Design and Analysis of a Novel Centrifugal Braking Device for a Mechanical Antilock Braking System Cheng-Ping Yang1 Mechanism and Machine Theory Laboratory, Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwan e-mail: [email protected]
Ming-Shien Yang Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwan e-mail: [email protected]
Tyng Liu Associate Professor Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwan e-mail: [email protected]
A new concept for a mechanical antilock braking system (ABS) with a centrifugal braking device (CBD), termed a centrifugal ABS (C-ABS), is presented and developed in this paper. This new CBD functions as a brake in which the output braking torque adjusts itself depending on the speed of the output rotation. First, the structure and mechanical models of the entire braking system are introduced and established. Second, a numerical computer program for simulating the operation of the system is developed. The characteristics of the system can be easily identified and can be designed with better performance by using this program to studying the effects of different design parameters. Finally, the difference in the braking performance between the C-ABS and the braking system with or without a traditional ABS is discussed. The simulation results indicate that the C-ABS can prevent the wheel from locking even if excessive operating force is provided while still maintaining acceptable braking performance. [DOI: 10.1115/1.4030014] Keywords: centrifugal braking device, mechanical antilock braking system, braking performance, braking safety
1
Introduction
The braking system is a critical component of vehicles, and extensive research on ABSs has been published recently. Locking of the wheel while braking is in progress can be dangerous because the driver can lose control of the vehicle, resulting in an increased braking distance. Therefore, for safety, ABSs are installed on most general passenger cars and certain heavy vehicles. In 1936, Bosch developed a hydraulic–electric braking system suitable for cars [1]. The braking pressure can be adjusted appropriately by using an electronic sensor to measure the rotational speed of the wheel. Girling developed a hydromechanical ABS in the mid-1980s [1]. This system uses a centrifugal clutch instead of an electronic sensor. Its friction force changes with the rotational 1 Corresponding author. Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 26, 2014; final manuscript received March 4, 2015; published online April 2, 2015. Assoc. Editor: Qi Fan.
Journal of Mechanical Design
speed of the wheel to adjust the output braking pressure. Wakabayashi et al. developed a motor-actuated ABS in 1988 [2]. The antilock motor drives the driving disk through a planet gear and then pulls the braking wire to reduce the braking force. Lu and Shin developed a hydraulic-modulating ABS in 2005 [3]. In this system, the volume of the brake fluid container can be changed by an internal push rod, which is controlled by an electromagnetic coil; in this manner, the braking pressure can be adjusted. Siemens developed an electronic wedge braking system in 2006 [4]. The braking force can be changed directly by measuring the rotational speed of the wheel and controlling the voltage and current. In 2007, Choi et al. developed an ABS with an electro-rheological valve pressure modulator [5]. The braking force can be adjusted by controlling the viscosity of the brake fluid by changing the current producing the magnetic field. Huang developed a mechanical antilock braking device suitable for a bicycle in 2008 [6]. The maximum braking force can be fixed by using an antilock spring and wedge braking pad. Therefore, the wheel will not lock even if the driver provides excessive operating force. This ABS was further analyzed by our group in 2013 [7]. In addition, several patents have presented various ABS designs for light two-wheeled vehicles [8–12]. Electronic ABSs have been commonly installed on both general passenger cars and heavy vehicles. Electronic ABSs contain electronic sensors and a central control unit. These ABSs can control the braking force by rapidly adjusting the pressure of the brake fluid. However, there are some disadvantages to this operating mode. First, the braking force is discontinuous. When the ABS is used, the braking force changes over time, i.e., the vehicle could lose a portion of the braking force during the braking period. Second, the system includes many complex and expensive components. Therefore, this system is unsuitable for use in light two-wheeled vehicles. To overcome the disadvantages of electronic ABSs, we attempt to develop a mechanical ABS, i.e., C-ABS, which prevents the wheel from locking by using centrifugal force to automatically adjust the braking force. A patent search revealed that there are some braking devices that use the same concept as C-ABS [13–15]. These devices provide a braking force based on the rotational speed. However, when the rotational speed is slow, there is a lack of braking force generated or even a loss of brakes. Therefore, these problems should be overcome to apply these devices to braking systems. The C-ABS is designed with two brakes and a gearbox to increase the total braking force, and the antilock function is achieved through the improved brake fluid pressure distribution. Additionally, the proposed system increases the braking efficiency by applying a continuous braking force. In this paper, we use a commercial scooter as our model of analysis, establishing a numerical program to realize the characteristics of the system. Then, preferred design parameters can be determined from the results of the simulated braking performance.
2
Principle of the C-ABS
2.1 Basic Concept of the C-ABS. The output torque of the centrifugal brake shoe will change according to its rotational speed, i.e., the output torque increases as the rotational speed increases, and vice versa. Therefore, the CBD can adjust the braking force automatically as the rotational speed of the wheel changes, preventing excessive braking torque, which locks the wheel. The proposed system consists of a CBD, two brakes, and a speed-increasing gearbox. The first brake is the original brake of the vehicle, whereas the second brake is the proposed CBD. The function of the speed-increasing gearbox is to increase both the rotational speed of the centrifugal brake shoe and the output braking torque to the wheel. When the driver operates the brake lever, two braking torques are applied to the wheel simultaneously. The first braking torque is applied to the wheel directly. The second braking torque acts on the housing initially but is then transmitted from the centrifugal brake shoe to the gearbox. This second torque increases the braking torque before acting on the wheel. If the
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rotational speed of the wheel decreases sharply due to excessive braking torque, the centrifugal brake shoe will not contain sufficient centrifugal force, leading to a lack of friction force with the housing. This lack of friction force will cause a slip between the centrifugal brake shoe and the housing. In other words, the static friction transitions to kinetic friction, thus reducing the braking torque acting on the wheel. After the rotational speed decreases to the minimum engagement speed of the CBD, the centrifugal brake shoe separates from the housing and stops transmitting braking torque to the wheel. At this stage, a continuous braking force is applied by the first braking system only. The basic C-ABS is illustrated in Fig. 1. The section outlined by the dotted line is the proposed CBD, which is connected to the wheel through the speed-increasing gearbox. The C-ABS prototype is shown in Fig. 2. The mechanism is developed according to the basic concept outlined in Fig. 1. This structure is designed to be easily fabricated and measured. 2.2 Mechanical Model of the CBD. The main components of the CBD are three centrifugal brake shoes, a bearing, and a housing with a brake disk. Figure 3 shows the free body diagram of one single centrifugal brake shoe analyzed in the counterclockwise direction. The forces shown include the centrifugal force FCBD , the spring force Fspr , the friction force of rubber bushing Frbr , the normal force dN, and the friction force with the housing ldN l represents the friction coefficient between the centrifugal brake shoe and the housing. The angular velocity x1 of the CBD, with a mass m, generates a centrifugal force at the mass center. This force is represented by the equation FCBD ¼ mx21 rcm
(1)
where k is the elastic coefficient of the spring and DS0 is the prestretched length of the spring. When the brake shoe engages with the housing, the spring stretches an additional amount DS. From the geometrical configuration of the brake shoe, the equation of the spring force can be described as Fspr ¼ kðDS0 þ DSÞ
(2)
Assuming that there is a unit pressure p acting on the brake shoe at an angle hc from the rotational axis, the applied pressure will be proportional to the vertical distance between the acting point and rotational axis [16]. The equation can be described as p pm ¼ sin hc sin hm
Fig. 1 Basic composition of the C-ABS
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(3)
Fig. 2 C-ABS prototype
where pm and hm represent the maximum pressure and the angle of the maximum pressure, respectively. If the angle between the frictional material on the brake shoe and the end position is less than 90 deg, then ha ¼ hc2 ; if hc2 > 90 deg, then ha ¼ 90 deg. The normal force acting on the brake shoe can be derived as dN ¼ pbr dhc ¼
pm br sin hc dhc sin hm
(4)
where b is the width of the frictional material. Considering all of the forces acting on the centrifugal brake shoe, the force balance along the rotational axis can be expressed as FCBD r2 Fspr rs1 Fspr rs2 Frbr r3 Mn Mt ¼ 0
(5)
where Mn and Mt are the vertical direction moment and tangent direction moment of the friction material, respectively. By rewriting the equation, we can derive the output torque of the CBD shown as below ð ð nlpm br2 hc2 sin hc dhc (6) TCBD ¼ n lrdN ¼ sin hm hc1 where n is the number of centrifugal brake shoes in the CBD. When the centrifugal brake shoe begins to engage with the housing, the equation of motion can be written as
Fig. 3 The mechanical model of the centrifugal brake shoe
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FCBD;0 r2 Fspr rs1 Fspr rs2 Frbr r3 ¼ 0
(7)
Therefore, we can derive the angular velocity of the CBD when it is engaging as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fspr ðrs1 þ rs2 Þ þ Frbr r3 x0 ¼ (8) mrcm r2 2.3 Model of the Friction Coefficient of the CBD. The friction coefficient is affected by not only the frictional material but also the surface temperature. Therefore, it is necessary to establish a model for the friction coefficient that can describe its variation with temperature. When kinetic friction is generated between the centrifugal brake shoe and the housing, their surface temperatures will rise and change the friction coefficient. The energy conservation equation can be used to calculate the amount of kinetic energy that has been converted to thermal energy at each moment. Some assumptions should be made to simplify the model. First, the motional energy of the CBD is considered negligible. Second, the energy losses generated by the slip between the tire and flywheel are negligible. Third, there is no energy loss from the transmission and resistance of the bearings. The energy conservation equation can be written as Ef0 þ Ew0 TCBD Dx dt ¼ Ef þ Ew þ Q
Variation in the friction coefficient with temperature [17]
After determining the friction coefficient between the centrifugal brake shoe and the housing, the exact output torque of the CBD can be derived.
