4 Accelerazione/decelerazione (marcia in rettilineo) F = m x aTRCZona di stabilitàLimite FisicoF = m x a < l x m x gAcceleration, decelerationTo change a vehicle speed (acceleration or deceleration) or its direction, a force is needed.Accelerating or decelerating:F = m . a Where m = vehicle mass and a = acceleration (+ or -)This force is transmitted to the road surface through the tires. The braking force and the accelerating force are proportional to the weight of the car times the friction coefficient. Since the weight is equal to the mass times g (acceleration of gravity), the maximum force, which can be transmitted equals:Fmax = µl . m. g . k**k = vehicle weight on the used wheels/ total vehicle weight. (rear spoilers on racing cars increase the load on the traction wheels)g = 9,81 m/s²µl = friction coefficient between road and tire (In longitudinal direction)From this can be concluded that every 2WD car can brake faster as it can accelerate (independent from engine power).Q: If Porsche claims that the 911 is able to stop in 5 sec. from 200 km/h to 0; What kind of deceleration is than required, and which µ it could be possible?ABSF = m x aDecelerazione
5 Accelerazione laterale (marcia in curva) F = m x aLimite FisicoF = m x v2/r < l x m x gTRCZona di stabilitàCurvaVSCVSCCurvaFc = m x v2/rCorneringTo control cornering in a safe way, the VSC system is used.Cornering creates a centrifugal force the vehicle has to withstand:Fc = m . v²/r , where v = vehicle speed and r = corner radiusMaximum force, which can be transmitted through the tires: Fmax s .m.gFmax = m. vmax²/ r and Fmax = .m.gSo vmax = µr . r . gDuring braking, accelerating and cornering, the vehicle behaviour is always limited by the friction coefficient between tire and road surface.Tire and road surface are the most important items when we are talking about vehicles possibilities.Even if a vehicle is equipped with the most advanced and high-tech systems is NOT able to go faster through a corner, brake shorter or accelerate faster as that same vehicle w/o these systems.ABSF = m x aDecelerazione
6 Riferimenti Slittamento: Decelerazione: S=(vV-vW)/ vV Dove: S=SlittamentovV=velocità veicolovW=velocità ruoteDecelerazione:a=(v1-v2)/ta=decelerazionev1=velocità inizialev2=velocità finalet=tempo impiegato per passare da v1 a v2
7 Coefficiente d’attrito (marcia in rettilineo) StabileInstabileIntervallo di slittamentotollerato dall’ABSForza frenante:Fb= b.m.gSlip = 10÷30% Fb = max.Asfalto asciuttoCoefficente di attrito in frenata bAsfalto bagnatoSlip = v vehicle – v wheel %v vehicleThis is the most famous graph used to discus all systems to control vehicle stability under the 3 circumstances, such as braking, accelerating and turning (see 2 slides further).Since tires deform due to the force(s) applied on it, is it impossible to transmit any force without slip. Remarkable is that the highest friction coefficient is reached with a slip between 10 and 30%, depending on road surface, tire construction and vehicle speed. Once over this critical slip, the coefficient drops.The friction coefficient on dry concrete is about 10 times higher than it is on ice. (Dry concrete: +/- 1,0 – Ice: +/- 0,1)These phenomena can be explained by the characteristics of rubber friction. With this type of materials (viscous-elastic) tensions and deformations create a combination of viscous and elastic behavior. Therefore a tire should not be seen as a spring with a constant spring force, but as a combination of a spring and a liquid damper. This means that the internal tensions not only depending on the deformation, but also on the speed in which these deformations occur.Ghiaccio102030406080100Rapporto di slittamento (%)BloccaggioRotolamento
