report on vehicle dynamics pdf
- 1. 1 1. INTRODUCTION Vehicle dynamics is the study of how the vehicle will react to driver inputs on a given road. Vehicle dynamics is a part of engineering primarily based on classical mechanics. Vehicles Wheels Motion Self-powered Dynamics Greek “DYNAMIS” power Vehicle Ride and Handling Ride is associated with comfort and grip Handling is associated with path following Driving task has two components: Command and control Acceleration forces, braking forces and steering forces acting on the vehicle are dynamic forces that depend upon the tyre-to-road friction. The amount of friction depends on the type and surface condition of tyre and road as well as the weight on the tyre. Control is lost on any wheel if the dynamic load exceeds the friction between tyre and road, because the tyre slips or skids. Ideally, the tyre should contact the ground squarely and should roll without my sidewise force or thrust. This is not practically possible with a moving automobile encountering road irregularities, wind gust, required directional control, changes in weight, acceleration and braking, and in addition the presence of movable suspension systems to absorb shock. Tyres encounter both large and small bumps as they roll over the road surface. Deflections due to small bumps are absorbed by the tyre, but the vertical deflections from the larger bumps are carried through the wheels, drums and bearings to the vehicle suspension system. Suspension, if designed for large deflection, absorbs these bumps and allows the body to run smooth. Suspension with limited deflection bounces the vehicle body. The suspension system, therefore, must not only absorb shock and support the automobile weight, but it keeps the tyre in contact with the road to ensure vehicle control. The suspension system, therefore, must not only absorb shock and support the automobile weight, but it keeps the tyre in contact with the road to ensure vehicle control. Its proper design produces minimum wear on the tyre and other parts of the suspension system.
- 2. 2 2. ASPECTS OF VEHICLE DYNAMICS Some attributes or aspects of vehicle dynamics are purely dynamic. These include: 1. Body flex 2. Body roll 3. Bump Steer 4. Bundorf analysis 5. Directional stability 6. Understeer, oversteer 7. Pitch 8. Roll 9. Yaw 10. Noise, vibration, and harshness 11. Ride quality 12. Speed wobble 13. Weight transfer and load transfer 2.1. BODY FLEX Body flex is a lack of rigidity in a motor vehicle's chassis. It is often something to be avoided by car manufacturers as higher levels of body flex is a sign of structural weakness, and means that the vehicle's suspension cannot work as efficiently - the body takes up some of the 'slack', rather than the parts of the car which were specifically designed for this purpose. A chassis that flexes may be prone to fatigue and further "softening" with use will eventually result in failure. 2.2. BODY ROLL Body roll is the load transfer of a vehicle towards the outside of a turn. When a vehicle is fitted with a suspension package, it works to keep the wheels or tracks in contact with the road, providing grip for the driver of the vehicle to control its direction. This suspension is compliant to some degree, allowing the vehicle body, which sits upon the suspension, to lean in the direction of the perceived centrifugal force acting upon the car. 2.3. BUMP STEER Bump steer or roll steer is the term for the tendency of the wheel of a car to steer itself as it moves through the suspension stroke. It is typically measured in degrees of steer per metre of upwards
- 3. 3 motion or degrees per foot. 2.4. BUNDORF ANALYSIS A Bundorf analysis is a measure of the characteristics of a vehicle that govern its understeer balance. The understeer is measured in units of degrees of additional yaw per g of lateral acceleration. 2.5. DIRECTIONAL STABILITY Directional stability is stability of a moving body or vehicle about an axis which is perpendicular to its direction of motion. Stability of a vehicle concerns itself with the tendency of a vehicle to return to its original direction in relation to the oncoming medium (water, air, road surface, etc.) when disturbed (rotated) away from that original direction. If a vehicle is directionally stable, a restoring moment is produced which is in a direction opposite to the rotational disturbance. This "pushes" the vehicle (in rotation) so as to return it to the original orientation, thus tending to keep the vehicle oriented in the original direction. 2.6. UNDERSTEER AND OVERSTEER Understeer and oversteer are vehicle dynamics terms used to describe the sensitivity of a vehicle to steering. Oversteer is what occurs when a car turns (steers) by more than the amount commanded by the driver. Conversely, understeer is what occurs when a car steers less than the amount commanded by the driver. Figure 1. Oversteer
- 4. 4 Figure 2. Understeer 2.7. PITCH Pitch is the front-and-rear motion of a car about an axis that extends from the left to right of a vehicle and trough the center of gravity, or transverse (side-to-side) Y - axis. Pitch is typically taken to be positive (+) for upward movement of the vehicle nose and negative (-) for downward movement of the vehicle nose. The effects of pitch will increase as a function of vehicle altitude. Pitch is happening in response to acceleration and deceleration forces, and is hard to flight. Figure 3. Pitching, Rolling, Yawing