(9)
where Ef0 and Ew0 are the rotational energies of the flywheel and wheel, respectively, at the previous time step; Dx is the variation of rotational speed per unit time; Ef and Ew are the rotational energies of the flywheel and wheel at the next step, respectively; and Q is the thermal energy generated in this system. The following equations represent the relationship between these parameters: 8 1 > > Ef ¼ If x2f > > 2 > > < 1 Ew ¼ Iw x2w (10) 2 > > > > Dx ¼ Kx Kx w0 w > > : Q ¼ Qabs þ Qloss where If and Iw are the inertias of the flywheel and the wheel, respectively, and K is the speed-increasing gear ratio of the gearbox that increases the rotational speed of the CBD. The heat absorbed by the centrifugal brake shoe Qabs and the heat lost to the air Qloss can be described from thermodynamics and heat transfer as ( Qabs ¼ mcp DT ¼ mcp ðT T 0 Þ (11) Qloss ¼ Q_ conv dt ¼ hAs ðTs T 1 Þdt where cp and As represent the specific heat and the surface area of the CBD, respectively, and h is the forced convection heat transfer coefficient of gases. We assume that the centrifugal brake shoe is evenly heated, i.e., the variation of the surface temperature equals the temperature variation of the entire material, Ts ¼ T. The environmental temperature is set to 25 C, which is also the initial temperature of the centrifugal brake shoe, i.e., T 0 ¼ T 1 ¼ 25 C. The temperature of the centrifugal brake shoe at each moment can be derived from the previous equations. Huang et al. acquired a relationship for the kinetic friction coefficient of the centrifugal clutch experimentally. As shown in Fig. 4, we can draw three trend lines from these data. The trend lines can be described as 8 1 1 > > if T 250 Tþ > > 1500 3 > < 1 89 lðTÞ ¼ (12) if 250 < T 330 Tþ > 1600 160 > > > 1 15 > : if T 330 Tþ 480 16 Journal of Mechanical Design
Fig. 4
2.4 Mechanics of the Wheel. A wheel acting on the flywheel during the braking process is considered. When the brake engages, there is a total braking torque Tb generated on the wheel, and a braking force Fb is simultaneously generated on the surface of the tire. Because the tire is elastic, it will deform as the wheel rolls under a load. The energy consumption results in a rolling resistance for the wheel, which equals the rolling resistance torque resulting from the normal force N acting on off-set distance d. The value d can be derived from the product of the radius of the wheel and the coefficient of rolling resistance fr [18]. Thus, the torque equation can be described as Fb Rw Tb Nd ¼ Iw aw
(13)
where Rw and aw are the radius and the angular acceleration of the wheel, respectively. Similarly, the torque equation for the flywheel can be expressed as Fb Rf þ Nd ¼ If af
(14)
where Rf and af are the radius and angular acceleration of the flywheel, respectively. We can derive the angular velocity at each moment through our numerical simulation program by obtaining the angular accelerations of the wheel and flywheel. The function of the flywheel is to simulate the motion of the kinetic energy of the vehicle so that the inertia of the flywheel can be derived from the energy conservation equation as 1 1 MV 2 ¼ If x2f 2 2
(15)
If ¼ MR2f
(16)
where M and V are the mass and velocity of the vehicle, respectively. After the inertia of the flywheel is determined, the motion of the vehicle can be derived from the flywheel in the simulation program. 2.5 Skid Ratio of the Wheel. In an ideal condition, the wheel rolls entirely on the ground when no force is acting on it. Therefore, the vehicle speed can be determined from the wheel speed. The wheel speed refers to the tangential speed of the wheel, i.e., it is different from the rotational speed of the wheel. However, when the brake engages, the wheel speed and the vehicle speed differ. The relationship describing this difference can be defined as the skid ratio s, which is expressed as JUNE 2015, Vol. 137 / 065002-3
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s¼
V xw Rw 100 % V
(17)
where V is the speed of the vehicle. The tangential speed of the wheel can be derived from the product of the angular velocity xw and the radius Rw . If the skid ratio is zero, then the wheel is rolling purely without slip; if the skid ratio is 100%, then the wheel stops rolling but the vehicle continues to move. In other words, the wheel is locked, and only pure slip occurs. The vehicle speed can be derived from the tangential speed of the flywheel under the assumption that the variation in the speed of the flywheel is equal to the true motion of the vehicle. Many studies have focused on the skid ratio and friction models. In this study, we use the friction model introduced by Kiencke and Daiss [19]. The relationship between the friction coefficient and the skid ratio can be expressed as lg ðsÞ ¼
as b þ cs þ s2
(18)
where the parameters in Eq. (18) are defined as 8 lp l1 > a¼ ð1 sp Þ2 > > l > p l1 > > < b ¼ s2p > > > > l1 ð1 þ s2p Þ 2lp l1 > > :c ¼ lp l1
3 (19)
In the above equation, lp is the peak value of the friction coefficient, sp is the skid ratio at the peak value of the friction coefficient, and l1 is the friction coefficient when the skid ratio is 100%. The values of the parameters are taken from Ref. [20]. We set the parameter values for a road surface with dry asphalt as ðsp ; lp ; l1 Þ ¼ 0:2; 0:85; 0:75, whereas the parameter values for a road with wet asphalt are ðsp ; lp ; l1 Þ ¼ 0:2; 0:6; 0:5. When designing a braking system, the skid ratio should be controlled between approximately 10% and 30% to achieve maximum braking performance. If the skid ratio is smaller than 10%, the braking force is insufficient, resulting in less braking efficiency. In contrast, the vehicle will be unstable if the skid ratio is larger than 30%, making it easier to lock the wheel. 2.6 Operating Force and Braking Torque. The braking mechanism transmits the operating force provided by the driver to the brake calipers to generate the braking torques. The operating force is assumed to be equally distributed to the two brakes, i.e., brakes 1 and 2. The braking torques applied to the two brake disks are expressed as 1 (20) T1 ¼ 2ld Fo Lr P1 Rd1 2 1 (21) T2 ¼ 2ld Fo Lr P2 Rd2 2 where Fo is the operating force. The braking lever ratio Lr and the brake fluid pressure ratios P1 and P2 can increase the operating force. ld is the friction coefficient between the brake disk and brake caliper lining, and Rd1 and Rd2 are the effective radii of the two brake disks. The braking torque of brake 1 T1 provides a continuous braking torque on the wheel during the braking process. The braking torque of brake 2 T2 can transmit a braking torque that depends on the rotational speed of the CBD. We establish a numerical simulation program that can calculate the total braking torque acting on the wheel. Then, the angular acceleration and angular velocity of the wheel can be derived from the equations in the previous discussion. The characteristics of the C-ABS can be determined from the simulations. 065002-4 / Vol. 137, JUNE 2015
2.7 Estimation of Power Losses. Compared with the original system, the proposed system generates extra power losses due to the additional components, i.e., the CBD and gearbox. Because the inertia of the CBD is minor, the power loss due to the CBD is low and can be ignored. However, the power loss resulting from the gearbox is significant, and it can be estimated by calculating the resistances of the gears under mesh conditions. In the study by Heingartner and Mba, the power losses included windage loss, oil churning loss, sliding friction loss, and rolling friction loss [21]. Because the proposed gearbox for the C-ABS does not require immersion in lubricant, the primary source of power loss in the system is sliding friction loss. Kuria and Kihiu analyzed the power losses for multistage gear trains [22]. According to the simulation data charts, the average power loss resulting from sliding friction is 35 W at an input speed of 1500 rpm. Comparatively, the proposed gearbox is designed with only two-pair gears. Therefore, we can estimate that the power loss is approximately 17.5 W. Because a general scooter engine can provide almost 1600 W at the same rotational speed, according to calculations, the ratio between the power loss and output power is less than 1.1%. In other words, the gearbox is not a considerable source of energy consumption for the C-ABS.
