DESIGN AND ANALYSIS OF A CHASSIS FOR A 60 TON PAY LOAD

Abstract:

As the chassis frame forms the backbone of a heavy vehicle, its principal function is to safely carry the maximum load for all designed operating conditions. To achieve a satisfactory performance, the construction of a chassis is the result of careful design and rigorous testing. Various manufacturers have individual design concepts and different methods of achieving the desired performance standards for the complete chassis, not all chassis components are interchangeable between various makes and models of vehicles. So, there is no standard design for chassis frame. Even though start with the chassis frame design start with selection of the section for side rails and cross members.

In this paper we have designed a chassis for storage cum resting fixture. Storage cum resting fixture is a structure of length 11000mm & width 2300mm, used to store cylindrical specimens of various sizes and weights in horizontal configuration. The storage cum resting fixture is used to carry the propellant stored in the cylindrical specimens. The trolley fixture should be designed for a maximum pay load of 60 tons.

The Objective of my project is to design a chassis for a pay load of 60 Tons. The design process involves manual design calculations, 3d modeling using UNIGRAPHICS software and analysis to validate the design. Ansys package has been implemented to perform the structural analysis.

INTRODUCTION

The storage cum resting fixture is used to carry the propellant stored in the cylindrical specimens. During storage, these specimens are also required to be rotated periodically. The trolley fixture should withstand for a maximum load of 60 tons, which is weight of the specimen and four rollers.

FIXTURE OVERVIEW:
The functionality of this fixture is as below • Cylindrical specimens of various sizes and weights are required to be stored in horizontal configuration.

• During Storage these specimens are also required to be rotated periodically.

• The trolley fixture should be designed for a maximum pay load of 60 tons.

• The Trolley shall move on a 2.07m track width rails, the rails are straight.

• There shall be one/two axles for the trolley and two/one equalizing wheels on each end of the axles.

• One of the eight wheels/Four Wheels has to be driven by geared air motor with manual override.

• Diameter of the specimen loaded on the fixture varies from 1m to 2.5m.

• Length of the Specimen varies from 2m to 10m.

• 6 Roller stands shall be there in the fixture and each roller stand contains two sets of rollers.

• Two roller stands will support one specimen.

• There can be cases of three specimens kept on the fixture (Different Length and Diameter).

• Each alternate roller stand should be provided with planetary gear drive for rotating the specimen manually with least effort .

• Each roller stand has to be provided with end stoppers with rollers at the middle along the center line of the platform. The rollers of the end stoppers butt against the annular end face of the specimen and prevent the specimen moving axially due to skewing effect during rotation.

• Provision to be made for positioning the roller stand at different locations in the platform.

Technical Specifications of the Fixture

• Overall dimensions of the platform: L=11000mm & W=2300mm

• Loading Platform Level from Rail Top : 1000mm (Approximate)

• Load carrying capacity of Each Trolley: 60 tons

• Distance between the Rails (Center of rail to center of rail): 2.07m, Width of the Rails: 75mm

• No. of Axles for Each Trolley: 2

• No. of Wheels on each Axle: One/Two Balancing double flanged wheels on either side of the axle

• Minimum Diameter of the Axle Wheel 400mm

• Tread Width of the Axle Wheel to suit the rail track (Rail Track Width=75mm)

• Type of Drive: Pneumatic with manual override

• Type of Motor: Vane Motor of suitable capacity with planetary gear box and pneumatic brake, Possible to release the brake when driving manually with handle through gear box. Globe make pneumatic motor to be used

• Air motor drive control: It should be possible to move the trolley with/without payload both in forward and reverse directions. It should also be possible to move the trolley at low speeds by inching. However the maximum speed should not exceed 6m/min. The drive control shall be provided on the trolley itself.

• In case of necessity , it should be possible to drive the trolley with 60tons payload by manual effort through the air motor gear box using a handle. The effort required to rotate the air motor should not exceed 3Kg(f)

• Parking Brake: Each trolley should be provided with manually operated parking brake.

• Roller Stands: Each Trolley should be provided with 6 No. of roller Stands, each roller stand has two wheels of 400mm diameter (Min)

SCOPE OF PROJECT

Following are the main subsystems of the resting fixture.

• Pneumatic Motor and Planetary Gear mechanism

• Rail Wheel and Axle Assembly Design

• Chassis Design

• Roller Stand & Rollers Assembly Design

• Planetary Gear Design

The objective of my project is to do design calculations for chassis, develop 3D model using UNIGRAPHICS and to perform structural analysis on the Chassis using Ansys.
[pic]
Figure 1.1 Overview of the trolley assembly

LITERATURE SURVEY

Lonny L. Thompson, K. Lampert and E. Horry had written a journal on “Design of a twist fixture to measure the torsional stiffness of Winston cup chassis” explain the torsional stiffness of the vehicles chassis significantly affects its handling characters tics and therefore an important parameter to measure. In this work a new twist fixture apparatus designed to measure the torsional stiffness of chassis. [1] Sertac Pehlivan, Joshua D. Summers Farhad Aemi had written a journal on “Tolerance analysis of fixture layout design” explain the development of an integrated computer aided fixture design. And explain the fundamental differences various distributed design architectures. [2] G.S.A Shawki suggested a book “Rigid considerations in fixture design” explained the fixture behavior design theory and methodology. [3] Panos Y. Papalambros had presented a journal on “Journal on Mechanical Design” explained design theory and methodology (including creativity in design and decision analysis). [4] William F. Milliken, Douglas L. Milliken has suggested a book “Chassis Design” and explained the principle to design chassis and analysis of chassis. [5] Keith J. Wakeham has suggested a book “Introduction to chassis design” and explained various factors influences the chassis design. He explained different types of forces acting on the chassis and the chassis response because of these forces. In this book he mentioned that “The key to good chassis design is that the further mass is away from the neutral axis the more ridgid it will be.” [6] William B. Riley and Albert R. George had presented a paper on “Design, Analysis and Testing of a Formula SAE Car Chassis” discusses several of the concepts and methods of chassis design. In this paper he introduces several of the key concepts of chassis design both analytical and experimental. Finite element method was used to analyze the chassis at different loading conditions. [7] Michael Broad and Terry Gilbert were presented a paper on “Design, Development and Analysis of the NCSHFH.09 Chassis” and explained proper design methodology for the development of chassis. He investigated several loads acting on the chassis. Finally, he implemented Finite element analysis using Ansys. [8] Ashutosh Dubey and Vivek Dwivedi were suggested a paper “Vehicle chassis analysis” explained the load cases and boundary conditions for the stress analysis of chassis using Finite element analysis over Ansys. Shell elements have been used for the longitudinal members & cross members of the chassis. The results of finite element analysis have been checked by experimental methods too. [9] Cicek Karaoglu and N Sefa Kuralay were presented a paper “Stress analysis of a truck chassis” and explained the different loading conditions. Stress analysis of a truck chassis was performed by using FEM. ANSYS was used for the solution of the problem. [10] Mohd Husaini, Abd Wahab was suggested a paper “Stress analysis on truck chassis” and explained the functions of the chassis. In this paper he presented an analysis of the static stress that acting on the upper surface of the truck chassis. Finite element analysis has been used in this numerical analysis. [11] Bathe K.J written a book “Finite Element Procedures” explain principles of the finite element methods. The book then presents an over view of Ansys technologies before moving on to cover key applications areas in detailed. This book develops the readers understanding of FEA and ability to use ansys software tools to solve their own particular Ansys problems. [12] Dr.R.B choudary written a book “Introduction to Ansys 10.0”, this book helps the new ansys users in getting started. This book introduces reader to effective finite problem solving by demonstrating the use of comprehensive Ansys software in a series of step by step examples. This book explains the basics of Ansys. [13]

CHASSIS

DEFINITION OF A CHASSIS

The chassis is the framework that is everything attached to it in a vehicle. In a modern vehicle, it is expected to fulfill the following functions:

• Provide mounting points for the suspensions, the steering mechanism, the engine and gearbox, the final drive, the fuel tank and the seating for the occupants; • Provide rigidity for accurate handling; • Protect the occupants against external impact.

While fulfilling these functions, the chassis should be light enough to reduce inertia and offer satisfactory performance. It should also be tough enough to resist fatigue loads that are produced due to interaction between the driver, engine, power transmission and road conditions.

LADDER FRAME

The history of the ladder frame chassis dates back to the times of the horse drawn carriage. It was used for the construction of ‘body on chassis’ vehicles, which meant a separately constructed body was mounted on a rolling chassis. The chassis consisted of two parallel beams mounted down each side of the car where the front and rear axles were leaf sprung beam axles. The beams were mainly channeled sections with lateral cross members, hence the name. The main factor influencing the design was resistance to bending but there was no consideration of torsion stiffness.

