Report Example - Car Suspension Design

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REDESIGN AND CALCULATION OF BRISTOL FIGHTER CAR’S SUSPENSION SYSTEM FINAL REPORT OF THE GROUND VEHICLE COURSE By : Group 4 Indria Herman(13102108) Yudha Azali(13102117) Robin(13103085)

MECHANICAL ENGINEERING ITB 2007

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CONTENTS CONTENTS ...................................................................................................................ii CHAPTER I INTRODUCTION ..................................................................................1 CHAPTER II BASIC THEORY ..................................................................................2 CHAPTER III BRISTOL FIGHTER CAR’S DATA ................................................8 3.1 Performance......................................................................................................9 3.2 Chassis, structure and safety.............................................................................10 3.3 Packaging..........................................................................................................10 3.4 Interior ..............................................................................................................11 3.5 Handling and Roadholding ...............................................................................11 3.6 Steering .............................................................................................................12 3.7 Brake.................................................................................................................12 3.8 Additional Information .....................................................................................13 CHAPTER IV CALCULATION .................................................................................14 CHAPTER V RESUME................................................................................................22 REFERENCES ..............................................................................................................23

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CHAPTER I INTRODUCTION Ground vehicle course is optional course which should be taken by the students who took the construction and design sub-major in Mechanical Engineering ITB. One of the part in this course cover about ride and handling of ground vehicle. This part describe about several considerations in order to have a comfort in riding and handling. On covering about ride and handling of ground vehicle, suspension system is the main system that become the basic consideration. Since suspension system has become the most influential factor that really important, nowadays, several modification have been implemented to have a better suspension system. In this part of ground vehicle course the students were introduced the basic knowledge about the definition of suspension system, the parameters that influence the characteristics of the suspension system, and the design and calculation of suspension system. By given about all of this material course, the students are expected to have a more comprehension which lead to a better skill if they were work in automotif bisnis. The most practical implementation of the suspension system theory are suspension system in car and motorcycle. In Order to accomplish the Ground Vehicle Course, students are divided inte groups. Each group consist of three students. Each group should make a report about the design calculation of a ground vehicle which they are choosen before. On this opportunity the writers choose the Bristol Fighter car which is sports car as a ground vehicle which suspension system will be analyzed and redesign..The information about the bristol city car is given by searching the web.

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CHAPTER II BASIC THEORY Suspension System Before we started about how to measure the suspension system parameters, let’s talk about what the suspension system used to. Suspension is the term given to the system of springs, shock absorbers and linkages that connects a vehicle to its wheels as can be seen in Picture 1. Suspension systems serve a dual purpose - contributing to the car's handling and braking for good active safety and driving pleasure, and keeping vehicle occupants comfortable and reasonably well isolated from road noise, bumps, and vibrations. The suspension also protects the vehicle itself and any cargo or luggage from damage and wear.

Picture 1. The Arrangement of the complete suspension system In suspension system, there are two main components that make us feel comfort in riding a vehicle: springs and shock absorbers/dampers. In this chapter, we won’t discuss about the types of the springs and dampers. We only talk about the properties of the suspension system: ‐

Spring rate/stiffness

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Spring rate is a major component in setting the vehicles ride height or its location in the suspension stroke. Vehicles which carry heavy loads will often have heavier than desired springs to compensate for the additional weight that would otherwise collapse a vehicle to the bottom of its travel (stroke). Heavier springs are also used in performance applications when the suspension is constantly forced to the bottom of its stroke causing a reduction in the useful amount of suspension travel which may lead to harsh bottoming. This may vary with deflection. For active suspensions, it may depend on other things. The softer the springs, the more important the other requirements are. Spring rate is often a compromise between comfort and handling, but when other things are compromised instead, as in the 1960s Lotus Elan, both may be achieved. ‐

Damping Damping is the control of motion or oscillation, as seen with the use of hydraulic gates and valves in a vehicles shock absorber. This may also vary, intentionally or unintentionally. Like spring rate, the optimal damping for comfort may be less than for control. Damping controls the travel speed and resistance of the vehicles suspension. An un-damped car will oscillate up and down. With proper damping levels, the car will settle back to a normal state in a minimal amount of time. Most damping in modern vehicles can be controlled by increasing or decreasing the resistance to fluid flow in the shock absorber.

