it will vibrate differently. To understand this, let’s make use of the concept of single and multiple-degree-of-freedom systems.

1.2.2.1 Single Degree of Freedom

A single-degree-of-freedom (SDOF) system (see Figure 3) where the mass m can only move along the vertical x-axis. It is described by the following equation m풙̈ (t) c풙̇ (t) kx(t) f (t) (1) with m the mass, c the damping coefficient, and k the stiffness. This equation states that the sum of all forces acting on the mass m should be equal to zero with f (t) an externally applied force,m푥̈ (t) the inertial force, c푥̇(t) the (viscous) damping force, and kx(t) the restoring force. The variable x(t) stands for the position of the mass m with respect to its equilibrium point, i.e. the position of the mass when f (t) 0.

Figure 1-3 Single DOF System

Although very few practical structures could realistically be modeled by a single-degree- of-freedom (SDOF) system, the properties of such a system are important because those of a more complex multiple-degree-of-freedom (MDOF) system can always be represented as the linear superposition of a number of SDOF characteristics.

1.2.2.2 Multiple Degree of Freedom

Multiple-degree-of-freedom (MDOF) systems are described by the following equation.

M풙̈ (t) C풙̇ (t) Kx(t) f (t)

In Figure 4, the different matrices are defined for a 2-DOF system with both DOF along the vertical x-axis.

Figure 1-4 2-DOF System

Chapter 2

Literature Review and Background

2.1 Literature Review

A sub-frame is a key aspect of vehicle design. The first appearance of sub-frame was in the late 1960’s. The initial occurrence was to provide a way to balance the riding comfort and handling for a luxury car. Subframes are structural modules which are designed to carry specific automotive components such as the engine or the axle and suspension. The purpose of using a subframe in an automobile is to distribute high local loads over a wider area of the body structure and to isolate vibration and harshness from the rest of the body. The subframes are bolted or welded to the vehicle body. Bolted subframes are sometimes equipped with rubber bushings or springs to dampen noise and vibrations. An additional benefit is that subframes can be separately assembled and integrated into the vehicle on an automated assembly line when required.

As a natural development from a car with a full chassis, separate front and rear axle subframes are used in modern vehicle designs to reduce the overall weight and cost. Axle subframes can have various forms and fulfill different functions:

• subframes for rear and front axles

• perimeter frames which carry both the axle and the engine. 8

Simple axle subframes usually carry the axle, the lower control arms and, in case of the front axle, the steering rack. Subframes which also support the engine and possibly other components (e.g. transmission) would be particularly useful on front wheel drive cars.

Such more complex, but also more expensive designs would result in better road isolation and less harshness since these components are not anymore directly connected to the main body structure.

Typical engine sub-frames are fabricated by stamping heavy steel sheets into concave sections, which are welded together to form a tubular structure that is bolted to the vehicle frame or chassis. Another benefit is engine cradles provide a way to build the steering, engine, and transmission assemblies in a separate location from where this finished assembly is installed in the finished vehicle. This modular approach to assembly allows for improved flexibility and efficiency, which results in fast assembly time and reduced costs. Furthermore, engine cradles also serve the maintenance side of the automotive industry, allowing mechanics to remove broken parts more easily, thus reducing repair time and maintenance cost.

As a result of the realization of advantages provided by engine cradles, a rear subframe with similar structure has been developed and received widespread adoption in the automotive industry. Rear sub-frames serve the purpose of carrying the rear suspension and occasionally drivetrain components for rear-wheel or all-wheel drive vehicles.

Figure 2-1: BMW 5 series model with front and rear axle subframes

Source: BMW

Shock absorption in automobiles is performed by suspension system that carries the weight of the vehicle while attempting to reduce or eliminate vibrations which may be induced by a variety of sources, such as road surface irregularities, aerodynamics forces, vibrations of the engine and driveline, and non-uniformity of the tire/wheel assembly.

Usually, road surface irregularities, ranging from potholes to random variations of the surface elevation profile, acts as a major source that excites the vibration of the vehicle body through the tire/wheel assembly and the suspension system (Wong, 1998).

