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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 62, NO. 3, MARCH 2013
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Electromagnetic Energy-Harvesting Shock Absorbers: Design, Modeling, and Road Tests Zhongjie Li, Lei Zuo, George Luhrs, Liangjun Lin, and Yi-xian Qin
Abstract—This paper presents the design, modeling, bench experiments, and road tests for a retrofit regenerative shock absorber based on a permanent magnetic generator and a rack–pinion mechanism for the purposes of energy harvesting and vibration damping. Results show that variable damping coefficients and the asymmetric feature in jounce and rebound motions are achieved by controlling the electrical load of the shock absorber. Improved efficiency and reliability are achieved by utilizing a roller to guide the rack and preload on the gear transmission to reduce backlash and friction. A peak power of 68 W and average power of 19 W are attained from one prototype shock absorber when the vehicle is driven at 48 km/h (30 mi/h) on a fairly smooth campus road. Index Terms—Electromagnetic, energy harvesting, regenerative, road test, shock absorber, vehicle suspension.
I. I NTRODUCTION Fig. 1. Schematic of the regenerative suspension system.
V
EHICLES are widely used all around the world and cause a lot of energy and environmental issues. In the United States, transportation accounts for over 70% of oil consumption [1]; however, only 10%–16% fuel energy in the vehicles is utilized for driving to overcome resistance from road friction and air drag [2]. In addition to thermal efficiency and braking energy, one important loss is kinetic energy dissipated by shock absorbers. The primary function of vehicle suspension is to reduce the vibration disturbance from road roughness, acceleration, deceleration, and cornering to the chassis for better ride comfort and to maintain good tire–ground contact force for better vehicle handling and mobility. Traditional suspension systems consist of springs and viscous shock absorbers. Hydraulic shock absorbers dissipate the vibration energy into waste heat to ensure ride comfort and road handling. Due to simplicity and reliability, passive dampers are favored and used in almost all vehicles nowadays. Generally speaking, softer dampers provide a more comfortable ride, whereas stiffer dampers provide better stability and, thus, better road handling. However, the passive dampers’ characteristics have been determined during their design and cannot be changed. To help vehicles break the Manuscript received June 4, 2012; revised September 19, 2012 and October 15, 2012; accepted November 12, 2012. Date of publication January 4, 2013; date of current version March 13, 2013. This work was supported in part by the New York State Energy Research and Development Authority and in part by the State University of New York Research Foundation Technology Accelerator Fund. The review of this paper was coordinated by Dr. M. Kazerani. The authors are with the State University of New York at Stony Brook, Stony Brook, NY 11794 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2012.2229308
tradeoff between ride quality and road handling, semiactive and active suspension systems have been proposed over the past several decades. However, power consumption and fuel efficiency are a concern. Tests in the literature indicate that the full-active suspension consumes 10%–30% engine power [3]. Regenerative shock absorbers have the potential to not only harvest the kinetic energy traditionally wasted in suspension vibration but for use as actuators for suspension control as well. Moreover, it can increase fuel efficiency by reducing the electrical demand to the car alternators and, thus, reduce the engine’s workload (see Fig. 1). Energy dissipated by shock absorbers is calculated and modeled by a number of researchers. Segel and Lu [4] did some simulation, indicating that approximately 200 W of power are wasted by four dampers when a passenger car drives on a road. Zuo and Zhang [5] modeled road roughness and vehicle dynamics, concluding 100–400-W energy potential from the shock absorbers of a typical vehicle at 96 km/h (60 mi/h). It is also noted that typical vehicles use about 300 W of electricity when the optional electric accessories are turned off [6], which demands five to six times more fuel power, considering 25%–45% engine efficiency and 50%–65% alternator efficiency [7]. To improve the fuel efficiency of vehicles, regenerative shock absorbers are designed to harvest energy from the vibration. Karnopp [8] first proposed a linear electromagnetic absorber consisting of moving coils with a magnetic field around them. Suda et al. [9] developed a hybrid suspension system, in which a linear dc generator was used to harvest energy from vibration. Zhang et al. [10] proposed and characterized one type of regenerative shock absorber, which consists of a ball-screw mechanism and a permanent-magnet dc generator.
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Martins [11] improved electromagnetic active suspension on power electronics, permanent magnetic materials, and microelectronic systems. Choi et al. [12] designed a self-powered semiactive suspension system with a controllable electrorheological shock absorber and an energy generator. Chen and Liao developed a self-powered and self-sensing magnetorheological damper and demonstrated controllable damping force while utilizing wasted vibration energy [13]. Avadhany et al. [14] patented a regenerative shock absorber with a hydraulic piston, a hydraulic motor, and an electrical generator. Zuo et al. [15] designed an electromagnetic energy harvester and built a 1 : 2 scale prototype to verify its capabilities of generating power under vibration. Li et al. [16] proposed a rack– pinion-based design and analyzed its characterizations with a nonlinear dynamic model. This paper aims at introducing the design principles of a regenerative shock absorber, modeling the dynamics, characterizing it with laboratory-based experiments, and eventually demonstrating it in vehicle road tests. The contribution of this paper is threefold. We first present a truly retrofitable design of an energy-harvesting shock absorber. Second, we create physical-based modeling, which can be used to guide the design and parameter selection. Third, we characterize the damping property and demonstrate energy-harvesting capacity in road tests. It should be noted that although this work has been featured in some popular new media, such as PhysOrg [17], R&D 100 Award [18], and Newsday [19], none of these journalists have reported the technical design, modeling, bench test, and road test data. This paper is organized as follows: Section II describes the design principles. Section III introduces the modeling and analysis of the energy-harvesting shock absorber. In Section IV, the prototype is characterized with bench tests. In Section V, road tests are conducted to verify the capabilities of energy harvesting in a Chevrolet full-size SUV. Conclusions, including design guidelines, are then given in Section VI.
Fig. 2. Experiment setup for suspension vibration tests. The laser head of the displacement sensor (Micro-Epsilon ILD1401) is mounted on the inner cylinder of the absorber, and the target is mounted on the outer cylinder.