Measurement On this assignment, we are using formulas from the book Fundamentals of Vehicle Dynamics by T. D. Gillespie and The Shock Absorber Handbook by J. C. Dixon to calculate the spring stiffness and damping characteristic of a car. From these books, we have received so much information about how to measure the spring stiffness and damping characteristic; the parameters; the assumption that we have to make; and the data that we must collect first before doing the calculation. To do this calculation; first of all, we must know about total weight of the vehicle including the passengers and their luggage that might be able to put on the car. For ground vehicle, the standard weight of one passenger is about 68 kilos with 7 kilos of GROUND VEHICLE COURSE FINAL REPORT

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luggage (for car). Next is we must know about the wheelbase of the car and the location of the center of gravity (CG). From this information, we could measure the mass that being distributed on the front wheels and the rear wheels. We could also measure the distance between the center of gravity to the front and rear wheels. All of this information is the main information that we must have in order to do this calculation. After received all of the information above, we should take an assumption about the natural frequency that we wanted to appear in our suspension system design. Usually we took the value about 1-1.5 Hz (human comfort zone) for the passenger car. From the natural frequency that we have chosen, we could measure the spring stiffness by using this formula:

k = 4π 2 f n m where :

k = spring stiffness/rate (N/m) fn = natural frequency (Hz) m = sprung mass (kg)

We could start this calculation from the front or from the rear wheels and then calculate the others based on Olley’s criteria.

Olley’s Criteria The Olley’s criteria are: 1. The front suspension should have a 30% lower ride rate than the rear suspension, or the spring center should be at least 6.5% of the wheelbase behind the CG.The geometry of the car can be seen in picture 2. Although this does not explicitly determine the front and rear natural frequencies, since the front-rear weight distribution on passenger cars is close to 50-50, it will generally assure that the rear frequency is greater than the front. The formula that related to this criteria is:

kf kr where :

≅

1 b 1.44 a

kf = front spring stiffness (N/m) kr = rear spring stiffness (N/m)

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a = distance between front suspension and CG (m) b = distance between rear suspension and CG (m)

Picture 2. Geometry of the car 2. The pitch and bounce frequencies should be less than 1.2 times the pitch frequency. For higher ratios, “interference kicks” resulting from the superposition of the two motions are likely. In general, this condition will be met for modern cars because the dynamic index is near unity with the wheels located near the forward and rearward extremes of the chassis.

f bounce < 1.2 f pitch Pitch is an angular motion of the car body with the center of rotation located between the wheelbases; while center of rotation of bounce located outside the wheelbase. This means that bounce is more likely a vertical motion; especially when the center of rotation located far away in front/rear of the car. In order to fulfill these criteria, we should do some earlier calculation:

α = (K f + K r ) / M

β = (K r b − K f a ) / M

γ = (K f a 2 + K r b 2 ) / Mk 2 k=

Iy M

→ radius of Gyration

Radius of Gyration could be measure using another calculation; that is:

k 2 = DI .a.b where :

k = radius of Gyration

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a = front-CG b = rear-CG DI = dynamic index (1.1 – 1.2) M = total mass To calculate the value of pitch and bounce frequency, we are using the formulas below:

ω1 =

(α + γ ) + (α − γ )2 / 4 + β 2 / k 2

ω2 =

(α + γ ) − (α − γ )2 / 4 + β 2 / k 2

2

2

Where the value of the frequency is:

f =

ω 2π

3. Neither frequency should be greater than 1.3 Hz, which means that the effective static deflection of the vehicle should exceed roughly 6 inches. 4. The roll frequency should be approximately equal to the pitch and bounce frequencies. In order to minimize roll vibrations, the natural frequency in roll needs to be low just as for the bounce and pitch modes.

Damping Coefficient Next thing that we should do is to calculate the value of the damper. The damping coefficient could be determined just using a simple formula:

ζ =

c 2 km

hence :

c = 2ζ km But before we calculate the value of the damping coefficient, we must first check the ridehandling parameter below:

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f RH = f 3 2ζ f RH = 1 ⇒ ride − optimized f RH = 2 ⇒ handling − optimized f RH = 1.25 − 1.75 ⇒ compromized − design where :

fRH = ride-handling parameter f = natural frequency of the suspension system ζ = damping ratio ζ = 0.2 – 0.4 → passenger car ζ = 0.4 – 1.0 → competition car

The value of ζ (damping ratio) can be assumed depending on what kind of car that we want to design.