A ladder frame acts as a grillage structure with the beams resisting the shear forces and bending loads. To increase the torsion stiffness of the ladder chassis cruciform bracing was added in the 1930’s. The torque in the chassis was retrained by placing the cruciform members in bending, although the connections between the beams and the cruciform must be rigid. Ladder frames were used in car construction until the 1950’s but in racing only until the mid 1930’s. A typical ladder frame shown as below in Figure 2.5.

[pic]

Figure 2.5: Ladder frame chassis

TWIN TUBE

The ladder frame chassis became obsolete in the mid 1930’s with the advent of all-round independent suspension, pioneered by Mercedes Benz and Auto Union. The suspension was unable to operate effectively due to the lack of torsion stiffness. The ladder frame was modified to overcome these failings by making the side rails deeper and boxing them. A closed section has approximately one thousand times the torsion stiffness of an open section. Mercedes initially chose rectangular section, later switching to oval section, which has high torsion stiffness and high bending stiffness due to increased section depth, while Auto Union used tubular section. The original Mercedes design was further improved by mounting the cross members through the side rails and welding on both sides. The efficiency of twin tube chassis’ is usually low due to the weight of the large tubes. They were still in use into the 1950’s, the 1958 Lister-Jaguar being an example of this type.

SPACE FRAME

Although the space frame (Figure 2.7) demonstrated a logical development of the four-tube chassis, the space frame differs in several key areas and offers enormous advantages over its predecessors. A space frame is one in which many straight tubes are arranged so that the loads experienced all act in either tension or compression. This is a major advantage, since none of the tubes are subject to a bending load. Since space frames are inherently stiff in torsion, very little material is needed so they can be lightweight. The growing realization of the need for increased chassis torsion stiffness in the years following World War II led to the space frame, or a variation of it, becoming universal among European road race cars following its appearance on both the Lotus Mk IV and the Mercedes 300 SL in 1952. While these cars were not strictly the first to use space frames, they were widely successful, and the attention they received popularized the idea.

[pic]

Figure 2.7: 1952 Lotus Mk.IV space frame

DESIGN OF CHASSIS

The storage cum resting fixture is used to carry the propellant stored in the cylindrical specimens. During storage, these specimens are also required to be rotated periodically. The trolley fixture should withstand for a maximum load of 60 tons, which is weight of the specimen and four rollers.

As the chassis frame forms the backbone of a heavy vehicle, its principal function is to safely carry the maximum load for all designed operating conditions. To achieve a satisfactory performance, the construction of a chassis is the result of careful design and rigorous testing. Various manufacturers have individual design concepts and different methods of achieving the desired performance standards for the complete chassis, not all chassis components are interchangeable between various makes and models of vehicles. So, there is no standard design for chassis frame. Even though start with the chassis frame design start with selection of the section for side rails and cross members.
[pic]
Figure shows the assembly of the Fixture used to carry the cylindrical specimens
[pic]
Figure shows the Chassis assembly of the Fixture used to carry the cylindrical specimens

Design of Chassis Assembly

The objective of my project is to do design calculations for a maximum pay load of 65tons

Design of Cross Members

[pic]

Figure 6.1 Line Diagram of Roller Load Point and Cross Member of Chassis

Required Sectional Modulus of Box Section (Cross)

• Assumed as a simply supported beam with two point loads (Roller Locations)

• Shear load (σ) = 24 kg(f)/mm^2(Shear Load Considered with Factor of Safety of greater than 4)

• Total Load on the Chassis (w) = 65 tons (60Tons is maximum Specimen weight + 5 Tons as factor considered for Roller's, Stands, Planetary unit )

• Weight trasmitted at each Roller Point Load(W) = w*1000/4 = 65*1000/4 = 16250kgs

• Distance between Rails(L) = 2070 mm

• Distance between Shaft Loading Brackets(Lb) =1760 mm (Considered the Roller Load Points)

• Maximum Bending Moment(Bmax1) = w*(L-Lb)/2 = 16250*(2070-1760)/2 = 2518750 Kg-mm

• Max Bending Moment(Bmax) = Bmax1/1000 = 2518750/1000 = 2518.75 kg(f)-m

• Required Sectional Modulus(Zr) = Bmax1/σ = 104947.9167 mm^3

Considered Sectional Modulus of Box Section (Roller Resting Section)

• Type of Construction : Box Section Made from two channels of Height : 225; Width: 80 ; Thickness of Flange:12.4; Thickness of Web:6.5 as per IS:226

• Height of the cross box section (h) = 225 mm

• Width of the cross box section (w) = 160mm

• Web Thickness of the cross box section (tw) = 6.5 mm

• Flange of the cross box section Thickness (tf) = 12.4 mm Moment of Inertia (I) = (w*h^3-((w-2*tw)*(h-2*tf)^3))/12 = (160*225^3-((160-2*6.5)*(225-2*12.4)^3))/12 = 53580705.9 mm^4

• Sectional Modulus(Z2) = I/(h/2) = 53580705.9/(225*0.5) = 119068.2353 mm^3

Sectional Modulus of I Section (Roller Resting Section)

• Height of the I-Section (h1) = 250 mm

• Width of the I-Section (w1) = 100 mm

• Web Thickness of the I-Section (tw1) = 15 mm

• Flange Thickness of the I-Section (tf1) = 15 mm

• Moment of Inertia of the I-Section (I1) = (w1*h1^3-((w1-2*tw1)*(h1-2*tf1)^3))/12 = (100*250^3-((100-2*15)*(250-2*15)^3))/12 = 54785000 mm^4

• Sectional Modulus of the I-Section (Z3) = I1/(0.5*h1) =54785000/(0.5* 250) = 109570 mm^3

• Considered Sectional Modulus of Box Section is greater than Required Sectional Modulus & I-Section Sectional Modulus.

6.2.2 Design of Long Members

[pic]

figure 6.2 Line Diagram of Roller Load Point and Cross Member of Chassis

Required Sectional Modulus of Long Member Box Section

• Considered type Cantilever as the long member of Chassis is constrained all the sides

• Shear load (σ) = 24 kg(f)/mm^2 (Shear Load Considered with Factor of Safety of greater than 4)

• Total Load on the Chassis (w) = 65 tons (60Tons is maximum Specimen weight + 5 Tons as factor considered for Roller's, Stands, Planetary unit )

• Distance between Rail Wheels along length (L) = 7850 mm

• Distance between Roller Support and load Left Side (L1) = 1325mm

• Distance between Roller Support and load Right Side (L2) = 1000 mm

• Left Side Reaction(Rl) = w*1000/4 = 16250 Kgs

• Right Side Reaction(Rr)= w*1000/4 = 16250 Kgs

• Bending Moment Left Side(Bl) = Rl*L1 =16250*1325 = 21531250 Kg(f)-mm

• Bending Moment Right Side(Br) = Rr*L2 = 16250*1000= 16250000 Kg(f)-mm

• Maximum Bending Moment on the long member (Bmax2) = Max(Bl, Br) = Max (21531250, 16250000) = 21531250 Kg(f)-mm

• Max Bending Moment(Bmb) = Bmax2/1000 = 21531250/1000 = 21531.25 kg(f)-m

• Required Sectional Modulus(Z4) = Bmax2/ σ = 21531250/24 = 897135.4167 mm^3

Considered Section of the Long Member Section Modulus

[pic]

Figure 6.3 Cross Section of the Long Member Section

• Type of Construction : Box Section Made from two channels of Height : 300; Width: 90 ; Thickness of Flange:13.6; Thickness of Web:7.8 as per IS:226 , A channel of Height : 175; Width: 75 ; Thickness of Flange:10.2; Thickness of Web:5.7 welded as shown above to achieve higher Sectional modulus

• Height of long box section (h2) = 300 mm

• Width of long box section (w2) = 180 mm

• Flange thickness of long box section (Ft2) = 13.6 mm

• Web thickness of long box section (t2) = 7.8 mm

• Length of Box Section (L2) = 11000 mm

• Weight of the Box Section (Wb) = 798.6kgs (36.3 Kg/meter is wt of channel)

• Bottom Channel Height (hc) = 175 mm

• Bottom Channel Width (hw) = 75 mm

• Bottom Channel Flange thickness (tcf) = 10.2 mm

• Bottom Channel Web thickness (tcw) = 5.7 mm

• Bottom Weight of the Channel (Wc) = 211.2 kgs (19.2 kg/meter is wt of channel)

• Moment of Inertial for Box Section(MI2) = (w2*h2^3-(w2-2*t2)*(h2-2*Ft2)^3)/12 = 126866266.8 mm^4