Fig. 3. Suspension velocity between the sprung and unsprung masses recorded on a local road at 32 km/h (20 mi/h). TABLE I MEASURED SUSPENSION VIBRATION VELOCITY AND C ALCULATED P OWER
II. R EGENERATIVE S HOCK A BSORBER D ESIGN A. Suspension Vibration Input To evaluate the suspension’s vibration induced by road roughness, we performed some experimental study using a Chevrolet Suburban (2002 model). A laser displacement sensor (Micro-Epsilon ILD1401, 1000 Hz, resolution 50 μm) is mounted on the traditional shock absorber of the rear suspension to directly measure the compression/extension of the shock absorber, as shown in Fig. 2. The suspension velocity is calculated from the measured relative displacement by taking a derivative and applying a fourth-order Butterworth filter of bandwidth 0.1–100 Hz [5]. The vehicle is driven on different roads, including Stony Brook Road near Stony Brook University, Stony Brook, NY, and the Long Island Expressway (I-495). The suspension vibration highly depends on road conditions and vehicle speed. Fig. 3 shows a recorded relative vibration velocity between the sprung and unsprung masses obtained in the test at the vehicle speed of 32 km/h (20 mi/h). The instant peak-to-peak velocity can be 0.15 m/s, but the root-meansquare (RMS) value of the velocity data is only 0.026 m/s.
Table I shows the measured relative velocities of the suspension when the SUV was driven at different vehicle speeds. In Table I, it is shown that the suspension velocity increases with the increase in vehicle driving speed. In addition, road conditions have a great influence on the suspension velocity. Based on the measured equivalent damping coefficient 4700 N/m of the traditional shock absorber on this SUV vehicle, we also calculated the table power dissipated by the suspension system with four shocks, as shown in Table I.
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Fig. 4.
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Overall structure of the regenerative shock absorber.
B. Design Principle In general, spring stiffness is very important for the vibration energy harvester design since we would like to make the resonant frequency the same as the excitation frequency. However, the main excitation to vehicle suspension is road roughness, which is generally random and, often, can be modeled as whitenoise velocity input to the tires [5]. In addition, retrofit design is important for economic implementation without changing the suspension structure or suspension stiffness. Therefore, we would like to design regenerative shock absorbers that can directly replace the traditional oil damper to achieve the desired damping while harvesting the energy. There are generally two types of configurations of regenerative shock absorbers, i.e., linear design and rotary design. The linear-type shock absorbers utilize the relative motion between magnetic field and coils to directly generate power based on Faraday’s law of electromagnetic induction. The rotary shock absorbers transfer linear motion of suspension vibration to rotary motion to drive permanent magnetic dc generators. Usually, rotary shock absorbers are capable of generating more power and getting a larger damping coefficient for the given space [20]. To change the linear motion into rotary motion, different mechanisms could be adopted including ball-screw and rack–pinion mechanisms. However, considering the poor performance of the ball-screw harvester in high frequencies [21], we choose the rack–pinion mechanism, as shown in Fig. 4. A pair of bevel gears are also used to change the transmission by 90◦ . As the output voltage is proportional to the rotational speed, a planetary gearbox is used for motion magnification. C. Prototype Introduction The principle of regenerative shock absorber is shown in Fig. 4, and a prototype is showed in Fig. 5. It is mainly composed of rack–pinion, bevel gears, planetary gears, and an electrical generator. The electric generator assembly is mounted on a cylinder, and an outer cylinder is used to enclose the system. The rack is connected with the end of the outer cylinder and will drive the pinion gear when there is a relative motion between the two ends of the shock absorbers. Through bevel gears, the rotational motion of the pinion gear is transferred by 90◦ to the rotational motion of the generator. The planetary gears are used to magnify the motion, and a dc motor is used as a generator. It should be noted that Li et al. [16] previously built a rack–pinion-based shock absorber prototype, but the size of the shock absorber prototype is not retrofittable for common vehicles (101.6 mm of overall diameter, in comparison with
Fig. 5. Three-dimensional model and photo of the shock absorber prototype.
the 72-mm outside diameter in this prototype). Moreover, there are large backlash and friction in the transmission. To reduce friction forces and backlash impacts, in this design, a roller is used to guide the rack and preload of rack on the opposite side of the pinion gears. In addition, we put a Teflon ring between the outer and inner cylinders to further reduce the dry friction forces. We also put a filter with a steel wire screen at the top of the shock absorber to prevent the dirt from being sucked into the cylinders during the motion. The selection of gears for this system is critical for its overall performance. With a higher transmission ratio, the system can achieve a higher damping coefficient (which we will see in the modeling, Section III), but a large gear ratio usually means low transmission efficiency. A smaller transmission ratio has higher transmission efficiency and better compactness, but the expected damping coefficient would be lower. Hence, the selection of gears is a compromise between performance, efficiency, and compactness. In this prototype, we choose ratio 50 to bring the typical RMS suspension velocity to the rated generator rotation speed. The bevel and rack–pinion gears are the two most important components in the system that may cause failure; hence, contact fatigue, strength of teeth surface, and strength of teeth root bending should be checked. III. M ODELING AND A NALYSIS The regenerative shock absorber has several parts, including a generator, a planetary gearbox, bevel gears, rack–pinion, etc. The objective of this session is to investigate the influence of these components and the parameters on the dynamics of the system. A. DC Motor and DC Generator Permanent magnetic dc motors can be directly used as generators. Although the modeling of a dc motor is well known, it is a very common mistake that people may directly take a 100-W
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the maximum continuous current due to the thermal limit of this electrical machine. For a short time, the instant speed can be higher than the rated speed, and thus, the instant voltage generated can be higher. Moreover, the maximal permissible speed is limited by the ball bearings in this motor. B. Dynamics Modeling
Fig. 6. Two working modes of electrical machines. (a) As a motor. (b) As a generator.
motor to be a 100-W generator. In this session, we analyze the characteristics of motors and generators and illustrate the difference of dc machines as a generator and as a motor (see Fig. 6). When the electrical machine of internal resistance ri is used as a motor, the relation between input voltage Um and back electromotive force (EMF) voltage Uemf at nominal current In is Um = In ri + Uemf .