Damping Force Characteristic Damping force characteristic described about how many forces that can be absorbed by the damper in certain condition. To design this characteristic, we must calculate the damping force in certain speed of the piston (inside the damper) with certain tension/compression force ratio (usually between 50/50 – 80/20). Therefore, we use the formula below:

F = ζ km × V where :

F = tension or compression force V = piston velocity

The basic standard of damping characteristic is by calculated the tension and compression forces at the velocity of the piston 0.05, 0.1, 0.3, and 0.6 m/s (both tension and compression) with tension/compression force ratio between 50/50 – 80/20.

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CHAPTER III BRISTOL FIGHTER CAR’S DATA In the Bristol’s car, the V-10 engine and transmission have been specially developed to suit Bristol requirements. The rest of the vehicle has been designed to meet the uniquely demanding requirements of a sports car capable of more than 200 miles an hour. Fighter is one of the very few cars ever designed where aerodynamic efficiency has been placed ahead of all other considerations. Innovative design features are shared with aircraft, high-speed missiles and even submarines. The teardrop form of the passenger area ensures the lowest possible lift and drag. It also offers uninterrupted all-round vision whilst the dramatic gullwing doors are an intelligent solution on a sporting car to ensure easy entry and exit even in confined spaces. Supremely elegant but with a steely hint of aggression, the Fighter is a perfect example of the beauty that inevitably results when form exactly follows function. This superior characteristic can be seen in picture 3.

Picture 3. Bristol fighter car’s aerodynamic design

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A summary about the technical and design features of Bristol Fighter car will be explained bellow. 3.1

Performance •

All-aluminium V-10 engine is unusually light and compact. Specific output of one horsepower per pound of weight sets a new benchmark for class.

•

Power output of 525 bhp increases further at very high speed due to aerodynamically induced supercharging effect. Maximum speed approximately 210 mph.

•

Excellent traction permits 0-60 mph in approximately 4 secs.

•

Generous torque, high gearing and low drag ensure pleasing fuel economy. Even our "lead-footed" factory test drivers regularly return over 20 mpg.

•

6-speed, close ratio manual gearbox allows 60 mph in first gear, 100 mph cruising at 2,450 rpm in 6th.

•

Engine produces an effortless flow of torque. Even at tickover there is 350 lb.ft (476 Nm) available. Generous peak torque of 525 lb.ft (714 Nm) is achieved at 4,200 rpm.

Picture 4. Chassis of the Bristol car

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Chassis, Structure and Safety •

Immensely strong chassis structure which can be seen in picture 4, with steel sill boxes and cross members, honeycomb aluminium floors, aluminium torsional bulkheads.

•

Inner structure in aluminium with hand formed aluminium outer body panels to ensure longevity.

•

Carbon fibre doors and tailgate ensure maximum stiffness and contribute to a lower centre of gravity.

•

Massive steel tube rollover structure and safety cage provides advanced levels of passenger protection in a really severe impact.

•

Optional four point racing type seatbelts.

•

As with expensive racing cars, Fighter is built over a steel surface plate enabling each part to be accurately positioned in three dimensions. There is thus none of the build up of tolerances that occur in mass produced and normal hand-built cars.

•

Use of aerospace materials and design techniques trim weight to a moderate 1,475 kg (3,310 lb).

•

3.3

Electronic tyre pressure monitors and alarms are a standard fitment. Packanging

•

Generous accommodation for occupants up to 6'7" tall. Ample electric adjustment for seats and steering wheel makes all sizes comfortable.

•

Boot area accessible from within and without, accommodates luggage for long distance touring or two large golf bags.

•

23-gallon (105 litre) fuel tank gives touring range in excess of 400 miles. 28.5gallon (130 litre) tank is optional.

•

In the event of tyre trouble a full sized spare tyre is standard so that you may safely and conveniently continue your journey.

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Genuinely compact external dimensions make driving in traffic or on challenging smaller roads a pleasure.

•

Panoramic visibility for maximum safety and driving enjoyment.

•

Turning circle rivals most city cars, 100% Ackerman steering geometry avoids unseemly tyre scrub.

