Development of a Hardware-in-the-Loop Test Bench for Validation of an ABS System on an e-Bike
Nicolas Ramosaj, 
Emmanuel Viennet This work presents the development of a Hardware-in-the-Loop (HIL) test bench that can be used to validate an electric bicycle (e-bike) anti-lock braking system (ABS) for different test scenarios. The approach involves interfacing a virtual bicycle simulation model running on a real-time target machine with the physical ABS hardware under test. This setup allows to test and evaluate ABS behavior in a safe and reproducible way, before starting testing on the track. This article describes the derivation of an equation-based model considering six degree-of-freedom (dof) representing the in-plane longitudinal dynamics of an e-bike. The simulation model is experimentally validated against measurements made on an instrumented test bike. The test apparatus used and the comparison of simulation results with measurements are presented. The characteristics of the HIL test bench developed are presented, and its applicability to an ABS validation process is illustrated by evaluating the braking performance of an ABS tested on a crossover bike.
Show LessType of the Paper: Conference Paper
Development of a Hardware-in-the-Loop Test Bench for Validation of an ABS System on an e-Bike
N. Ramosaj1, C. Fusco1,2, E. Viennet1,*
1School of Engineering and Architecture of Fribourg, HES-SO University of Applied Sciences and Arts Western Switzerland; nicolas.ramosaj@hefr.ch; christia.fusco@hes-so.ch; emmanuel.viennet@hefr.ch ORCID 0009-0004-0922-2934
2Dipartimento di Ingegneria Meccanica e Aerospaziale, Politecnico di Torino, Italy
*corresponding author.
Name of Editor: Jason Moore
Submitted: 15/09/2023
Accepted: 21/09/2023
Published: 27/09/2023
Citation: Ramosaj, N., Fusco, C. & Viennet, E. (2023).
Development of a Hardware-in-the-Loop Test Bench for Validation of an
ABS System on an e-Bike. The Evolving Scholar - BMD 2023, 5th
Edition.
This work is licensed under a Creative Commons Attribution License
(CC-BY).
Abstract:
This work presents the development of a Hardware-in-the-Loop (HIL) test bench that can be used to validate an electric bicycle (e-bike) anti-lock braking system (ABS) for different test scenarios. The approach involves interfacing a virtual bicycle simulation model running on a real-time target machine with the physical ABS hardware under test. This setup allows to test and evaluate ABS behavior in a safe and reproducible way, before starting testing on the track. This article describes the derivation of an equation-based model considering six degree-of-freedom (dof) representing the in-plane longitudinal dynamics of an e-bike. The simulation model is experimentally validated against measurements made on an instrumented test bike. The test apparatus used and the comparison of simulation results with measurements are presented. The characteristics of the HIL test bench developed are presented, and its applicability to an ABS validation process is illustrated by evaluating the braking performance of an ABS tested on a crossover bike.
Keywords: Bicycle, Longitudinal Dynamics, Abs,
Hardware In The Loop
Introduction
Electrically-assisted bicycles (e-bikes) are becoming increasingly popular and can facilitate active commuting. But this comes at the price of safety, as e-bikers have a higher risk of traffic accidents than traditional cyclists (Haufe et al. 2022). However, the availability of on-board electric power is enabling the emergence of active safety systems such as anti-lock braking systems (ABS), which could help to reduce the accident rate in the same way as has been observed in recent decades for cars and motorcycles (Maier, 2018). ABS have been widely used on cars since the 1970s (Leiber et al., 1979) and on motorcycles since the 1990s, but it was not until the 2010s that this technology was adapted to bicycles (Enisz et al., 2012) (Maier et al., 2015) (Corno et al., 2018).
ABS is a mechatronic device involving multi-domain expertise (electronics, mechanics, software) and therefore requires a specific development methodology, as proposed by the Association of German Engineers (VDI, 2004), with particular emphasis on the validation procedure. Sudden braking on two-wheelers, particularly when the front wheel locks, is a safety-critical maneuver. It is therefore particularly risky to carry out the initial validation of an ABS using road tests. Furthermore, in the case of road braking tests carried out by a human, it is difficult to achieve a sufficient level of reproducibility, particularly with regard to the application of braking force and the position, or movement, of the rider on the e-bike. In such a situation, a HIL test procedure offers an interesting way of validating an ABS in a safe and reproducible way.
