2017 2nd IEEE International Conference on Intelligent Transportation Engineering
Rapid Design of a Light Vehicle Hydraulic Brake System
Pier Giuseppe Anselma, Shirish Padmakar Patil, Giovanni Belingardi Department of Mechanical and Aerospace Engineering (DIMEAS) Politecnico di Torino Turin, Italy e-mail:
[email protected] design and for hot judder characteristic estimation was presented by Chung et al. in 2012 [8]. However, no previous study has been performed that relates to the brake system design that meets government standards. This paper aims at presenting an easy to use tool for the rapid design of brake systems. The design methodology is implemented in a MS-EXCEL tool in order to present a simple and intuitive user interface. The paper is organized as follows: firstly, an analytical model of the hydraulic brake system is presented. Each component of the system and its influence on the general performances is presented separately. Subsequently, the performance requirements imposed by the safety standard are illustrated that lay the foundations for the development of a design methodology. A few case studies are presented to demonstrate the rapid design tool for some production vehicles. Finally, conclusions of the study are presented.
Abstract—Brake system design is considered quite challenging due to conflicting safety constraints imposed on the system performance. As several components are integrated into the system, design focused exclusively on a single element does not guarantee efficient system performance. As a consequence, no general rules are provided in developing this type of system. This paper aims at proposing a quick and intuitive design methodology for the development of light vehicle hydraulic brake systems. An analytical model for the brake system is presented, that includes formulation for each system component. Subsequently, the two most important safety homologation standards for light vehicle brake systems (both US and EU legislations) are analyzed. Their requirements are integrated in a Microsoft Excel tool to enable a quick brake system design that meets the government safety standards. Design parameters include the master cylinder size, the vacuum-assisted booster size, the brake line pressures, the proportional valve kick-off pressure, and the number and size of the brake pistons.
II.
Keywords-analytical brake model; brake system design; rapid design; safety standards; vehicle braking dynamics
I.
A. Hydraulic Disc Brake System Modeling A schematic diagram of a hydraulic disc brake system is shown in Fig. 1. The input to the system is represented by the force applied by the driver on the brake pedal, which is magnified by the lever ratio and the vacuum assisted brake booster. Consequently, this enhanced force is transferred to the pushrod into the master cylinder generating the line pressure that leads the brake pistons to press the calipers/brake pads against the spinning rotor, thus generating braking torque by friction. Finally, a proportional valve is integrated in the system to regulate the distribution of brake line pressure between the front and rear axle. The following paragraph illustrates the analytical model for each component of the system. 1) Brake pedal, master cylinder and boost ratio The foot pedal force exerted on the brake pedal defines the value of generated brake line pressure (1).
INTRODUCTION
The safe operation of a motor vehicle requires continuous adjusting of its speed to meet changing traffic conditions. The brakes and the tires along with the steering system are the vehicle components that are responsible for accident avoidance. When dealing with the brake system design, challenges arise both from the amount of different components to consider and from the constraints imposed on the system performance. The two most relevant safety homologation standards for light vehicle braking system are the “Federal Motor Vehicle Safety Standard No. 135 – Light Vehicle Brake Systems” for the US legislation [1], and the “UNECE Regulation No. 13-H” for the EU legislation [2]. Their requirements need consideration and satisfaction when a car company designs a brake system for an actual vehicle. Several studies have been conducted on the brake system design: early in 1970, Puleo investigated the brake force distribution devices [3], while in 1977 Limpert established numerical and experimental procedures to evaluate braking force distribution [4], [5]. Jung et al. firstly developed a brake system design program for vehicles in 2008 [6], while Lee et al. introduced a semi-empirical program for predicting the braking performance of a passenger vehicle in 2011 [7]. Recently, a systematic process for hydraulic brake system
978-1-5090-6273-7/17/$31.00 ©2017 IEEE
ANALYTICAL MODELING OF A BRAKE SYSTEM
pl=( Fp· lp· ηp+ Fboost)/ AMC
(1)
Fp stands for the pedal force, lp and ηp are the pedal lever ratio and efficiency respectively. The first term of the numerator represents the ratio of pedal force transmitted to the master cylinder piston, while the second term Fboost is the contribution of the vacuum-booster. AMC in the denominator
30
can be identified. Particularly, this parameter defines how much longitudinal braking force is provided to the single wheel given a certain value of brake line pressure, as stated in (5). The equation is drawn with reference to the two free body diagrams of the rotor and the tire shown in Fig. 2.