•

8" ground clearance ahead of front wheels and 6" beneath car eliminates possibility of grounding over speed bumps or on steep driveways.

•

3.4

Sets new standards for space utilisation in fast cars. Interior

•

Modern and efficient in layout, stylish and elegant in appearance.

•

Extensive aircraft style instrumentation includes oil temperature and pressure, fuel system pressure, outside air temperature and engine hours displays.

•

Compact overhead aircraft-style console houses gauges and switch panel.

•

Special attention to tactile quality of switchgear.

•

Deeply bolstered armchair-type seats provide cosseting comfort with excellent lateral support in fast driving.

•

Excellent oddment space and access to luggage area from within.

•

Latest technology photo luminescent switch panels for glare-free operation at night.

•

Flawless soft hand stitched leather covers the interior surfaces.

•

Leather edge-bound Wilton carpeting with thick sound proofing layers.

•

Stylish gullwing doors make entry and exit a pleasure, especially in confined spaces.

3.5

Handling and Roadholding •

Front mid-engine design gives low polar moment of inertia for agile handling response.

•

52% of weight on rear wheels gives superior traction and braking performance.

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Unusually low centre of gravity minimises weight transfer and improves roadholding.

•

Fully independent double-wishbone suspension with coil-over racing type dampers for exceptional comfort and control.

•

Steering and suspension set entirely new standards for geometric precision and accuracy.

•

Fuel tank mounted around the centre of gravity to eliminate handling changes as fuel load varies.

•

Wide 285/40 x 18" tyres front and rear on 10" rims generate superb adhesion. Rated for speeds over 200 mph.

•

Every car individually set up to exact specification including adjusting to exact corner weights.

•

3.6

Adjustable electronic traction control fitted as standard. Steering

•

Rack and pinion with rapid 2.7 turns lock to lock.

•

Power assistance tailored to owner's individual preference.

•

Electric 4-way adjustable steering column. Unique steering wheel design enhances instrument visibility.

•

Steering mechanism optimised for accuracy and correct feedback.

•

Genuine feel of the road retained in slippery conditions.

3.7

Brakes •

Front 6-piston callipers with 343 x 32 mm ventilated discs.

•

Rear 4-piston callipers with 343 x 26 mm ventilated discs.

•

Careful thermodynamic design ensures freedom from fade in hard use.

•

Moderate servo assistance ensures progressive response and correct pedal feel.

•

Powerful separate emergency/parking brake callipers on rear.

•

All Bristol Cars are subject to continuous development and this specification can change and may differ from that outlined above.

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Additional Information •

FIGHTER 'S' (optional) Max power 628/660 bhp* at 5900 rpm. Max torque 580 lb.ft 3900 rpm. * Horsepower increases at high speed due to aerodynamic overpressure in inlet system

•

Drivetrain - 6-speed manual or optional 4-speed automatic. Final drive 3.07:1 with limited slip function.

•

Structure - Massively strong steel and aluminium platform chassis. Steel rollover safety cage. Aluminium exterior panels fanned by hand. Carbon fibre doors and tailgate.

•

Suspension - Front: unequal length wishbones with concentric spring/damper units. Anti-roll bar. Anti dive geometry. Rear: unequal length wishbones with supplementary toe control arm and concentric spring/damper units. Anti-roll bar. Anti-squat geometry.

•

brakes - Front: ventilated disc with six piston calipers. Rear: ventilated disc with four piston calipers. Servo assistance.

•

wheels - 18 X 10" forged aluminium

•

tyres - Front and Rear: 285/40 X 18. Spare: full size wheel and tyre. Space saver optional.

•

Fuel Capacity : 100 litres standard, normal range 350-500 miles. 135 litres optional range 425-650 miles.