Hardware-in-the-loop testing is a well-established method for the development of mechatronic systems in the automotive industry, particularly when it comes to active systems such as ABS (Gietelink, 2006) (Heidrich et al. 2013). It enables the design of a component (unit under test) to be validated without the complete system hardware, and relies on a real-time plant simulator that acts as a digital twin of the missing parts of the system. Setting up a HIL test bench for the validation of an ABS device involves capturing the longitudinal dynamic behaviour of an electric bicycle in a virtual model that is run on a real-time plant simulator. The virtual bike model and the ABS hardware under test are then interfaced and interact in a real-time closed loop. Figure 1a) presents the operating principle of a HIL test setup and Figure 1b) shows the necessary components used in a real-time plant simulator.
Figure 1. Operating principle of the HIL test bench; a) Unit under test and real-time plant simulator in closed-loop; b) Components of a real-time plant simulator. Adapted from (Gomez, 2001)
Inputs to the real-time plant simulator may be provided by the software or graphical user interface (input software) or by the unit under test (input hardware), and must be sampled at the test bench operating frequency in order to be interpreted by the virtual model. The outputs of the virtual model must also be conditioned so that they can be interpreted by the hardware (output software). The numerical solvers generally available for real-time operation require that the model can be formulated mathematically without algebraic loops. In addition, the level of modeling must be carefully chosen to avoid overloading the simulator processor.
This paper aims to present the development of a HIL test bench that can be used to validate an e-bike ABS for multiple load and test scenarios, a work inspired by and built upon (Pfeiffer et al., 2020). The derivation of a simulation model based on six-degree-of-freedom equations representing the in-plane longitudinal dynamics of an e-bike is presented in section 2. The mobile test apparatus implemented on the e-bike and the specific measurements carried out to experimentally characterize its front suspension and tires are presented in section 3. The validation of the virtual bike model is presented in section 4. Finally, section 5 details the developed HIL test bench and illustrates how it can be used to evaluate the braking performance of an ABS tested on a crossover bike.
Equation-Based Modeling of In-Plane Dynamics
In this section, the mechanical model describing the longitudinal in-plane dynamics of a semi-rigid e-bike (front suspension only) is described. The model consists in 4 rigid bodies, namely the main body (bicycle frame + rider), the lower part of the fork, the rear and front wheels. It is assumed that the rider does not move with respect to the bicycle frame, therefore their masses and inertias are lumped together at a common center of gravity\(\ G\) (CoG). The inertia of the lower part of the fork is neglected. In order to capture the in-plane motion of the frame, the travel of the front suspension and the possible slip of the wheels, a model with 6 degrees of freedom has been chosen. The generalized coordinates are grouped in a column vector denoted \(q\) and given by Equation (1):
| \[q = \left\lbrack x_{G}\ \ z_{G}\ \ \theta_{G}\ \ z_{FW}\ \ \delta_{FW}\ \ \delta_{RW} \right\rbrack^{T}\] | (1) |
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Where \(x_{G}\) and \(z_{G}\) are the longitudinal and vertical displacement of the CoG, \(\theta_{G}\) is the main body pitch angle, \(z_{FW}\) is the vertical displacement of the front wheel and \(\delta_{RW}\) and \(\delta_{FW}\) are the angular positions of the rear and front wheels relatively to the frame.
A typical front suspension is characterized by a caster angle \(\epsilon\) but we choose to reduce this to an equivalent vertical suspension as described in (Cossalter, 2006). The equivalent stiffness \(k_{F}\) and damping \(c_{F}\) of the suspension can be expressed in terms of the actual stiffness \(k\) and damping \(c\). In addition, a Coulomb friction force \(F_{CF}\) is considered in the suspension. A hyperbolic tangent function, associated with a gain \(k\) and the maximum friction force \(F_{C}\), are used to relate the Coulomb friction force to the sign of the relative velocity \(v_{rel}\) of the suspension, as shown in Equation (2):
| \[k_{F} = \frac{k}{\cos^{2}\epsilon}\ \ ,\ \ \ c_{F} = \frac{c}{\cos^{2}\epsilon}\ \ ,\ \ \ F_{CF} = {- F}_{C} \bullet \tanh\left( k \bullet v_{rel} \right)\] | (2) |
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The contact of the tire on the ground is modeled with a linear spring in parallel with a viscous friction. The modeling assumptions are summarized graphically in Figure 2 and the notations used are given in Table 1.