(1)
Furthermore, when it is used as a generator, output voltage Ug at nominal current In is Uemf = In ri + Ug
(2)
where the back EMF voltage is proportional to rotation speed ωn with gain ke of the back electromotive voltage constant. Thus Uemf = ke ωn .
(3)
From (1) and (2), we see that when the motor is used as a generator, at the same speed ωn and current In , output voltage Ug may be much smaller than the nominal input voltage Um of the motor. Thus Ug = Uemf − In ri = Um − 2In ri
(4)
and the nominal output power Pg as a generator is also smaller than the nominal power Pm of the motor, i.e., Pg = Ug In = Um In − 2In2 ri = Pm − 2In2 ri .
(5)
Equations (4) and (5) indicate how we should take the internal resistance and the nominal current into account in the generator selection. In this prototype, we select a dc motor (Maxon Motor, model 218010) as a generator. The parameters are shown in Table II. Plugging the motor parameters into (4) and (5), we see that the output voltage at the rated rotational speed and rated current will be 38.9 V, and the output power is only 41.1 W, much smaller than the rated power 48 V × 1.38 A = 66 W as a motor. One may think that the maximal output power happens when the external resistor is the same as the internal resistor: (48 V/2)2 /6.6 Ω = 87.3 W. However, a simple calculation indicates that the current in the electrical machine in such a case will be 3.6 A = 48 V/(2 × 6.6 Ω), which is much larger than the rated current 1.38 A, which is
The analysis in Section III-A is the capacity of steady power generation when an electrical motor is used as a generator. To model the dynamics of the system, we have to consider the inertia and inductance of the electrical generator. Fig. 7 shows the dynamic modeling of a dc generator. Electric current i in the generator coil will produce torque τi following the relationship τi = kt i
(6)
where kt represents the torque constant. Based on Newton’s second law, we can get τm − τi = J m
d2 θ dt2
(7)
where τm is the input mechanical torque on the generator, and Jm is the inertia of the rotor. Based on Kirchhoff’s voltage laws, we have Uemf − L
di − iR = 0 dt
(8)
where back EMF voltage Uemf = ke (dθ/dt), L represents the generator’s internal inductance, and R is the sum of generator internal resistance ri and electric load resistance Re . Take (6)–(8) into consideration, the overall expression of the generator’s dynamics can be written as L d dθ d2 θ d2 θ R = ke τm − Jm 2 . (9) τm − J m 2 + dt kt dt dt kt dt This equation can be written in the Laplace domain with Laplace operators, i.e., kt ke s Tm = + Jm s2 . Θ R + Ls
(10)
If we express the torque in mass–spring-damping form, i.e., Tm = Jm Θs2 + cm Θs + km Θ
(11)
then we can obtain the equivalent torsional damping of coefficient cm (frequency dependent), i.e., cm =
kt ke R R 2 + L2 ω 2
(12)
and the equivalent torsional stiffness km , i.e., km =
kt kt Lω 2 . R 2 + L2 ω 2
(13)
Equations (12) and (13) indicate that the coil resistance contributes to torsional damping, and the coil inductor appears to be a stiffness. Considering that the vibration induced by road irregularities is usually in the frequency range 1–10 Hz, and the inductance
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TABLE II PARAMETERS OF THE DC “MOTOR” USED IN THE PROTOTYPE
where kg , ηg , and Jg are the overall transmission ratio, efficiency, and rotation inertia of the gear transmission system from the pinion gear to the generator rotor, as explained in Section III-C; r is the radius of pinion gears; mr and mc are the masses of the rack and the moving casing; ke and kt are the voltage and torque constants of the generator; R is the electrical loop resistance; and kv is the viscous damping between the inner and outer cylinders. Therefore, the equivalent can be obtained as Fig. 7. Dynamics modeling of the electromagnetic generator, where Re can be the equivalent resistance of the power charge circuit.
of the generator (motor) is very small compared with the resistance (Lω R), the influence of the generator’s inner inductance can be neglected. Therefore, the generator can be simplified as a torsional damper: cm ≈ ke kt /R and km ≈ 0. The inertia of the motor will be considered together with the gear transmission as an equivalent mass. C. Gear Transmission The gear transmissions in our prototype system include planetary gears in the gearbox, bevel gears, and rack–pinion gears, as shown in Fig. 4. Considering that friction and backlash are comparatively small, the gears’ large stiffness and small damping effect, the whole transmission gears can be modeled together as one transmission system with an overall transmission ratio kg = kp · kb /r, efficiency ηg = ηp · ηb · ηr , and rotation inertia Jg = Jp · kp2 kb2 + Jb · kb2 + Jr , where Jp , kp , and ηp represent the rotation inertia, transmission ratio, and efficiency of the planetary gears; Jb , kb , and ηb represent the rotation inertia, transmission ratio, and efficiency of the bevel gears; and Jr , r, and ηb represent the rotation inertia, pinion radius, and efficiency of the rack and pinion. D. Linear Model Under Sinusoidal Vibration The backlash and Coulomb friction in this design are much smaller than those in the previous prototype [16]. Therefore, a linear model can be obtained with the equivalent mass, stiffness, and damping coefficient. Based on the models of the generator and gear transmission, we can obtain the relationship between the driving force and the motion displacement, i.e., ⎤ ⎡ J k2 Jg + mηg g + (mr + mc )⎦ F =⎣ r2 d2 x · 2 + dt
kg2 ke kt + kv r 2 ηg R
dx · dt
meq =
Jm kg2 ηg r2
Jg +
+ (mr + mc ).