Analysis of the Numerical Simulation
3.1 Structure and Method of the Simulation Program. In this study, we use MATLAB to simulate and analyze the C-ABS. We choose a 125 c.c. scooter as the basis of our numerical analysis model. In this scooter model, an excessive braking torque is applied on a single wheel as it advances at an initial speed. The braking force is held constant until the flywheel stops completely. The rotational speeds of the wheel and flywheel and the braking torque during the braking process can be determined from the numerical results. The skid ratio between the wheel and the flywheel can be derived from a simple calculation, from which we can determine whether the wheel is locked up and whether slip occurs. 3.2 Procedure for the Simulation Program. First, the program checks whether the flywheel, which has an initial rotational speed, is stopped. Second, the braking torque of brake 2 T2 and the braking torque of brake 1 T1 are calculated. Then, the program determined whether the CBD works and can transmit a braking torque TCBD . If so, the program checks whether the operating torque is larger than the CBD static friction torque, the maximum transmitting torque of the CBD. Then, the braking torque of the CBD can be determined. Finally, the total braking torque Tb acting on the wheel and other related parameters are calculated. This procedure is repeated until the flywheel stops. 3.3 Parameter Settings. In this paper, the parameter analysis process can be classified into three steps. First, the dimensions of the original vehicle are determined. We use a Kymco Racing 125 scooter as our model in the simulations. Second, the system parameters are set. These parameters consist of the weight and material characteristics of each component of the CBD. Third, the simulation parameters are set in the program. The parameters for the simulation include the initial speed of the vehicle and the variation of operating force. The detailed values of these parameters are presented in the Appendix. 3.4 Simulation Results and Parameter Studies. Different design parameters in the C-ABS will affect the braking performance. Therefore, the braking performance can be determined for various combinations of design parameter values to determine the most efficient design configuration. In this simulation, two road surface conditions, dry and wet asphalt surfaces, are considered. However, the simulated results show that it is meaningful and worthy to analyze in wet surface conditions. Therefore, we only show these figures simulated in wet surface conditions in this Transactions of the ASME
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parameter studies section. A better set of parameter values should not only yield a functioning ABS but also provide a higher braking performance. The design parameters analyzed here include the brake fluid pressure ratios of the original brake P1 and the CBD brake P2 , the speed-increasing gear ratio K and the effective radii of the brake disks Rd1 and Rd2 . The simulation results indicate that adjusting P2 and Rd2 influences the system only slightly. Therefore, the parameter values of the original vehicle can be used, and an additional parameter optimization study is not necessary. In addition, because changing Rd1 causes the same behavior as changing P1 , we can use the original effective radius value of the vehicle without varying Rd1 . The design parameters will be discussed in Secs. 3.4.1 and 3.4.2. 3.4.1 Changing the Fluid Pressure Ratio of the Original Brake P1 . We set P1 to be between 2 and 4, and the curves are drawn in 0.5 unit intervals. Figure 5 shows the variation of the braking torque acting on the wheel as a function of time. In wet surface conditions, the curves decline rapidly between 3.5 and 4.0 during the braking process and then maintain a constant value, at which point the wheel is locked. Figure 6 shows the skid ratio between the wheel speed and vehicle speed. It illustrates that the maximum two values of the fluid pressure ratio P1 result in the skid ratio becoming 100% in wet surface conditions, i.e., the wheel is locked. The simulations results demonstrate that the value of the fluid pressure ratio of the original brake should be designed to be between 3 and 3.5, as this range provides the best braking performance with an antilock braking function. 3.4.2 Changing the Speed-Increasing Gear Ratio K. We vary K between 3 and 5, and the curves obtained from the simulations are drawn at 0.5 unit intervals. Figure 7 presents the variations in the braking torque acting on the wheel. In wet surface conditions, the braking torque increases with increases in the speed-
increasing gear ratio. In addition, the curve will converge to a constant value regardless of the value of K. The convergent point is the point at which the output braking torque of the CBD stops due to insufficient rotational speed. Therefore, adjusting the speedincreasing gear ratio only affects the braking performance of the C-ABS in the earlier braking process. Figure 8 presents the skid ratio, which increases with increases in the speed-increasing gear ratio. From the skid ratio model discussed in Sec. 3.2, the best operating range for the skid ratio is between 10% and 30%. Therefore, the speed-increasing gear ratio should be designed such that the skid ratio in the braking process does not exceed 30%. The simulation results indicate that the value of the speedincreasing gear ratio should be designed to be lower than 4.5 so that the vehicle can provide safer braking. Adjusting the design parameter values led to the more effective set of design parameter values shown in Table 1 of the Appendix. The fluid pressure ratio and effective radius of the brake disk were not changed from their original values.