represents the master cylinder cross-sectional area. The pedal lever ratio, produced through the mechanical connection relates the pedal travel to the master cylinder stroke and it can be calculated with (2). lp= xp / (stMC - clMC)
(2)
xp is the maximum pedal travel imposed by packaging constraints, stMC the master cylinder stroke and clMC the master cylinder clearance. In a vacuum-assisted booster, the assist force provided to the master cylinder piston is generated by the difference in pressure across the booster diaphragm between the vacuum pressure on the master cylinder side and the atmospheric pressure on the input side, as shown in (3). Fboost=( patm - pvacuum) · Aboost
(3) Figure 2. Schematic diagram of the braking force generated by the hydraulic system.
patm and pvacuum are the atmospheric and vacuum pressures respectively, while Aboost represents the booster diaphragm circular area. 2) Proportional valve Due to the weight transfer during braking as discussed in the next paragraph, it is desirable to reduce the brake pressure for the rear axle for higher deceleration levels. This is achieved through the proportional valve, characterized by two parameters: the kick-off pressure (activation of the valve) and ratiop the ratio between the rear and the front brake line pressure when the valve is activated.
BG=Fx_wheel / pl= AWC ·2·μpad · (rrotor-rWC-clWC )/Rtire
AWC represents the total wheel cylinder (brake pistons) area, μpad the brake pad coefficient of friction, clWC the wheel cylinder to the rotor edge clearance, while rrotor, rWC and Rtire are the radii of the rotor, the wheel cylinder and the tire, respectively. In case more than one wheel cylinders were present, the total wheel cylinder area is given by the sum of the individual wheel cylinder area. Finally, the total developed braking force acting on the vehicle is given by (6).
pl < pkick-off Î pfront =pl ; prear =pl pl ≥ pkick-off Î pfront =pl ; prear =(pl - pkick-off)· ratiop+ pkick-off
(5)
(4)
Fbraking =Ʃ Fx_wheel =2·( BGfront·pfront + BGrear·prear)
(6)
B. Vehicle Braking Dynamics The vehicle deceleration during braking causes a load transfer having the front axle overloaded and the rear axle unloaded and consequently increasing the front axle braking capacity. Due to the Center of Gravity (COG) position, a load distribution between the front and rear axle can be observed even when the vehicle is not braking. Two vehicle parameters are defined in (7): Ψ quantifies the load distribution between the axles, while χ is a geometric parameter depending on the position of the COG. Based on these parameters, the static loads on the axles can be computed using (8).
Equation (4) defines the distribution of brake line pressure between front and rear axle depending on the proportional valve being activated or not. 3) Brake pistons, calipers and rotor
Ψ =Wrear / Wvehicle= Wvehicle· χ / L ; χ=hCOG/aCOG
(7)
Wrear = Ψ ·Wvehicle ; Wfront = (1-Ψ) ·Wvehicle
(8)
hCOG and aCOG are the COG height and distance from the front axle respectively, and L is the vehicle wheelbase. These parameters are dependent on the vehicle load condition and the COG position. Ψ and χ allow tracing the well-known brake performance diagram shown in Fig. 3. For a given tire-
Figure 1. Schematic diagram of a hydraulic brake system.
Based on the design characteristics of the brake pistons, the rotor, the calipers and the tire, a Brake Gain (BG) factor
31
road friction coefficient, two red lines are sketched that define the adherence limits. All the front/rear braking force combinations contained within the adherence limits can decelerate the vehicle without any axle locking. If the braking force combination of the system gets out of the allowed area through the upper-horizontal branch, the front axle will lock. On the other hand, rear axle will lock if the right-hand-vertical limit is crossed. Intersection of the two red lines results in simultaneous locking of the front and rear axles and represents the optimal braking force distribution targeted by the system performance. Analytical expressions of front and rear limit braking forces for a given road surface condition μ can be found in [5]. III.
Tests 2 to 6 are all run on a test surface with the value of road friction coefficient equal to 0.9. The pedal force exerted during each test is constant and must be within 65 and 500 N. No lockup of any wheel is allowed during these tests. Both tests 2 and 3 are run with the brake system in normal operational condition, even with different values of initial vehicle speed. Test 4 aims at simulating a functional failure of the variable brake proportioning system. As a consequence, brake pressure distribution will be the same for both the front and rear during the entire braking maneuver. A rupture or leakage failure for the hydraulic circuit is considered in Test 5. The presence of this specific standard constrains the vehicle manufacturers to install a dual-circuit system so that partial braking effectiveness is provided in the event of a circuit failure. Finally, Test 6 defines a standard where a functional failure causes the vacuum booster assist unit being inoperative.