8 Coefficiente di attrito (longitudinale) max1,0Slittamento criticoCoefficiente d’attrito-40%s0,5Attrito di rotolamentoAttrito di slittamentoSlittamento di scorrimento Fs = s.m.gRubber is a visco-elastic material: It can be represented by a spring combined with a hydraulic damper.Rubber friction can be divided into adhesion and hysteresis.The adhesion is the phenomena that the outer atoms of the deformed molecule structures of the rubber are in direct contact with the structured atoms of the road.Due to the relative speed difference between rubber and road (slip), the molecule structures are expanded and atom bindings are torn apart. After that, the molecule structure recovers and takes other atoms in its outer orbits. This component of friction force reaches its maximum at a speed difference between tire and road of 0,05 m/s and remains constant at higher speeds. Due to the fact the relative share of adhesion to the total slip reduces until negligible values, µ reaches its max. at a slip around 20%.The hysteresis component is the result of the deformation of the rubber of the tire. Due to the internal damping, compression of rubber costs more energy than the expansion of it. The energy difference as a result of this hysteresis is dissipated as heat, and is compensated by a force, opposite to the direction of travel.When the slip increases to 100%, the sliding friction by hysteresis has by far the biggest share in the total friction and reaches a coefficient of 40% less than the maximum.In short terms we can say that the max. possible force that can be transmitted from tire to road surface, is reached at the point µl is maximum.For acceleration (TRC) and deceleration (ABS) this is where slip is around 20%. For cornering or side slip, due to the construction of the tire, a different µ (µr) is reached, although the graph shape, based on the properties of rubber would be the same, if a certain % side slip was expressed on the axis.20406080100Slittamento longitudinaleSlittamento di deformazione Fr = r.m.g
9 Coefficiente d’attrito (marcia in curva) Intervallo di slittamentotollerato dall’ABSForza di aderanza laterale:Fs= s.m.gSlip* = 0% s = max. Fs = max.Slip* = 100% s = 0 Fs = 0*riferito allo slittamentolongitudinaleCoefficiente d’attrito in curva s Coefficente di attrito in frenata bAsfalto asciuttoSince µs (in lateral direction) is expressed in relation to longitudinal slip, maximum side force is reached when the slip is 0% and becomes 0 when the slip is 100%.Maximum side force is at 0% slip ratio in longitudinal direction.Asfalto bagnatoGhiaccio20406080100Rapporto di slittamento (%)
10 Massima trazione o massima forza frenante Cerchio di KammDirezione di marcia teoricaFmax= maxxmxgmax al 20% dello slittamentoLimite di aderenza del pneumaticoFmaxFS (forza laterale)Kamm's Circle is a model illustrating the distribution of forces on the wheels and the connection between dynamic driving forces and friction.The surface of the circle represents the contact surface between the tire and the road. The radius of the circle represents the strength of the grip force, so the circumference of the circle represents the limit to the tire's grip (Fmax = . m .g). The power vector, resulting from the combination of the two adds up (Fb and Fs), provides the total force Fr acting on the tires. Should this arrow extend beyond the circle, the force involved is greater than the grip of the wheels and the car will start to drift .In the circle diagram (circle of Kamm), the size and direction of the resulting force of braking / traction and cornering can be easily displayed.Maximum brake or acceleration force is with the 20% slip. If in this case side force is added, the vector result of the two forces will be out of the circle……more than 20% longitudinal slip and also side slip.From this circle it becomes clear that when a side force is combined with the maximum braking force (steering during emergency brake operation), the vehicle will drift.Q: Which situation is this, understeer or oversteer?Massima trazione o massima forza frenanteFB (forza fenante)FR (forza risultante)
11 Cerchio di Kamm Direzione di marcia teorica Fmax Fd max, Fb max ≠ Fs maxLimite di aderenza del pneumaticoFmaxFS (forza laterale)Since maximum side force, braking force and accelerating (drive) force are all different in size, the circle should actually be an ellipse.FR (forza risultante)Massima trazione o massima forza frenanteFB (forza fenante)Max forza di aderenza laterale
12 Cerchio di KammDal momento che la forza laterale (FS), la forza frenate (FB) e la trazione sono diverse, il cerchio di Kamm diventa un’ellisse.Es. dati:m=1500kg (massa veicolo)=0,2 (coefficiente d’attrito)r=100m (raggio di curvatura)FB=2300N (forza frenante)k1=10% (massimo slittamento longitudinale)Angolo di deriva?