• Centroid of Bottom Channel (Cb) =((hc*hw^2/2)-(hc-2*tcf)*(hw-tcw)*(tw*0.5+hw*0.5))/((hc*hw)-(hc-2*tcf)*(hw-tcw)) = 24.84mm

• Moment of Inertia for Channel as Solid (MIc1) = hc*hw^3/12 = 6152343.75 mm^4

• Moment of Inertial of Channel Hollow Portion (MIc2) = (hc-2*tcf)*(hw-tcw)^3/12 =4287735.11 mm^4

• Centroid of Complete Section(Cs) = (Wb*(hw+0.5*h2)+Wc*Cb)/(Wb+Wc) = 183.14 mm

• Moment of Inertia of BOX Section WRT to Section Centroid(MI2) = MIc1+hc*hw*(Cs-0.5*hw)^2 = 284530623.4 mm^4

• Moment of Inertia of Channel (MI3) = MIc2+(hc-2*tcs)*(hw-tcw)*((cs (hw*0.5+tcw*0.5))^2) = 222717843 mm^4

• Channel Moment of Inertial WRT to Centroid of Section(MI4) = MI2-MI3 = 61812780.4 mm^4

• Box Section Moment of Inertial WRT to Centroid(MI5) = MI2+(h2*w2-(h2-2*Ft2)*(w2-2*t2))* ((hw+h2*0.5-Cs)^2) = 142905637 mm^4

• Distance of the Outer surface from Centroid(Lc) = Max(Cs,(h2+hw-Cs)) = 191.86 mm

• Sectional Modulus(Z5) = (MI4+MI5)/Lc = 1066996.196 mm^3

Sectional Modulus of I Section for Long Member

• Height of I-Section (h3) = 420 mm

• Width of I-Section (w3) = 200 mm

• Web Thickness of I-Section (t3) = 25 mm

• Flange Thickness of I-Section (Ft3) = 25mm

• Moment of Inertia(MI6) = (w3*h3^3-(w3-2*t3)*(h3-2Ft3)^3)/12 = 496110416.7 mm^4

• Sectional Modulus(Z6) = MI6/h3/2 = 590607.64 mm^3

Considered Sectional Modulus of Long Member is greater than Required Sectional Modulus & I-Section Sectional Modulus.

5 Design of Cross Member at Rail Support Structure

This particular cross member will be subjected to only the loads from the Roller Assembly

Required Sectional Modulus of Cross Member

\

• Shear load (σ) = 24 kg(f)/mm^2(Shear Load Considered with Factor of Safety of greater than 4)

• Total Load on the Chassis (w) = 65 tons (60Tons is maximum Specimen weight + 5 Tons as factor considered for Roller's, Stands, Planetary unit )

• Load on at each Roller Point (Wc) = w*1000/4 = 16250 kgs

• Distance between Rails(Lr) = 2070 mm

• Distance between Shaft Loading Brackets(Lb) = 1760 mm (Considering the Roller Load Points)

• Maximum Bending Moment(Bmax3) = Wc*(Lr-Lb)/2 = 2518750 Kg-mm

• Max Bending Moment(Bmc) = Bmax3/1000 = 2518.75 kg(f)-m

• Required Sectional Modulus(Z7) = Bmax3/σc = 104947.92 mm^3

Considered Sectional Modulus of Box Section (Cross)

• Type of Construction : Box Section Made from two channels of Height : 300; Width: 90 ; Thickness of Flange:13.6; Thickness of Web:7.8 as per IS:226

• Height of Box Section (h4) = 300 mm

• Width of Box Section (w4) = 180 mm

• Web Thickness of Box Section (t4) = 7.8 mm

• Flange Thickness of Box Section (Ft4) = 13.6mm

• Moment of Inertia of Box Section (MI7) = (w4*h4^3-(w4-2*t4)*(h4-2Ft4)^3)/12 = 126866266.8 mm^4

• Sectional Modulus of Box Section (Z7) = MI7/h4/2 = 211443.78 mm^3

Considered Sectional Modulus of Cross Member is greater than Required Sectional Modulus. This Box Section is Used as the Stiffener only, the complete load of the Specimen and Fixture is transferred to wheels through the box section along the length. Hence the Box Section of 300 X 180 can be considered.

INTRODUCTION TO UNI-GRAPHICS Overview of Solid Modeling The Unigraphics NX Modeling application provides a solid modeling system to enable rapid conceptual design. Engineers can incorporate their requirements and design restrictions by defining mathematical relationships between different parts of the design. Design engineers can quickly perform conceptual and detailed designs using the Modeling feature and constraint based solid modeler. They can create and edit complex, realistic, solid models interactively, and with far less effort than more traditional wire frame and solid based systems. Feature Based solid modeling and editing capabilities allow designers to change and update solid bodies by directly editing the dimensions of a solid feature and/or by using other geometric editing and construction techniques.
Advantages of Solid Modeling Solid Modeling raises the level of expression so that designs can be defined in terms of engineering features, rather than lower-level CAD geometry. Features are parametrically defined for dimension-driven editing based on size and position.
Features
• Powerful built-in engineering-oriented form features-slots, holes, pads, bosses, pockets-capture design intent and increase productivity • Patterns of feature instances-rectangular and circular arrays-with displacement of individual features; all features in the pattern are associated with the master feature
Blending and Chamfering • zero radius • Ability to chamfer any edge • Cliff-edge blends for designs that cannot accommodate complete blend radius but still require blends

Advanced Modeling Operations • Profiles can be swept, extruded or revolved to form solids • Extremely powerful hollow body command turns solids into thin-walled designs in seconds; inner wall topology will differ from the outer wall, if necessary • Fixed and variable radius blends may overlap surrounding faces and extend to a Tapering for modeling manufactured near-net shape parts • User-defined features for common design elements (Unigraphics NX/User-Defined Features is required to define them in advance
3.1 General Operation

• Start with a Sketch

Use the Sketcher to freehand a sketch, and dimension an "outline" of Curves. You can then sweep the sketch using Extruded Body or Revolved Body to create a solid or sheet body. You can later refine the sketch to precisely represent the object of interest by editing the dimensions and by creating relationships between geometric objects. Editing a dimension of the sketch not only modifies the geometry of the sketch, but also the body created from the sketch.

• Creating and Editing Features

Feature Modeling lets you create features such as holes, slots and grooves on a model. You can then directly edit the dimensions of the feature and locate the feature by dimensions. For example, a Hole is defined by its diameter and length. You can directly edit all of these parameters by entering new values. You can create solid bodies of any desired design that can later be defined as a form feature using User Defined Features. This lets you create your own custom library of form features.

• Associativity Associatively is a term that is used to indicate geometric relationships between individual portions of a model. These relationships are established as the designer uses various functions for model creation. In an associative model, constraints and relationships are captured automatically as the model is developed.For example, in an associative model, a through hole is associated with the faces that the hole penetrates. If the model is later changed so that one or both of those faces moves, the hole updates automatically due to its association with the faces. See Introduction to Feature Modeling for additional details.

• Positioning a Feature

Within Modeling, you can position a feature relative to the geometry on your model using Positioning Methods, where you position dimensions. The feature is then associated with that geometry and will maintain those associations whenever you edit the model. You can also edit the position of the feature by changing the values of the positioning dimensions.

• Reference Features You can create reference features, such as Datum Planes, Datum Axes and Datum CSYS, which you can use as reference geometry when needed, or as construction devices for other features. Any feature created using a reference feature is associated to that reference feature and retains that association during edits to the model. You can use a datum plane as a reference plane in constructing sketches, creating features, and positioning features. You can use a datum axis to create datum planes, to place items concentrically, or to create radial patterns.

• Expressions The Expressions tool lets you incorporate your requirements and design restrictions by defining mathematical relationships between different parts of the design. For example, you can define the height of a boss as three times its diameter, so that when the diameter changes, the height changes also.

• Boolean Operations Modeling provides the following Boolean Operations: Unite, Subtract, and Intersect. Unite combines bodies, for example, uniting two rectangular blocks to form a T-shaped solid body. Subtract removes one body from another, for example, removing a cylinder from a block to form a hole. Intersect creates a solid body from material shared by two solid bodies. These operations can also be used with free form features called sheets.

• Undo You can return a design to a previous state any number of times using the Undo function. You do not have to take a great deal of time making sure each operation is absolutely correct, because a mistake can be easily undone. This freedom to easily change the model lets you cease worrying about getting it wrong, and frees you to explore more possibilities to get it right.