- 5. 5 2.8. ROLL The rolling moment acts about the longitudinal axis and is produced by that side wind forces it has only minor influence on the vehicle stability depending on the suspension system. 2.9. YAW Angular oscillation of the vehicle about the vertical axis is called yawing. It is the vertical movement of the complete vehicle body so the complete body rises up and down and known as Bouncing. 2.10. NOISE, VIBRATION, AND HARSHNESS Noise, vibration, and harshness (NVH), also known as noise and vibration (N&V), is the study and modification of the noise and vibration characteristics of vehicles, particularly cars and trucks. While noise and vibration can be readily measured, harshness is a subjective quality, and is measured either via "jury" evaluations, or with analytical tools that can provide results reflecting human subjective impressions. These latter tools belong to the field known as "psychoacoustics." 2.11. RIDE QUALITY Ride quality refers to a vehicle's effectiveness in insulating the occupants from undulations in the road surface (e.g., bumps or corrugations). A vehicle with good ride quality provides a comfort for the driver and passengers. 2.12. SPEED WOBBLE Wobble, shimmy, tank-slapper, speed wobble, and even death wobble are all words and phrases used to describe a quick (4–10 Hz) oscillation of primarily just the steerable wheel(s) of a vehicle. 2.13. WEIGHT TRANSFER Mechanism Of weight transfer The mechanism (cause) of fractional weight transfer may be understood by the free body diagram showing forces and moments acting on a vehicle at the time of braking. From mechanics it is known that when a body is accelerated in a straight path, the inertia force IF acts on its centre of gravity (C.G.) and whose magnitude is given by : IF = m × f(= W G × f)
- 6. 6 where m is mass of the vehicle and f is its acceleration. The braking force FR acts on the road surface in the opposite direction to IF. When brakes are applied, the forces IF and FR form an anticlockwise couple whose tendency is to cause overturning effect on the vehicle. The magnitude of this overturning couple is given by C = W g × f × h However, the vehicle is not going to overturn due to a righting couple produced on the establishment of forces Q between the wheels and the ground .The directions of Q on front and rear wheels are such so as to cause clockwise moment of righting couple whose magnitude is Cright = Q × L Where L is the wheelbase of the vehicle. Its consequence is to increase the perpendicular reaction between front wheels and the ground by an amount equal to Q, and to decrease it between the rear wheels and the ground by the same amount. Initially the weight of the vehicle is shared equally by each wheel. In a 4-wheeler, it is W/4 which now becomes, W/4+Q on front wheels, and W/4-Q on rear wheels. It is thus seen that a fraction of vehicle weight is transferred to the front from the rear wheels. Figure 4. Forces and moments to explain as to why a part of weight is transferred on braking
- 7. 7 3. POWER AND TORQUE CHARACTERISTICS OF AUTOMOBILE Figure 5. Variation of IP, BP, FP and torque as a function of engine speed in rpm. 4. ENGINE POWER OUTPUT The charge (fresh fuel-air mixture) on ignition converts into gas, and impinges upon the piston inside the cylinder. This causes movement of the piston, and thus the work is done on it. The rate at which this work is done, is called power and is measured in terms of power (in kW) or horsepower (hp). An engine that can deliver 75 kgf-m of work in 1 second is known to be a 1 hp engine. Following types of powers are being quoted with reference/to engines. 1. Indicated power (IP) 2. Brake power (BP) 3. Frictional power (FP) 4. Taxable horsepower (THP) 5. Drawbar power (DHP) 4.1. INDICATED POWER The power developed inside the cylinder by combustion of gases is called indicated horsepower. An indicating device an oscilloscope is used to determine IP. This device measures the pressure in the cylinder by Electronic means during all the four piston stroke. IP = pLANk 1000 kW
- 8. 8 4.2. BRAKE POWER The power available at the crankshaft (for onward transmission to drive the vehicle) is called the brake power. Rating of automotive engines is done m terms of BP. Brake power can be measured by dynamometer. The brake horsepower of an engine is calculated by the following formula : BHP = 2πNT 4500 where N is in rpm and T in kgf-m. If N is in rps and T in Nm, then 4500 will be replaced by 1000 and power will be kW. Then it will be calculated by, BP = 2πNT 1000 4.3. FRICTION POWER Loss of power due to friction occurs at many places inside the engine despite proper lubrication. One of the major causes of this loss is friction between piston-rings and the cylinder. It normally accounts for about 75% of all frictional losses in the engine. Other sources of friction losses are crankpin and connecting rod big end joint, crankshaft and main bearings etc. Friction