4
Comparison of the Braking Performance
In this paper, the braking performance of the C-ABS is analyzed in comparison with an original braking system and traditional ABS. First, we consider both dry and wet road surface conditions. We assume that the driver creates excessive operating force on the brake lever when encountering an emergency situation. The maximum operating force is set to be 460 N. Second, we discuss the difference in the working characteristics between the C-ABS and a traditional ABS. In particular, the C-ABS can provide a continuous braking torque during the ABS function so that the braking mechanism will provide better braking performance. 4.1 Comparison of the C-ABS and Original Braking System. Figure 9 shows the comparison of the braking torque from the C-ABS and from the original braking system. The thick
Fig. 5 Variations in the braking torque with changes in the fluid pressure ratio P1
Fig. 7 Variations in the braking torque with changes in the speed-increasing gear ratio K
Fig. 6 Variations in the skid ratio with changes in the fluid pressure ratio P1
Fig. 8 Variations in the skid ratio with changes in the speedincreasing gear ratio K
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and dotted lines represent the performance curve of the C-ABS and the general braking system, respectively. The curve illustrates that the slope of the thick line is greater than that of the dotted line in the rising stage. That is, the braking torque and braking force of the CABS increase more rapidly than those of the other systems because the speed-increasing gearbox increases the braking torque. Figure 9(a) illustrates that the braking torque of the original braking system is greater than that of the C-ABS in dry surface conditions. However, in wet surface conditions, as shown in Fig. 9(b), the braking torque curve of the C-ABS is higher than the original braking system. Figure 10 illustrates the dependence of the braking performances on the wheel and vehicle speeds. From an initial inspection of Fig. 10(a), the braking performance of the original braking system appears to be better than that of the C-ABS because the original braking system causes the vehicle to stop more rapidly. However, the wheel speed of the original braking system declines to 0 rapidly after the application of the brake, which will cause the wheel to lock and the vehicle to lose control. This situation is dangerous for a two-wheeled vehicle because it may cause the vehicle slip or turn over. In contrast, for the C-ABS, the wheel speed and vehicle speed decline in a stable manner during the braking process. Therefore, the vehicle maintains adequate control. 4.2 Comparison of the C-ABS and Traditional ABS. The simulation results illustrate that the mechanism of the antilock function of the C-ABS is different from that of the traditional ABS. The traditional ABS uses an electronic sensor to measure the wheel speed. The braking torque is then controlled by adjusting the brake fluid pressure. Therefore, the braking force supplied to the vehicle is discontinuous. This discontinuity causes not only vibration during the braking process but also a loss in some braking force while the fluid pressure is reduced. However, as shown in Fig. 9, when the antilock function of the C-ABS is used, the braking torque maintains a constant value with good performance rather than periodic variation, i.e., the wheel receives a continuous
Fig. 10 Comparison of the wheel speed and vehicle speed between the C-ABS and original braking system: (a) Dry surface conditions and (b) wet surface conditions
braking torque. Therefore, the C-ABS not only provides better braking performance than the traditional ABS but also generates less vibration during the ABS process.
5
Discussion
The C-ABS is simulated using an asphalt road with dry and wet surfaces. The results demonstrate that the system provides antilock brake functionality while maintaining sufficient braking performance. However, if the surface condition of the road is worse, e.g., an icy surface with an extremely low friction coefficient, the braking torque provided by brake 1 may lock the wheel because of the insufficient static friction coefficient between the wheel and ground. Therefore, the proposed system is not suitable for vehicles required to operate on snow or for vehicles such as off-road vehicles. The factors that affect the performance of the C-ABS include the temperature of the CBD and the wear of the frictional material. High temperatures decrease the friction coefficient when continuously operating the brake for a long period of time, as shown in Fig. 4. Therefore, heat elimination needs to be considered. Furthermore, the wear of the frictional material of the centrifugal brake shoes may change the rotational speed of engagement. The brake shoes should be adjusted or replaced regularly.
6
Fig. 9 Comparison of the braking torque between the C-ABS and original braking system: (a) dry surface conditions and (b) wet surface conditions
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Conclusion
This paper presents a mechanical C-ABS. A numerical simulation program is developed based on the mechanical model of the entire braking system. The simulation results demonstrate the antilock capability of the C-ABS for both wet and dry road surfaces when an excessive operating force is applied. The working characteristics of the proposed system are shown in the parameter studies, from which better design parameters are derived. The differences in the antilock mechanism between the proposed and traditional ABS are discussed. The C-ABS is more efficient than the traditional ABS due to its continuous braking force. The C-ABS can also reduce vibrations during the braking process. In addition, Transactions of the ASME
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the absence of any electronic components makes it easy to use in two-wheeled vehicles. This paper presented the details of the C-ABS to facilitate the development of a higher safety standard for braking systems, which can contribute to fields beyond only two-wheeled vehicles.
Acknowledgment The support provided by Giant Lion Know-How Co., Ltd., for this study is gratefully appreciated. Furthermore, we especially thanks to Mr. Tai-Her Yang for his helpful discussions.
Appendix
Table 1 Parameter value settings in the simulation Parameters
Value
1 More effective main parameter values Fluid pressure ratio of brake 1 P1 Fluid pressure ratio of brake 2 P2 Speed-increasing gear ratio K Effective radius of the brake disk Rd (m)
3.2 8 3.8 0.0871
2 Dimensions of the original vehicle Vehicle weight (kgw) Driver weight (kgw) Radius of the wheel (m) Inertia of the wheel (kg m2 ) Effective radius of the brake disk (m) Lever ratio of the brake Fluid pressure ratio of the original brake
113 70 0.2435 0.112 0.0871 3.125 8
3 Setting of the system parameters CBD weight (kgw) Friction coefficient of the braking pad [23] Centrifugal brake shoe—static friction coefficient [23] Centrifugal brake shoe—kinetic friction coefficient [23] Specific heat of the CBD [24] Surface area of the CBD (m2 ) Forced convection heat transfer coefficient of gases (W=m2 C) [24] Rolling resistance coefficient of the tire [25] Radius of the flywheel (m) Inertia of the flywheel (kg m2 ) 4 Simulation parameter values setting in the program Initial vehicle speed (km=hr) Surrounding temperature ( C) Maximum operating force (N) [26]
Journal of Mechanical Design
1.36 0.31 0.41 0.35 (T ¼ 25o C) 502 0.0363 200 0.013 0.25 11.4375 60 25 460