Figure 2. Bike model diagram
Table 1. List of parameters.
| Name | Title | Unit |
|---|---|---|
| \[main\ body\] | “Frame + rider” | - |
| \[m_{b}\] | Mass of “main body + rear wheel” | kg |
| \[m_{FW}\] | Mass of the front wheel | kg |
| \[I_{b}\] | Inertia of “main body + rear wheel” | kgm2 |
| \(I_{FW}\), \(I_{RW}\) | Inertia of the front and rear wheels | kgm2 |
| \[p\] | Wheelbase | m |
| \[b\] | Horizontal length from the front wheel axis to CoG | m |
| \[h\] | Height from the front wheel axis to CoG at static equilibrium | m |
| \(R_{FW}\), \(R_{RW}\) | Front and rear wheel radius at static equilibrium | m |
| \(x_{G}\), \(z_{G}\) | Displacement of G along X and Z-axis | m |
| \[\theta_{G}\] | Pitch angle | rad |
| \[z_{FW}\] | Displacement of front wheel along Z-axis | m |
| \(\delta_{FW}\), \(\delta_{RW}\) | Angular position of front and rear wheels | rad |
| \[k_{F}\] | Stiffness of the equivalent vertical front suspension | N/m |
| \[c_{F}\] | Damping of the equivalent vertical front suspension | Ns/m |
| \[F_{C}\] | Coulomb friction in equivalent vertical suspension | N |
| \[k\] | Numerical gain for tanh function | - |
| \[k_{T}\] | Stiffness of the front and rear tires | N/m |
| \[c_{T}\] | Damping of the front tire | Ns/m |
| \[M_{FB}\] | Brake torque on front wheel | Nm |
| \[M_{RD}\] | Driving torque on rear wheel | Nm |
For our 6-dof problem with generalized coordinates \(q_{j}\) and generalized velocities \(\dot{q_{j}}\), it is possible to formulate the Lagragian \(L = T - V\) where \(T\) is the kinetic energy and \(V\) is the potential energy. The Lagrange equations are given by Equation (3):
| \[\frac{d}{dt}\left( \frac{\partial L}{\partial\dot{q_{j}}} \right) - \left( \frac{\partial L}{\partial q_{j}} \right) = Q_{j}\] | (3) |
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Where \(Q_{j}\) are the non-conservative generalized forces, the conservative forces being considered in the potential energy \(V\).
The generalized coordinates are measured from the static equilibrium position. Therefore, gravity is canceled by initial spring forces and can be omitted in the potential energy. Hence the potential energy of the system can be expressed as Equation (4):
| \[V = \frac{1}{2} \cdot k_{F} \cdot \left( z_{G} - \theta_{G} \cdot b - z_{FW} \right)^{2} + \frac{1}{2} \cdot k_{T} \cdot z_{FW}^{2} + \frac{1}{2} \cdot k_{T} \cdot \left( z_{G} + \theta_{G} \cdot (p - b) \right)^{2}\] | (4) |
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While the kinetic energy is given in Equation (5):
| \[T = \frac{1}{2} \cdot m_{tot} \cdot {\dot{x}}_{G}^{2} + \frac{1}{2} \cdot m_{b} \cdot {\dot{z}}_{G}^{2} + \frac{1}{2} \cdot I_{tot} \cdot {\dot{\theta}}_{G}^{2} + \frac{1}{2} \cdot I_{RW} \cdot {\dot{\delta}}_{RW\ } + \frac{1}{2} \cdot m_{FW} \cdot {\dot{z}}_{FW}^{2} + \frac{1}{2} \cdot I_{FW} \cdot {\dot{\delta}}_{FW}\] | (5) |
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With inertias \(m_{tot}\) and \(I_{tot}\) as expressed in Equation (6):
\[m_{tot} = m_{b} + m_{FW}\] \[I_{tot} = I_{b} + I_{FW} + \left( h^{2} + b^{2} \right) \cdot m_{FW} = I_{frame} + I_{RW} + \left( h^{2} + (p - b)^{2} \right) \cdot m_{RW} + I_{FW} + \left( h^{2} + b^{2} \right) \bullet m_{FW}\] |
(6) |
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The generalized forces projected in the direction of each generalized coordinates are defined in Equation (7):