2.2 Manufacturability

Typically cradles are manufactured using multiple stampings of steel sheet metal welded together to form tubular structures. Another method of manufacturing cradle designs is the use of hydroforming. Hydroforming is a metal forming process where structural

members with closed sections are created from tubes. The process usually starts with a round tube being placed in a die, frequently with a mostly square or rectangular profile, then the tube is filled with fluid and hydraulic pressure is applied causing the walls of the tube to conform to the die creating the desired cross-section. Hydroforming is typically done with a constant wall thickness tube.

Both stamping and hydroforming metal forming operations are useful for large scale production operation such as those implemented by automotive manufacturers.

2.3 Design Considerations

Designing a sub-frame has many aspects to consider. Most of the automotive manufacturers take years in designing, validating, optimizing and testing. The list of considerations included are static stiffness, NVH performance, crashworthiness, strength and fatigue, weight, corrosion resistance, clearance, temperature and fluid exposure.

Many of these aspects are considered in this study.

Chapter 3

Tools and Resources

3.1 FEM & FEA

Finite Element method (FEM) simulates a physical part or assembly’s behavior by dividing the geometry of the part into a number of elements of standard shapes, applying loads and constraints, then calculating variables of interest – deflection, stresses, temperature, pressures etc. The behavior of an individual element is usually described by a relatively simple set of equations. Just as the set of elements would be joined together to build the whole structure, the equation describing the behavior of the individual elements are joined into a set of equations that describe the behavior of the whole structure.

FEM is

- A numerical method

- Mathematical representation of actual problem

- Approximate method

Basic definition is to make calculation at only limited number of points and then interpolate the result for entire domain (surface & volume).

3.1.1 FEA Process Introduction

FEA was used to validate the design prior to creating a prototype. This tool allowed for multiple iterations of the design to be modeled and tested against the harshest potential loading conditions without expending the time and effort required to create and test a prototype structure for each iteration of the design. There are many types of FEA software available to perform the analysis for this design. We have used Altair

Hyperworks® for this study.

Figure 3.1. Graphic window of Altair Hypermesh®

3.1.2 Pre-Analysis Processing

There are several actions necessary to convert the solid model into a simplified geometry that can be used for generating a finite element mesh that is both accurate to the original solid model design and stable enough for both mesh generation and solving. This section will identify these actions in five sub-sections including: Converting Solid Bodies to

Surface Bodies, Creating New Simulation and Finite Element Model, Manipulating

Surfaces for Optimal Mesh Generation, Creating Points for Load and Constraint

Application, and Ridged Connections for Simulating Weld and Bushing Connections.

3.2 Mesh Generation

After the proceeding, FEM preparation is completed the FEM is ready for 2D mesh generation. This process consists of generating a series of quadrilateral surface elements across the entire FEM geometry. These elements create the links and nodes that define the equation set used to calculate the stress and displacement the loads create in the cradle geometry. The properties of these elements define the material properties and wall thickness of the material. This makes it critical that the correct properties are assigned to the correct surface bodies for the results to be accurate.

3.2.1 Mesh Setup

Before we start 2D mesh of the components of the sub-frame, we need to setup

the settings, this is done using the tab meshing options present in the preferences

panel.

Figure 3-2 Graphic window for preference options

The next step is to set the mesh settings to the following settings and clicking return. This would mean the settings are saved for the current session. This is done to ensure the mesh does not alter every time we save the file or change the mesh.

Figure 3-3 Graphic window for mesh options

Next, we again have to go to preferences panel and choose the Check Element Settings. 15

Figure 3-4 Graphic window for Check element window

The following window pops up to select the Min. Length checks and Jacobian and Solver settings for the current window. After selecting the options, first Apply the settings and then click OK to save the set settings.

Figure 3-5 Graphic window for Check element settings

3.3 Converting Solid Bodies to Surface Bodies

After we set up the graphic window, the reference solid catia file is imported and the geometry contains large number of lines, points and other geometry features essential for designing the sub-frame geometry. The catia file also contain the geometry in solid form in which they act as a single solid part which is a major hurdle in extracting mid surfaces of individual components present in the sub-frame. This solid catia part cannot be modified or used for modeling/meshing of the components inside the solid geometry.