• Additional Capabilities Other Unigraphics NX applications can operate directly on solid objects created within Modeling without any translation of the solid body. For example, you can perform drafting, engineering analysis, and NC machining functions by accessing the appropriate application. Using Modeling, you can design a complete, unambiguous, three dimensional model to describe an object. You can extract a wide range of physical properties from the solid bodies, including mass properties. Shading and hidden line capabilities help you visualize complex assemblies. You can identify interferences automatically, eliminating the need to attempt to do so manually. Hidden edge views can later be generated and placed on drawings. Fully associative dimensioned drawings can be created from solid models using the appropriate options of the Drafting application. If the solid model is edited later, the drawing and dimensions are updated automatically. • Parent/Child Relationships If a feature depends on another object for its existence, it is a child or dependent of that object. The object, in turn, is a parent of its child feature. For example, if a HOLLOW (1) is created in a BLOCK (0), the block is the parent and the hollow is its child.A parent can have more than one child, and a child can have more than one parent. A feature that is a child can also be a parent of other features. To see all of the parent-child relationships between the features in your work part, open the Part Navigator.
3.2 Creating A Solid Model Modeling provides the design engineer with intuitive and comfortable modeling techniques such as sketching, feature based modeling, and dimension driven editing. An excellent way to begin a design concept is with a sketch. When you use a sketch, a rough idea of the part becomes represented and constrained, based on the fit and function requirements of your design. In this way, your design intent is captured. This ensures that when the design is passed down to the next level of engineering, the basic requirements are not lost when the design is edited. The strategy you use to create and edit your model to form the desired object depends on the form and complexity of the object. You will likely use several different methods during a work session. The next several figures illustrate one example of the design process, starting with a sketch and ending with a finished model. First, you can create a sketch "outline" of curves. Then you can sweep or rotate these curves to create a complex portion of your design.
3.3 Introduction to Drafting The Drafting application is designed to allow you to create and maintain a variety of drawings made from models generated from within the Modeling application. Drawings created in the Drafting application are fully associative to the model. Any changes made to the model are automatically reflected in the drawing. This associativity allows you to make as many model changes as you wish. Besides the powerful associativity functionality, Drafting contains many other useful features including the following: • An intuitive, easy to use, graphical user interface. This allows you to create drawings quickly and easily. • A drawing board paradigm in which you work "on a drawing." This approach is similar to the way a drafter would work on a drawing board. This method greatly increases productivity. • Support of new assembly architecture and concurrent engineering. This allows the drafter to make drawings at the same time as the designer works on the model. • The capability to create fully associative cross-sectional views with automatic hidden line rendering and crosshatching. • Automatic orthographic view alignment. This allows you to quickly place views on a drawing, without having to consider their alignment. • Automatic hidden line rendering of drawing views. • The ability to edit most drafting objects (e.g., dimensions, symbols, etc.) from the graphics window. This allows you to create drafting objects and make changes to them immediately. • On-screen feedback during the drafting process to reduce rework and editing. • User controls for drawing updates, which enhance user productivity. Finally, you can add form features, such as chamfers, holes, slots, or even user defined features to complete the object.

• Updating Models

A model can be updated either automatically or manually. Automatic updates are performed only on those features affected by an appropriate change (an edit operation or the creation of certain types of features). If you wish, you can delay the automatic update for edit operations by using the Delayed Update option. You can manually trigger an update of the entire model. You might, for example, want to use a net null update to check whether an existing model will successfully update in a new version of Unigraphics NX before you put a lot of additional work into modifying the model. (A net null update mechanism forces a complete update of a model, without changing it.)
The manual methods include: • The Unigraphics NX Open C and C++ Runtime function, UF_MODL_update_all_features, which logs all the features in the current work part to the Unigraphics NX update list, and then performs an update. See the Unigraphics NX Open C and C++ Runtime Reference Help for more information. • The Playback option on the Edit Feature dialog, which recreates the model, starting at its first feature. You can step through the model as it is created one feature at a time, move forward or backward to any feature, or trigger an update that continues until a failure occurs or the model is complete.
The Edit during Update dialog, which appears when you choose Playback, also includes options for analyzing and editing features of the model as it is recreated (especially useful for fixing problems that caused update failures).Methods that users have tried in the past that has led to some problems or is tricky to use: • One method uses the Edit Feature dialog to change the value of a parameter in each root feature of a part, and then change it back before leaving the Edit Feature dialog. This method produces a genuine net null update if used correctly, but you should ensure that you changed a parameter in every root feature (and that you returned all the parameters to their original values) before you trigger the update. • Another method, attempting to suppress all of the features in a part and then unsuppressed them, can cause updates that are not net null and that will fail.The failures occur because not all features are suppressible; they are left in the model when you try to suppress all features. As the update advances, when it reaches the point where most features were suppressed, it will try to update the features that remain (this is like updating a modified version of the model). Some of the "modifications" may cause the remaining features to fail. For these reasons, we highly recommend that you do not attempt to update models by suppressing all or unsurprising all features. Use the other options described here, instead.
3.4 ASSEMBLIES Concepts
Components
Assembly part files point to geometry and features in the subordinate parts rather than creating duplicate copies of those objects at each level in the assembly. This technique not only minimizes the size of assembly parts files, but also provides high levels of associativity. For example, modifying the geometry of one component causes all assemblies that use that component in the session to automatically reflect that change. Some properties, such as translucency and partial shading (on the Edit Object Display dialog), can be changed directly on a selected component. Other properties are changed on selected solids or geometry within a component. Within an assembly, a particular part may be used in many places. Each usage is referred to as a component and the file containing the actual geometry for the component is called the component part . • Top-down or Bottom-up Modeling You are not limited to any one particular approach to building the assembly. You can create individual models in isolation, then later add them to assemblies (bottom-up), or you can create them directly at the assembly level (top-down). For example, you can initially work in a top-down fashion, then switch back and forth between bottom-up and top-down modeling. • Design in Context When the displayed part is an assembly, it is possible to change the work part to any of the components within that assembly (except for unloaded parts and parts of different units). Geometry features, and components can then be added to or edited within the work part. Geometry outside of the work part can be referenced in many modeling operations. For example, control points on geometry outside of the work part can be used to position a feature within the work part. When an object is designed in context, it is added to the reference set used to represent the work part. • Associativity Maintained Geometric changes made at any level within an assembly result in the update of associated data at all other levels of affected assemblies. An edit to an individual piece part causes all assembly drawings that use that part to be updated appropriately. Conversely, an edit made to a component in the context of an assembly results in the update of drawings and other associated objects (such as tool paths) within the component part. See the next two figures for examples of top-down and bottom-up updates. • Mating Conditions Mating conditions let you position components in an assembly. This mating is accomplished by specifying constraint relationships between two components in the assembly. For example, you can specify that a cylindrical face on one component is to be coaxial with a conical face on another component. You can use combinations of different constraints to completely specify a component's position in the assembly. The system considers one of the components as fixed in a constant location, then calculates a position for the other component which satisfies the specified constraints. The relationship between the two components is associative. If you move the fixed component's location, the component that is mated to it also moves when you update. For example, if you mate a bolt to a hole, if the hole is moved, the bolt moves with it.

• Using Reference Sets to Reduce the Graphic Display Large, complex assemblies can be simplified graphically by filtering the amount of data that is used to represent a given component or subassembly by using reference sets. Reference sets can be used to drastically reduce (or even totally eliminate) the graphical representation of portions of the assembly without modifying the actual assembly structure or underlying geometric models. Each component can use a different reference set, thus allowing different representations of the same part within a single assembly. The figure below shows an example of a bushing component used twice in an assembly, each displayed with a different reference set. When you open an assembly, it is automatically updated to reflect the latest versions of all components it uses. Load Options lets you control the extent to which changes made by other users affect your assemblies. Drawings of assemblies are created in much the same way as piece part drawings. You can attach dimensions, ID symbols and other drafting objects to component geometry. A parts list is a table summarizing the quantities and attributes of components used in the current assembly. You can add a parts list to the assembly drawing along with associated callout symbols, all of which are updated as the assembly structure is modified. See the following figure. • Machining of Assemblies Assembly parts may be machined using the Manufacturing applications. An assembly can be created containing all of the setup, such as fixtures, necessary to machine a particular part. This approach has several advantages over traditional methods: • It avoids having to merge the fixture geometry into the part to be machined. • It lets the NC programmer generate fully associative tool paths for models for which the programmer may not have write access privilege.
It enables multiple NC programmers to develop NC data in separate files simultaneously

3D MODEL OF THE CHASSIS

The steps involved while developing the 3D model of the roller assembly:

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Figure 6.4 3D model of the chassis cross beam

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Figure 6.5 3D model of the chassis cross beams

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Figure 6.6 3D model of the chassis cross beams with a side rail

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Figure 6.6 3D model of the chassis