References [1] Heisler, H., 2002, Advanced Vehicle Technology, 2nd ed., Elsevier Ltd., London. [2] Wakabayashi, T., Matsuto, T., Tani, K., and Ohta, A., 1998, “Development of Motor Actuated Antilock Brake System for Light Weight Motorcycle,” JSAE Rev., 19(4), pp. 373–377. [3] Lu, C.-Y., and Shih, M.-C., 2005, “Design of a Hydraulic Anti-Lock Braking Modulator and an Intelligent Brake Pressure Controller for a Light Motorcycle,” Veh. Syst. Dyn., 43(3), pp. 217–232. [4] Ho, L. M., Roberts, R., Hartmann, H., and Gombert, B., 2006, “The Electronic Wedge brake—EWB,” Siemens AG, Siemens VDO Automotive, SAE Technical Paper No. 2006-01-3196. [5] Choi, S.-B., Sung, K.-G., Cho, M.-S., and Lee, Y.-S., 2007, “The Braking Performance of a Vehicle Anti-Lock Brake System Featuring an ElectroRheological Valve Pressure Modulator,” Smart Mater. Struct., 16(4), pp. 1285–1297. [6] Huang, T.-C., 2008, “Antilock Brake System Structure,” Taiwan Patent No. 200,942,708. [7] Yang, C.-P., and Liu, T., 2013, “Analysis of a New Mechanical Anti-Lock Brake System for Two-Wheeled Vehicle,” Appl. Mech. Mater., 437, pp. 313–320. [8] Ruan, Z.-C., 1999, “Bicycle Antilock Brake Device,” Taiwan Patent No. 363,576. [9] Chen, J.-W., 2000, “Anti-Lock Brake Device for Bicycle,” Taiwan Patent No. 450,243. [10] Huang, C.-H., 2006, “Stepwise Brake Structure,” Taiwan Patent No. I353943. [11] Xu, Z.-H., Gu, W.-Q., and Hong, W.-J., 2002, “Anti-Lock Braking Device of Bicycle,” Taiwan Patent No. 559,179. [12] Lv, C.-M., Lv, Y.-W., and Lv, Y.-X., 2011, “Two-Wheel Braking Control Device,” Taiwan Patent No. M402254. [13] Swift, D. P., LaCroix, T. R., and Bullock, W. E., 1997, “Centrifugal Shopping Cart Brake,” U.S. Patent No. 5,607,030. [14] Kidd, M. T., and Cline, G. L., 2008, “Centrifugal Brakes for Wheels,” U.S. Patent No. 7,464,797 B2. [15] Ferdman, L., 2013, “Wheel Speed Regulator,” U. S. Patent No. 0025984 A1. [16] Shigley, J. E., and Mischke, C. R., 2001, Mechanical Engineering Design, 6th ed., McGraw-Hill, New York. [17] Huang, F., Mo, Y.-M., and Lv, J.-C., 2010, “Study on Heat Fading of Phenolic Resin Friction Material for Micro-Automobile Clutch,” Proceedings of the IEEE International Conference on Measuring Technology and Mechatronics Automation (ICMTMA), Vol. 3, pp. 596–599. [18] Cossalter, V., 2006, Motorcycle Dynamics, 2nd ed., Race Dynamics, Greendale, WI. [19] Kiencke, U., and Daiss, A., 1994, “Estimation of Tyre Friction for Enhanced ABS-Systems,” JSAE Rev., 16(2), pp. 221–221(1). [20] Wong, J. Y., 2008, Theory of Ground Vehicles, 4th ed., Wiley, Ottawa, ON, p. 27. [21] Heingartner, P., and Mba, D., 2005, “Determining Power Losses in the Helical Gear Mesh,” Proceedings of the Gear Technology, pp. 32–37. [22] Kuria, J., and Kihiu, J., 2011, “Prediction of Overall Efficiency in Multistage Gear Trains,” World Acad. Sci., Eng. Technol., 5(2), pp. 50–56. [23] Shigley, J. E., and Mischke, C. R., 1996, Standard Handbook of Machine Design, 2nd ed., McGraw-Hill, New York. [24] C¸engel, Y. A., 2004, Heat Transfer, 2nd ed., McGraw-Hill, New York. [25] Wong, J. Y., 2008, Theory of Ground Vehicles, 4th ed., Wiley, Ottawa, ON, p. 17. [26] Haidar, S. G., Kumar, D., Bassi, R. S., and Deshmukh, S. C., 2004, “Average Versus Maximum Grip Strength: Which is More Consistent?,” J. Hand Surg.Br. Eur., 29(1), pp. 82–84.
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Ming-Shien Yang Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwan e-mail: [email protected]
Tyng Liu Associate Professor Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwan e-mail: [email protected]
A new concept for a mechanical antilock braking system (ABS) with a centrifugal braking device (CBD), termed a centrifugal ABS (C-ABS), is presented and developed in this paper. This new CBD functions as a brake in which the output braking torque adjusts itself depending on the speed of the output rotation. First, the structure and mechanical models of the entire braking system are introduced and established. Second, a numerical computer program for simulating the operation of the system is developed. The characteristics of the system can be easily identified and can be designed with better performance by using this program to studying the effects of different design parameters. Finally, the difference in the braking performance between the C-ABS and the braking system with or without a traditional ABS is discussed. The simulation results indicate that the C-ABS can prevent the wheel from locking even if excessive operating force is provided while still maintaining acceptable braking performance. [DOI: 10.1115/1.4030014] Keywords: centrifugal braking device, mechanical antilock braking system, braking performance, braking safety
1
Introduction
The braking system is a critical component of vehicles, and extensive research on ABSs has been published recently. Locking of the wheel while braking is in progress can be dangerous because the driver can lose control of the vehicle, resulting in an increased braking distance. Therefore, for safety, ABSs are installed on most general passenger cars and certain heavy vehicles. In 1936, Bosch developed a hydraulic–electric braking system suitable for cars [1]. The braking pressure can be adjusted appropriately by using an electronic sensor to measure the rotational speed of the wheel. Girling developed a hydromechanical ABS in the mid-1980s [1]. This system uses a centrifugal clutch instead of an electronic sensor. Its friction force changes with the rotational 1 Corresponding author. Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 26, 2014; final manuscript received March 4, 2015; published online April 2, 2015. Assoc. Editor: Qi Fan.
Journal of Mechanical Design
speed of the wheel to adjust the output braking pressure. Wakabayashi et al. developed a motor-actuated ABS in 1988 [2]. The antilock motor drives the driving disk through a planet gear and then pulls the braking wire to reduce the braking force. Lu and Shin developed a hydraulic-modulating ABS in 2005 [3]. In this system, the volume of the brake fluid container can be changed by an internal push rod, which is controlled by an electromagnetic coil; in this manner, the braking pressure can be adjusted. Siemens developed an electronic wedge braking system in 2006 [4]. The braking force can be changed directly by measuring the rotational speed of the wheel and controlling the voltage and current. In 2007, Choi et al. developed an ABS with an electro-rheological valve pressure modulator [5]. The braking force can be adjusted by controlling the viscosity of the brake fluid by changing the current producing the magnetic field. Huang developed a mechanical antilock braking device suitable for a bicycle in 2008 [6]. The maximum braking force can be fixed by using an antilock spring and wedge braking pad. Therefore, the wheel will not lock even if the driver provides excessive operating force. This ABS was further analyzed by our group in 2013 [7]. In addition, several patents have presented various ABS designs for light two-wheeled vehicles [8–12]. Electronic ABSs have been commonly installed on both general passenger cars and heavy vehicles. Electronic ABSs contain electronic sensors and a central control unit. These ABSs can control the braking force by rapidly adjusting the pressure of the brake fluid. However, there are some disadvantages to this operating mode. First, the braking force is discontinuous. When the ABS is used, the braking force changes over time, i.e., the vehicle could lose a portion of the braking force during the braking period. Second, the system includes many complex and expensive components. Therefore, this system is unsuitable for use in light two-wheeled vehicles. To overcome the disadvantages of electronic ABSs, we attempt to develop a mechanical ABS, i.e., C-ABS, which prevents the wheel from locking by using centrifugal force to automatically adjust the braking force. A patent search revealed that there are some braking devices that use the same concept as C-ABS [13–15]. These devices provide a braking force based on the rotational speed. However, when the rotational speed is slow, there is a lack of braking force generated or even a loss of brakes. Therefore, these problems should be overcome to apply these devices to braking systems. The C-ABS is designed with two brakes and a gearbox to increase the total braking force, and the antilock function is achieved through the improved brake fluid pressure distribution. Additionally, the proposed system increases the braking efficiency by applying a continuous braking force. In this paper, we use a commercial scooter as our model of analysis, establishing a numerical program to realize the characteristics of the system. Then, preferred design parameters can be determined from the results of the simulated braking performance.