Figure 3-6 Graphic window for solid geometry

The solid part of the model is deleted and the surface part of the catia geometry is preserved for further use in development and finite element modeling. The solid is deleted from the catia file imported by the following method.

Figure 3-7 Delete option in tool bar

The delete option available can be used to delete almost everything in Altair

Hypermesh®. The delete option basically in default cases shows “elems” as an entity. For deleting “solids”, I use the options available in delete and use solids among the various options available.

Figure 3-8 Delete panel for solid geometry

The “solids” selected can be used by selecting the model using a graphic window and solids available can be deleted in one step.

Figure 3-9 Graphic window for Solid geometry deletion 18

After the solids are deleted, the next step is to separate the single sheet metal component into different components for organizing and ease of modeling.

Figure 3-10 Components of the sub-frame

The mid surface of the solid geometry file is extracted using the help of geometry panel available.

Figure 3-11 Midsurface extraction

The solid model for each component is used to extract mid surfaces separately and placed in separate collectors for further use of finite element modeling/mesh and model fix so that to make it easier to assign material and physical properties to them. Generally, Sheet metal parts mid surface are extracted using this method because of the symmetry in the solid component and thickness is assigned as per the thickness of the solid model. The sheet metal mid surface parts are then isolated and the solid part is hidden for the 2D mesh to be placed on the sheet metal mid parts for finite element analysis.

Figure 3-12 Midsurfaces of Sub-frame

3.3 Creating New Simulation and Finite Element Model

To convert the existing surface model into a FEM, the mid surfaces need to be 2D modeled using the options available in Altair Hypermesh®. Altair Hypermesh® is used extensively in Automotive and other industries for Finite Element Modeling/Mesh.

Meshing in Altair Hypermesh® contains of a few steps which is quite easy considering manual meshing in other commercial software packages.

Figure 3-13 2D panel

Figure 3-14 Automesh options

The components present are manually modelled using the 2D automesh panels and elements are connected regardless of the change in surface. The manual 2D modeling is considered the best modeling technique because it eliminates the chance of minimum element size and other element deformities which contribute towards higher solver time and memory.

Figure 3-15 Midsurface component with 2D mesh

Altair Hypermesh® also has an option for 3D modeling which helps us capture the geometry in detail and as per our requirement. 3D modeling is generally used in geometry which have a solid geometry almost greater than the element size used to model the geometry.

Figure 3-16 Component with 3D mesh

Subframe is a part in the automobile which is bonded with the help of CO2 weld or also called Arc weld. For the simulation to take place accurately the weld and its properties should be assigned accordingly. In Altair Hypermesh®, welding is performed in the following way. The weld process is done by using the option of connectors and all welds are generally developed using connectors in Altair Hypermesh®. In Altair Hypermesh®, the components to be welded are first selected and isolated and the region of weld is selected by the Finite Element Nodes available. The nodes are then considered as path of the seam weld. The components are then selected between whom the weld needs to be formed. Certain criteria such as type, tolerance and width of weld element are selected and the weld is created. This process creates 2 types of result, one of them is the weld element with the RBE3 elements attached to it and the other of the weld geometry which can be used for editing or change in weld due to design modifications. The seam weld process is described in figure as follows.

Figure 3-17 1D panel

Figure 3-18 Connectors Tab

Figure 3-19 Seam weld Tab

The seam weld is done to the sheet metal parts using the above method and the sub-frame is formed as per the seam weld geometry. The subframe thus formed is shown in figure below.

Figure 3-20 Seam weld visual representation

3.4.1 Element Simulated Physical and Material Properties

For the Physical Property section of the mesh collector settings, the PSHELL type is used for all collectors using 2D elements in this analysis. The specification of the PSHELL properties is set by selecting the wrench symbol in the Physical Property section. Once the wrench symbol is selected the PSHELL settings window.

Figure 3-21 Physical Properties of components

As each mesh is generated, it is assigned to a mesh collector, so the PSHELL assigned to each mesh collector determines the simulated thickness and material of all the meshes stored within that mesh collector. The material thickness types are each assigned to a different 2D mess collector for the simulation. After all collectors are created and all materials and thickness intended for use in the design are loaded in to the proper

PSHELL and assigned to the correct mesh collector.