| \[\left\{ \begin{array}{r} Q_{x_{G}} = - F_{x_{FW}} - F_{x_{RW}} \\ Q_{Z_{G}} = - \left( \left( c_{F} + c_{T} \right) \cdot {\dot{z}}_{G} + \left( c_{T} \cdot (p - b) - c_{F} \cdot b \right) \cdot {\dot{\theta}}_{G} - c_{F} \cdot {\dot{z}}_{FW} \right){+ F}_{C} \bullet \tanh\left( k \bullet {(\dot{z}}_{FW} + {\dot{\theta}}_{G} \cdot b\ {- \ \dot{z}}_{G}) \right) \\ Q_{\theta_{G}} = - ({(c}_{T} \cdot (p - b) - c_{F} \cdot b) \cdot {\dot{z}}_{G} + \left( c_{T} \cdot (p - b)^{2} + c_{F} \cdot b^{2} \right) \cdot {\dot{\theta}}_{G} - c_{F} \cdot b \cdot {\dot{z}}_{FW}) + \left( F_{x_{FW}} + F_{x_{RW}} \right) \cdot h\ \ \ \ \ \ \\ {+ F}_{C} \bullet \tanh{\left( k \bullet {(\dot{z}}_{G} - {\dot{\theta}}_{G} \cdot b\ {- \ \dot{z}}_{FW}) \right) \cdot b} \\ Q_{Z_{FW}} = - \left( - c_{F} \cdot {\dot{z}}_{G} - c_{F} \cdot b \cdot {\dot{\theta}}_{G} + \left( c_{F} + c_{T} \right) \cdot {\dot{z}}_{FW} \right){+ F}_{C} \bullet \tanh\left( k \bullet {(\dot{z}}_{G} - {\dot{\theta}}_{G} \cdot b\ {- \ \dot{z}}_{FW}) \right) \\ Q_{\delta_{FW}} = F_{x_{FW}} \cdot R_{W} - M_{FB} \\ Q_{\delta_{RW}} = M_{RD} + F_{x_{RW}} \cdot R_{W} \\ \end{array} \right.\ \] | (7) |
|---|
By computing all quantities and returning to Equation (3), the Lagrange equations can be expressed by the following set of coupled ordinary differential equations such as Equation (8):
| \[\left\{ \begin{array}{r} \begin{array}{r} \left( m_{tot} \right) \cdot {\ddot{x}}_{G} = - F_{x_{RW}} - F_{x_{FW}} \\ \ \\ \left( m_{b} \right) \cdot {\ddot{z}}_{G} + \left( c_{F} + c_{T} \right) \cdot {\dot{z}}_{G} - c_{F} \cdot {\dot{z}}_{FW} + \left( c_{T} \cdot (p - b) - c_{F} \cdot b \right) \cdot {\dot{\theta}}_{G} \\ + \left( k_{F} + k_{T} \right) \cdot z_{G} - k_{F} \cdot z_{FW} + \left( k_{T} \cdot (p - b) - k_{F} \cdot b \right) \cdot \theta_{G} - F_{C} \bullet \tanh\left( k \bullet {(\dot{z}}_{FW} + {\dot{\theta}}_{G} \cdot b\ {- \ \dot{z}}_{G}) \right) = 0 \\ \end{array} \\ \ \\ \ \\ \left( I_{tot} \right) \cdot {\ddot{\theta}}_{G} + \left( c_{F} \cdot b^{2} + c_{T} \cdot (p - b)^{2} \right) \cdot {\dot{\theta}}_{G} + \left( c_{T} \cdot (p - b) - c_{F} \cdot b \right) \cdot {\dot{z}}_{G} + c_{F} \cdot b \cdot {\dot{z}}_{FW} \\ + \left( k_{F} \cdot b^{2} + k_{T} \cdot (p - b)^{2} \right) \cdot \theta_{G} + \left( k_{T} \cdot (p - b) - k_{F} \cdot b \right) \cdot z_{G} + k_{F} \cdot b \cdot z_{FW} \\ {\ - F}_{C} \bullet \tanh{\left( k \bullet {(\dot{z}}_{G} - {\dot{\theta}}_{G} \cdot b\ {- \ \dot{z}}_{FW}) \right) \cdot b} = \left( F_{x_{RW}} + F_{x_{FW}} \right) \cdot h \\ \ \\ m_{wheel} \cdot {\ddot{z}}_{FW} - c_{F} \cdot {\dot{z}}_{G} + c_{F} \cdot b \cdot {\dot{\theta}}_{G} + \left( c_{F} + c_{T} \right) \cdot {\dot{z}}_{FW} - k_{F} \cdot z_{G} + k_{F} \cdot b \cdot \theta_{G} + \left( k_{F} + k_{T} \right) \cdot z_{FW} \\ - {\ F}_{C} \bullet \tanh{\left( k \bullet {(\dot{z}}_{G} - {\dot{\theta}}_{G} \cdot b\ {- \ \dot{z}}_{FW}) \right) = 0}\ \\ \ \\ I_{FW} \cdot {\ddot{\delta}}_{FW} = F_{x_{FW}} \cdot R_{w} - M_{FB} \\ \ \\ I_{RW} \cdot {\ddot{\delta}}_{RW} = F_{x_{RW}} \cdot R_{w} + M_{RD} \\ \end{array} \right.\ \] | (8) |