losses in an engine are expressed in terms of friction power (FP). This loss is less at low speed of an engine, and increases rapidly at higher speeds. Variation of frictional horsepower (a loss) as a function of engine speed is shown in Figure. It is related to indicated power and brake power by FP = IP - BP 4.4. TAXABLE HORSEPOWER The taxable horsepower (THP) rating of engines is used to assess engines for taxation purposes. It is also used to categorize engines on a uniform basis. To illustrate, we consider a race event of auto vehicles in which all types of vehicles ranging from mopeds, scooters, motorcycles, cars etc. are the participants. Question arises whether all these vehicles should run together, or they be grouped in different categories. It is expressed by THP = D2 N 2.5
- 9. 9 A logical answer is, of course, the latter alternative i.e. the participating vehicles should be grouped in different categories. This is similar to weightlifting or boxing games in which the players are grouped on the basis of their weights. Grouping of vehicles is done on the basis of their THP. Thus a 2- wheeler and a car will run in the same group if their engines are of the same THP rating . 4.5. DRAWBAR HORSEPOWER A larger proportion of brake horsepower goes waste in overcoming various resistances in a moving vehicle. Rest of the Power is utilized to propel the vehicle. This power which is utilized to propel the vehicle is known as drawbar horsepower (DHP). Thus DHP = BHP - RESISTANCES 5. AUTOMOTIVE RESISTANCES AND PROPULSIVE POWER The brake horsepower available at the crankshaft of an automotive engine is not fully utilized to Speed up the vehicle much of it goes waste to overcome various resistances which are given as under. 1. Road resistances: (a) Rolling resistance (b) Frictional resistances 2. Road gradient resistance 3. Air (or wind) resistance 4. Accelerating resistance 5.1. (a) Rolling Resistance It mainly occurs due to the deformation of road and tyre, and dissipation of energy through impact. The toning resistance depends upon, Mass of the vehicle Material of the road surface such as; asphalt, macadam, gravel, clay, wood or sand. Nature (quality) of the road surface such as poor, good, dry or wet. Material of the tyres Inflation of the tyres It is greater on soft muddy and sandy road than the hard, dry or wooden paving. Also it is less with pneumatic tyres than the solid tyres. It is directly proportional to the gross vehicle weight.
- 10. 10 The rolling resistance R, can be expressed by, Rr = Cr mg where Cr is rolling resistance constant and m is mass of the vehicle. The value of Cr, depends upon the condition of tyre and road surfaces in contact. A reasonable value of 0.015 may be taken for it when Rr, is expressed in newton and m in kilogram. The rolling resistance may also be determined empirically by the following formula which includes the effect of velocity V of the auto vehicle. Rr = (0.0112 + 0.00006V) mg Here Rr is in newton, m in kg and V in kmph. This formula has been suggested by General Motors Company of USA, and is valid for steady speed on level paved road. A comparison equations shows that the rolling resistance constant is related with the vehicle’s velocity as Cr = 0.0112 + 0.00006V Rolling resistance for different road surfaces and tyres can be approximated from the values given in Table for speeds between 20 to 50 kmph. Table 1. Road resistances for different road surfaces 5.1. (b) Frictional resistances Another kind of road resistance is frictional resistance that includes resistance due to transmission losses also. Such losses are owing to Lower gear efficiencies in first, second, and top gears. Churning of oil in gearbox and the rear axle system. Adhesion of tyre which is about 65% of the total losses in chassis. The frictional resistance R can be approximated by Rf =132.5 + 50.5 m
- 11. 11 The frictional resistance also depends upon the driving conditions driving habits and maintenance of the vehicle. Those losses are comparatively low in privately owned vehicles single hand driven vehicles and periodically maintained vehicles. 5.2. Road gradient resistance Slope (Gradient) of the road has considerable effect on the resistance to motion of the vehicle. The gradient resistance depends upon mass of the vehicle slope of the Road on which vehicle is moving The road gradient resistance Rg is expressed by Rg = mg sin θ where m is the mass of the vehicle and ϴ is slope of the road gradient resistance is higher on a steeper road than on the road with mild slope it is zero on the level road since ϴ is equal to zero for such roads. Figure 6. Gradeability of vehicle 5.3. Air (or wind) resistance The air resistance faced by an automobile depends upon Speed of the vehicle Size and shape of the vehicle Speed of moving air Direction of wind with respect to direction of the vehicles motion The effect of speed on the air resistance is illustrated in figure the air resistance varies such as the square of speed it means that if the speed is doubled the resistance increases by four times. For slow speed vehicles such as trucks and Lorries, the air resistance is small but for higher speed vehicles it is considerable.