The most important parameter of this energy-harvesting absorber is the equivalent of the damping ratio. Thus Ceq =
kg2 ke kt + kv . r 2 ηg R
(16)
We see that the equivalent damping coefficient is mainly determined by generator constants ke and kt , transmission ratio kg from the pinion gear to the generator rotor, loop resistance R = ri + Re , and viscous friction coefficient kv between the inner and outer cylinders. Equation (16) can be used to guide the selection of the generator, gearbox ratio, and pinion gear diameter. Equation (16) also indicates that electrical resistance R = ri + Re is important to the damping coefficient. As a result, the damping coefficient can be controlled with resistance Re of external load or charging circuit. It should be noted that an electrical charging circuit is very important for energyharvesting suspension, which is out of the scope of this paper. However, it is useful to note that the charging circuit with a dc/dc converter can be modeled as a pure resistor Re controlled with pulsewidth modulation under moderate assumption [22], [23]. Although the equivalent stiffness of the electrical generator due to inductor L [see (13)] is negligible, the equivalent mass meq will appear to have a negative slope in the force–displacement loops under sinusoidal vibration input, which we will see in the bench tests. Thus x = A cos(ω0 t + ϕ0 ) + x0 2
d x = −Aω02 cos(ω0 t + ϕ0 ) = ω02 x. dt2
(17)
Hence, the force can be expressed as ⎡ ⎤ J k2 Jg + mηg g F = −⎣ + (mr + mc )⎦ r2
(14)
(15)
·
ω02 x
+
kg2 ke kt + kv r 2 ηg R
·
dx . dt
(18)
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Fig. 10. Force–displacement loop for different frequencies with 30-Ω external load and 30-mm displacement input, where the negative slope is due to the effect of mass inertias. Fig. 8. Equivalent dynamic model of the shock absorber. (a) For general input excitation. (b) For harmonic excitation.
Fig. 11. Force–displacement loops for different electrical loads at displacement input of 0.1-Hz frequency and 30-mm amplitude.
Fig. 9. Bench test setup for the regenerative shock absorber.
The coefficient of x is a negative stiffness. Thus ⎡
⎤ J k2 Jg + mηg g Keq = −meq ω02 = −⎣ +(mr +mc )⎦ ω02 . r2
(19)
We will see this phenomenon as a negative slope in the force–displacement loops in Section IV-A. Hence, the whole system can be viewed as mass meq and damper Ceq in series or a negative spring element Keq and damper Ceq in parallel, as shown in Fig. 8. IV. B ENCH T ESTS The experiment setup for the laboratory test of the energy harvester prototype is shown in Fig. 9. The bench tests are conducted on an 858 Mini Bionix II material testing system from MTS. A dynamic signal analyzer HP 3567A is used to record the voltage signal from the generator. Force and displacement signals are measured with a displacement sensor and a load cell (integrated in the 858 Mini Bionix II testing system). A. Symmetric Test of the Damping and Harvesting The prototype was first tested with sinusoidal displacement input. Power resistors were used as the external electrical load.
The force–displacement damping loops are shown in Figs. 10 and 11 at different frequencies and external electrical loads. It is shown in Fig. 10 that the orientation of the loop is not horizontal, and the slope changes when the frequencies increase. This can be explained using (19). The slope is mainly caused by the inertia of moving parts, and the orientation represents the negative stiffness Keq of the system, where Keq = −meq ω02 . In Figs. 10 and 11, the area of the loop means the mechanical work input of the shock absorber ΔW in one cycle; hence, the mechanical power input can be calculated as Pin = ΔW · ω0 /2π. Moreover, the equivalent damping coefficient can be calculated as Ceq =
ΔW πω0 X 2
(20)
where ω0 means the input frequency, and X means the displacement magnitude. The force–displacement loops in Figs. 10 and 11 are not smooth. The fluctuating waves on the force–displacement loops are due to the imperfect engagement of the gear teeth of bevel gears and rack–pinion gears. This problem may be taken care of by more precise machining and tolerance control. Fig. 12 shows the relationship between force and velocity. We can see that the relationship is almost linear, and the slopes correspond to the damping coefficients. In addition, the slopes increase when the electrical load decreases, which means we attend larger damping.
LI et al.: ENERGY-HARVESTING SHOCK ABSORBERS: DESIGN, MODELING, AND ROAD TESTS
Fig. 12. Force–velocity relationship for different electrical loads at displacement input of 0.5-Hz frequency and 30-mm amplitude.
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Fig. 14. Output electrical power for different resistors at displacement input of 0.5-Hz frequency and 30-mm vibration amplitude.
Fig. 13. Damping coefficients with different electrical loads.
Equation (16) predicts that the damping coefficient of the regenerative shock absorber depends on the electrical loads: Ceq = (kh2 ke kt /r2 ηg R) + kv . Such a prediction very well matches with the experiment, as shown in Fig. 13. Therefore, the shock absorber can be controlled in a large range by controlling the external resistances or the PMW of the circuit circuitry [22], [23]. In this prototype, a 30-Ω electrical load corresponds to a damping coefficient of around 5000 Ns/m, which is close to the value of the commercial shock absorber used in the test SUV. In addition, a 94-Ω electrical load corresponds to a damping coefficient of 1800 Ns/m, which is good for a typical passenger car. We also recorded the voltage of the external load. The instant output electrical power is calculated based on the recorded voltage and resistor value Pout = V 2 /Re , as shown in Fig. 14. The peak output power attains 22 and 12 W, respectively, on 42- and 94-Ω external loads and at 0.5-Hz and 30-mm vibration amplitude. It should be noted that the energy-converting efficiency is an important index of the harvester performance. However, we have rarely seen such a number in the published papers. After we obtain the input mechanical power and output electrical power, we can then calculate the total efficiency of the regenerative shock absorbers. The total efficiency is further
Fig. 15. Mechanical efficiency under different vibration frequencies with 94-Ω resistive load, where the vibration amplitude is 10 mm.
deconvoluted into mechanical and electrical efficiencies. The electrical efficiency is the ratio of the external resistance and the loop resistance (sum of the external resistance and the generator internal resistance, 6.6 Ω in the prototype). The mechanical efficiency ranges from 33% to 63% with different vibration frequencies (see Fig. 15) and different electrical loads (see Fig. 16). It is shown that the mechanical efficiency achieves the maximum at around 1-Hz frequency input, and the efficiency decreases at high frequency. The mechanical efficiency at 0.5 Hz increases from 47% to 60% when the vibration amplitude increases from 10 to 30 mm. In addition, the mechanical efficiency also varies with the change in electrical load, as shown in Fig. 16. B. Asymmetry in the Jounce and Rebound Asymmetric damping coefficients are essential for the vehicle suspension system because they can help vehicles keep good contact with roads and reduce shock to the vehicle body. The regenerative shock absorber is symmetrically designed; however, the asymmetric characteristics can be achieved by shunting the regenerative shock absorber with different electric loads during the jounce and rebound motions. Considering
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Fig. 18.