Material Properties of the steel used in the study is given in the table below

Table 3.1 Physical properties of steel

Property Value

E 2.1e+05 MPa

Nu 0.300

RHO 7.9e-09 t/mm3

3.4.2 1D,2D & 3D Mesh

For all the 2D analysis in this study the CQUAD4 element was used. This is a quadrilateral plate with membrane-bending or plain strain behavior. This it is the most robust and versatile element for use on this kind of analysis, given the settings and geometry used.

Figure 3-22 1D, 2D & 3D Element types

The mesh parameters section is when the element size is specified. Smaller element sizes provide more accurate results, but increase the number of equations the solver needs to process, so if the elements are set too small the solver will take an excessive amount of time to solve the model or may run out of memory and not be able to produce results at all. For the analysis conducted in this study an element size of 10 mm was selected because it was small enough that two or more elements are needed to span the material

thickness of the all the pieces of the design, which is generally considered a good starting point for element sizing.

3.4.3 Simulation Constraints and Loading Application

The meshes are the framework used to create the equations, that when solved, maps the stress and displacement in the structure, but the loads and constraints are the inputs and boundaries that drive those equations. This section describes the process used to apply constraints and loads to the analysis. Figure shows the four constraints located in the center of the bushing sleeves used to mount the cradle to the vehicle chassis, and several of the loading forces and moments being applied to the center of the mounting points.

Figure 3-23 SPC Constraint

3.4.3.1 Constraints

The four constraints are created by selecting the Load Collectors icon located in the toolbar. The Load Collectors icon appears as shown in Figure 27

Figure 3-24 Load Collector Tab

The Constraints option is then used to create constraints with known degrees of freedom and the size of the constraint for visual purpose can also be determined. In creating this type of constraints, SPC comes up which means Single Point Constraint.

Figure 3-25 Constraint panel in Analysis Tab

3.4.3.2 Loads & Other Factors:

The loads which are defined and discussed in detail in are created by first selecting the

Load Collectors icon. For carrying out normal mode analysis, we need the range of frequency that we want our model to run/execute. For selecting Frequency, we need to create load collector and name the collector. The next step is to select the card image and for frequency input we use EIGRL card which helps us in setting frequency range.

Figure 3-26 Load Collector create panel

The next step after selecting the card image is to select create/edit option and input the frequency range for the model.

Figure 3-27 Frequency Range setup

3.5 Solving Simulation

Solving the simulation is accomplished by selecting the options available in Analysis option and normal mode analysis is performed using the RADIOSS® option present in

Analysis. The optimization of sub-frame and further development such as gauge optimization can also be performed in Optistruct® solver available in Altair

Hyperworks®.

Figure 3-28 Analysis Panel 29

The RADIOSS® option basically contains the option for saving the file as an “save as” option and other options such as “export options”, “run options” and “memory options”.

RADIOSS® is a leading structural analysis solver for highly non-linear problems under dynamic loadings. It is used across all industries worldwide to improve the crashworthiness, safety, and manufacturability of structural designs.

OptiStruct® is an industry proven, modern structural analysis solver for linear and nonlinear problems under static and dynamic loadings. It is the market-leading solution for structural design and optimization. OptiStruct® is used by thousands of companies worldwide to analyze and optimize structures for their strength, durability and NVH characteristics. It accurately handles nonlinearity of materials, geometries, and contact for applications including gasket analysis, bolt pre-tensioning, rotor dynamics and Thermo- structural analysis.

3.6 Post-Processing Results

For cases in this study, most runs take around 15-20 mins. After the solver finishes, the results are examined by opening the Altair Hyperview®. In the normal mode analysis, the result obtained is the natural frequency of the system. The natural frequency of a system is unique to its system. In manufacturing of a system, it is taken care to avoid obtaining the same frequency again to avoid resonance.

Figure 3-29 Normal Mode of original sub-frame

To examine the eigen frequency results, the frequency value is available in the window on the right top corner. The first three frequency of the subframe is given in the table below.