SAFETY STANDARD SPECIFICATIONS
Brake system requirements can be classified among the most restrictive federal standards for vehicle components. In this work both the US and EU standards have been analyzed, their major tests are considered and reported in Table I. All the tests must be run with the transmission position in neutral. Moreover, each test must be performed considering two different load cases: the Gross Vehicle Weight Rating (GVWR) representing the maximum operating weight of a vehicle as specified by the manufacturer and the Lightly Loaded Vehicle Weight (LLVW) meaning unloaded vehicle weight plus the weight of a mass of 180 kg (approximately driver and one passenger). The first test, called the “Wheel Lockup Sequence”, ensures that the lock up of front wheels occur either simultaneously or at lower deceleration rate than the lock up of the rear wheels. The observation of which axle is locking first during an emergency braking is vital for safety reasons. Rear axle locking first is prohibited as a loss of rear adherence can possibly degenerate into vehicle spinning without control. Front axle locking first ensures that the vehicle preserves straight direction. Moreover, the driver could eventually regain control over the vehicle if the road friction coefficient suddenly rose. In this test, the pedal force is increased at a linear rate to provoke abrupt lockup of the first axle. Referring to Fig. 3, the line representing the braking force distribution of the system must cross the allowed area through the upper-horizontal branch for different values of road friction coefficients between 0.15 and 0.8.
Figure 3. Brake system performance diagram.
Figure 4. Graphical requirements of the safety standard tests.
TABLE I. SAFETY STANDARD REQUIREMENTS FOR BRAKE SYSTEMS PERFORMANCE
Test Name
Initial vehicle speed
1
Wheel Lockup Sequence
-
2
Cold Effectiveness
100 Km/h
3
High Speed Effectiveness
v=0.8·vveh-MAX
4
Proportional Valve Failure
5
Hydraulic Circuit Failure Vacuum Booster Assist Failure
6
Each test is characterized by an initial speed of the vehicle and a required stopping distance. Knowing these two parameters, the required minimum deceleration can be easily found. With reference to the performance diagram illustrated in Fig. 3, the lines of constant deceleration run under an angle of 45 degrees. Fig. 4 illustrates the performance diagram highlighting the test requirements. On one hand, the braking force distribution must be contained within the nolock up area (red lines). On the other hand, it must be greater than the minimum deceleration requirement (green line). As a result, the tip of the braking force line, correlated to the applied pedal force, must fall within the area highlighted in yellow to meet the test requirements. The last column on the
Requirements Deceleration [m/s2] Stopping distance
5.51
100 Km/h
70 m 0.1v+ 0.0067v2 110 m
100 Km/h
168 m
2.30
100 Km/h
168 m
2.30
̴ 5.30 3.21
32
right of Table I illustrates the obtained deceleration requirement for each standard test. The requirement of Test 3 depends on the vehicle maximum speed and it can be calculated through the given formula in Table I. IV.
The brake engineer has the flexibility to choose the appropriate combination of the number and the size of the brake piston as well as the maximum system pressure to provide the required maximum clamp force for the front and rear brakes. Once the design is finalized, the ratio of the maximum brake pressures (Rear/Front) will define the brake force distribution as controlled by the proportional valve.
DESIGN METHODOLOGY
In this section, a brake system design procedure based on the safety standard requirements is presented. The system design parameters include the number and diameters of the brake pistons for each brake (front and rear), the line pressures, the proportioning valve kick off pressure, the diameter and stroke of the master cylinder, the vacuum booster diaphragm diameter and the pedal lever ratio. Fig. 5 illustrates the design methodology where each step corresponds to the selection of a particular design parameter. Particularly, design steps are displayed in black, while verification steps are shown in red. Details are as follows: Step 1 – The first step aims to ensure that the brake pistons can provide the required longitudinal braking force to the wheels. Note that, if the road friction coefficient increases, the allowed brake utilization area in Fig. 4 enlarges and subsequently more braking force can be applied without losing adherence. Since the most safety standard tests are run on skid 90 surfaces, it is important that the maximum braking capacity is at least 0.9g. Brake diagram (μ=0.9) is thus considered in this paper to represent the standard tests. The total clamp force provided should allow the brake system to reach the optimum point Op, identified through the intersection of the adherence limit lines. With reference to Fig. 4, the efficiency of the system for the specific surface condition can thus be evaluated considering the ratio between the length of the line a and the sum of the lengths of the lines a and b. BFR_MAX and BRE_MAX define the coordinates of the optimum point in Fig. 4. Consequently, the expressions of the required clamp load for the front and rear brakes are: Fclamp_req_FR(μ)=BFR_MAX (μ)·Rtire/(4·μpad·rm_pad) ; Fclamp_req_RE(μ)=BRE_MAX (μ)·Rtire/(4·μpad·rm_pad)
Figure 5. Flowchart of the design methodology.