13 Cerchio di Kamm Soluzione: Fmax= m x g x x k (in direzione longitudinale)= 1500 x 9,81 x 0,2 x 1=2.943NFS = m x v2/r= 1500 x (40/3,6)2/100=1851NL’angolo di deriva ricavato dal diagramma successivo è di 56°
14 Circle of Kamm (°): angolo di deriva Deriva Fs Forza traente Fd (N) (°): angolo di deriva3000Deriva2000CurvaSx1000Fs1234567Forza laterale Fs (N)FbForza longitudinale (N)10001851200030001From the above diagram, the so-called drift angle (difference between the wheel angle and the angle of the direction in which the wheel moves) can be read out directly.l = longitudinal slip max 10%Q: Given: m = 1500kg, µ = 0.2, v = 40 km/h (11,11 m/s), r = 100m , Fb= 2300Nk = 1 (vehicle weight on the used wheels/ total vehicle weight)Question: drift angle?Solution: Fmax = m x g x µ x k (in longitudinal direction)= 1500 x 9.81 x 0,2 x 1 = 2943 NFs = m x v² / r= 1500 x 11,11² / 100Fs = 1851 NFrom the graph we can see; the drift angle is 5 - 6°Q: Does the ABS operate? No, slip is less than 10%.Result of this manoeuvre? Understeer100022000323005Forza risultante Fr7300010Forza frenante Fb (N)Brake slip (%)
17 Sistemi frenanti Pompa freni Tipo Lockheed, tipo PortlessServo freno idraulicoSistemi di ripartizione della forza frenateValvola “P”, valvola LSPVEBD: Sistema di distribuzione elettronica della forza frenante (Electronic Brake force Distribution)On modern vehicles brake systems become very complex due to the ABS, TRC and VSC system integration. Therefore, some brake system manufacturers (ATE, KNORR, BOSCH) are investigating in electro-mechanical brake systems.Nevertheless, most of the production vehicles, however, still use hydraulic brake systems.
18 Pompa freni – Tipo Lockheed Master cylinder construction and operationWhen the brakes are not applied, the piston cups of No.1 and No.2 pistons are between the inlet port and compensation port, providing a passage between the cylinder and the reservoir. The hydraulic pressure becomes compensated between the two sides of the piston.
19 Pompa freni – Tipo Lockheed PressurizationWhen the brake pedal is depressed, No.1 piston moves to the left and the piston cup seals the compensating port to block the passage towards the reservoir. As the piston moves further, it increases the hydraulic pressure inside the cylinder. This pressure acts directly on the rear wheels. Since this pressure also acts on the piston No.2, this piston moves also, creating hydraulic pressure behind the piston, which acts on the front wheels.Note: The actual brake circuit configurations can differ vehicle to vehicle.
20 Pompa freni – Tipo Lockheed Pedale dei freni rilasciato:Il liquido freni scorre nella vaschetta attraverso la porta di compensazioneLa porta di compensazione assorbe anche eventuali cambiamenti di volume del liquido freni dovuti a variazioni di temperaturaWhen the brake pedal is released, the pistons return to their original position by the hydraulic pressure force and spring force. However, the brake fluid does not return immediately from the wheel cylinders and momentarily a vacuum is created inside the master cylinder.Through the orifices at the tip of the piston and around the periphery of the cups, brake fluid enters the cylinder.After the piston has returned to its original position, the brake fluid that gradually returns from the wheel cylinders flows into the reservoir through the compensating ports. The compensating ports also absorb changes in brake fluid volume due to temperature changes, when the brakes aren’t used.
21 Pompa freni – Tipo Lockheed Lockheed type master cylinder:When the ABS is operating, there are complex forces acting on the piston cups, created by the motor of the ABS actuator. As the piston cup is near the compensating port, if there are strong opposing forces it is possible for the piston cup to be damaged by the edge of the port.On the latest ABS systems therefore, a solenoid valve (Master Cut Solenoid Valve) is closing off the hydraulic pressure from ABS actuator and master cylinder. This avoids pressure waves acting on the cups during ABS operation.
22 Pompa freni – Tipo Portless Portless type master cylinder:The portless type does not have a compensating port on the front side. Therefore the cup never travels through the cylinder ports.When the brake pedal is not depressed, the No.2 piston is not in contact with the center valve seat, and thus the center valve creates a passage between the valve head and the No.2 piston. Through this small passage brake fluid can flow back to the reservoir.
23 Pompa freni – Tipo Portless When the brakes are applied, the No.2 piston moves and the center valve closes of the passage. When the piston moves further, hydraulic pressure is created.The disadvantage of portless type master cylinders is their higher sensitivity for dirt and foreign particles in the brake fluid. It can prevent the center valve from sealing during brake operation.Therefore on ABS equipped brake systems, the rear brakes receive pressure from a Lockheed type cylinder, while the front wheels are controlled by a portless type cylinder.Furthermore, the tandem master cylinder is designed so, that the No.1 piston moves before the No.2. It is therefore not necessary to have portless type on the No.1 piston because he passed the compensating port before opposing force can act on the cup.