FINITE ELEMENT METHOD
4.1 INTRODUCTION The Basic concept in FEA is that the body or structure may be divided into smaller elements of finite dimensions called “Finite Elements”. The original body or the structure is then considered as an assemblage of these elements connected at a finite number of joints called “Nodes” or “Nodal Points”. Simple functions are chosen to approximate the displacements over each finite element. Such assumed functions are called “shape functions”. This will represent the displacement with in the element in terms of the displacement at the nodes of the element. The Finite Element Method is a mathematical tool for solving ordinary and partial differential equations. Because it is a numerical tool, it has the ability to solve the complex problems that can be represented in differential equations form. The applications of FEM are limitless as regards the solution of practical design problems. Due to high cost of computing power of years gone by, FEA has a history of being used to solve complex and cost critical problems. Classical methods alone usually cannot provide adequate information to determine the safe working limits of a major civil engineering construction or an automobile or an aircraft. In the recent years, FEA has been universally used to solve structural engineering problems. The departments, which are heavily relied on this technology, are the automotive and aerospace industry. Due to the need to meet the extreme demands for faster, stronger, efficient and lightweight automobiles and aircraft, manufacturers have to rely on this technique to stay competitive. FEA has been used routinely in high volume production and manufacturing industries for many years, as to get a product design wrong would be detrimental. For example, if a large manufacturer had to recall one model alone due to a hand brake design fault, they would end up having to replace up to few millions of hand brakes. This will cause a heavier loss to the company. The finite element method is a very important tool for those involved in engineering design; it is now used routinely to solve problems in the following areas. • Structural analysis • Thermal analysis • Vibrations and Dynamics • Buckling analysis • Acoustics • Fluid flow simulations • Crash simulations • Mold flow simulations

Nowadays, even the most simple of products rely on the finite element method for design evaluation. This is because contemporary design problems usually cannot be solved as accurately & cheaply using any other method that is currently available. Physical testing was the norm in the years gone by, but now it is simply too expensive and time consuming also. [pic]
Basic Concepts: The Finite Element Method is based on the idea of building a complicated object with simple blocks, or, dividing a complicated object into small and manageable pieces. Application of this simple idea can be found everywhere in everyday life as well as engineering. The philosophy of FEA can be explained with a small example such as measuring the area of a circle. Area of one Triangle: Si = ½ * R2* Sin (I
Area of the Circle: SN = ½ * R2 * N * Sin (2 ( / N) ( ( R2 as N ( ( Where N = total number of triangles (elements) If one needs to evaluate the area of the circle without using the conventional formula, one of the approaches could be to divide the above area into a number of equal segments. the area of each triangle multiplied by the number of such segments gives the total area of the circle.

A BRIEF HISTORY OF THE FEM:
WHO
The reference credited is to Courant (Mathematician), Turner(air craft industry), clough(California university), Martin(air craft industry), argyris(German university),…., However, it was probably established by several pioneers independently.
WHEN
✓ Initial idea in mathematical terms was put in 1940s. ✓ Application to simple engineering problems in 1950s. ✓ Implementation in large computer is 1960s. ✓ Development of pre and post processors in 1980s. ✓ Analysis of large structural problems in 1990s.
WHERE
Implementation and application were mainly in aircraft industry and automobile sectors (large and fast computers were available only in these industries)
WHAT
Field problems in the form matrix methods of organizing large numbers of algebraic equations are used and matrix equations are solved. Differential equations are transformed into an algebraic form. Blocks with different geometry are hooked together for creating complex geometry of the engineering problem
WHY
The advantage of doing FEM analysis is that it is fairly simple to change the geometry, material and loads recomputed stresses for modified product rather than build and test. The method can be used to solve almost any problem that can be formulated as a field problem. The entire complex problem can be cast as a larger algebraic equation by assembling the element matrices with in the computer and solved.
Available Commercial FEM software packages • ANSYS (General purpose, PC and workstations) • SDRC/I-DEAS (Complete CAD/CAM/CAE package) • NASTRAN (General purpose FEA on mainframes) • LS-DYNA 3D (Crash/impact simulations) • ABAQUS (Nonlinear dynamic analysis) • NISA (A General purpose FEA tool) • PATRAN (Pre/Post processor) • HYPERMESH (Pre/post processor)

More about FEA Finite Element Analysis was first developed for use in the aerospace and nuclear industries where the safety of the structures is critical. Today, the growth in usage of the method is directly attributable to the rapid advances in computer technology in recent years. As a result, commercial finite element packages exist that are capable of solving the most sophisticated problems, not just in structural analysis. But for a wide range of applications such as steady state and transient temperature distributions, fluid flow simulations and also simulation of manufacturing processes such as injection molding and metal forming. FEA consists of a computer model of a material or design that is loaded and analyzed for specific results. It is used in new product design, and existing product refinement. A design engineer shall be able to verify the proposed design, which is intended to meet the customer requirements prior to the manufacturing. Things such as, modifying the design of an existing product or structure in order to qualify the product or structure for a new service condition. Can also be accomplished in case of structural failure, FEA may be used to help determine the design modifications to meet the new condition.
The Basic Steps Involved in FEA Mathematically, the structure to be analyzed is subdivided into a mesh of finite sized elements of simple shape. Within each element, the variation of displacement is assumed to be determined by simple polynomial shape functions and nodal displacements. Equations for the strains and stresses are developed in terms of the unknown nodal displacements. From this, the equations of equilibrium are assembled in a matrix form which can be easily be programmed and solved on a computer. After applying the appropriate boundary conditions, the nodal displacements are found by solving the matrix stiffness equation. Once the nodal displacements are known, element stresses and strains can be calculated. Basic Steps in FEA • Discretization of the domain • Application of Boundary conditions • Assembling the system equations • Solution for system equations • Post processing the results.

Discritization of the domain: The task is to divide the continuum under study into a number of subdivisions called element. Based on the continuum it can be divided into line or area or volume elements.

Application of Boundary conditions: From the physics of the problem we have to apply the field conditions i.e. loads and constraints, which will help us in solving for the unknowns.

Assembling the system equations: This involves the formulation of respective characteristic (Stiffness in case of structural) equation of matrices and assembly.

Solution for system equations: Solving for the equations to know the unknowns. This is basically the system of matrices which are nothing but a set of simultaneous equations are solved.

Viewing the results: After the completion of the solution we have to review the required results. The first two steps of the above said process is known as pre-processing stage, third and fourth is the processing stage and final step is known as post-processing stage.

What is an Element? Element is an entity, into which a system under study can be divided into. An element definition can be specified by nodes. The shape(area, length, and volume) of the element depends upon the nodes with which it is made up of.
What are Nodes? Nodes are the corner points of the element. Nodes are independent entities in the space. These are similar to points in geometry. By moving a node in space an element shape can be changed. This is a volume element, can take the shape of a Hexahedron or a Wedge or a Tetrahedron order elements. For linear elements the edge is defined by a linear function called shape function whose degree is one. For the elements having mid side nodes on the edge quadratic function called shape function whose degree is two is used. The higher order elements when over lapped on geometry can represent complex shapes very well within few elements. Also the solution accuracy more with the higher order elements. But higher order elements will require more computational effort and time.
Brief Over View of Structural Static Analysis: Static analysis is one in which the loads/boundary conditions are not the functions of time and the assumption here is that the load is applied gradually. The most common application of FEA is the solution of stress related design problems.
Typically in a static analysis the kind of matrix solved is [K] * [X] = [F]
Where K is called the stiffness matrix, X is the displacement vector and F is the load matrix. This is a force balance equation. Some times, the K matrix is the function X. Such systems are called non-linear systems.
Nodal Displacements ui, uj
Nodal Forces fi, fj
Spring constant k
Spring force displacement relationship F = k ( with ( = uj – ui
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K = F/( (>0) is the force needed to produce a unit stretch
Consider the equilibrium forces for the spring. At node i, we have fi = -F = -k(uj – ui) = kui – kuj
And at node j, fj = F = k(uj – ui) = - kui + kuj

Element Quality Requirements: There are certain parameters that determine the quality of the results. The engineer has to ensure that these parameters maintained within the acceptable limits of the software for obtaining the good results. These are called mesh quality parameters.

Warp age: Warp age occurs only on Quad and Hexa elements. Since three points define a plane, one of the four nodes being in different plane by an angle causes warp age. The perfect warp age value desired is zero.

Aspect Ratio: It checks the ration of the length of the longest side of an element to the shortest length of the same element. A perfect value is one. The quickest way is to correct high aspect ratio is to increase the length of the shortest side or decrease the length of the longest side.

Skew: Skew measures the angle that is created as the square is turned into a parallelogram or rhombus. A perfect skew value is zero.

