MEC 540 Final Project

7/26/2019 MEC 540 Final Project

http://slidepdf.com/reader/full/mec-540-final-project 1/18

Design optimization of Composite Bicycle frame using HyperMesh and OptiStruct

Plinio Guzman

107885638

MEC 540

In this paper I explore the theory of mechanics of structures and composites and couple it with

techniques of Finite Element Analysis in order to study the parameters that come into play in

the design of a bicycle frame. The research uses a bicycle frame as a focal point for the

knowledge to gravitate around, but the learning and results of this project can be generalized

to have a wide range of applications in fields relating to the optimization of structural design

using composite materials. Thinking in terms of bicycles gives me a more tangible feel for these

topics and helps me better understand them. I hope you as a reader have a similar experience.

Introduction

Bicycles are a mainstream means of transportation and recreation. They are found amid busy

streets of dense urban centers, on seemingly endless roads that stretch out alongside

breathtaking sceneries, and across remote mountaintops that only some dare to ride. As a

result of the various disciplines, terrains, riders and riding styles that exist, there is no universal

truth to what makes the perfect bicycle. In this paper I will incorporate theoretical principles

with computational techniques with the intention of designing a bicycle frame.



More than any other part, the frame is what gives a bicycle its distinct feel. It determines the

handling of a bike and the way it behaves in corners and at high speeds. Up to the beginning of

the last decade, bicycle design used to be a trial and error process in which new models were

made based on a combination of what had worked in the past and heuristics. With the

development of new materials and computational tools, engineers are now able to fine tune

design parameters of their choosing in an attempt to make the best bicycle possible.

Finite Element Analysis integrates the theoretical understanding of the behavior of materials

with computational techniques to create an interactive visual environment to analyze

performance. This allows engineers to know how particular design is going to behave before

having to actually build it. This is a time and money saving technique, as it allows designers to

quickly and inexpensively go through several iterations of ideas while searching for an optimal

design. It has become a standard methodology for pre-production analysis.

Altair HyperWorks is a high-performance Finite Element Analysis software used in the

engineering industry to model, visualize, analyze and optimize design problems. It offers

modules directed toward the study of structures, motion, composites and optimization, which I

use throughout this study.

Bicycle Design

The ultimate goal of bicycle design is to maximize how much of the rider's input energy is used

to promote forward motion. That is to say, to make bicycles that can be ridden faster and for

longer, not to mention, that are comfortable and less prone to breaking. Bicycles must meet

safety and performance requirements as well as in some cases comply with design regulations

set by authorities such as the Union Cycliste International.

Owing to improvements in the field of composites, industries ranging from aeronautics to naval

have adopted these improved materials to make lighter, stronger and more durable

components that are better apt to meet the needs of specific applications. The use of

composites in these industries can be traced back as far as 1940. More recently, the bicycle

industry has began to use composite materials to replace heavy steel and aluminum tubing in

the making of frames; notably carbon fiber.

Traditionally bicycle frames have been made out of aluminum and steel but, thanks to advent

technological advances in composite manufacturing, the cycling industry has been shifting its

focus into implementing composite materials into the manufacturing of components. Forexample, a carbon/epoxy bicycle frame can be made to weigh less than a kilogram, compared

to the average aluminum frame weighing around 5 kilograms.

In addition to shaving weight, composite materials allow bicycles to have improved elastic

properties. Based on how you manufacture composites you can customize how much they

bend and how much they resist bending; these properties are called compliance and stiffness,

respectively, and are opposites of each other. Because energy is most efficiently transferred



through stiff members, a torsionally stiff bottom bracket and head tube are desirable. although

it may not be noticeable, if a frame has a tendency to twist from side to side with each pedal

stroke the rider will expend unnecessary energy. In addition to conserving energy, lateral

stiffness also provides better handling. Improved in-plane vertical compliance means that the

bicycle can flex up and down a little in order to absorb sudden shocks and vibrations for the

road, ultimately resulting in a more comfortable and stable ride.

Composite Materials

Several materials can be combined in different configurations to create composite materials

which can be given enhanced properties than those found in each one of the composing

materials individually. Such is the case with carbon fiber, which is made by bounding a series of

long thin fibers of carbon with epoxy to create a lamina. By themselves, epoxy and carbon are

rather weak materials, but by strategically combining them they can be given properties that

surpass those of common metals.