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\(F_{x_{FW}}\) and \(F_{x_{RW}}\) are the friction forces due to the tire-road interaction and they are computed using Pacejka Magic Formula (Pacejka, 2005) with constant coefficients as expressed in Equation (9). The formula uses dimensionless coefficients B, C, D, and E which depend on the road condition, the slip factor \(\kappa\) and the vertical load \(F_{z}\) acting on considered wheel.
| \[F_{x} = F_{z} \cdot D \cdot sin\left( C \cdot arctan\left( B \cdot \kappa - E \cdot \left( B \cdot \kappa - arctan(B \cdot \kappa) \right) \right) \right)\] | (9) |
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\(M_{FB}\) is the brake torque acting on the front wheel. It is modelled as a Coulomb friction and is computed as in Equation (10):
| \[M_{FB} = 2 \bullet F_{BP} \bullet R_{disc} \bullet \mu_{disc} \cdot \tanh\left( k \cdot {\dot{\delta}}_{FW} \right)\] | (10) |
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Where \(F_{BP}\) is the force acting on the brake pad, \(R_{disc}\) is the effective brake disc radius and \(\mu_{disc}\) is the friction coefficient. A hyperbolic tangent function and a gain \(k\) are used to relate the friction torque to the sign of the relative front wheel velocity \(\dot{\delta_{FW}}\). The factor 2 stands for the number of friction interfaces in the brake.
Test Apparatus
In this section, the mobile test apparatus implemented on the e-bike and the specific measurements conducted to characterize experimentally its front suspension and tire are presented.
Figure 3. Experimental bike and equipment, different sensors used are circled.
Figure 3 shows the Flyer Goroc 2, a crossover type bike that will serve as reference for the validation of the virtual model. It is instrumented with various sensors, described in Table 2, to capture the in-plane dynamics of the bike during a strong braking maneuver with the front brake only.
Table 2. Sensor characteristics.
| Measurand | Brake lever force | Fork displacement | Front wheel speed | Accelerations / Rotation rates |
|---|---|---|---|---|
| Sensor name | 2-D Debus Diebold SA-BS04-000 | 2-D Debus Diebold SA-LP150 | 2-D Debus Diebold SD-VI05-000 | 2-D Debus Diebold BC-3A4_3G500-000 |
| Application | Brake lever | Fork | Front / Rear wheels | Luggage rack |
| Principle | Strain gauge | Potentiometer | Inductive | Capacity effects / Coriolis vibratory gyroscope |
| Range | 0...500 N | 0...150 mm | 0...1500 Hz | ± 4 g / ± 500 °/s |
| Accuracy | ± 0.5 % | ± 1.5 mm | Depends on phonic wheel resolution | ± 1 % / ± 1 % |
| Resolution | < 0.01 N | < 0.01 mm | Depends on data logger frequency | ± 0.00125 g / ± 0.02 °/s |
| Sampling rate | 1 kHz | unlimited | < 50 kHz | 1 kHz |
| Signaling | Voltage | Voltage | Voltage | CAN |
The data logger, “AXX” circled in dark green, records data from every channel and stores them on an external USB stick. It is mounted on the luggage rack and it is supplied by an external battery. The data acquisition system is also connected to a sensor switch, “AYY” circled in red, which is able to collect data from 4 analog sensors and 1 frequency sensor. An inertial measurement unit (IMU) is directly included into the data logger, it measures accelerations and rotation rates in the 3 directions. A force lever sensor, “A01” circled in light green, is mounted on the front brake lever to measure the force applied by the rider when braking. The travel of the front suspension is logged by using a linear potentiometer adjusted parallel to the fork, “A02” circled in purple.