Step 2 – The next step concerns the selection of the “knee point”, i.e. the minimum value of the brake line pressure that activates the operation of the proportioning valve. The decision is made based on a pictorial representation in the software where the generated braking force is compared to the optimal one. The optimal braking force distribution is represented by a parabola whose shape depends on the vehicle properties (i.e. dimensions and distribution of weight), as known from the theory [5]. It should be noted that GVWR and LLVW load cases present different optimal braking force parabolas; as a consequence the choice of kickoff pressure should be made seeking a good compromise between the two cases. Step 3 – This step aims at the selection of the master cylinder to meet the design requirements. The procedure is established for designing the cylinder capacity in order to compensate for all the brake system fluid losses as well as to provide the required pressure for generating the clamping force. The list of all the brake system volume losses, as well as the related formulas can be found in [5]. As a good practice, a safety factor is considered when determining the minimum master cylinder capacity. Many possible combinations of the diameter (thus cross-sectional area) and stroke can provide the required capacity, but the balanced design is the one that provides an acceptable hydraulic gain as well as an acceptable pedal lever ratio. Since the master cylinder cross-sectional area relates the brake line pressure to the pedal force, a reasonable value has to be selected to get acceptable values of pedal force [9]. At the same time, a proper value of the master cylinder stroke
(11)
In this paper, an approximation is made in estimating rm_pad=(rm_rotor - 20). On the other hand, the generalized expression for the clamp load provided by the brake system is given by (12). Fclamp_prov =pl_MAX ·AWC
(12)
The LLVW case is considered in a conservative strategy in terms of load distribution. However, the GVWR case demands higher values of clamp load than the LLVW. The clamp load required is consequently increased by a safety factor represented by the vehicle weight ratio between GVWR and LLVW cases. Thus, the clamp load requirement for both front and rear brakes can be expressed by (13). Fclamp_prov_FR ≥Fclamp_req_FR ·Wveh_GVWR/Wveh_LLVW ; Fclamp_prov_RE ≥Fclamp_req_RE ·Wveh_GVWR/Wveh_LLVW
(13)
33
TABLE II. VEHICLE DATA USED IN THE STUDY
should be selected to provide reasonable pedal lever ratios, generally within 3 and 4 for ergonomic requirements [5]. Step 4 –The first verification step ensures that the brake system is capable to pass the vacuum booster assist failure test. Equations (1) to (6) are implemented to calculate the braking force developed without any contribution from the vacuum boost. The test must be passed by applying a pedal force between 65-500 N (the range in the safety standard) and generating a braking force that falls in the target area shown in Fig. 4. Safety factors of 1.2 are considered appropriate to ensure the system performance is more than adequate to meet the deceleration requirement and at the same time avoid the lock-up. At this point in the design process, an unsuccessful test suggests that the system is not capable of providing enough braking force. In this instance, an increase in the clamp load is required until enough braking force is furnished to pass the test. Step 5 –The last design parameter to be determined is the vacuum booster diaphragm diameter. The constraint to this specification is the achievement of the cold effectiveness test. The same procedure of step 4 is followed, considering the deceleration requirement of the cold effectiveness test and adding the booster force term in (1). Appropriate value of diaphragm diameter can be selected until the test is passed. Step 6 –The finishing step regards the achievement of the remaining federal standards to validate the designed system. In the locking sequence test, the brake system performance is compared to the adherence limit for several surface conditions with μ=0.15-0.8. The test is passed if, for all the considered surfaces, the brake system characteristic line crosses the adherence limit through the upper-horizontal branch. The high speed effectiveness test differentiates from the cold effectiveness test only for the value of deceleration requirement. The proportional valve failure test is run considering at each point the rear line pressure is equal to the front line pressure. In most cases, each of the two brake subsystems of a light vehicle involves diagonal wheels (frontleft and rear-right, front-right and rear-left), consequently during a single circuit failure a braking action of the nonfailed system is produced. In other words, the hydraulic circuit failure test has to be passed considering only half of the braking potential. If any of the tests of Step 6 is failed, the methodology suggests reconsidering previous design steps and modifying parameters in order to achieve all the safety standards. The MS-EXCEL format allows easy management and handling of design data in adjustment steps. V.