When manufacturing composites using unidirectional fiber composites, each lamina can be

arranged with a different orientation. The overall fiber layup can therefore be tailored to

optimize the behavior of the structure it composes.

Using HyperWorks I find optimal the fiber orientation and layer thickness to better respond to

the loading conditions.

Force Analysis

The frame of the bicycle is the main structure designed to support the main external loads. A

pedaling force from the rider is transmitted through a chain mechanism and is made to rotate arear wheel thus propelling the bicycle and rider forward. Doing a simplified analysis of the

transmission of power the bicycle experiences it can be seen that forces come from the rider at

five key locations: two at the handlebar, one on each pedal and one on the saddle. As the rider

shifts position . A rider may alternate between sitting and standing positions effectively shifting

his weight between the front and read of the bicycle, as well as vary the application of forces

from side to side. During intense pedaling a left pedal stroke is couple with a downward and

upward force on the left and right end of the handlebar respectively.

An often overlooked point noted by L Maestrelli in [] is that due to the standard placement of

the chain on the right side of the bicycle causes that the loading conditions associated to thepush of the right and left pedal are asymmetric.

There is a contact point at the location where each wheel meets the ground. At each of these

contact points the play of forces aboard the bicycle is countered by a normal force and a

traction force perpendicular to the direction of travel of the wheel. The balance of forces and

its relationship to the geometry of the bicycle determines the direction of travel or whether the

bicycle is able to stay up or go around turns.



Structural Analysis

It is important to overstate the importance of structural analysis of the frame when designing a

bicycle. The strength and stiffness of a bicycle can be predicted and modified by coupling the

theoretical understanding of mechanics of composites and structures with the use of computermodeling techniques such as Finite Element Analysis.



Motivations

Design lighter bikes that can be ridden faster and for longer.

Optimize performance, minimize weight.

Flexing of rear triangle to absorb shock.



Hypermesh

The bicycle frame model was designed on SolidWorks based on the general dimensions of a

Rocky Mountan Blizzard bicycle.

Each tube that composes the frame was considered as an individual section.



Based on the paper by Maestrelli loading is considered to be asymmetric about the main axis

due to the chain being located on the right hand side of the bicycle.

Bottom bracket concentrated loading from rider’s weight as well as a moment



Material

The material used for this simmulation is AS4/3502-6 carbonn fiber, and its properties are as

follows:

AS4/3502-6

t=0.005

E1=20.6e6

E2=1.42e6

V12=0.3

G12=0.87e6

XT=330e3

XC=-180e3

YT=7.5e3

YC=-35e3

S=14e3



Deflection analysis



Optimization

Finite Element Structural Optimization methods are ways of applying traditional optimization

algorithms to structural design problems using Finite Element Analysis. Compared to standard

mathematical techniques these methods have the advantage of being able to analyze

otherwise cumbersome numerical problems and of providing a visual representation of theoptimal results. [Marco Cavazzuti]

Common optimization methods in mechanical engineering

Topology optimization

Topometry optimization

Topography optimization

Size optimization

Shape optimization

As with the numerical methods, necessary elements used for structural optimization are:

Design space (mesh)

Variables (thickness, angle, mass…)

Optimization constraints, measurement (stiffness, displacement, stress, strain, failure

(hill, etc))

Objective function(min/max/minmax/maxmin) Minimize mass, maximize vertical

compliance, maximize lateral stiffness, etc

Optimization Algorithm (gradient based, mma)

In the case of topology, topometry, topography(2D or shell elements), and sizeoptimization the element density can vary between 0 (void) and 1 (present)



Optimization

Objective: Minimize Volume (mass) of chain stay

Constraint: Displacement

Lower bound=1.4

Upper bound=2.4

Variables: thk1, thk2, thk3, thk4

The 7 layers are symmetric about the middle axis. This results in there being 4 different ply

orientations, 3 of which have a corresponding match about the mid-plane. This allows for the

use of only 4 design variables, which simplifies calculations.



Optimization results

Through the OptiStruct Module the objective function was minimized throughout 15 iterations.

The volume of the chain stay can be seen to go from around 1.3 to 0.626 cm^3.

It can be seen that in iteration 4 and 8 the maximum constraint on displacement was violated.

The thickness was reduced too much which caused the displacement to go over the constrain

limit.



The following image shows the final thickness of each set of layers. The results show that themid plane should be the thickest layer.



Conclusion

The analysis shows results that are numerically off to those that would apply to a real life

model, but give insight to how much effect each variable has in the behavior of the frame.