- 12. 12 For racing cars, it is of paramount importance the air resistance Ra is expressed by :- Ra = Ca A V2 Figure 7. Effect of speed on Air resistance where Ca is coefficient of air resistance A is projected frontal area of the vehicle and V is speed of the vehicle if Ra is expressed in a Newton, A in square metre and V in kmph then value of Ca for different categories of auto vehicles as given below in the chart. Table 2. Value of Ca for different categories of auto vehicles 6. TRACTIVE RESISTANCE AND PROPELLING POWER The sum of the resistances discussed earlier is known as the tractive resistance RT and is considered at the axle of the vehicle. Thus Rt = Rr + Rf + Rg + Ra + Racc
- 13. 13 here Racc is the accelerating resistance expressed as a mf and is required when and the vehicle is to be accelerated now the power required to propel the vehicle can be determined as follows by finding the work required to be done at the axle. Thus, WR = RT × V (N-km/hr) = RT × V × 1000 60 × 60 watt therefore required power is obtained as : HP = RT × V × 1000 60 × 60 watt if the efficiency of transmission between the engine crankshaft and the driving axle is η HP = RT × V 60 × 60 × η The transmission efficiency is generally taken as 85 %. 7. MEASUREMENT OF THE TEST VEHICLES Many of the following tests are correlated against results from instrumented test vehicles. 7.1. BENCH TESTS 7.1.1. LOCATION OF CENTRE OF GRAVITY The location of centre of gravity of the test vehicle is determined in a longitudinal, lateral and vertical direction. Below, the longitudinal direction is called the x coordinate, the lateral direction y coordinate and the vertical direction z coordinate. The location of centre of gravity in the x and y directions is determined by measuring the four wheel loads by means of wheel-load scales, onto which the vehicle is placed. Alongside the overall weight of the vehicle determined in this way, the position of the centre of gravity in an x and y direction can be calculated with the known wheel base and track width variables by production of torque equilibria. The height of the centre of gravity is determined by weight displacement when lifting an axle. In this process, the brakes are released and the transmission is in neutral, through which the wheels can be freely turned. The efficiency lines of the axle loads pass through the wheel centre lines. To detect the axle load of the axle which has not been lifted, two wheel- load scales are used.
- 14. 14 Figure 8. Measurement of the vehicle’s centre-of-gravity height hcog As a function of the inclination of the vehicle, the axle loads on the front and rear axle change. The height h of the centre of gravity above the level passing through the front and rear wheel centre line can be calculated via the torque equilibrium around the rear wheel centre line from the difference of the axle loads and the angle of inclination of the vehicle in question: The dynamic wheel radius is measured with the vehicle at a standstill. 7.1.2. MOMENT OF INERTIA The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rotation rate. It is an extensive (additive) property: for a point mass the moment of inertia is just the mass times the square of the perpendicular distance to the rotation axis. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). Its simplest definition is the second moment of mass with respect to distance from an axis.