Quad Angles: The perfect Quad angles would be all 90 degrees min and max. The acceptable value for min angle is 45 degrees and 135 degrees is the max angle

Trial Angles: The perfect trial angle would be 60 degrees min and max. The acceptable values for min angle are 20 degrees and max angle is 120 degrees.

Jacobian: To simplify the description of what Jacobin measures is to say that it compares the element to the perfect square. A perfect Jacobin value is one. In other words Jacobin measures the deviation of the element from a perfect square.

Normals: The element normal is defined by the ordering of element node ids. An element normal of a continues mesh should face in the same direction as the element normal of the adjacent element.

NOTES ON ANSYS ELEMENT MANUAL
General element Features: Element Input: Many features that are common to all ANSYS elements in the element library are described here. Element Name: An element type is identified by a name, such as BEAM3, consisting a group label (BEAM) and a unique, identification number (3). Nodes: The nodes associated with the element are listed as I, J, K, etc. The node order determines the element coordinate system orientation for some element types. Degrees of Freedom: Each element type has DOF set, which constitutes the primary nodal unknowns to be determined by the analysis. They may be displacements, rotations, temperatures, pressures, voltage, etc. DOF are not defined on the nodes explicitly by the user, but rather are implied by the element types attached to them Real Constants: This data is required for the calculation of element matrix, but which cannot be determined from node locations or material properties, are input as “real constants”. Typical real constants include area, thickness, diameter and etc. Material Properties: Typical material properties include Young’s modulus, density, thermal conductivity and etc. Surface Loads: These loads are typically pressures for structural element types, convictions and heat fluxes for thermal element type and etc. Body Loads: Body loads are typically temperatures for structural element type, heat generation rates for thermal element type and etc. Special Features: The keywords in the special features list indicate that certain additional capabilities are available for the element. Most often these features make the element the element nonlinear and require an iterative solution be done. KEY Opts: These are the switches, used to turn various element options on or off. KEYOPT options include stiffness formulation choices, printout controls, element co-ordinate system choices and etc.

Solution Output: The output from the solution consists of the nodal solution (or the primary DOF solution) and the element solution (or the derived solution). Each of these solutions are described here. Solution output is written to output file “jobname.out” and the results are “jobname.rst”. The output file can be viewed through the GUI, while the database and results file data can be postprocessor.

Nodal Solution: The nodal solution form of analysis consists of (1) the degree of freedom solution, such as nodal displacements, temperatures, and pressures and (2) the reaction solution calculated at constrained nodes, such as forces at displacement constraints, heat flows at temperature DOF constraints, fluid flows at pressure DOF constraints, and so on.

Element Solution: The element output items are shown along with the element type description. Not all of the items shown in the output table will appear at all the times for the element. Items not appearing are either not applicable to the solution or have all zero results and are suppressed to save the space. The output is, in some cases, dependent on the input. For example, for thermal elements accepting either surface convection or nodal heat flux, the output will be either in terms of convection or heat flux.

Coordinate Systems: a). Element coordinate systems: The element co-ordinate system is used for orthotropic material input directions, applied pressure directions and stress output directions. Element co-ordinate systems are right-handed. For line elements, the default orientation is generally with the X-axis along the element. For solid elements (such as PLANE42 or SOLID45) the default orientation is generally parallel to the global Cartesian co-ordinate system. For area shell elements (such as SHELL63), the default orientation generally has the X- axis aligned with element I-J side, the Z-axis normal to the shell surface. b). Elements that operate on nodal co-ordinate system:
A few special elements operate totally in the nodal co-ordinate system
COMBIN14 Spring Damper with KEYOPT (2) = 1, 2,3,4,5, or 6
MASS21 Structural Mass with KEYOPT (2) = 1
MATRIX27 Stiffness, Damping or Mass Matrix
COMBIN37 Control element
FLUID38 Dynamic Fluid Coupling
COMBIN39 Non Linear Spring with KEYOPT (4) = 0
COMBIN40 Combination Element These elements are defined in the nodal co-ordinate system. This allows for easy directional control, especially for case of two node elements with coincident nodes. If Ux, Uy, or Uz degrees of freedom are being used, the nodes are not coincident, and the load is not acting parallel to the line connecting the two nodes, there is no mechanism for the element to transfer the resulting moment load, resulting in total loss of moment equilibrium. The one exception is MATRIX27 which can include moment coupling when appropriate additional terms are added to the matrix. There are some things to consider if any of the nodes have been rotated, for example with the NROTAT command. If the nodes of the element containing more than one node are not rotated in the exact same way, force equilibrium may not be maintained.

Accelerations operate normally in the Global co-ordinate system, But since there is no transformation done between the nodal and global systems, the accelerations will effectively act on any element mass in the nodal system, giving unexpected results. Therefore, it is recommended not to apply. Mass and inertia relief calculations will not be correct.

Linear Material Properties: The material properties used by the element type are listed under “Material Properties” in the input table for each element type. These properties are called linear properties, because typical non-thermal solutions with these properties require only a single iteration. Properties such as stress-strain data are called nonlinear properties, because an analysis with these properties requires an iterative solution. For orthotropic materials, the X, Y, and Z part of the label refers to the direction that the particular property acts in. Poisson’s ratio may be input in either major or minor form, but not both for a particular material. The major form is converted to the minor form during the solve operation.
Data Tables: A data table is a series of constants that are interpreted when they are used. Data tables are always associated with a material number and are most often used to define nonlinear material data. For some element types, the data table is used for special element input data other than material properties. The form of data table depends upon the data being defined. Where the form is peculiar to only one element type.

Node and Element Loads: Loadings are defined to be two ways: nodal and element. Nodal loads are defined at the nodes and are not directly related to the elements. These nodal loads are associated with DOF at the nodes. Element loads are surface loads, body loads and inertia loads. Element loads are always associated with a particular element type. Certain elements may also have “flags”. Flags are not actually loads, but are used to indicate that a certain type calculation is to be performed. For example, when the FSI(fluid structure interaction) flag is turned on, a specified face of an acoustic element is treated as an interface between a fluid portion and a structural portion of the model.
Triangle, Prism and Tetrahedron Elements: Degenerated elements are elements whose characteristic face shape is quadrilateral, but is modeled with at least one triangular face. For example, PLANE42 triangles, SOLID45 wedge, and SOLID$% tetrahedral are all degenerated shapes. Degenerated elements are often used for modeling transition regions between fine and course meshes, for modeling irregular and warped surfaces, etc. Degenerated elements formed with quadrilateral and brick elements without midsize nodes are much less accurate than those formed from elements with midside nodes and should not be used in high stress gradient regions. An exception where triangular shell elements are preferred is for severely skewed or warped elements. Warping occurs when the four nodes of a quadrilateral shell element are not in the same plane. Warp age is measured by the relative angle between the normal to the face at the nodes. A flat face has all normal parallel to i.e. a zero relative angle. Degenerated triangular 2-D solid and shell elements may be formed from four noded quadrilateral elements by defining duplicate node numbers for the third and fourth(K and L) node locations. The node pattern then becomes I, J, K, K. If the L node is not input, it defaults to node K. If extra shape functions are included in the element, they are automatically suppressed (degenerating the element to lower order). Element loads specified on nodal basis should have the same loads specified at the duplicate node locations. Degenerated triangular prism elements may be formed from eight noded 3-D solid elements by defining duplicate node numbers for the third and fourth and the seventh and eighth node locations. The node pattern then becomes I, J,K,K,M,N,O,O. A degenerated tetrahedron element may be formed from a triangular prism element by further condensation of face 6 to a point. The input node pattern should be I, J,K,K,M,M,M,M. If extra shape functions are included in the element are automatically suppressed.
Axisymmetric Elements with Nonanisymmetric Loads: The use of ax symmetric model greatly reduces the modeling and analysis time compared to that of 3-D model. A special class of ANSYS ax symmetric elements (called harmonic elements) allows a nonaxisymmetric load. For these elements (PLANE25, SHELL61, PLANE75, PLANE78, PLANE83 and FLUID81), the load is defined as a series of harmonic functions.