Force–velocity relationship of the regenerative shock absorber.
Fig. 16. Mechanical efficiency for different external resistances under harmonic vibration of 30-mm amplitude.
Fig. 17. Control circuit for asymmetric characteristics.
that the upward and downward motions will generate voltages with opposite polarities in the dc generator (i.e., positive and negative voltages), a simple circuit can be built to achieve the asymmetry, as shown in Fig. 17. Such a circuit connects R2 in positive voltage direction and R1 in negative voltage direction. Hence, the damping coefficient of the regenerative shock absorber is ⎧ 2 ⎨ k2g ke kt + kv , positive voltage direction r ηg R 2 (21) Casym = 2 ⎩ k2g ke kt + kv , negative voltage direction.
Fig. 19. Asymmetric forces of the regenerative shock absorber in jounce and rebound motions. TABLE III VEHICLE INFORMATION
r ηg R 1
Figs. 18 and 19 show the regenerative shock absorber with asymmetric damping coefficients. We can see that the regenerative shock absorber can act similarly as the traditional hydraulic shock absorber for the asymmetric characteristics. Hence, the regenerative shock absorber can replace traditional shock absorbers for its complete function while harvesting energy from vehicle vibration. In addition, if the external load resistor can be controlled with semiactive control laws, it can further improve the vehicle dynamics and harvest energy at the same time. V. ROAD T ESTS To validate the given analysis and demonstrate energy harvesting from the shock absorbers, we carried out road tests us-
ing a Chevrolet Surburban SUV (2002 model). Its information is shown in Table III. The experiment setup is shown in Fig. 20. The displacement of the rear shock absorber was recorded by a laser displacement sensor from Micro-Epsilon with a sampling rate of 1000 points/s. The output voltage is recorded with a digital signal analyzer HP 35670A. The road tests were conducted on the campus road of Stony Brook University, Stony Brook, NY, at different speeds, including 30 and 20 mi/h (or 48 and 32 km/h). The recorded voltages on an external electrical load of 30 Ω generated from the energy-harvesting shock absorber at these two vehicle speeds are shown in Figs. 21 and 22, respectively. It is shown that the peak voltages were over 40 V. Correspondingly, the peak
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powers are 67.5–58.2 W. The average power values are 4.8 and 3.3 W, respectively, at 48 and 32 km/h (30 and 20 mi/h), or 19.2 and 13.2 W can be harvested on four shock absorbers at 48 and 32 km/h. Recall in Table I, we estimate 54.1- and 13.5-W energy dissipation on a local road at 48 and 32 km/h. The results from the road tests are encouraging, although the harvesting efficiency in road tests cannot be drawn from these values since the suspension vibration highly depends on the road conditions. VI. C ONCLUSION
Fig. 20. Setup of the road tests. (Top) Vehicle. (Bottom left) Instruments. (Bottom right) Mounting of sensors and the regenerative shock absorber.
A retrofit rack–pinion-based electromagnetic regenerative shock absorber is developed and tested, which can generate electric power from the road-induced suspension vibration of vehicles. The working principle and design are presented. A dynamic modeling for a rack–pinion-type shock absorber system has been derived and analyzed. The prototype is evaluated on a testing machine with sinusoidal displacement input. The results show that the equivalent damping coefficient depends on the external electrical resistances. As a result, the regenerative shock absorber can be used as a controllable damper, and the damping coefficient can be handled by controlling equivalent external electrical load. A total energy conversion efficiency of up to 56% is achieved under +/−30-mm 0.5-Hz vibration and 94-Ω external load. We also demonstrated the asymmetric characteristics of the regenerative shock absorber in jounce and rebound motions by connecting it with asymmetric electrical loads. Road tests were carried out to verify the performance of the new designed regenerative shock absorber. The experiment results indicate that the generated voltage reflects the road irregularities well. A peak power of 67.5 W and an average power of 19.2 W can be obtained from four energy-harvesting shock absorbers when the vehicle travels at 48 km/h (30 mi/h) on a fairly smooth campus road. ACKNOWLEDGMENT
Fig. 21. Displacement and voltage measured at 48 km/h (30 mi/h) on a paved campus road.
The authors would like to thank the people who helped greatly with this project, including Mr. D. McAvoy and J. T. O’Connor of the Stony Brook University Transportation Department, for providing the test vehicles, and X. Tang, P. Li, T. Lin, and W. Zhou, for assistance with the road test. R EFERENCES
Fig. 22. Displacement and voltage measured at 32 km/h (20 mi/h) on a paved campus road.
[1] Energy Information Administration Basic Petroleum Statistics. [Online]. Available: http://www.eia.gov/energyexplained/index.cfm?page=oil_ home#tab2 [2] Advanced Technologies and Energy Efficiency. [Online]. Available: http://www.fueleconomy.gov/FEG/atv.shtml [3] M. Donahue, “Implementation of an active suspension preview controller for improved ride comfort,” M.S. thesis, Univ. California, Berkeley, CA, 2001. [4] L. Segel and X. P. Lu, “Vehicular resistance to motion as influenced by road roughness and highway alignment,” Aust. Road Res., vol. 12, no. 4, pp. 211–222, Dec. 1982. [5] L. Zuo and P. Zhang, “Energy harvesting, ride comfort, and road handling of regenerative vehicle suspensions,” in Proc. DSCC, 2012, pp. 295–302. [6] J. Yang and F. Stabler, “Automotive applications of thermoelectric materials,” J. Electron. Materials, vol. 38, no. 7, pp. 1245–1251, Jul. 2009. [7] Automotive Handbook, p. 813, Stuttgart, Germany: Robert Bosch GmbH, 1996.