24 Servo-freno idraulico From the reservoir brake fluid is entering to the electric pump. This pump pressurizes the fluid into an accumulator. Pressure switches control the pump motor and warning buzzer.If the accumulator pressure becomes lower than the specified pressure in the PH (“Pressure Low”) switch, the switch turns OFF. The ABS and booster ECU turns the pump ON, until the PH switch goes ON. After several seconds the ECU turns off the pump motor.In case the PH switch should malfunction, which causes the pump to operate continuously, a relief valve opens to drain brake fluid back to the reservoir to prevent overpressure.When the pressure drops under the predetermined level of the PL (“Pressure High”) switch, this switch goes OFF, thus activating through the ECU the warning buzzer and light.At this moment, the ABS is prohibited from operating.
25 Servo-freno idraulico FunzionamentoConstruction:The master cylinder is the center port type single master cylinder, which is used for the front brakes only. The brake booster is integrated with the master cylinder. The operating portion, master cylinder, and regulator are positioned coaxially to achieve a simple and compact construction. This construction enables the hydraulic pressure that is generated by the brake booster to be applied directly to the rear brakes.No brake pedal action:Here, on this drawing, the yellow color shows the location of brake fluid. In this case the system is not activated. No pressure present.
26 Servo-freno idraulico Aumento della pressione (bassa pressione)No brake pedal action:In light blue, brake fluid is not pressurized by the pump but only by the pedal force, whilst darker green represents pressurized fluid by the pump, and we will see dark blue as fluid pressurized by the action of the brake piston later.Follow the flow of fluid through the master cylinder and see that front and rear brake calipers receive fluid non-pressurized (Brakes not applied before Spool Valve moved forward and close passage from reservoir), so that bleeding air can be done by applying pressure onto the reservoir.Pressure increase (low pressure):The pedal effort that is applied to the brake pedal is transmitted via the operating rod, power piston and master cylinder piston. However, because the load setting of the master cylinder’s return spring is higher than that of the regulator piston’s return spring, the regulator piston gets pushed before the volume in the master cylinder becomes compressed. As a result, the spool valve moves moves leftward.The spool valve closes the path between the reservoir and the booster chamber (behind the power piston) and opens the path between the accumulator and the booster chamber. Then, the pressurized brake fluid enters into the booster chamber to provide a power assist to the pedal effort.When the pressure is introduced into the booster chamber, the power assist overcomes the force of the master cylinder’s return spring. This causes the volume in the master cylinder to become compressed and increases the pressure that is applied to the front brakes.At the same time, the pressure in the booster chamber increases the pressure that is applied to the rear brakes as well.During the initial stage of brake operation, the booster pressure that is applied to the rubber reaction piece is small. Therefore, a return force in the rightward direction does not apply to the spool valve via the reaction rod.
27 Servo-freno idraulico Aumento della pressione (alta pressione)Pressure increase (high pressure):However, when the pressure is high, the booster pressure that is applied to the rubber reaction piece increases and, thus it becomes deformed and applies higher reaction force to the push rod (in fact to the pedal)
28 Servo-freno idraulico Mantenimento della pressionePressure holding:This is a state in which the force that is applied via the brake pedal and the master cylinder pressure are in balance.The forces that are applied to the front and rear of the regulator piston, in other words, forces that are generated by the master cylinder pressure and the regulator pressure become balanced. This causes the spool valve to close both path (B) from the booster chamber to the accumulator and path (A) to the reservoir. As a result, the brake system is in the holding state.
29 Servo-freno idraulico Riduzione della pressionePressure release:When the pressure that is applied to the brake pedal is released, the master cylinder pressure decreases. Then, the regulator piston’s return (rightward) force becomes relatively greater, causing the regulator piston to retract and the spool valve to also retract. As a result, the path (A) between the reservoir and the booster chamber opens.The booster pressure becomes reduced in this state, creating a balance that corresponds to the force that is newly applied via the brake pedal. This process is performed repetitively to reduce the booster pressure and the master cylinder pressure in accordance with the force applied via the brake pedal.
30 Servo-freno idraulico Nessuna pressurizzazioneNo booster operation:If the booster does not operate, there is no pressure applied on the rear brake cylinders.Braking is only possible on the front wheels without power assist.
