1 Longitudinal and lateral dynamics Lecturer dr. Arunas Tautkus Kaunas University of technology Powering the Future With Zero Emission and Human Powered Vehicles Terrassa
2 Content of lecture Basic terms and descriptions; Forces affecting a vehicle; Longitudinal and lateral dynamics of vehicles; Active Safety Systems which control forces of vehicles Electronic Stability-Program
3 Basic terms and descriptions
4 Basic terms and descriptions Force What is a Force? A force is a Push or a Pull that one body exerts on another.
5 Basic terms and descriptions Net Force The sum of the forces is called the net force.
6 Basic terms and descriptions Net Force Two forces acting in different directions. When the forces are equal and acting in different directions they balance each other out.
7 Basic terms and descriptions Weight The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, w = mg. At the Earth's surface, where g=9.8 m/s 2
9 Speed Speed is equal to distance travelled divided by the time taken. If s is the length of the path traveled until time t, the speed equals the time derivative of distance s:
10 Speed units Erasmus LLP Intensive Programme Basic terms and descriptions
11 Basic terms and descriptions Kinetic Energy Kinetic energy is a term that describes the energy a vehicle has due to its mass and speed. Kinetic energy is energy of motion. Kinetic energy = ½ (mass) x (velocity) 2
12 Basic terms and descriptions INERTIA Inertia is the resistance to change the direction or velocity of a body in motion.
13 Inertia moments Examples of inertia moments
14 Basic terms and descriptions Moments of Inertia A. Pitch the force felt in acceleration or braking movement around (Horizontal axis) of vehicle B. Roll the force felt in cornering, side to side movement (Lateral axis) of the vehicle C. Yaw the force felt in a spin movement around (Vertical axis) of the vehicle
15 Centripetal Force Any motion in a curved path represents accelerated motion, and requires a force directed toward the center of curvature of the path. This force is called the centripetal force.
16 Centrifugal Force Centrifugal Force
17 Basic terms and descriptions FRICTION Friction is defined as the resistance to motion between two surfaces. There are four basic types of friction. A. Static the holding force between two surfaces at rest; B. Sliding the resistance to motion between two surfaces which are moving across each other; C. Rolling the resistance to motion of a rolling object like a ball, cylinder or wheel; D. Internal the resistance to motion within elastic objects (tires get warm from internal friction as they flex);
18 Normal Forces and Frictional Forces Reaction Force From Ramp Friction Force Normal means perpendicular Normal Force Decompose Vector Weight of block Weight of block Friction Force = Normal Force (coefficient of friction) F friction = F normal μ - frictional coefficient
19 Tyre Friction Coefficient
20 Traction TRACTION Traction is defined as the adhesive friction of the tire to the road surface. There are three traction forces: 1) Driving Traction To accelerate the vehicle 2) Braking Traction To slow or stop the vehicle 3) Cornering Traction To turn the vehicle
21 Longitudinal and lateral dynamics of vehicles
22 SAE vehicle axis system
23 Moments affecting a vehicle
24 Moments affecting a vehicle
25 Moments affecting a vehicle
26 Forces affecting a vehicle
27 Forces affecting a vehicle If the car starts to slide on any of the wheels, that means that the lateral, motive or braking force exceeds the force that wheel can handle and then slides in lateral and or longitudinal axis
28 Longitudinal and lateral dynamics 1. Resistance a. Aerodynamic b. Rolling c. Up hill 2. Tractive Effort 3. Acceleration 4. Braking Force
29 Longitudinal dynamics. Resistance Resistance is defined as the force impeding vehicle motion. 1. Aerodynamic resistance 2. Rolling resistance 3. Up hill resistance
30 Aerodynamic Resistance R a Aerodynamic Resistance Composed of: 1. Turbulent air flow around vehicle body (85%) 2. Friction of air over vehicle body (12%) 3. Vehicle component resistance, from radiators and air vents (3%)
31 Aerodynamic Resistance R a
32 Aerodynamic Resistance. Drag force. The drag force is acting at height h D above the ground. F D = 0.5ρC D Av 2 ; Whereρ : - Atmospheric air density (= kg/m³) C D - Drag factor A - Area of vehicle frontal projection v speed of vehicle
33 Aerodynamic Resistance. Drag factor.
34 Aerodynamic Resistance. Lift force. The front lift force (F Lf = 0.5ρC Lf Av 2 ) and the rear lift force (F Lr = 0.5ρC Lr Av 2 ).
35 Aerodynamic Resistance. Aerodynamic lift and drag forces with different vehicle styles
36 Aerodynamic Resistance Rolling moment Pitching moment Yawing moment The result of air stream interacting with the vehicle is forces and moments.
37 Rolling Resistance R rl Composed primarily of : 1. Resistance from tire deformation ( 90%) 2. Tire penetration and surface compression ( 4%) 3. Tire slippage and air circulation around wheel( 6%) R rl f rl W Where: R rl f rl W - roling resistance coeficient; f W rl - weight of vehicle.
38 Up hill Resistance R g Composed of : Gravitational force acting on the vehicle: R g W sin g For small angles, R g W tan sin g tan g G R g WG tan g g
39 Up hill Resistance R g R g = W =
40 Up hill Resistance R g UP hill: 1- Increase the car motion resistance; R g = W sin (against the direction of motion) 2-Increase the load on rear axle and decrease the load on the front one. 3-Decrease the stopping distance when using the brakes
41 When you are driving uphill, the force of gravity is working against you. Your traction could be reduced depending upon road conditions.