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[8] D. Karnopp, “Permanent magnet linear motors used as variable mechanical dampers for vehicle suspensions,” Veh. Syst. Dyn., vol. 18, no. 4, pp. 187–200, 1989. [9] Y. Suda, S. Nakadai, and K. Nakano, “Hybrid suspension system with skyhook control and energy regeneration,” Veh. Syst. Dyn., vol. 28, no. S1, pp. 619–634, 1998. [10] Y. Zhang, F. Yu, and K. Huang, “A state of the art review on regenerative vehicle active suspension,” in Proc. 3rd ICMEM, Beijing, China, Oct. 21–23, 2009, pp. 1689–1695. [11] I. Martins, “Permanent-magnets linear actuators applicability in automobile active suspensions,” IEEE Trans. Veh. Technol., vol. 55, no. 1, pp. 86– 94, Jan. 2006. [12] S.-B. Choi, M.-S. Seong, and K.-S. Kim, “Vibration control of an electrorheological fluid-based suspension system with an energy regenerative mechanism,” Proc. Inst. Mech. Eng. D, J. Autom. Eng., vol. 223, no. 4, pp. 459–469, Apr. 2009. [13] C. Chen and W-H. Liao, “A self-sensing magnetorheological damper with power generation,” Smart Mater. Struct., vol. 21, no. 2, pp. 025014-1– 025014-14, Feb. 2012. [14] S. Avadhany, P. Abel, V. Tarasov, and Z. Anderson, “Regenerative shock absorber,” U.S. Patent 0 260 935, 2009. [15] L. Zuo, B. Scully, J. Shestani, and Y. Zhou, “Design and characterization of an electromagnetic energy harvester for vehicle suspensions,” Smart Mater. Struct., vol. 19, no. 4, pp. 1007–1016, Apr. 2010. [16] Z. Li, Z. Brindak, and L. Zuo, “Modeling of an electromagnetic vibration energy harvester with motion magnification,” in Proc. ASME Int. Mech. Eng. Congr., Denver, CO, 2011, pp. 285–293. [17] L. Zyga, (2011, Jul. 14). Energy-harvesting shock absorber that increases fuel efficiency wins R&D 100 award, PhysOrg News. [Online]. Available: http://phys.org/news/2011-07-energy-harvesting-absorber-fuel-efficiencyaward.html [18] 2011 R&D 100 Award Winners. [Online]. Available: http://www. rdmag.com/Awards/RD-100-Awards/2011/06/R-D-100-2011-WinnersOverview/ [19] S. Chang, (2011, Jul. 15). Professor’s shock absorber wins award, Newsday. [Online]. Available: http://www.newsday.com/classifieds/cars/ professor-s-shock-absorber-wins-award-1.3026134. [20] A. Gupta, A. J. Jendrzejczyk, M. T. Mulcahy, and R. J. Hull, “Design of electromagnetic shock absorbers,” Int. J. Mech. Mater. Design, vol. 3, no. 3, pp. 285–291, Sep. 2006. [21] Y. Kawamoto, Y. Suda, H. Inoue, and T. Kondo, “Electro-mechanical suspension system considering energy consumption and vehicle manoeuvre,” Veh. Syst. Dyn., vol. 46, no. 1, pp. 1053–1063, Sep. 2008. [22] E. Lefeuvre, D. Audigier, C. Richard, and D. Guyomar, “Buck–boost converter for sensorless power optimization of piezoelectric energy harvester,” IEEE Trans. Power Electron., vol. 22, no. 5, pp. 2018–2025, Sep. 2007. [23] X. Tang and L. Zuo, “Simultaneous energy harvesting and vibration control of structures with tuned mass dampers,” J. Intell. Mater. Syst. Struct., vol. 23, no. 18, pp. 2117–2127, Dec. 2012.
Zhongjie Li was born in China in 1988. He received the B.S. degree in mechanical engineering from Harbin Institute of Technology, Harbin, China, in 2010. He is currently working toward the M.S. degree with the Department of Mechanical Engineering, State University of New York at Stony Brook. His current research is in the areas of design, modeling, and testing of regenerative shock absorbers.
Lei Zuo received the B.S. degree in automotive engineering from Tsinghua University, Beijing, China, in 1997 and two M.S. degrees in electrical and mechanical engineering and the Ph.D. degree in mechanical engineering from Massachusetts Institute of Technology, Cambridge, in 2005. In 2008, after working four years in industry, he joined the State University of New York at Stony Brook as an Assistant Professor and founded the Energy Harvesting and Mechatronics Research Laboratory. His research is currently supported by the U.S. National Science Foundation, the U.S. Department of Energy, the U.S. Department of Transportation, the New York Energy Research and Development Authority, and industry. His research interests include vibration and thermoelectric energy harvesting, mechatronics design, control systems, smart structures, and biosensors. Dr. Zuo received an R&D 100 Award by R&D 100 Magazine for his work on energy-harvesting shock absorbers.
George Luhrs, photograph and biography not available at the time of publication.
Liangjun Lin, photograph and biography not available at the time of publication.
Yi-xian Qin, photograph and biography not available at the time of publication.
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Electromagnetic Energy-Harvesting Shock Absorbers: Design, Modeling, and Road Tests Zhongjie Li, Lei Zuo, George Luhrs, Liangjun Lin, and Yi-xian Qin
Abstract—This paper presents the design, modeling, bench experiments, and road tests for a retrofit regenerative shock absorber based on a permanent magnetic generator and a rack–pinion mechanism for the purposes of energy harvesting and vibration damping. Results show that variable damping coefficients and the asymmetric feature in jounce and rebound motions are achieved by controlling the electrical load of the shock absorber. Improved efficiency and reliability are achieved by utilizing a roller to guide the rack and preload on the gear transmission to reduce backlash and friction. A peak power of 68 W and average power of 19 W are attained from one prototype shock absorber when the vehicle is driven at 48 km/h (30 mi/h) on a fairly smooth campus road. Index Terms—Electromagnetic, energy harvesting, regenerative, road test, shock absorber, vehicle suspension.