GVWR
LLVW
Vehicle
L [mm]
Wveh [N]
aCOG [mm]
hCOG [mm]
A B C D
2612 2570 2636 2300
12459 13636 12704 9565
1488 1338 1373 1279
595 617 543 586
Wveh [N]
aCOG [mm]
hCOG [mm]
18099 18688 18099 14175
1097 977 949 897
630 653 575 620
TABLE III. BRAKE SYSTEM DESIGN FOR THE STUDIED VEHICLES Vehicle Brake pistons (Front) Brake pistons (Rear) Line pressures
Number
A 3
B 3
C 3
D 3
Diameter [mm]
41.28
44.45
50.8
34.93
Number
1
1
1
1
Diameter [mm]
41.28
38.1
41.28
28.58
Front [MPa]
6
6
4.4
7
Rear [MPa]
4.6
4.3
3.85
5.4
Kick-off [MPa]
2
1
1
3
Master cylinder
Diameter [mm]
28.57
28.57
31.75
26.99
Stroke [mm]
42
42
42
42
Vacuum booster
Diaphragm diameter [mm]
153
153
153
153
0.61
0.56
0.56
0.56
System overall efficiency
The maximum pedal travel imposed by vehicle packaging is assumed to be 125 mm. The values of 0.8 and 0.35 are retained for the pedal lever efficiency and the brake pad coefficient of friction respectively, while the master cylinder clearance is assumed to be 2 mm. Following the illustrated methodology and using the MS-EXCEL aided visualization no more than 1 hour is required to develop each brake system. Parameters of the obtained systems are illustrated in Table III, where efficiencies for skid 15, 30 ,45, 65 and 80 surfaces for both GVWR and LLVW cases are averaged to obtain the system overall efficiency. Adopting the proposed methodology, considerable values of system efficiency can be achieved. VI. x x x
CASE STUDIES
This design procedure has been applied to develop brake system designs for some actual vehicles. Vehicle data are illustrated in Table II. The tire sizes are assumed to be 205/55 R16 for vehicles A and D, and 215/60 R16 for vehicles B and C. In this paper, an assumption is made that all the brake pistons on the same axle have equal piston diameters. Up to four brake pistons are considered for each wheel.
x x x
34
CONCLUSION
A design methodology that enables quick development of hydraulic brake systems for light vehicles is presented. The brake system is modeled through analytical equations for each component. Safety standard homologation requirements are presented and analyzed. After each test is considered to establish design targets, a procedure is proposed to develop the brake system meeting the standard requirements. MS-EXCEL software is involved to quickly observe the impact of changes of the design parameters on the system performance. The developed tool is tested by quickly coming up with effective brake systems for four actual vehicles.
[5]
REFERENCES [1]
[2]
[3] [4]
U.S. Department of Transportation - NHTSA, “Federal Motor Vehicle Safety Standard No. 135; Light vehicle brake systems.” Dec 2, 2005. [Online]. Available: https://www.nhtsa.gov/DOT/NHTSA/.../TP-135-01.pdf Economic Commission for Europe, “Regulation No. 13-H - Uniform provisions concerning the approval of passenger cars with regard to braking,” Feb. 24, 2014. [Online]. Available: https://www.unece.org/fileadmin/DAM/trans/doc/2007/wp29/ECETRANS-WP29-2007-03e.pdf Puleo G., “Automotive brake proportioning devices.,” SAE Paper No. 700375, 1970. Limpert R., “An investigation of brake balance for straight and curved braking,” SAE Paper No. 741086, 1974.
[6]
[7]
[8]
[9]
35
Limpert R., “Brake Design and Safety”, SAE, USA, 1999, pp. 293350. S. P. Jung , K. J. Jun, T. W. Park, and J. H. Yoon, “Development of the brake system design program for a vehicle,” International Journal of Automotive Technology 9(1):45-51, 2008. Lee, C.H., Lee, J.M., Choi, M.S. et al.,” Development of a semiempirical program for predicting the braking performance of a passenger vehicle,” Int.J Automot. Technol. (2011) 12: 193. Chung, W.S., Song, H.S., Jung, D.H. et al., “Development of a systematic process for hydraulic brake system design and for hot judder characteristic estimation,” J Mech Sci Technol (2012) 26: 3893. R. G. Mortimer, “Foot Brake Pedal Force Capability of Drivers,” Ergonomics, (1974) 17:4, 509-513.