There is more work and learning to be done in order to improve the modeling and optimization.

In the future a large part of the frame will be created using simplified hollow pipe structures

directly on HyperMesh to avoid the meshing complications that file importing brought along.



Literature Review

An early use of Finite Element Methods for bicycle design was done by Paterson and Londry in

1986 [] who represented a tubular frame structure using eulerian beam elements and

measured their respective deflection, von Mises stress and strain energy under various loadingconditions. Their rudimentary study laid down important grounndwork and proved the

usefulness of FEM techniques in the design of bicycle frames. Their findings showed that energy

dissipation in the vertical direction could be increased with minimal negative effect on hill

climbing when pedaling out of the saddle and that the down tube was the greatest ebsorber of

train energy.

In 1994 Lessard et al also modeled tubular frames using beam elements and compared the

analysis of several frame designs to experimental measurements, focusing on maximizing the

vertical compliance and lateral stiffness. He emphasized that in the classical tubular diamond

shape frame structure problems arose at the junction between tubes.. In his study Lessard

studied and identified the boundary conditions that a frame would encounter during realistic

riding conditions, and narrowed them down to three generalized loading cases: braking, front

impact, and stand up peadling. He used arbitrary loads and comments that the choice of load to

apply is arbitrary since he was only studying displacement and the tests are done within the

elastic limit of the material.

He suggests that composite bicycle frames should be composed of a monocoque structure in

which loads are supported through a low mass skin of a large surface area, therefore improving

stiffness characteristics. Because the ideal racing frame should effectively transfer human

energyt hat the rider puts into the pedals and handlebar with minimal losses due to the frame.

He suggests a torsionally stiff bottom bracket and head tube, as energy is most effectivelytransfered through stiff members. He adds that the frame should allow for in-plane vertical

compliance to dissipate road surface forces. Lessard comments that there is room for study of

the relationship between quantifiable frame stiffness characteristics and qualitative description

of the experience of the rider.

Derek Covill used parametric finite element analysis of bicycle frame geometries to study the

vertical compliance and lateral stiffness characteristics of 82 existing bicycle frames. His results

showed that smaller frames behave most favourably in terms of vertical compliance and lateral

stiffness, and that a shorter top tube length and larger head tube angle result ina laterally stiffer frame. He suggests that there is further room for development of the study

regarding a more detailed tube geometry, the use of alternative materials, and analysis of of

other structural characteristics.

Paolo Balisedra used the FEM software HyperMesh to study four different bicycle fork designs

and used eight different quasi-isotrpoic laminates generated using the HyperLaminate module.

He notes that the virtual model represents an ideal component and neglects possible defects



that may occurr during the manufacturing process such as porosity, wavyness or ply drops. The

results were used to validate the use of a manufactured frame which was subsequently used

for races through a total distance of around 500 km. The fork was later submitted to lateral

static load tests and showed no significant redution in stiffness.

Noting the incorrect assumptions that can be made about the location of stresses on a bicycleduring real riding conditions, professional cycling company Cervelo created an instrumented

'strain gage' bike outfitted with sensors and 'ridden hard'. They accounted for different

situations and riding styles in their tests and concluded that bending and torsion loads were

distributed differently than previously believed. Being a private company these results were not

released to the public.

Cervelo's analysis showed that a large 1.2 inch axle increased the stiffness of the bottom

bracket and allowed the seat tube and down tube to be lighter as well, at a lower weight. They

cite that they use carbon/epoxy prepreg of diferent moduli (supplied by Ntwport Adhesives and

Composites and Nippon Graphite Fiber Corp.) in different areas of the frame to tailor the

mechanical properties of each section, and use a fiberglass scrim in the places where the

carbon layup comes in contact with metal components.

Cervelo manufactures the frame's top tube, head tube, down tube, seat tube and bottom

bracket as a monocoque shell, and chain stay and seat stay molded as separate pieces; using

inflatable latex bladders to achieve an accurate fiber architecture and a consistent all thickness.

Xiang introduces in 2011 the principles of biomechanics and ergonomic knowledge, noting that

feature parameters of the rider are often not included in the frame design. He defines the

relative position between the saddle, the handlebar and the central axis as the bicycle'sthreepivot and uses it as a main parameter in order to improve rider confort. The optimization

goal of his methods is to keep the rider comfortable by maintaining the back muscles in a

relaxation state and minimizing leg fatigue.

MEC 540 Final Project

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