I. I NTRODUCTION Fig. 1. Schematic of the regenerative suspension system.
V
EHICLES are widely used all around the world and cause a lot of energy and environmental issues. In the United States, transportation accounts for over 70% of oil consumption [1]; however, only 10%–16% fuel energy in the vehicles is utilized for driving to overcome resistance from road friction and air drag [2]. In addition to thermal efficiency and braking energy, one important loss is kinetic energy dissipated by shock absorbers. The primary function of vehicle suspension is to reduce the vibration disturbance from road roughness, acceleration, deceleration, and cornering to the chassis for better ride comfort and to maintain good tire–ground contact force for better vehicle handling and mobility. Traditional suspension systems consist of springs and viscous shock absorbers. Hydraulic shock absorbers dissipate the vibration energy into waste heat to ensure ride comfort and road handling. Due to simplicity and reliability, passive dampers are favored and used in almost all vehicles nowadays. Generally speaking, softer dampers provide a more comfortable ride, whereas stiffer dampers provide better stability and, thus, better road handling. However, the passive dampers’ characteristics have been determined during their design and cannot be changed. To help vehicles break the Manuscript received June 4, 2012; revised September 19, 2012 and October 15, 2012; accepted November 12, 2012. Date of publication January 4, 2013; date of current version March 13, 2013. This work was supported in part by the New York State Energy Research and Development Authority and in part by the State University of New York Research Foundation Technology Accelerator Fund. The review of this paper was coordinated by Dr. M. Kazerani. The authors are with the State University of New York at Stony Brook, Stony Brook, NY 11794 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2012.2229308
tradeoff between ride quality and road handling, semiactive and active suspension systems have been proposed over the past several decades. However, power consumption and fuel efficiency are a concern. Tests in the literature indicate that the full-active suspension consumes 10%–30% engine power [3]. Regenerative shock absorbers have the potential to not only harvest the kinetic energy traditionally wasted in suspension vibration but for use as actuators for suspension control as well. Moreover, it can increase fuel efficiency by reducing the electrical demand to the car alternators and, thus, reduce the engine’s workload (see Fig. 1). Energy dissipated by shock absorbers is calculated and modeled by a number of researchers. Segel and Lu [4] did some simulation, indicating that approximately 200 W of power are wasted by four dampers when a passenger car drives on a road. Zuo and Zhang [5] modeled road roughness and vehicle dynamics, concluding 100–400-W energy potential from the shock absorbers of a typical vehicle at 96 km/h (60 mi/h). It is also noted that typical vehicles use about 300 W of electricity when the optional electric accessories are turned off [6], which demands five to six times more fuel power, considering 25%–45% engine efficiency and 50%–65% alternator efficiency [7]. To improve the fuel efficiency of vehicles, regenerative shock absorbers are designed to harvest energy from the vibration. Karnopp [8] first proposed a linear electromagnetic absorber consisting of moving coils with a magnetic field around them. Suda et al. [9] developed a hybrid suspension system, in which a linear dc generator was used to harvest energy from vibration. Zhang et al. [10] proposed and characterized one type of regenerative shock absorber, which consists of a ball-screw mechanism and a permanent-magnet dc generator.
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Martins [11] improved electromagnetic active suspension on power electronics, permanent magnetic materials, and microelectronic systems. Choi et al. [12] designed a self-powered semiactive suspension system with a controllable electrorheological shock absorber and an energy generator. Chen and Liao developed a self-powered and self-sensing magnetorheological damper and demonstrated controllable damping force while utilizing wasted vibration energy [13]. Avadhany et al. [14] patented a regenerative shock absorber with a hydraulic piston, a hydraulic motor, and an electrical generator. Zuo et al. [15] designed an electromagnetic energy harvester and built a 1 : 2 scale prototype to verify its capabilities of generating power under vibration. Li et al. [16] proposed a rack– pinion-based design and analyzed its characterizations with a nonlinear dynamic model. This paper aims at introducing the design principles of a regenerative shock absorber, modeling the dynamics, characterizing it with laboratory-based experiments, and eventually demonstrating it in vehicle road tests. The contribution of this paper is threefold. We first present a truly retrofitable design of an energy-harvesting shock absorber. Second, we create physical-based modeling, which can be used to guide the design and parameter selection. Third, we characterize the damping property and demonstrate energy-harvesting capacity in road tests. It should be noted that although this work has been featured in some popular new media, such as PhysOrg [17], R&D 100 Award [18], and Newsday [19], none of these journalists have reported the technical design, modeling, bench test, and road test data. This paper is organized as follows: Section II describes the design principles. Section III introduces the modeling and analysis of the energy-harvesting shock absorber. In Section IV, the prototype is characterized with bench tests. In Section V, road tests are conducted to verify the capabilities of energy harvesting in a Chevrolet full-size SUV. Conclusions, including design guidelines, are then given in Section VI.
Fig. 2. Experiment setup for suspension vibration tests. The laser head of the displacement sensor (Micro-Epsilon ILD1401) is mounted on the inner cylinder of the absorber, and the target is mounted on the outer cylinder.
Fig. 3. Suspension velocity between the sprung and unsprung masses recorded on a local road at 32 km/h (20 mi/h). TABLE I MEASURED SUSPENSION VIBRATION VELOCITY AND C ALCULATED P OWER
II. R EGENERATIVE S HOCK A BSORBER D ESIGN A. Suspension Vibration Input To evaluate the suspension’s vibration induced by road roughness, we performed some experimental study using a Chevrolet Suburban (2002 model). A laser displacement sensor (Micro-Epsilon ILD1401, 1000 Hz, resolution 50 μm) is mounted on the traditional shock absorber of the rear suspension to directly measure the compression/extension of the shock absorber, as shown in Fig. 2. The suspension velocity is calculated from the measured relative displacement by taking a derivative and applying a fourth-order Butterworth filter of bandwidth 0.1–100 Hz [5]. The vehicle is driven on different roads, including Stony Brook Road near Stony Brook University, Stony Brook, NY, and the Long Island Expressway (I-495). The suspension vibration highly depends on road conditions and vehicle speed. Fig. 3 shows a recorded relative vibration velocity between the sprung and unsprung masses obtained in the test at the vehicle speed of 32 km/h (20 mi/h). The instant peak-to-peak velocity can be 0.15 m/s, but the root-meansquare (RMS) value of the velocity data is only 0.026 m/s.
