1. Financial analysis for vehicle program
What is needed?
Units
Description
Source
Sales demand estimate
Number of vehicles
How many vehicles can be sold?
Sales & marketing
Sales price estimate
$/unit
What is the customer willing to pay?
Sales & Marketing
Investment cost estimate
$$$$
Plant cost
Tooling cost
Engineering cost
Company overhead
Vehicle Engineering, Finance, Manufacturing & Assembly, Suppliers
Variable cost estimate
Material cost
Production cost including labor

2. Profit Analysis Profit = Revenue – cost Where
Revenue = selling price*number of vehicles sold
Cost = investment cost + variable cost* number of vehicles produced
Break even volume is the number of vehicles need to be sold so that there is no loss
Break even Volume = Investment cost/(selling price – variable cost)

3. Examples of Successful & Unsuccessful Programs
Entity
Estimate
Actual
Sales Volume
150,000
120,000
75,000
150, 000
Sale Price ($/unit)
22,000
18,000
Investment Cost ($)
500 M
Variable Cost ($/unit)
17,000
Total Profit (M$)
250 M
100 M
- 125 M
-350 M
Break even volume = 500,000,000/(22,000-17,000) = 100,000 vehicles

4. Your Calculations
Estimate selling price for your car from market survey
Estimate the number of vehicles that can be sold
Assume variable cost to be about X% of the selling price
Assume investment cost to be Y RM
Figure out break even volume and profit
Figure out a way to distribute investment and variable cost to systems
Investment
Cost
Variable
Cost
Body
Chassis
Powertrain
Climate Control
Electrical
Body
Chassis
Powertrain
Climate Control
Electrical

5. Weight Analysis Curb Weight : Weight of an assembled vehicle
Gross Vehicle Weight (GVW) = Curb weight + passenger & cargo weight
Corner weight = weight on each suspension
Curb
Weight
Body
Chassis
Powertrain
Climate Control
Electrical

6. Vehicle-fixed Coordinate System
ISO (International Standards Organization) coordinate system
Defines directions with respect to the vehicle

7. Forces Acting on a Car, Truck or Motorcycle
Gravity
Tire normal forces (loads)
Tire shear forces (driving or braking)
Aerodynamic forces and moments
D’Alembert (acceleration) forces
Trailer hitch loads

8. Static Loads
Sitting statically on a level surface:

9. Longitudinal Dynamics
Dynamic load transfer
Acceleration limits
Braking limits
Aerodynamic forces/moments

10. Acceleration at Low Speed
Acceleration on a level surface with no aerodynamic reactions

11. Climbing a Grade No aerodynamic or acceleration effects
For small angles: cosq = 1, sinq = q
q = Grade angle (in radians)

12. Aerodynamic Resistance Load
Aerodynamic drag load
DA = 0.5 ρ V2 CD A
Where:
CD = Aerodynamic drag Coefficient
ρ = Air density
A = Frontal Area of the vehicle

13. Tire Rolling Resistance Load
Rx = Rxf + Rxr = fr Wf + fr Wr
Where:
fr = Rolling Resistance Coefficient
Wr = Rear axle load
Wf = Front axle load
fr = or 0.01*(1+ V/160)
Where, V is vehicle speed in km/h

14. Powertrain Applications
Powertrain development
Architecture evaluation (FWD, RWD, 4WD)
Acceleration (0-100 kph, passing), top speed
Tuning (engine, torque converter, transmission matching)
Traction limits
Fuel economy

15. Powertrain Architecture
Traction-limited acceleration depends on loads on the drive wheels
I.e.,
Front wheel drive
Rear wheel drive
Four wheel drive

16. Powertrain Architecture
Components in a solid axle rear drive

17. Engine Dyno Performance
Steady speed; Wide Open Throttle (WOT)

18. Basic Acceleration Model
Simple acceleration model used by highway engineers
Acceleration is:
Proportional to power to weight ratio
Inversely proportional to speed

19. Example of Simple Model
Simple acceleration model used by highway engineers
It over-predicts performance with actual P/W ratios
Models are calibrated with effective P/W ratio
Simulated Vehicle (250 kw, 1833 kg, with all losses)
100% Efficient
50% Efficient

20. Tractive Force Performance
Tractive force vs. speed:
Reflects engine torque curve
Depends on gear
Low (1st) gear
High tractive effort
Limited speed range
Higher gears expand the speed range but reduce tractive effort
Multiple gears approximate constant engine power
Continuously variable transmission (CVT) can follow constant engine power curve

21. Acceleration Performance
(M+Mr) ax = T Ngf ηgf/r – Rx – DA – Rhx – W sinθ
Where
M = vehicle mass = W/g
Mr = equivalent mass of rotating components
ax = longitudinal acceleration
T = Engine Toerque
Ngf = combined ratio of transmission & final drive
ηgf = combined efficiency of transmission & final drive
Rx = Rolling resistance forces
DA = Aerodynamic forces
Rhx = Hitch forces
θ = Inclination angle
Mr = [(Ie+It)Ngf2 + IdNf2 + Iw]/r2 or Mr/M = 0.04Ngf Ngf2
and Ie,It and Iw are engine, transmission, axle inertias