2
Principle of the C-ABS
2.1 Basic Concept of the C-ABS. The output torque of the centrifugal brake shoe will change according to its rotational speed, i.e., the output torque increases as the rotational speed increases, and vice versa. Therefore, the CBD can adjust the braking force automatically as the rotational speed of the wheel changes, preventing excessive braking torque, which locks the wheel. The proposed system consists of a CBD, two brakes, and a speed-increasing gearbox. The first brake is the original brake of the vehicle, whereas the second brake is the proposed CBD. The function of the speed-increasing gearbox is to increase both the rotational speed of the centrifugal brake shoe and the output braking torque to the wheel. When the driver operates the brake lever, two braking torques are applied to the wheel simultaneously. The first braking torque is applied to the wheel directly. The second braking torque acts on the housing initially but is then transmitted from the centrifugal brake shoe to the gearbox. This second torque increases the braking torque before acting on the wheel. If the
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rotational speed of the wheel decreases sharply due to excessive braking torque, the centrifugal brake shoe will not contain sufficient centrifugal force, leading to a lack of friction force with the housing. This lack of friction force will cause a slip between the centrifugal brake shoe and the housing. In other words, the static friction transitions to kinetic friction, thus reducing the braking torque acting on the wheel. After the rotational speed decreases to the minimum engagement speed of the CBD, the centrifugal brake shoe separates from the housing and stops transmitting braking torque to the wheel. At this stage, a continuous braking force is applied by the first braking system only. The basic C-ABS is illustrated in Fig. 1. The section outlined by the dotted line is the proposed CBD, which is connected to the wheel through the speed-increasing gearbox. The C-ABS prototype is shown in Fig. 2. The mechanism is developed according to the basic concept outlined in Fig. 1. This structure is designed to be easily fabricated and measured. 2.2 Mechanical Model of the CBD. The main components of the CBD are three centrifugal brake shoes, a bearing, and a housing with a brake disk. Figure 3 shows the free body diagram of one single centrifugal brake shoe analyzed in the counterclockwise direction. The forces shown include the centrifugal force FCBD , the spring force Fspr , the friction force of rubber bushing Frbr , the normal force dN, and the friction force with the housing ldN l represents the friction coefficient between the centrifugal brake shoe and the housing. The angular velocity x1 of the CBD, with a mass m, generates a centrifugal force at the mass center. This force is represented by the equation FCBD ¼ mx21 rcm
(1)
where k is the elastic coefficient of the spring and DS0 is the prestretched length of the spring. When the brake shoe engages with the housing, the spring stretches an additional amount DS. From the geometrical configuration of the brake shoe, the equation of the spring force can be described as Fspr ¼ kðDS0 þ DSÞ
(2)
Assuming that there is a unit pressure p acting on the brake shoe at an angle hc from the rotational axis, the applied pressure will be proportional to the vertical distance between the acting point and rotational axis [16]. The equation can be described as p pm ¼ sin hc sin hm
Fig. 1 Basic composition of the C-ABS
065002-2 / Vol. 137, JUNE 2015
(3)
Fig. 2 C-ABS prototype
where pm and hm represent the maximum pressure and the angle of the maximum pressure, respectively. If the angle between the frictional material on the brake shoe and the end position is less than 90 deg, then ha ¼ hc2 ; if hc2 > 90 deg, then ha ¼ 90 deg. The normal force acting on the brake shoe can be derived as dN ¼ pbr dhc ¼
pm br sin hc dhc sin hm
(4)
where b is the width of the frictional material. Considering all of the forces acting on the centrifugal brake shoe, the force balance along the rotational axis can be expressed as FCBD r2 Fspr rs1 Fspr rs2 Frbr r3 Mn Mt ¼ 0
(5)
where Mn and Mt are the vertical direction moment and tangent direction moment of the friction material, respectively. By rewriting the equation, we can derive the output torque of the CBD shown as below ð ð nlpm br2 hc2 sin hc dhc (6) TCBD ¼ n lrdN ¼ sin hm hc1 where n is the number of centrifugal brake shoes in the CBD. When the centrifugal brake shoe begins to engage with the housing, the equation of motion can be written as
Fig. 3 The mechanical model of the centrifugal brake shoe
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FCBD;0 r2 Fspr rs1 Fspr rs2 Frbr r3 ¼ 0
(7)
Therefore, we can derive the angular velocity of the CBD when it is engaging as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fspr ðrs1 þ rs2 Þ þ Frbr r3 x0 ¼ (8) mrcm r2 2.3 Model of the Friction Coefficient of the CBD. The friction coefficient is affected by not only the frictional material but also the surface temperature. Therefore, it is necessary to establish a model for the friction coefficient that can describe its variation with temperature. When kinetic friction is generated between the centrifugal brake shoe and the housing, their surface temperatures will rise and change the friction coefficient. The energy conservation equation can be used to calculate the amount of kinetic energy that has been converted to thermal energy at each moment. Some assumptions should be made to simplify the model. First, the motional energy of the CBD is considered negligible. Second, the energy losses generated by the slip between the tire and flywheel are negligible. Third, there is no energy loss from the transmission and resistance of the bearings. The energy conservation equation can be written as Ef0 þ Ew0 TCBD Dx dt ¼ Ef þ Ew þ Q
Variation in the friction coefficient with temperature [17]
After determining the friction coefficient between the centrifugal brake shoe and the housing, the exact output torque of the CBD can be derived.
(9)
where Ef0 and Ew0 are the rotational energies of the flywheel and wheel, respectively, at the previous time step; Dx is the variation of rotational speed per unit time; Ef and Ew are the rotational energies of the flywheel and wheel at the next step, respectively; and Q is the thermal energy generated in this system. The following equations represent the relationship between these parameters: 8 1 > > Ef ¼ If x2f > > 2 > > < 1 Ew ¼ Iw x2w (10) 2 > > > > Dx ¼ Kx Kx w0 w > > : Q ¼ Qabs þ Qloss where If and Iw are the inertias of the flywheel and the wheel, respectively, and K is the speed-increasing gear ratio of the gearbox that increases the rotational speed of the CBD. The heat absorbed by the centrifugal brake shoe Qabs and the heat lost to the air Qloss can be described from thermodynamics and heat transfer as ( Qabs ¼ mcp DT ¼ mcp ðT T 0 Þ (11) Qloss ¼ Q_ conv dt ¼ hAs ðTs T 1 Þdt where cp and As represent the specific heat and the surface area of the CBD, respectively, and h is the forced convection heat transfer coefficient of gases. We assume that the centrifugal brake shoe is evenly heated, i.e., the variation of the surface temperature equals the temperature variation of the entire material, Ts ¼ T. The environmental temperature is set to 25 C, which is also the initial temperature of the centrifugal brake shoe, i.e., T 0 ¼ T 1 ¼ 25 C. The temperature of the centrifugal brake shoe at each moment can be derived from the previous equations. Huang et al. acquired a relationship for the kinetic friction coefficient of the centrifugal clutch experimentally. As shown in Fig. 4, we can draw three trend lines from these data. The trend lines can be described as 8 1 1 > > if T 250 Tþ > > 1500 3 > < 1 89 lðTÞ ¼ (12) if 250 < T 330 Tþ > 1600 160 > > > 1 15 > : if T 330 Tþ 480 16 Journal of Mechanical Design
Fig. 4
2.4 Mechanics of the Wheel. A wheel acting on the flywheel during the braking process is considered. When the brake engages, there is a total braking torque Tb generated on the wheel, and a braking force Fb is simultaneously generated on the surface of the tire. Because the tire is elastic, it will deform as the wheel rolls under a load. The energy consumption results in a rolling resistance for the wheel, which equals the rolling resistance torque resulting from the normal force N acting on off-set distance d. The value d can be derived from the product of the radius of the wheel and the coefficient of rolling resistance fr [18]. Thus, the torque equation can be described as Fb Rw Tb Nd ¼ Iw aw
(13)
where Rw and aw are the radius and the angular acceleration of the wheel, respectively. Similarly, the torque equation for the flywheel can be expressed as Fb Rf þ Nd ¼ If af
(14)
where Rf and af are the radius and angular acceleration of the flywheel, respectively. We can derive the angular velocity at each moment through our numerical simulation program by obtaining the angular accelerations of the wheel and flywheel. The function of the flywheel is to simulate the motion of the kinetic energy of the vehicle so that the inertia of the flywheel can be derived from the energy conservation equation as 1 1 MV 2 ¼ If x2f 2 2
(15)
If ¼ MR2f
(16)
where M and V are the mass and velocity of the vehicle, respectively. After the inertia of the flywheel is determined, the motion of the vehicle can be derived from the flywheel in the simulation program. 2.5 Skid Ratio of the Wheel. In an ideal condition, the wheel rolls entirely on the ground when no force is acting on it. Therefore, the vehicle speed can be determined from the wheel speed. The wheel speed refers to the tangential speed of the wheel, i.e., it is different from the rotational speed of the wheel. However, when the brake engages, the wheel speed and the vehicle speed differ. The relationship describing this difference can be defined as the skid ratio s, which is expressed as JUNE 2015, Vol. 137 / 065002-3
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s¼
V xw Rw 100 % V
(17)