Shear Deflection: Shear deflection effects are often significant in the lateral deflection of short beams. The significance decreases as the ratio of the radius of gyration of the beam cross section to the beam length becomes small compared to unity. Shear deflection effects are activated in the stiffness matrices of ANSYS beam element by including a nonzero shear deflection constant (SHEAR) in the real constant list for the element type. The shear deflection constant is defined as the ratio of the actual beam cross sectional area to the effective area resisting shear deformation. The shear constant should be equal to or greater than zero. The element shear stiffness decreases with increasing the value of shear deflection constant. A zero shear deflection constant may be used to neglect shear deflection.
Element Characteristics List of Element Types: The ANSYS element library consists of more than 100 different element formulations. An element type is identified by a name (8 characters maximum), such as BEAM3, consisting a group label (BEAM) and a unique identification number (3) 2-D versus 3-D Models: ANSYS models may be 2-D or 3-D, depending on the element type used. The axisymmetric modes are also considered as 2-D models. Some elements (such as COMBIN14) may be 2-D or 3-D, depending upon the KEYOPT value selected.
Element Characteristic Shape In general, four shapes are possible: Point, Line, Area or Volume. A point element typically dented by a node, e.g., a mass element. A line element is typically represented by a line or arc connecting two or three nodes. E.g., beams spars, pipes and axisymmetric shells. An area element has a triangular or quadrilateral shape and may be a 2-D solid element or shell element. A volume element has a tetrahedral or brick shape usually a 3-D solid element
Degrees of Freedom and Discipline The DOF of the element determine the discipline for which the element is applicable: Structural, Thermal, Fluid, Electric, Magnetic or Coupled field. The element type should be chosen such that the DOF’s are sufficient to characterize the model’s response. Including the unnecessary DOF increases the solution memory requirements and run time.

THEORIES OF FAILURE:
Determining the expected mode of failure is an important first step in analysing a part design. The failure mode will be influenced by the nature of load, the expected response of the material and the geometry and constraints. In an engineering sense, failure may be defined as the occurrence of any event considered to be unacceptable on the basis of part performance. The modes of failure considered here are related to mechanical loads and structural analysis. A failure may include either an unacceptable response to a temporary load involving no permanent damage to the part or an acceptable response which does involve permanent, and sometimes catastrophic, damage. The purpose of theories of failure is to predict what combination of principal stresses will result in failure. There are number of theories to describe failure criteria, of them these are the widely accepted theories.

Maximum principal stress theory (rankine’s) σ1 or σ2 or σ3 (which ever is maximum) = σy.
According to this theory failure of the material is assumed to have taken place under a state of complex stresses when the value of the maximum principal stress reaches a value equal to that of the elastic limit stress (yield stress) as found in a simple tensile test.
Maximum shear theory (guest’s or coulomb’s) (σ1-σ2) or (σ2-σ3) or (σ3-σ1) = σ y (Which ever is maximum). According to this theory the failure of the material is deemed to have taken place when the maximum shear stress exceeds the maximum shear stress in a simple tension test.
Maximum principal strain theory (St.Venant’s) σ1-ν (σ2+σ3) or σ2-ν (σ3+σ1) or σ3-ν (σ1+σ2) (which ever is maximum) = σ y. According to this theory, failure of the material is deemed to have taken place when the maximum principal strain reaches a value calculated from a simple tensile test.
Maximum strain energy theory (Beltrami-Haigh’s) σ1²+σ2²σ3²-2ν (σ1σ2+σ2σ3+σ3σ1) = σ y². According to this theory failure is assumed to take place when the total strain energy exceeds the strain energy determined from a simple tensile test.
Octahedral or distortion energy theory (von mises-hencky) σ1²+σ2²+σ3²-σ1σ2-σ2σ3-σ3σ1 = σy². According to this theory failure is assumed to take place when the maximum shear strain energy exceeds the shear strain energy in a simple tensile test. This is very much valid for ductile material; in this the energy which is actually responsible for the distortion is taken into consideration.

Soderberg’s equations (recommended for ductile materials only):
1/n= σm/σy + Kf σa/σ-1
1/n= tm/ty + Kf ta/t-1
Where, σm =mean stress σy = yield stress σa = stress amplitude (σmax-σmin)/2 σ-1 = endurance limit stress tm = mean shear stress ty = yield shear stress 1/n = factor of safety

Goodman’s equations (for brittle materials)
1/n=Kt [σm/σu +σa/σ-1]
1/n=Kt[tm/tu +ta/t-1]
Where, σu = ultimate stress K = stress concentration factor

Choice of the theories of failure: Well documented experimental results by various authors on the various theories of failure, indicate that the distortion energy theory predicts yielding with greatest accuracy. Compared to this maximum shear stress theory predicts results which are always on safer side. Maximum principal stress theory gives conservative results only if the sign of the two principal stresses is the same (2-D case). Therefore, the use of maximum principal stress theory for pure torsion is ruled out where the sign of the two principal stresses are opposite. When the fracture of a tension specimen loaded up to rupture is examined, it shows that for ductile materials, failure occurs along lines at angles 45 degrees with the load axis. This indicates a shear failure. Brittle materials on the other hand, rupture on planes normal to the load axis, indicating that maximum normal stress determines failure. Because of the above mentioned observations, it is universally accepted that for a brittle materials, the maximum normal stress theory is the most suitable. For ductile materials, the maximum shear stress theory gives conservative results and it is simpler to use as compared to distortion energy theory, so it is universally accepted as the theory of failure for ductile materials. But, where low weight is desired, the distortion energy theory is recommended.
In brief:
Ductile material Under combined static loading, the machine parts made of ductile material will fail by yielding. The working or allowable stress is therefore, passed on the yield point stress. The maximum shear stress theory will be used for the design because it is conservative and easy to apply.

Brittle materials Failure in brittle materials, takes place by fracture. Brittle materials do not have a distinct yield point and so, the ultimate strength is used as the basis for determining the allowable or design stress. Separate design equations should be used in tension and compression, since for materials like cast iron; the ultimate compressive strength is considerably greater than the ultimate tensile strength. The maximum principal stress theory will be used for the design. Due consideration will be given to the sign of principal stresses. If both the principal stresses (2-D case) are of the same sign, the effect of the smaller stress is neglected. If the two principal stresses are of opposite sign, then the maximum principal stress theory does not give conservative results. In that case another equation should be used.

ANSYS The ANSYS program is self contained general purpose finite element program developed and maintained by Swason Analysis Systems Inc. The program contain many routines, all inter related, and all for main purpose of achieving a solution to an an engineering problem by finite element method.
ANSYS finite element analysis software enables engineers to perform the following tasks: • Build computer models or transfer CAD models of structures, products, components, or systems. • Apply operating loads or other design performance conditions • Study physical responses ,such as stress levels, temperature distributions, or electromagnetic fields • Optimize a design early in the development process to reduce production costs. • Do prototype testing in environments where it otherwise would be undesirable or impossible The ANSYS program has a compressive graphical user interface (GUI) that gives users easy, interactive access to program functions, commands, documentation, and reference material. An intuitive menu system helps users navigate through the ANSYS Program. Users can input data using a mouse, a keyboard, or a combination of both. A graphical user interface is available throughout the program, to guide new users through the learning process and provide more experienced users with multiple windows, pull-down menus, dialog boxes, tool bar and online documentation.
5.1 ORGANIZATION OF THE ANSYS PROGRAM The ANSYS program is organized into two basic levels: • Begin level • Processor (or Routine) level The begin level acts as a gateway in to and out of the ANSYS program. It is also used for certain global program controls such as changing the job name, clearing (zeroing out) the database, and copying binary files. When we first enter the program, we are at the begin level.

At the processor level, several processors are available; each processor is a set of functions that perform a specific analysis task. For example, the general preprocessor (PREP7) is where we build the model, the solution processor(SOLUTION)is where we apply loads and obtain the solution, and the general postprocessor(POST1) is where we evaluate the results and obtain the solution. An additional postprocessor (POST26), enables we to evaluate solution results at specific points in the model as a function of time.
5.2 PERFORMING A TYPICAL ANSYS ANALYSIS The ANSYS program has many finite element analysis capabilities, ranging from a simple, linear, static analysis to a complex, nonlinear, transient dynamic analysis. The analysis guide manuals in the ANSYS documentation set describe specific procedures for performing analysis for different engineering disciplines.
A typical ANSYS analysis has three distinct steps: • Build the model • Apply loads and obtain the solution • Review the results

The following table shows the brief description of steps followed in each phase.
|PRE-PROCESSOR |SOLUTION PROCESSOR |POST-PROCESSOR |
|Assigning element type |Analysis definition |Read results |
|Geometry definition |Constant definition |Plot results on graphs |
|Assigning real constants |Load definition |View animated results |
|Material definition |Solve | |
|Mesh generation | | |
|Model display | | |

5.3 PRE-PROCESSOR:
The input data for an ANSYS analysis are prepared using a preprocessor. The general preprocessor (PREP 7) contains powerful solid modeling an mesh generation capabilities, and is also used to define all other analysis data with the benefit of date base definition and manipulation of analysis data. Parametric input, user files, macros and extensive online documentation are also available, providing more tools and flexibility
For the analyst to define the problem. Extensive graphics capability is available through out the ANSYS program, including isometric, perceptive, section, edge, and hidden-line displays of three-dimensional structures-y graphs of input quantities and results, ands contour displays of solution results.