22. Top Speed Calculation T Ngf ηgf/r >= Rx + DA + Rhx + W sinθ
If LHS > RHS, acceleration to higher speed is possible
LHS = RHS corresponds to top speed in that gear

23. Powertrain System Design
Aerodynamic Drag
Rolling Resistance
Climbing Grade
Mass, Driveline Inertias
Gear Inefficiencies
Uncontrolled
Variables
Vehicle
Acceleration
Top Speed
Engine torque/power
Transmission Gear Ratios
Final Drive Gear Ratio
Torque Converter
Tire Size
Tire Traction Limit
Axle Roll
Design Specifications

24. What is needed?
Procedure for calculating top speed and time to reach 100 km/h from 0
Procedure to calculate top speed
spreadsheet

25. Torque Converter Fluid coupling between engine and transmission
Stator:
Deflects return flow in direction of the impeller
Adds to torque of impeller
Turbine torque > engine torque
Zero output/input speed ratio is “stall”
Turbine input to transmission is typically two times engine torque

26. Differential

27. Differential Rules

28. Torques on a Chassis

29. Traction Limits

30. Differential Performance

31. Brake Systems Applications
Proportioning evaluation
Weight variations (curb weight to GVWR)
High and low friction
Testing for regulatory compliance (FMVSS 105, 121..)
Stability in braking (e.g., split mu, FMVSS 135)
Evaluating effect of partial system failures

32. Typical Braking System

33. Tire Slip

34. Wheel Lockup
Front wheel lockup will cause loss of ability to steer the vehicle
With rear wheel lockup, any yaw disturbance will initiate rotation of the vehicle making it unstable
Brake proportioning strategy should allow the front brakes to lock first if ABS is not provided

35. Anti-lock Brakes

36. FMVSS Regulatory Requirements
A fully loaded passenger car with new brakes will stop from speeds 30/60 mph in distance with average deceleration of 17/18 ft/s^2
A fully loaded passenger car with burnished brakes will stop from speeds 30/60/80 mph in distance with average deceleration of 17/19/18 ft/s^2
A lightly loaded passenger car with burnished brakes will stop from speeds 60 mph in distance with average deceleration of 20 ft/s^2
A fully and lightly loaded passenger car with brake failure will stop from speeds 60 mph in distance with average deceleration of 8.5 ft/s^2

37. Brake Proportioning
Maximum brake force an axle can carry without locking
μp(Wfs + Fxr*h/L)
Front Axle Fxmf =
1 – μp*h/L
μp(Wrs - Fxf*h/L)
Rear Axle Fxmr =
1 + μp*h/L
Where Fxf and Fxr are front and rear brake forces
Wfs and Wrs are front and rear static weights
μp is the peak brake coefficient
h is the c.g. height
L is the wheelbase

38. Brake Proportioning Brake Force Fx = Tb/r = G Pa/r Where
Fx is front or rear brake force (N)
Tb is front or rear brake torque (Nm)
r is the tire rolling radius (m)
G is front or rear brake gain (N.m/MPa)
Pa is brake application pressure

39. What is needed Explanation on how to draw braking limits on the chart
How to draw FMVSS requirement
How to draw applied brake force diagram
Brake pressure/brake torque relation
Brake proportion strategy graph

40. Performance Triangles
Front Lockup Boundary
2000
1500
Front Brake Force
Ideal Proportioning
Proportioning
Range
1000
Rear Lockup Boundary
500
500
1000
1500
2000
Rear Brake Force

41. Brake Proportioning

42. Braking Efficiency Eb = Dx/μp Where Eb is the braking efficiency
Dx is the actual deceleration
μp is the braking coefficient

43. Braking Efficiency Calculation
Assume front and rear brake proportioning strategy such as
Pf = Pa and Pr = 0.8 Pa
Calculate front and rear axle brake forces
Fxf = 2Gf*Pf/r and Fxr = 2Gr*Pr/r
Calculate deceleration Dx
Dx = (Fxf+Fxr)/W
Calculate front and rear axle loads
Wf = Wfs + (h/L)(W/g)Dx
Wr = Wrs – (h/L)(W/g)Dx
Calculate braking coefficients μf and μr
μf = Fxf/Wf and μr = Fxr/Wr
Calculate braking efficiency Eb
Eb = Dx/ (higher of μf or μr)
7. Increase Pa till desired level of Dx is reached

44. Brake System Design Vehicle Uncontrolled Variables
Aerodynamic Drag
Rolling Resistance
Mass, C.G., wheelbase
Uncontrolled
Variables
Vehicle
Deceleration
Efficiency
Locking Strategy
Brake Pressure
Brake Torque Gains
Brake Proportioning
Tire Size
Tire Friction Limit
Design Specifications

45. Energy/Power Absorption
Energy and power absorbed by the brake system during braking
E = MV2/2
P = MV2/(2ts)
Where
M is the mass of the vehicle
V is the initial speed
ts is the time to stop