Table 3.2 Frequency and Mode shape of original sub-frame

Frequency Mode Shape

129.11 Hz

188.98 Hz

194.73 Hz

Chapter 4

Simulation Loading Scenarios

4.1 Loading Conditions

To assure that the rear sub-frame design could withstand the wide variety of loading conditions capable of being generated during most possible driving scenarios, 7 loading scenarios represent the loads the suspension components could transmit into the rear subframe design due to symmetry in the original design. The SAE Vehicle Axis System was used for this analysis and is defined relative to general vehicle structure in Figure below.

Figure 4-1 Z-direction for car

4.1.1 Two-Wheel Bump

The Two-Wheel Bump loading scenario simulates both rear wheels hitting a bump simultaneously, like the loading seen when a vehicle travels over a speed bump at high speed.

4.1.2 Forward Braking

The Forward Braking loading scenario simulates heavy braking being applied to both rear wheels simultaneously, while the vehicle is traveling at high speed in the forward direction, like the loading seen when a vehicle has to brake suddenly when coming to an unexpected red light.

4.1.3 Reverse Braking

The Reverse Braking loading scenario simulates heavy braking being applied to both rear wheels simultaneously, while the vehicle is traveling in the reverse direction, similar to the loading seen when a vehicle has to brake suddenly when backing up out of a driveway and an unexpected vehicle moves into the path.

4.1.4 Cornering

The Cornering loading scenarios simulate traveling around tight turns at a velocity close to the maximum the vehicle can achieve while maintaining control though the entire turn.

This scenario is similar to those seen by a vehicle traveling through a round-about at speeds above the recommended limits.

4.1.5 Forward Acceleration

The Forward Acceleration loading scenario simulates the loads applied to the cradle when the vehicle accelerates quickly in the forward direction, similar to when a driver punches the gas when a light turns green trying to get up to speed limit quickly.

4.1.6 Reverse Acceleration

The Reverse Acceleration loading scenario simulates the loads applied to the cradle when the vehicle accelerates quickly in the reverse direction, such as backing quickly out of a parking spot.

4.1.7 Max Torque

The Maximum Torque loading scenario simulates the loads transmitted into the cradle when the powertrain generates and transmits maximum torque to the wheels.

Chapter 5

Sub-frame Modified Design

5.1 Design Space:

The design space of the subframe is decided using the actual subframe design available and the design space is created so as to eliminate any possible interactions with nearby sub systems and nearby components. It is vital to design the new design as per other adjacent systems as any intersection with the existing model is not favorable and preferred.

Figure 5-1 Design space for sub-frame

The design space is divided into 2 parts. The first being the “non-design space” and the other being “design space”. The non-design space is considered as the region which remains unchanged after the design optimization. In this study, we have considered the region which holds the mounting as regions with other sub systems are unchanged. The design space is the part which is considered for the topology optimization and is modeled considering the intersections with other sub systems.

Topology optimization is concerned with material distribution and how the members within a structure are connected. It treats the equivalent density” of each element as a design variable. Another “view” on topology optimization is in classical FEA you ask for loads and test the component subsequently. In topology optimization, you ask for loads and deliver a structure which is capable to carry the loads.

The design space is modeled using tetra elements and contains CTETRA elements. These elements generally create a volume for the design space. The inner volume of the design space is shown below.

Figure 5-2 3D Tetra Mesh cross-section view 37

5.2 Optimization and Results

The design space after being finalized is given physical property and material is assigned as per the original model. The physical property of the design and non-design space is given as shown in the figure.

Figure 5-3 Physical Property Creation for design & non-design space

After the Physical and Material properties of the design space are assigned the loads and constraints are assigned as per the original model. The constraints and loads are assigned as per the 7 loading conditions described and the optimization is carried out to create new design which can sustain the above loading conditions and can be further developed for manufacturing. The design space is now analyzed using Optistruct® solver available in

Hypermesh®. The file is saved as needed and the other options of the tab are set as shown in figure.

Figure 5-4 Optistruct solver panel

After using “Optistruct” solver, the solver takes time of around 15-20 mins to solve the input file, and the output is determined after the solver completes the optimization process.