The front wheel speed is recorded by an inductive sensor located near the front wheel axis, “A3X” circled in yellow, used together with a phonic wheel with 60 ticks per revolution. It is used to measure the slip ratio of the front wheel during braking maneuver. The rear wheel speed is also measured in a similar way, “A03” circled in blue, but is used only as bike speed reference. During the validation tests, only the front brake is used so that the slip ratio of the rear wheel can be neglected. Furthermore, for safety reasons, the amount of braking force is kept in a range where no lift up of the rear wheel can occur. All signals are logged with a sample frequency of 1 kHz. The measurement system is setup prior to the test on a personal computer (PC) with the appropriate software and uploaded on the data logger.
While the force on the front brake pad cannot be measured on the bike during tests, it is possible to determine experimentally the amplification factor between the force applied on the lever and the effective force on the brake caliper. For this purpose, the brake system is removed from the bike and an additional force sensor is mounted between the brake pads. It is used together with the force sensor mounted on the brake lever. A measurement is conducted by applying force steps on the brake lever and recording information delivered by both sensors. The measured points with the most significant population (steady state points) are averaged while the points with less population (transient points) are not considered. Finally, a function is designed that goes through averaged points and interpolates linearly between them as illustrated in Figure 4. This function allows to transform the force measured at the brake lever during the validation tests into a force at the front brake pad that serves as an input to the virtual bike model. It is interesting to notice that the interpolation function that is based on steady state measured points still provides good accuracy during transients.
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Figure 4. Interpolation function used to transform the force measured on brake lever into a force at brake pad. Left picture shows measures and right picture shows the correlation between measures and interpolation function.
For the experimental characterization of the front suspension, SR Suntour Raidon 34-120mm, and the front tire, Maxxis Forekaster SilkShield 29 x 2.35, a servo-hydraulic double-rod test cylinder is used. It is able to test components statically with a force of ± 25 kN and dynamically with a force of ± 20 kN ; the maximal displacement allowed is 150 mm (± 75 mm) at a maximal speed of 1.8 m/s and a maximal frequency of 100 Hz. It is used to apply a displacement cycle as an input on the upper part of the fork.
Figure 5 shows the test setups that have been used to identify the behavior of the front suspension and the tire. The rod of the hydraulic cylinder is equipped with a force sensor and a displacement sensor directly connected to the steerer tube. In a first test setup a sinusoidal displacement is applied to the suspension alone and the reaction force is measured for different amplitudes and frequencies. This permits the identification of suspension stiffness, damping and Coulomb friction. A second setup is used with the suspension and the front tire to determine in turn the compression stiffness and damping of the tire for different inflation pressures. In this later setup a mount supports the wheel axis vertically (direction normal to the picture plane) to prevent any bending of the assembly under test load.
The stiffness, damping and friction parameters for the suspension and the tire, namely \(k_{F}\), \(c_{F}\), \(F_{CF}\), \(k_{T}\), \(c_{T}\) could be estimated and a good agreement is found between the proposed model and the measurements, as displayed in Figure 6.
Figure 5. Experimental setups on dynamical test bench to characterize suspension and tire behavior. Left picture shows the setup with fork suspension alone. Right picture is the setup with both fork and front tire.
Figure 6. Validation of the suspension model in response to sinusoidal displacement of different input amplitudes, displayed here for a frequency of 0.1 Hz.