The pre-processor stage involves the following: • Specify the title, which is the name of the problem. This is optional but very useful, especially if a number of design iterations are to be completed on the same base mode. • Setting the type of analysis to be used ,e.g., Structural, Thermal, Fluid, or electromagnetic, etc • Creating the model. The model may be created in pre-processor, or it can be imported from another CAD drafting package via a neutral file format. • Defining element type, these chosen from element library. • Assigning real constants and material properties like young’s modules, Poisson’s ratio, density, thermal conductivity, damping effect, specific heat, etc • Apply mesh. Mesh generation is the process of dividing the analysis continuum into number of discrete parts of finite elements.

5.4 SOLUTION PROCESSOR Here we create the environment to the model, i.e, applying constraints &loads. This is the main phase of the analysis, where the problem can be solved by using different solution techniques. Her three major steps involved: • Solution type required, i.e. static, modal, or transient etc., is selected • Defining loads. The loads may be point loads, surface loads; thermal loads like temperature, or fluid pressure, velocity are applied. • Solve FE solver can be logically divided in o three main steps, the pre-solver, the mathematical-engine and post-solver. The pre-solver reads the model created by pre-processor and formulates the mathematical representation of the model and calls the mathematical-engine, which calculates the result. The result return to the solver and the post solver is used to calculate strains, stresses, etc., for each node within the component or continuum.

5.5 POST –PROCESSOR: Post processing means the results of an analysis. It is probably the most important step in the analysis, because we are trying to understand how the applied loads affects the design, how food your finite element mesh is, and so on. The analysis results are reviewed using postprocessors, which have the ability to display distorted geometries, stress and strain contours, flow fields, safety factor contours, contours of potential filed results; vector field displays mode shapes and time history graphs. The postprocessor can also be used for algebraic operations, database manipulators, differentiation, and integration of calculated results. Response spectra may be generated from dynamic analysis. Results from various loading may be harmonically loaded axis metric structures.

5.6 REVIEW THE RESULTS: Once the solution has been calculated, we can use the ANSYS postprocessor to review the results. Two postprocessors are available: POST1 and POST 26. We use POST 1, the general postprocessor to review the results at one sub step over the entire model or selected portion of the model. We can obtain contour displays, deform shapes and tabular listings to review and interpret the results of the analysis. POST 1 offers many other capabilities, including error estimation, load case combination, calculation among results data and path operations. We use POST 26, the time history post processor, to review results at specific points in the model over all time steps. We can obtain graph plots of results, data vs. time and tabular listings. Other POST 26 capabilities include arithmetic calculations and complex algebra. In the solution of the analysis the computer takes over and solves the simultaneous set of equations that the finite element method generates, the results of the solution are • Nodal degree of freedom values, which form the primary solution • Derived values which form the element solution

5.7 MESHING: Before meshing the model and even before building the model, it is important to think about weather a free mesh or a mapped mesh is appropriate for the analysis. A free mesh has no restrictions in terms of element shapes and has no specified pattern applied to it. Compare to a free mesh, a mapped mesh is restricted in terms of the element shape it contains and the pattern of the mesh. A mapped area mesh contains either quadrilateral or only triangular elements, while a mapped volume mesh contains only hexahedron elements. If we want this type of mesh, we must build the geometry as series of fairly regular volumes and/or areas that can accept a mapped mesh.
FREE MESHING: In free meshing operation, no special requirements restrict the solid model. Any model geometry even if it is regular, can be meshed. The elements shapes used will depend on whether we are meshing areas or volumes. For area meshing, a free mesh can consist of only quadrilateral elements, only triangular elements, or a mixture of the two. For volume meshing, a free mesh is usually restricted to tetrahedral elements. Pyramid shaped elements may also be introduced in to the tetrahedral mesh for transitioning purposes.

MAPPED MESHING We can specify the program use all quadrilateral area elements, all triangular area elements or all hexahedra brick volume elements to generate a mapped mesh. Mapped meshing requires that an area or volume be “regular”, i.e., it must meet certain criteria. Mapped meshing is not supported when hard points are used. An area mapped mesh consists of either all quadrilateral elements or all triangular elements
For an area to accept a mapped mesh the following conditions must be satisfied: • The area must be bounded by either three or four lines • The area must have equal numbers of element divisions specified on opposite sides, or have divisions matching one transition mesh patterns. • If the area is bounded by three lines, the number of element divisions must be even and equal on all sides • The machine key must be set to mapped. This setting result in a mapped mesh of either all quadrilateral elements or all triangular elements depending on the current element type and shape key. • Area mapped meshes shows a basic area mapped mesh of all quadrilateral elements and a basic area mapped mesh of all triangular elements.

5.8 STRUCTURAL STATIC ANALYSIS: A static analysis calculates the effects of study loading conditions on a structure, while ignoring inertia and damping effects, such as those caused by time varying loads. A static analysis can however include steady inertia loads and time varying loads that can be approximated as static equivalent loads. Static analysis is used to determine the displacements, stresses, strains and forces in structures or components caused by loads that do not induce significant inertia and damping effects. Steady loading and response conditions are assumed, i.e. the loads and the structure’s responses are assumed to vary slowly with respect to time. The kinds of loading that can be applied in static analysis include: • Externally applied forces and pressures. • Steady state inertial forces • Imposed displacement • Temperatures • Fluences (for nuclear swelling)

Finite Element Analysis of the chassis assembly

Objective

To Objective of this analysis is to check the High stressed locations and deflections on the chassis for the pay load of 60 tonnes.

Material Properties:

Young’s Modulus (Ex)=2e5N/mm2

Poisson’s Ratio = 0.3

Density = 7850Tons/mm3

Element Type Used:

Solid 45

Number of Nodes: 8

Number of DOF: 3 (Ux, Uy, Uz)

SOLID45:

SOLID45 is used for the three-dimensional modeling of solid structures. 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 is defined by eight nodes and the orthotropic material properties. Orthotropic material directions correspond to the element coordinate directions.

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This element takes less CPU time for element stiffness formation and stress/strain calculations.

In Finite element model SOLID 45 elements have been used for the longitudinal members & cross members of the chassis.

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Figure 6.7 3D Model of the Chassis Assembly

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Figure 6.8 FE Model of the Chassis Assembly

Weight of 60tons is distributed on the four roller mountings equally. All DOF constrained at all the four sided of the chassis, where wheels are attached. Figure 6.9 shows the loading conditions on the chassis assembly.
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Figure 6.9 Loading conditions
Figure 6.10 shows the displacement plot of the chassis assembly. Maximum nodal displacement is 0.34mm.

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Figure 6.10 Displacement plot
Figure 6.11 shows the Von mises stress plot of the chassis assembly. Max. stress of 37Mpa is observed on the chassis due to a pay load of 60 tonnes..

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Figure 6.11 Von mises stress plot

Conclusions

➢ Performed design calculations for the chassis for a pay load of 60 tonnes .

➢ Performed 3d modelling of the Chassis

➢ Performed Finite Element analysis of the chassis.The max deflection observed in the analysis is 0.34mm.

➢ The maximum vonMises stress observed on the chassis is 37 Mpa.

➢ The yield strength of the material used for chassis manufacturing is 260N/mm2.

➢ From the above results it is concluded that chassis design is safe for a pay load of 60Tonnes.

REFERENCES

1. Pomulo Rossi Pinto Filho, “Automotive Frame Optimization”, Universidad Federal de Uberlandia. November 2003. 2. Murali M.R.Krisna,“Chassis Cross-Member Design Using Shape Optimization”, International Congress and Exposition Detroit, Michigan. February 23-26, 1998. 3. Marco Antonio Alves Jr, Helio Kitagawa and Celso Nogueira, “ Avoiding Structural Failure Via Fault Tolerant Control – An Apllication on a Truck Frame”, Detroit, Michigen November 18-20, 2002.

4. Lonny L. Thomson, Pipasu H. Soni, Srikanth Raju, E. Harry Law, “ The Effects of Chassis Flexibility on Roll Stiffness of a Winston Cup Race car”, Departmental of Mechanical Engineering, Clemson University, 1998

5. C.Cosme, A.Ghasemi, J.Gandevia, “Application of Computer Aided Engineering in the Design of Heavy-Duty Truck Frames”, SAE Paper 1999-01-3760, International Truck & Bus Meeting & Exposition, Detroit, Michigan, 1999.

6. “FEMtools Theoretical Manual”, Dynamic Design Solution NV, Leuven, Belgium, 2002

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