where V is the speed of the vehicle. The tangential speed of the wheel can be derived from the product of the angular velocity xw and the radius Rw . If the skid ratio is zero, then the wheel is rolling purely without slip; if the skid ratio is 100%, then the wheel stops rolling but the vehicle continues to move. In other words, the wheel is locked, and only pure slip occurs. The vehicle speed can be derived from the tangential speed of the flywheel under the assumption that the variation in the speed of the flywheel is equal to the true motion of the vehicle. Many studies have focused on the skid ratio and friction models. In this study, we use the friction model introduced by Kiencke and Daiss [19]. The relationship between the friction coefficient and the skid ratio can be expressed as lg ðsÞ ¼
as b þ cs þ s2
(18)
where the parameters in Eq. (18) are defined as 8 lp l1 > a¼ ð1 sp Þ2 > > l > p l1 > > < b ¼ s2p > > > > l1 ð1 þ s2p Þ 2lp l1 > > :c ¼ lp l1
3 (19)
In the above equation, lp is the peak value of the friction coefficient, sp is the skid ratio at the peak value of the friction coefficient, and l1 is the friction coefficient when the skid ratio is 100%. The values of the parameters are taken from Ref. [20]. We set the parameter values for a road surface with dry asphalt as ðsp ; lp ; l1 Þ ¼ 0:2; 0:85; 0:75, whereas the parameter values for a road with wet asphalt are ðsp ; lp ; l1 Þ ¼ 0:2; 0:6; 0:5. When designing a braking system, the skid ratio should be controlled between approximately 10% and 30% to achieve maximum braking performance. If the skid ratio is smaller than 10%, the braking force is insufficient, resulting in less braking efficiency. In contrast, the vehicle will be unstable if the skid ratio is larger than 30%, making it easier to lock the wheel. 2.6 Operating Force and Braking Torque. The braking mechanism transmits the operating force provided by the driver to the brake calipers to generate the braking torques. The operating force is assumed to be equally distributed to the two brakes, i.e., brakes 1 and 2. The braking torques applied to the two brake disks are expressed as 1 (20) T1 ¼ 2ld Fo Lr P1 Rd1 2 1 (21) T2 ¼ 2ld Fo Lr P2 Rd2 2 where Fo is the operating force. The braking lever ratio Lr and the brake fluid pressure ratios P1 and P2 can increase the operating force. ld is the friction coefficient between the brake disk and brake caliper lining, and Rd1 and Rd2 are the effective radii of the two brake disks. The braking torque of brake 1 T1 provides a continuous braking torque on the wheel during the braking process. The braking torque of brake 2 T2 can transmit a braking torque that depends on the rotational speed of the CBD. We establish a numerical simulation program that can calculate the total braking torque acting on the wheel. Then, the angular acceleration and angular velocity of the wheel can be derived from the equations in the previous discussion. The characteristics of the C-ABS can be determined from the simulations. 065002-4 / Vol. 137, JUNE 2015
2.7 Estimation of Power Losses. Compared with the original system, the proposed system generates extra power losses due to the additional components, i.e., the CBD and gearbox. Because the inertia of the CBD is minor, the power loss due to the CBD is low and can be ignored. However, the power loss resulting from the gearbox is significant, and it can be estimated by calculating the resistances of the gears under mesh conditions. In the study by Heingartner and Mba, the power losses included windage loss, oil churning loss, sliding friction loss, and rolling friction loss [21]. Because the proposed gearbox for the C-ABS does not require immersion in lubricant, the primary source of power loss in the system is sliding friction loss. Kuria and Kihiu analyzed the power losses for multistage gear trains [22]. According to the simulation data charts, the average power loss resulting from sliding friction is 35 W at an input speed of 1500 rpm. Comparatively, the proposed gearbox is designed with only two-pair gears. Therefore, we can estimate that the power loss is approximately 17.5 W. Because a general scooter engine can provide almost 1600 W at the same rotational speed, according to calculations, the ratio between the power loss and output power is less than 1.1%. In other words, the gearbox is not a considerable source of energy consumption for the C-ABS.
Analysis of the Numerical Simulation
3.1 Structure and Method of the Simulation Program. In this study, we use MATLAB to simulate and analyze the C-ABS. We choose a 125 c.c. scooter as the basis of our numerical analysis model. In this scooter model, an excessive braking torque is applied on a single wheel as it advances at an initial speed. The braking force is held constant until the flywheel stops completely. The rotational speeds of the wheel and flywheel and the braking torque during the braking process can be determined from the numerical results. The skid ratio between the wheel and the flywheel can be derived from a simple calculation, from which we can determine whether the wheel is locked up and whether slip occurs. 3.2 Procedure for the Simulation Program. First, the program checks whether the flywheel, which has an initial rotational speed, is stopped. Second, the braking torque of brake 2 T2 and the braking torque of brake 1 T1 are calculated. Then, the program determined whether the CBD works and can transmit a braking torque TCBD . If so, the program checks whether the operating torque is larger than the CBD static friction torque, the maximum transmitting torque of the CBD. Then, the braking torque of the CBD can be determined. Finally, the total braking torque Tb acting on the wheel and other related parameters are calculated. This procedure is repeated until the flywheel stops. 3.3 Parameter Settings. In this paper, the parameter analysis process can be classified into three steps. First, the dimensions of the original vehicle are determined. We use a Kymco Racing 125 scooter as our model in the simulations. Second, the system parameters are set. These parameters consist of the weight and material characteristics of each component of the CBD. Third, the simulation parameters are set in the program. The parameters for the simulation include the initial speed of the vehicle and the variation of operating force. The detailed values of these parameters are presented in the Appendix. 3.4 Simulation Results and Parameter Studies. Different design parameters in the C-ABS will affect the braking performance. Therefore, the braking performance can be determined for various combinations of design parameter values to determine the most efficient design configuration. In this simulation, two road surface conditions, dry and wet asphalt surfaces, are considered. However, the simulated results show that it is meaningful and worthy to analyze in wet surface conditions. Therefore, we only show these figures simulated in wet surface conditions in this Transactions of the ASME
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parameter studies section. A better set of parameter values should not only yield a functioning ABS but also provide a higher braking performance. The design parameters analyzed here include the brake fluid pressure ratios of the original brake P1 and the CBD brake P2 , the speed-increasing gear ratio K and the effective radii of the brake disks Rd1 and Rd2 . The simulation results indicate that adjusting P2 and Rd2 influences the system only slightly. Therefore, the parameter values of the original vehicle can be used, and an additional parameter optimization study is not necessary. In addition, because changing Rd1 causes the same behavior as changing P1 , we can use the original effective radius value of the vehicle without varying Rd1 . The design parameters will be discussed in Secs. 3.4.1 and 3.4.2. 3.4.1 Changing the Fluid Pressure Ratio of the Original Brake P1 . We set P1 to be between 2 and 4, and the curves are drawn in 0.5 unit intervals. Figure 5 shows the variation of the braking torque acting on the wheel as a function of time. In wet surface conditions, the curves decline rapidly between 3.5 and 4.0 during the braking process and then maintain a constant value, at which point the wheel is locked. Figure 6 shows the skid ratio between the wheel speed and vehicle speed. It illustrates that the maximum two values of the fluid pressure ratio P1 result in the skid ratio becoming 100% in wet surface conditions, i.e., the wheel is locked. The simulations results demonstrate that the value of the fluid pressure ratio of the original brake should be designed to be between 3 and 3.5, as this range provides the best braking performance with an antilock braking function. 3.4.2 Changing the Speed-Increasing Gear Ratio K. We vary K between 3 and 5, and the curves obtained from the simulations are drawn at 0.5 unit intervals. Figure 7 presents the variations in the braking torque acting on the wheel. In wet surface conditions, the braking torque increases with increases in the speed-
increasing gear ratio. In addition, the curve will converge to a constant value regardless of the value of K. The convergent point is the point at which the output braking torque of the CBD stops due to insufficient rotational speed. Therefore, adjusting the speedincreasing gear ratio only affects the braking performance of the C-ABS in the earlier braking process. Figure 8 presents the skid ratio, which increases with increases in the speed-increasing gear ratio. From the skid ratio model discussed in Sec. 3.2, the best operating range for the skid ratio is between 10% and 30%. Therefore, the speed-increasing gear ratio should be designed such that the skid ratio in the braking process does not exceed 30%. The simulation results indicate that the value of the speedincreasing gear ratio should be designed to be lower than 4.5 so that the vehicle can provide safer braking. Adjusting the design parameter values led to the more effective set of design parameter values shown in Table 1 of the Appendix. The fluid pressure ratio and effective radius of the brake disk were not changed from their original values.