42 Down hill effect on the car Down hill: 1- Increase the tractive force, 2- Increase the load on front axle and decrease the load on the rear one. 3- Increase the stopping distance when using the brakes
43 Traction Traction is defined as the adhesive friction of the tire to the road surface. There are three traction forces: 1) Driving Traction To accelerate the vehicle; 2) Braking Traction To slow or stop the vehicle; 3) Cornering Traction To turn the vehicle.
44 F t Erasmus LLP Intensive Programme Tractive force
45 Tractive force The net power available for accelerating the vehicle will be: P t = T t ω t = (η t T e )[(1 i)ω e ] = η t (1 i)p e The engine power (P e ) is the product of its torque (T e ) and angular velocity (ω e ): Where: Pe = T e ω e η t - The efficiency of a power transmission system. It is η t =0.93; i - slip of a power transmission system;
46 Braking forces
47 Braking forces From the previous figure we can define the total friction force (F f ), the total rolling resistance (F r ) and the net vertical force (F v ): F f = F ff + F fr = μf v F v = mg F Lf F Lr = mg F L = (1 F L mg)mg = (1 0.5ρC L Av 2 /mg)mg Where: ρ= atmospheric air density (= kg/m³); C DA = drag factor; C LA = lift factor; m= vehicle mass; g= gravitational acceleration(= m/s²); μ= tyre road friction coefficient; f r = rolling resistance coefficient
48 Weight transfer The major effect of the basic vehicle dimensions is weight transfer. Weight transfer is unavoidable. Weight transfers occur as a result of the chassis twisting around the car's roll centre.
49 Rear Weight transfer due to acceleration When you accelerate, the weight of the car is thrown backwards. This causes the rear suspension to compress slightly and increases the available grip at the rear tires.
50 Weight transfer The major effect of the basic vehicle dimensions is weight transfer. Weight transfer is unavoidable.
51 Forwards Weight transfer due to braking Weight transfers under braking are thus more likely to affect the balance of the car.
52 Weight transfer as a result of steering
53 Rollover forces Forces acting to roll over a vehicle
54 Maximum Speed on Banked Roadway
55 Maximum Speed on Banked Roadway Equation of maximum speed:
56 Active Safety Systems which control forces of vehicles
57 History of main safety systems We can see that the hydraulic brakes were designed only in ABS anti-lock braking system only in Electronics Stability program only in Today we can see a lot of safety systems, as: dynamic cruise control, lane assist and others.
58 Active Safety Systems Antilock braking system ABS; Traction control system TCS; Electronic Stability-Program.
59 Antilock Braking System Prevents the wheels from locking and thus allows avoiding obstacles; The vehicle remains under control even while braking on one-sided slippery road; The stopping distance is usually shortened compared to locked wheels.
60 Traction Control System TCS prevents the vehicle from skidding when accelerating too much in a turn.
61 Electronic Stability-Program
62 Electronic Stabilization Program (ESP) Audi, Volkswagen Erasmus LLP Intensive Programme Different names for ESP Electronic Stability Program (ESP) - Holden, HSV, Hyundai, Kia, Mercedes Benz, Jeep, Renault, Saab,Chrysler, Citroen, Maybach, Peugeot, Ssangyong Dynamic Stability Control (DSC) - Ford, FPV, BMW, Mazda, Land Rover, Aston Martin, Jaguar Vehicle Stability Control (VSC) Suzuki, Toyota Vehicle Dynamic Control (VDC)- Nissan, Subaru, Alfa Romeo Dynamic Stability And Traction Control (DSTC) - Volvo
63 ESP Electronic Stability Program What does ESP do? ESP actively enhances vehicle stability (staying in lane and in direction); Through interventions in the braking system or the engine management; To prevent critical situations (skidding), that might lead to an accident;
64 ESP Electronic Stability Program What is so special about ESP? ESP watches out: Surveys the vehicle s behavior (longitudinal and lateral dynamics); Watches the driver s commands (Steering angle, brake pressure, engine torque);
65 ESP Electronic Stability Program What is so special about ESP? ESP knows: recognizes critical situations in many cases before the driver does; considers the possible ways of intervening: Wheel-individual brake pressure application Intervention in the engine management
66 ESP Electronic Stability Program Why is ESP so important? Frequent cause for accidents: The driver loses control of his vehicle. I.e. through: Speeding; misinterpretation of the course or the road condition; sudden swerving.
67 ESP Electronic Stability Program The parts of the ESP are: Hydraulic modulator with ESP ECU and integrated hydraulic valves (1) Wheel brakes and wheel-speed sensors (2) Steering wheel angle sensor (3) Yaw sensor with acceleration sensor (4) Engine management ECU (5) Brake master cylinder (6).
68 ESP Electronic Stability Program The input parameters of the ESP system are: Longitudinal velocity Lateral acceleration Yaw rate Brake pressure Throttle pedal position Steering wheel angle
69 ESP Electronic Stability Program How does ESP work? (1) ESP analyzes: What is the driver s intention? Position of the steering wheel + wheel speed + position of the accelerator + brake pressure = ECU recognizes driver s intention Steering Wheel Brake Pedal Wheel
70 ESP Electronic Stability Program How does ESP work? (2) ESP examines: How does the vehicle behave? Yaw speed + Lateral forces = ECU calculates the vehicle s behaviour.
71 ESP Electronic Stability Program ESP acts: It steers through brake-application The ECU calculates the required measures The hydraulic unit quickly and individually supplies the brake pressure for each wheel In addition, ESP can reduce the engine torque via connection to the motor management
72 ESP Electronic Stability Program In what situations is ESP needed? Examples: Avoiding an obstacle; Sudden wrenching of the steering wheel; Driving on varying road surfaces (especially important on the ice or snow surfaces);
73 ESP Electronic Stability Program The Electronic Stability Program keeps car safely on track.
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