- 15. 15 Now that the location of centre of gravity is known, the moments of inertia (MOI) around the longitudinal, lateral and vertical axes can be measured. This is done by the vehicle oscillating around the corresponding axes at the centre of gravity of the vehicle against springs of a known stiffness. By measurement of the oscillation time T, the moments of inertia can be calculated with known spring stiffness. To determine the moments of inertia around the lateral axis of the vehicle, the vehicle is placed on a cutting line transverse to the direction of travel. The cutting line is aligned in such a way that the centre of gravity of the vehicle in a horizontal position of the vehicle is vertically above the cutting line. In the longitudinal direction of the vehicle, springs on which the vehicle supports itself via the auxiliary frame are clamped in at identical distances. Figure 9. Measurement of the MOI around the transversal vehicle axis Euler's theorem is used to calculate the moment of inertia of the vehicle/frame unit around the cutting line axis from the frequency of the oscillations of this system: This approach for the calculation of the moment of inertia holds for the entire vehicle/frame unit around the cutting line axis. In order to obtain the MOI for the vehicle around its lateral axis passing through the centre of gravity alone, two items obtained up to now must be subtracted:
- 16. 16 On the one hand, an item is contained corresponding to the MOI of the frame. To remove it from the result up to now, the measurement with the auxiliary frame alone is repeated and the moment of inertia of the frame around the cutting line axis ϴy,Frame is calculated. By subtracting Θy,Frame from the overall moment of inertia around the cutting line Θy, total, the moment of inertia of the vehicle alone around the cutting line axis. Θ y,Veh = Θ y,total – Θ y,Frame The second item having an influence on the moment of inertia around the lateral axis is the so-called “Steiner ratio” of the vehicle. The Steiner ratio results from the distance between the rotary axis of the cutting line and the required reference axis, the axis through the centre of gravity of the vehicle. By subtracting the Steiner ratio in , the moment of inertia in a lateral direction of the vehicle through the centre of gravity is determined. Θy,CoG = Θy,Veh -mVeh ∆h2 y,Veh Figure 10. Test-bench structure for the MOI measurement around the transversal axis 7.2. BRAKE FORCE DISTRIBUTION In the course of this study, the connection between brake pressure applied by the hydraulic unit of the brake and the resulting brake power on the wheel must be determined. During the driving tests held at a later point in time, there can be a deduction of the brake power actually existing on the wheels with the help of this ratio.
- 17. 17 These measurements are done on the “ABS test bench” of the ika. The ABS test bench has four sets of rollers driven independently of one another onto which the vehicle is placed. Thanks to a movable frame for the rollers for the rear axle, the test bench can be adjusted to various wheel bases. All four wheels are driven evenly via the rollers with a speed corresponding to a traction of 6.5 kph. The reaction torque and thus the effective brake power up to a maximum of 5 kN are measured by a force transmitter interposed between the drive unit support and the frame. A detection roller measures the actual wheel speed in order to switch the test bench off automatically in the event of excessive slip between the rollers and the wheel. A principal diagram of the ABS test bench is shown in Figure. Figure 11. ABS test-bench While the test is being held, the ABS test bench drives all four wheels evenly to start with. Thanks to a continuous operation of the brake pedal, the brake power on all the wheels is increased until the blocking of one axle results, by which the vehicle is lifted out of the contact rollers. During this process, the four wheel brake powers and the brake pressures are recorded, the two brake powers of one axle being identical. 7.3. DRIVING TESTS In order to be able to hold the driving tests to examine the test vehicles and specifically the vehicle dynamics controller, the vehicles are equipped with extensive measurement technique. All the measurement devices used and the measurement variables recorded by them are listed in below table.
- 18. 18 . Table 3. Driving test instruments 8. CONCLUSION 1. Enhance vehicle steerability and stability Steerability is enhanced in normal driving condition. Braking is involved only when the vehicle tends to instability 2. Precise steering control requires understanding of interaction between tyre and road. Treated as disturbance to be cancelled out. 3. Vehicle state estimation uses interaction between tire and road as source of information. Seen by observer as force that govern vehicle’s motion. 4. Vehicle dynamics are important to enable a good overall design of such a complex product as a vehicle intended for mass production at affordable cost for the customers.
- 19. 19 9. REFRENCES 1. K.M. Gupta, “Automobile Engineering” by Umesh Publications, Third Edition, Page no. 78-84, 87- 90,. 2. R.S. Khurmi, J.K. Gupta, “ Theory Of Machines” by S. Chand Publications, Third Edition Page no. 253-255. 3. K.M. Moeed, “Automobile Engineering” by Katson Publications, Revised Edition 2016, Page no. 63- 64. 4. J. J. Uicker; G. R. Pennock; J. E. Shigley (2003). Theory of Machines and Mechanisms (3rd ed.). New York: Oxford University Press. ISBN 9780195155983. 5. Marion, JB; Thornton, ST (1995). Classical dynamics of particles & systems (4th ed.). Thomson. ISBN 0-03-097302-3.