Validation of the Simulation Model
In this section the fidelity of the simulation model is assessed by comparing its results with measurements. The scenario chosen for the model validation is simple and safe but nevertheless relevant for the application. It consists in accelerating the e-bike on a flat road until reaching a speed of approx. 25 km/h, measured on the bike native speedometer, then stabilizing the bike by stopping pedaling for about 1 second, and braking strongly with the front brake until the bike comes to a complete stop. The biker tries to remain immobile with respect to the bicycle frame during the braking phase although this is fairly impossible in the very late phase of the braking. For evident safety reasons, the tests are performed only on a clean, dry high-grip surface so that any locking of the front wheel is made impossible and braking intensity is kept in a range where no lift up of the rear wheel can occur.
The simulation model has only one input variable, namely the normal force applied at the front brake caliper which is obtained from the measured force at brake lever as detailed in section 3.
Figure 7 shows the comparison between simulation results and physical measurements of the bicycle based on the scenario described above. The agreement between simulation and measurements is good for front wheel speed and longitudinal acceleration, the two most important quantities for the application covered by this project. The overall deceleration of the front wheel speed is well reproduced by the model. Even the slight wheel slip at the start of braking is partially visible in the simulation results. The measurement of longitudinal acceleration is rather noisy, mainly due to the irregularities of the road, which is not totally smooth, and the driver, whose movement is not totally negligible. However, the simulated acceleration corresponds well to the average of the measured signal, which validates the model. It is interesting to note that, in order to compare the simulated longitudinal acceleration with the measured acceleration, it is necessary to take into account the terrestrial gravity component that appears on the IMU measurement axis when the bike undergoes a pitch angle, as this component can be significant even at small pitch angles.
Comparison of fork displacement and pitch velocity, however, highlights certain weaknesses in the approach taken to suspension modeling. Firstly, the suspension stiffness identified seems close to reality for limited compressions, but it was necessary to add a mechanical stop in the simulation to prevent suspension displacement beyond 84 mm and thus get closer to real suspension behavior in extreme compressions. Secondly, while the extension of the suspension model at the end of the braking phase occurs with a realistic slope, its compression at the beginning of the braking phase is slower than the measurements. In other words, the observed peak in pitch velocity during pitch-up is correctly reproduced, but the peak during dive is clearly underestimated compared to the measurement. One explanation is that the suspension may have different damping in compression and extension, particularly at high relative speeds, a behavior not taken into account by the identification procedure.
Figure 7. Comparison between simulation model (red) and physical bike (blue) when submitted to the same brake force input.
Hardware in the Loop Test Bench
In this section, the developed HIL test bench is presented and its applicability to an ABS validation process is discussed. Figure 8 presents an overview of the installation whose core part is the real-time target machine running the virtual bike model connected to the physical braking system of the bike. This setup allows the test engineer to first test and evaluate the ABS behavior in a safe place, before starting tests on the track.
The architecture of the HiL test bench is composed of a personal computer (PC), a Speedgoat Performance real-time target machine and the hardware. The PC is used to visualize the bike behavior thanks to a 3D animation. The animation is played live based on the simulation results computed on the real-time target machine and returned to the main PC via an UDP communication. The simulation model is integrated in a Matlab/Simulink environment; it includes the virtual bike model and the Simulink blocks needed to control the test scenarios. This configuration allows to compile an executable file on the real-time target machine and to run a test scenario with external inputs/outputs in real-time.
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| Figure 8. A complete overview of the hardware in the loop test bench. |
The HIL test bench features ergonomically positioned bicycle handlebars for use in real-life situations. The front brake lever is hydraulically connected to the ABS hydraulic module, which is then connected to the brake caliper. A force sensor is placed between the brake pads and adjusted to the same thickness as a brake disc. The measured force is the input variable for the virtual bike model. A phonic wheel is driven by a fast-reacting DC motor, whose speed set point is defined by the real-time simulation model. This emulates the rotation of the bike's front wheel, so that the ABS system's speed sensor can be used to acquire the rotation speed signal as in the real world. The ABS system under test also needs the bicycle's longitudinal acceleration as input signal. In real-life operation, this acceleration is received from an on-board IMU, but in the HIL configuration, this acceleration is calculated by the simulation model and sent to the ABS control unit via a CAN bus.