•

Dimension - Length: 4420 mm. (14'6"). Width: 1795mm. (5'10") Height: 1345mm. (4'5") Wheelbase 2750mm. (9") Front track and Rear track: 1470mm. (4'10") Kerb Weight: 1540kg. (3450lb) Turning circle: 11.5m (37'9")

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CHAPTER IV CALCULATION 4.1

Stifness Spring Rate Calculation

Bristol Fighter Car’s Information : •

Total Sprung Mass → mtotal = 1540kg (vehicle + 2 passenger + luggage)

•

Wheel Base = 2,75 m

•

mrear = 0,52.mtotal (gives superior traction and breaking performance)

•

Maximum Torque is 580 lb.ft at 3900 rpm

Assumption : •

ζ = 0,4 ( passenger car )

•

Front natural frequencies = 1 Hz

•

Rear natural frequencies = 1,5 Hz

Criteria : •

Human comfort zone natural frequency between 1-1,5 Hz

•

Olley’s Criteria

The Olley Criteria : 1. The front suspension should have a 30% lower ride than the rear suspension. k front k rear

≅

1 a . 1.44 b

Rear sprung mass → mrear = 0,52.1540kg = 800,8kg Front sprung mass → m front = 1540kg − 800,8kg = 739,2kg

Front to central of gravities → a = L.

mrear 800,8kg = 2,75m. = 1,43m 1540kg mtotal

Rear to central of gravities → b = 2,75m − 1,43m = 1,32m GROUND VEHICLE COURSE FINAL REPORT

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k = 4.π 2 f n m Calculation starts with front sprung mass N m 1,43m b N k rear = k front .1,44. = 29182,4 .1,44. 1,32m a m N k rear = 45542 m ∴ f nrear = 1,44 Hz → comfort k front = 4π 2 (1Hz ) 2 (739,2kg ) = 29182,4

Calculation start with rear sprung mass

N m 1 a N 1 1,32m = 47421,5 . . k front = k rear . 1,44 b m 1,44 1,43m N k front = 30398,4 m ∴ f n front = 1,04 Hz → comfort k rear = 4π 2 (1,5 Hz ) 2 (800,8kg ) = 47421,5

Result N m N ⇒ 45542,2 − 47421,5 m

∴ k front ⇒ 29182,4 − 30398,4 ∴ k rear

2. Neither frequency should be greater than 1,3 Hz

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For convenience in the analysis the following parameters are defined :

α= β= γ =

k front + k rear M

(k rear .b ) − (k front .a ) M k front .a + k rear . .b 2

(

2

) (

)

M .k 2

Iy

radius of gyration → k =

M

= DI .a.b

Motion of a simple vehicle : ••

z + αz + βθ = 0

••

θ+ β

Z + γθ = 0 k2

vertical motion → z = Z sin ωt

with :

pitch motion → θ = θ sin ωt ∴ − Zω 2 sin ωt + αZ sin ωt + βθ sin ωt = 0

(α − ω )Z + βθ = 0 2

Z

θ

=−

β α −ω2

∴ −θω 2 sin ωt + Z

θ

=−

β k2

Z sin ωt + γθ sin ωt = 0

(

k2 γ −ω2

)

β

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β k 2 (γ − ω 2 ) − =− β α −ω2 β2 2 2 (α − ω )(γ − ω ) = 2 k

⎛ β2 ⎞ ω 4 + (α + γ )ω 2 + ⎜⎜ αγ − 2 ⎟⎟ = 0 k ⎠ ⎝

( ( α +γ) α + γ )2 (ω1,2 ) = ±

⎛ β 2 ⎞ (α + γ ) ⎜ ± − ⎜ αγ − 2 ⎟⎟ = 2 k ⎠ ⎝

2

2

4

ω1 =

(α + γ ) + (α − γ )2 − β 2

ω2 =

(α + γ ) − (α − γ )2 − β 2

2

k2

4

k2

4

2

(α − γ )2 − β 2

k2

4

Dynamic Index → DI=1,1 Radius of gyration → k = DI .a.b = Chose

α= β=

→ k front = 30398,4 N → k rear = 45542 N

k front + k rear M

=

(k γ =

front

) (

m

1540kg 45542 N

( =

.a 2 + k rear . .b 2 M .k 2

m

(30398,4 + 45542) N m

(k rear .b ) − (k front .a ) M

(1,1)(1,43m )(1,32m ) = 1,505m

m

= 49,312 sec − 2

) (

.1,32m − 30398,4 N

m

1540kg

.1,43m

) = 10,809 m

) = {45542 N m .(1,32m) }+ {30398,4 N m .(1,43m) } 2

1540kg (1,505m )

s2

2

2

γ = 41,882 sec − 2

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ω1 =

ω1 =

(α + γ ) + (α − γ )2 − β 2 2

k2

4

(49,312 + 41,882) sec 2

−2

+

{(49,312 − 41,882)sec

} − (10,809 m s )