31 Servo-freno idraulico Hydraulic brake booster is located on the left side of the engine compartment (on this model). It is one compact unit which includes the actuator, hydraulic pump with DC motor, accumulator portion, pressure switches (PH & PL) and reservoir.
32 Valvola di ripartizione Tipo: proporzionaleAs we saw earlier, the maximum brake force that can be applied on a certain wheel is related to the weight and load on the braking wheels.Fbrake = .m.g, where m.g is the force acting on a certain wheel.Since due to inertia, the point of gravity shifts forward during braking, the front wheels receive a higher load (vertical force), while the rear wheel load reduces. The braking force of the rear wheels must be therefore reduced accordingly.The P-valve adjust the apportionment of the braking force between front and rear axles as determined by the brake’s particular dimensions in order to achieve a closer approximation to the ideal distribution, i.e parabolic curve. However, comparing P-valves with ABS (explained later) we can state, proportioning valves are open-loop control element, while ABS achieves closed-loop control.
33 Valvola di ripartizione Valvola tipo PA P-valve performs this pressure reduction function.If the hydraulic pressure in chamber A rises further, the piston moves to the right and opens valve C. As pressure in chamber B increases, the piston moves to the left due to the difference in surface areas, blocking the valve C. This process is constantly repeated to regulate the pressure, applied to the wheel cylinders.
34 Valvola di ripartizione Valvola tipo LSPLSPV-valveFor vehicles (pick-up, truck, van..) where the load on the rear wheels can differ a lot with the use, the maximum braking force that can be transmitted without locking the wheels differs as well.Using a load sensing spring, which acts in the same direction on the P-valve as the pressure coming from the master cylinder, the regulated pressure to the rear wheels changes in relation to the load sensing spring force.Load sensing proportioning valves achieve good approximation of ideal distribution. These valves respond to increased axle loads by displacing the trigger point upward.Vehicles with a hydraulic brake booster, the rear wheel pressure equals the booster pressure and is therefore in relation to but lower than the front wheel.Vehicles with the latest EBD system don’t have a P-valve. Brake pressure for the rear wheels is then controlled by the ABS.
35 Electronic Brake-force Distribution Il ripartitore elettronico della forza frenante (EBD) è un software che sostituisce la valvola “P” e garantisce:Maggior precisione (la pressione varia come la curva caratteristica ideale)Adattamento alle diverse condizioni di carico del veicoloRipartizione della forza frenante tra destra e sinistraThis brings us to the EBD. A brake system is developed in such a way, even w/o ABS operation (malfunction), the system should work as a normal brake system, w/o creating danger. Since locked rear wheels create unpleasantly uncontrollable situations, a P-valve (as a fail-safe device) reduces the rear brake pressure, so that this situation can never happen.However, in most of the braking situations, the rear brake force is not fully utilised. Over the years, ABS systems showed and proved their reliability. By deleting or increasing the gradient of the P valve, the ABS avoids locking of rear wheels.Detailed explanation of EBD operation can be found later in this course.
36 Assistenza Liquido DOT 4 Secco Umido Castrol LMA DOT4 230°C 155°C ATE super blue racing 280°C °CATE typ °C 200°CMotul racing °C 216°CCastrol SRF 310°C 270°CSecco: quantità d’acqua < al 3%Umido: quantità d’acqua > del 3%DOT4 brake fluid is glycol based and absorbs moisture over time. Moisture contamination causes fluid boiling point to drop (which could lead to fluid boil and brake fade during extensive use).Moisture contamination also contribute to internal corrosion in the calipers, wheel cylinders and brake lines.Leaving a brake fluid container open for one night can already ruin the brake fluid.Normally the brake fluid contents 3% water after 18 months, which is enough to lower the boiling temperature by 25% or more.The dry boiling point of DOT4 is around 230°C, while with 3% water (=wet boiling point) it becomes 155°C.DOT5 brake fluid is silicone based and therefor doesn’t attract moisture. Since DOT5 is not compatible with regular brake fluids, can react with rubber seals, its hard to poor without introducing bubbles into the braking system and moisture will pool to lower system areas such as calipers (encouraging corrosion) it isn’t used in our vehicles.Toyota has a DOT 5.1 brake fluid. This brake fluid is NOT a silicone based fluid but glycol based DOT 4 with higher boiling point (dry boiling point: 307°C, wet boiling point = 185°C). It still mixes with moisture from the air, and needs to be replaced regularly.Every two years or km brake and clutch fluid needs to be changed.
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