Figure 9 illustrates the current installation of the HIL test bench. A pneumatic cylinder acts on the brake lever and can apply a force up to 200 N. This makes it possible to run scenarios with different sets of parameters with a good reproducibility.
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| Figure 9. Developed HIL test bench. Left : overview ; right : handlebar, brake system and ABS |
The entire HIL test bench is clocked at a frequency of 1 kHz. Simulink's fixed-step Extrapolation solver (ODE14x) is used to numerically integrate the ordinary differential equations of the virtual bicycle model. The integration time step must be chosen carefully to ensure correct convergence even in the case of strong discontinuities in the inputs (e.g. sudden braking) or in the intrinsic behavior of the system (e.g. wheel slip). Although it is possible to reduce the time step to 0.2 ms without overloading the target machine's CPU in real time, it has been observed that a time step of 1 ms is sufficient in most cases. Figure 10 shows the typical results obtained for the following scenario: a large force is suddenly applied and held constant by the test bench's pneumatic cylinder. This force would correspond to a constant force of 2000 N on the front brake pads without ABS intervention. The scenario tested considers a flat road with low grip, so that the braking torque applied exceeds the maximum friction force the tire can transmit to the road. When wheel slip is detected, ABS triggers a pressure release in the hydraulic brake circuit, reducing the actual force measured at the front brake pad. When the front wheel is no longer slipping, the pressure in the hydraulic brake circuit increases again, thanks to the pump built into the ABS system under test.
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| Figure 10. Example results obtained with the HiL test-bench. Test scenario shows that ABS triggers a decrease of effective force at front brake when a slip condition is detected at the front wheel. |
Low-speed e-bikes can be used in a wide variety of ways. For example, the same bike can be used with a child seat, mounted on the front or rear, or with panniers attached to the front or rear. This means that ABS performance must be validated for a very wide range of load cases. The HIL test bench presented here is based on a virtual bike model which has been validated for a specific load case, but which is fully parameterizable, making it easy to simulate these different load cases by varying for example the position of the center of gravity, the sprung mass, or the bike rotational inertia.
One of the limitations of the test bench developed is the need to provide the ABS system under test with suitably conditioned inputs. In the case where the only input required by the ABS is the measurement of wheel speed, it is relatively simple to emulate the rotation of a phonic wheel and thus place the ABS sensor in operating conditions as close to reality as possible. However, if the ABS control logic requires acceleration information, it is not possible to have a device on the test bench that emulates this acceleration. This involves bypassing the IMU and sending the ABS control unit a signal representing the accelerations based on the simulation model. Ultimately, the disadvantage of this approach is that it makes interfacing between the virtual and physical worlds more complex, and requires the cooperation of the ABS manufacturer to enable the control unit to receive an external signal.
Conclusions and Outlook
In this paper the development of a HIL test bench is presented that can be used to test the correct operation of an ABS system on an e-bike. The HIL setup is based on a virtual bike model with 6 degrees of freedom, which has been validated by on-road measurements on an instrumented bike and additional dynamic testing of the front suspension. Tests carried out as part of this development have shown that the developed test bench can be interfaced with an existing ABS system, and that it can easily be used to test different scenarios, such as emergency braking on a flat road with low grip, and different load cases, such as with a child seat or panniers. The HIL test bench can be used by an ABS manufacturer to improve its development process using model-based design techniques or by an e-bike manufacturer to validate the performance of a supplier's ABS system in a quantitative, safe and reproducible way.
Although the simulation model proposed in this paper is adequate and sufficient for the targeted application, there is still room for improvement to reduce the discrepancies observed between measurements and simulation during strong braking. In particular, the non-linear behavior of the suspension needs to be modeled in greater detail.
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Figures (13)
More details
- License: CC BY
- Review type: Open Review
- Publication type: Conference Paper
- Submission date: 15 September 2023
- Publication date: 27 September 2023
- Conference: The Evolving Scholar - BMD 2023, 5th Edition
Citation
Ramosaj, N., Fusco, C. & Viennet, E. (2023). Development of a Hardware-in-the-Loop Test Bench for Validation of an ABS System on an e-Bike. The Evolving Scholar - BMD 2023, 5th Edition. https://doi.org/10.59490/6504843acc05ff8f18f36576