4
Comparison of the Braking Performance
In this paper, the braking performance of the C-ABS is analyzed in comparison with an original braking system and traditional ABS. First, we consider both dry and wet road surface conditions. We assume that the driver creates excessive operating force on the brake lever when encountering an emergency situation. The maximum operating force is set to be 460 N. Second, we discuss the difference in the working characteristics between the C-ABS and a traditional ABS. In particular, the C-ABS can provide a continuous braking torque during the ABS function so that the braking mechanism will provide better braking performance. 4.1 Comparison of the C-ABS and Original Braking System. Figure 9 shows the comparison of the braking torque from the C-ABS and from the original braking system. The thick
Fig. 5 Variations in the braking torque with changes in the fluid pressure ratio P1
Fig. 7 Variations in the braking torque with changes in the speed-increasing gear ratio K
Fig. 6 Variations in the skid ratio with changes in the fluid pressure ratio P1
Fig. 8 Variations in the skid ratio with changes in the speedincreasing gear ratio K
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and dotted lines represent the performance curve of the C-ABS and the general braking system, respectively. The curve illustrates that the slope of the thick line is greater than that of the dotted line in the rising stage. That is, the braking torque and braking force of the CABS increase more rapidly than those of the other systems because the speed-increasing gearbox increases the braking torque. Figure 9(a) illustrates that the braking torque of the original braking system is greater than that of the C-ABS in dry surface conditions. However, in wet surface conditions, as shown in Fig. 9(b), the braking torque curve of the C-ABS is higher than the original braking system. Figure 10 illustrates the dependence of the braking performances on the wheel and vehicle speeds. From an initial inspection of Fig. 10(a), the braking performance of the original braking system appears to be better than that of the C-ABS because the original braking system causes the vehicle to stop more rapidly. However, the wheel speed of the original braking system declines to 0 rapidly after the application of the brake, which will cause the wheel to lock and the vehicle to lose control. This situation is dangerous for a two-wheeled vehicle because it may cause the vehicle slip or turn over. In contrast, for the C-ABS, the wheel speed and vehicle speed decline in a stable manner during the braking process. Therefore, the vehicle maintains adequate control. 4.2 Comparison of the C-ABS and Traditional ABS. The simulation results illustrate that the mechanism of the antilock function of the C-ABS is different from that of the traditional ABS. The traditional ABS uses an electronic sensor to measure the wheel speed. The braking torque is then controlled by adjusting the brake fluid pressure. Therefore, the braking force supplied to the vehicle is discontinuous. This discontinuity causes not only vibration during the braking process but also a loss in some braking force while the fluid pressure is reduced. However, as shown in Fig. 9, when the antilock function of the C-ABS is used, the braking torque maintains a constant value with good performance rather than periodic variation, i.e., the wheel receives a continuous
Fig. 10 Comparison of the wheel speed and vehicle speed between the C-ABS and original braking system: (a) Dry surface conditions and (b) wet surface conditions
braking torque. Therefore, the C-ABS not only provides better braking performance than the traditional ABS but also generates less vibration during the ABS process.
5
Discussion
The C-ABS is simulated using an asphalt road with dry and wet surfaces. The results demonstrate that the system provides antilock brake functionality while maintaining sufficient braking performance. However, if the surface condition of the road is worse, e.g., an icy surface with an extremely low friction coefficient, the braking torque provided by brake 1 may lock the wheel because of the insufficient static friction coefficient between the wheel and ground. Therefore, the proposed system is not suitable for vehicles required to operate on snow or for vehicles such as off-road vehicles. The factors that affect the performance of the C-ABS include the temperature of the CBD and the wear of the frictional material. High temperatures decrease the friction coefficient when continuously operating the brake for a long period of time, as shown in Fig. 4. Therefore, heat elimination needs to be considered. Furthermore, the wear of the frictional material of the centrifugal brake shoes may change the rotational speed of engagement. The brake shoes should be adjusted or replaced regularly.
6
Fig. 9 Comparison of the braking torque between the C-ABS and original braking system: (a) dry surface conditions and (b) wet surface conditions
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Conclusion
This paper presents a mechanical C-ABS. A numerical simulation program is developed based on the mechanical model of the entire braking system. The simulation results demonstrate the antilock capability of the C-ABS for both wet and dry road surfaces when an excessive operating force is applied. The working characteristics of the proposed system are shown in the parameter studies, from which better design parameters are derived. The differences in the antilock mechanism between the proposed and traditional ABS are discussed. The C-ABS is more efficient than the traditional ABS due to its continuous braking force. The C-ABS can also reduce vibrations during the braking process. In addition, Transactions of the ASME
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the absence of any electronic components makes it easy to use in two-wheeled vehicles. This paper presented the details of the C-ABS to facilitate the development of a higher safety standard for braking systems, which can contribute to fields beyond only two-wheeled vehicles.
Acknowledgment The support provided by Giant Lion Know-How Co., Ltd., for this study is gratefully appreciated. Furthermore, we especially thanks to Mr. Tai-Her Yang for his helpful discussions.
Appendix
Table 1 Parameter value settings in the simulation Parameters
Value
1 More effective main parameter values Fluid pressure ratio of brake 1 P1 Fluid pressure ratio of brake 2 P2 Speed-increasing gear ratio K Effective radius of the brake disk Rd (m)
3.2 8 3.8 0.0871
2 Dimensions of the original vehicle Vehicle weight (kgw) Driver weight (kgw) Radius of the wheel (m) Inertia of the wheel (kg m2 ) Effective radius of the brake disk (m) Lever ratio of the brake Fluid pressure ratio of the original brake
113 70 0.2435 0.112 0.0871 3.125 8
3 Setting of the system parameters CBD weight (kgw) Friction coefficient of the braking pad [23] Centrifugal brake shoe—static friction coefficient [23] Centrifugal brake shoe—kinetic friction coefficient [23] Specific heat of the CBD [24] Surface area of the CBD (m2 ) Forced convection heat transfer coefficient of gases (W=m2 C) [24] Rolling resistance coefficient of the tire [25] Radius of the flywheel (m) Inertia of the flywheel (kg m2 ) 4 Simulation parameter values setting in the program Initial vehicle speed (km=hr) Surrounding temperature ( C) Maximum operating force (N) [26]
Journal of Mechanical Design
1.36 0.31 0.41 0.35 (T ¼ 25o C) 502 0.0363 200 0.013 0.25 11.4375 60 25 460
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