Figure 5-5 Optistruct solver run time visualization

The result is first viewed in Hyperview® and the optimized model is shown in figure below. The result is then post processed in Hypermesh® using the result files using the option “OSSmooth” option available.

Figure 5-6 Optimization result from Altair Hyperview®

The optimized result is then opened in Hypermesh® for further development. This option converts the design obtained into geometry for further use and development. The optimized design is further developed to make it feasible to manufacture and assemble as manufacturing the whole subframe as a casting is costly and not recommended in automotive industry due to high cost involved in casting and other assembling issues. The optimized design is made into sheet metal and assembled using seam weld. The non-

design space components are retained and the stability of the model is checked further development. The optimized model is as shown in figure.

Figure 5-7 Sheet metal design of optimization result

The optimized model is first tested for structural stiffness and although the structure is stiff enough, it’s not enough when compared to the original model and hence improvement in structure is carried out and iterations are carried out with change in structure to increase the frequency value and to decrease the mass of the obtained sub- frame structure.

Figure 5-8 Normal mode analysis result of Optimization result

The normal mode analysis performed shows the various mode shapes of the optimized model.

Table 5.1 Frequency and Mode shape of optimized result

Frequency Mode Shape

56.97 Hz

120.66 Hz

174.95 Hz

To increase the stiffness of the structure certain changes are applied to the design model and thickness of the sheet metal structure is altered. The changes help in decreasing the

mass of the sub-frame structure drastically and increasing the base frequency of the model. The structure is now refined, as from the simulation it appears the structure is weak at torsion at the center visible in the first mode shape and it needs reinforcement.

Figure 5-9 Final sub-frame design

Normal Mode Analysis is performed on the refined sheet metal optimized model and checked for structural stability and natural frequency. The mode shapes and frequency are shown in the table below. The refined model is low on mass and frequency levels are high enough to be considered for development.

Table 5.2 Frequency and Mode shape of Final sub-frame

Frequency Mode Shape

113.86 Hz

132.63 Hz

180.58 Hz

The final modified sub-frame design has the following dimensions and the mass of the sub-frame are given in the following table.

Table 5.3 Comparison between original and optimized model

Property in Consideration Original Model Optimized Model

Length in x-direction 551.10 mm 551.10 mm

Length in y-direction 1460.72 mm 1460.72 mm

Length in z-direction 232.74 mm 232.74 mm

Mass of the design space sub- 19.06 Kgs 17.67 Kgs frame

% Change in design space mass 7.29 %

The modified sub-frame model has a significant 7.29% less mass compared to the original model and that change in mass of about 1.39 Kgs in mass production of the car would significantly save millions of dollars for the manufacturer and would also decrease the mass of the vehicle down which would imply in higher mileage and performance of the automobile. The vehicle mass is always a factor for the manufacturers to look into development of new cars and use of various materials and designs to lower cost of manufacturing.

The von-mises stress value of the optimized design space sub-frame components when compared to the original sub-frame design helps understands that the new design has a large surface area and volume which helps in reducing the stress in the components compared to the original sub-frame. The values of von-mises stress are tabulated below. 45

Table 5.4 Von-Mises Maximum Stress Comparison of Optimized and Original model

Type of Load Case Optimized Model von-mises Original Model von-mises

stress (in MPa) stress (in MPa)

Static Condition 433.9 298.0

Braking Condition 229.6 287.4

Rollover Condition 395.7 401.3

The von-mises stress in static condition for the optimized model is more compared to original model but for all other cases the stress values are always less than the original sub-frame. It is mainly due to the higher stress in non-design space of the sub-frame which is being transferred to the design space because of greater contact area in optimized model. Even though the stress is high, the value is well within yield stress of steel so it can be accepted.

The new optimized model is a sheet metal geometry which can be manufactured using stamping, forging and other manufacturing techniques. The optimized model is better in terms of surface area and volume compared to the original model. This leads to better stress distribution over a large surface area and less displacement. The sheet metal geometry and its corresponding mass is described below.

Table 5.5 Component mass and name