−2 2

4

2

2

(1,505m )2

ω1 = 7,327 sec −1 → f 1 = 0,137 Hz

ω2 =

ω2 =

(α + γ ) − (α − γ )2 − β 2 2

4

(49,312 + 41,882) sec 2

k2

−2

−

{(49,312 − 41,882)sec 4

} − (10,809 m s )

−2 2

2

2

(1,505m )2

ω 2 = 6,125 sec −1 → f 2 = 0,163Hz

3. The pitch and bounce frequencies should be close together : the bounce frequency should be less than 1,2 times the pitch frequency.

f bounce < 1,2 f pitch

ω1 7,327 = = 1,196 → 1,196 < 1,2 ω 2 6,125

4. The roll frequency should be approximately equal to the pitch and bounce frequency.

4.2

Ride and Handling

Ride-handling parameter → f RH = f 3 2ζ f RH = 1 ⇒ ride - optimized

f RH = 2 ⇒ handling - optimized f RH = 1,25 − 1,75 ⇒ compromised – design

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Chose : •

Sport car → ζ = 0,45 ( first assumption is 0,4 )

•

f RH front = 1 ⇒ ride

•

f RH rear = 1,39 ⇒ compromised

4.2.1

Damping Coefficient Calculation

Damping calculation formula → ζ =

c 2 k .m

Front Damper : c f = 2ζ k front .m front = 2(0,45) 30398,4 N c f = 4266,275 kg

s

≈ 4,27 ton

m

.739,2kg

s

Rear Damper : c rear = 2ζ k rear .m rear = 2(0, 45) 45542 N c r = 5434,138 kg

4.2.2

s

≈ 5, 43 ton

m

.800,8kg

s

Damping Force Characteristic

Damping force F = ζ k .m.V where V = piston velocity Tension and compression damping force ratio Tension (m/s)

Compression (m/s)

Force ratio (T/C)

0.05

-0.05

50/50

0.1

-0.1

60/40

0.3

-0.3

70/30

0.6

-0.6

80/20

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Damping force calculation Speed(m/s) -0.6 -0.3 Tension -0.1 -0.05 0.05 0.1 Compression 0.3 0.6

front rear -2559.72 -1090.61 -3261 -1304.44 -1279.86 -767.81 -1630.5 -978.24 -426.62 -341.39 -543.5 -434.88 -213.31 -213.31 -271.75 -271.75 213.31 213.31 271.75 271.75 426.62 512.09 543.5 652.32 1279.86 1791.51 1630.5 2282.56 2559.72 4362.45 3261 5217.76

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Front Damping Characteristic ( total = left + right ) Front (Total left+right) Linear

Modif

5000 4000

damping force

3000 2000 1000 0 -0.8

-0.6

-0.4

-0.2

-1000

0

0.2

0.4

0.6

0.8

-2000 -3000 piston velocity

Rear Damping Characteristic ( total = left + right )

Rear (Total left+right) Linear

Modif

6000 5000

damping force

4000 3000 2000 1000 0 -0.8

-0.6

-0.4

-0.2

-1000 0

0.2

0.4

0.6

0.8

-2000 -3000 -4000 piston velocity

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CHAPTER V RESUME The redesign calculation of Bristol Figther car has accomplished. By satisfying the consideration of comfort in ride and handling based on the Olley’s Criteria, the characteristics of the suspension system of Bristol Fighter car are: 1. The value of spring stifnes are: → k front = 30398,4 N → k rear = 45542 N

m

m

2. The value of the damper coefficient are: Front Damper : cfront = 4, 27 ton Rear Damper : c rear = 5, 43 ton

s

s

3. The ratio of the pitch and bounce frequency is 1,19 < 1,2

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REFERENCES T. D. Gillespie, T. D. Gillespie, Fundamentals of Vehicle Fundamentals of Vehicle Dynamics, SAE, 1992 J. J. Reimpell & H. Stoll, The Automotive Chassis: Engineering Principles, SAE, 1996 J.C. Dixon, The Shock Absorber Handbook, SAE, 1999 R.Q.Riley,Automobile Ride, Handling, and Suspension Design,R.Q.Riley.Enterprise,1999

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