Table I shows the measured relative velocities of the suspension when the SUV was driven at different vehicle speeds. In Table I, it is shown that the suspension velocity increases with the increase in vehicle driving speed. In addition, road conditions have a great influence on the suspension velocity. Based on the measured equivalent damping coefficient 4700 N/m of the traditional shock absorber on this SUV vehicle, we also calculated the table power dissipated by the suspension system with four shocks, as shown in Table I.
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Fig. 4.
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Overall structure of the regenerative shock absorber.
B. Design Principle In general, spring stiffness is very important for the vibration energy harvester design since we would like to make the resonant frequency the same as the excitation frequency. However, the main excitation to vehicle suspension is road roughness, which is generally random and, often, can be modeled as whitenoise velocity input to the tires [5]. In addition, retrofit design is important for economic implementation without changing the suspension structure or suspension stiffness. Therefore, we would like to design regenerative shock absorbers that can directly replace the traditional oil damper to achieve the desired damping while harvesting the energy. There are generally two types of configurations of regenerative shock absorbers, i.e., linear design and rotary design. The linear-type shock absorbers utilize the relative motion between magnetic field and coils to directly generate power based on Faraday’s law of electromagnetic induction. The rotary shock absorbers transfer linear motion of suspension vibration to rotary motion to drive permanent magnetic dc generators. Usually, rotary shock absorbers are capable of generating more power and getting a larger damping coefficient for the given space [20]. To change the linear motion into rotary motion, different mechanisms could be adopted including ball-screw and rack–pinion mechanisms. However, considering the poor performance of the ball-screw harvester in high frequencies [21], we choose the rack–pinion mechanism, as shown in Fig. 4. A pair of bevel gears are also used to change the transmission by 90◦ . As the output voltage is proportional to the rotational speed, a planetary gearbox is used for motion magnification. C. Prototype Introduction The principle of regenerative shock absorber is shown in Fig. 4, and a prototype is showed in Fig. 5. It is mainly composed of rack–pinion, bevel gears, planetary gears, and an electrical generator. The electric generator assembly is mounted on a cylinder, and an outer cylinder is used to enclose the system. The rack is connected with the end of the outer cylinder and will drive the pinion gear when there is a relative motion between the two ends of the shock absorbers. Through bevel gears, the rotational motion of the pinion gear is transferred by 90◦ to the rotational motion of the generator. The planetary gears are used to magnify the motion, and a dc motor is used as a generator. It should be noted that Li et al. [16] previously built a rack–pinion-based shock absorber prototype, but the size of the shock absorber prototype is not retrofittable for common vehicles (101.6 mm of overall diameter, in comparison with
Fig. 5. Three-dimensional model and photo of the shock absorber prototype.
the 72-mm outside diameter in this prototype). Moreover, there are large backlash and friction in the transmission. To reduce friction forces and backlash impacts, in this design, a roller is used to guide the rack and preload of rack on the opposite side of the pinion gears. In addition, we put a Teflon ring between the outer and inner cylinders to further reduce the dry friction forces. We also put a filter with a steel wire screen at the top of the shock absorber to prevent the dirt from being sucked into the cylinders during the motion. The selection of gears for this system is critical for its overall performance. With a higher transmission ratio, the system can achieve a higher damping coefficient (which we will see in the modeling, Section III), but a large gear ratio usually means low transmission efficiency. A smaller transmission ratio has higher transmission efficiency and better compactness, but the expected damping coefficient would be lower. Hence, the selection of gears is a compromise between performance, efficiency, and compactness. In this prototype, we choose ratio 50 to bring the typical RMS suspension velocity to the rated generator rotation speed. The bevel and rack–pinion gears are the two most important components in the system that may cause failure; hence, contact fatigue, strength of teeth surface, and strength of teeth root bending should be checked. III. M ODELING AND A NALYSIS The regenerative shock absorber has several parts, including a generator, a planetary gearbox, bevel gears, rack–pinion, etc. The objective of this session is to investigate the influence of these components and the parameters on the dynamics of the system. A. DC Motor and DC Generator Permanent magnetic dc motors can be directly used as generators. Although the modeling of a dc motor is well known, it is a very common mistake that people may directly take a 100-W
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the maximum continuous current due to the thermal limit of this electrical machine. For a short time, the instant speed can be higher than the rated speed, and thus, the instant voltage generated can be higher. Moreover, the maximal permissible speed is limited by the ball bearings in this motor. B. Dynamics Modeling
Fig. 6. Two working modes of electrical machines. (a) As a motor. (b) As a generator.
motor to be a 100-W generator. In this session, we analyze the characteristics of motors and generators and illustrate the difference of dc machines as a generator and as a motor (see Fig. 6). When the electrical machine of internal resistance ri is used as a motor, the relation between input voltage Um and back electromotive force (EMF) voltage Uemf at nominal current In is Um = In ri + Uemf .
(1)
Furthermore, when it is used as a generator, output voltage Ug at nominal current In is Uemf = In ri + Ug
(2)
where the back EMF voltage is proportional to rotation speed ωn with gain ke of the back electromotive voltage constant. Thus Uemf = ke ωn .
(3)
From (1) and (2), we see that when the motor is used as a generator, at the same speed ωn and current In , output voltage Ug may be much smaller than the nominal input voltage Um of the motor. Thus Ug = Uemf − In ri = Um − 2In ri
(4)
and the nominal output power Pg as a generator is also smaller than the nominal power Pm of the motor, i.e., Pg = Ug In = Um In − 2In2 ri = Pm − 2In2 ri .
(5)
Equations (4) and (5) indicate how we should take the internal resistance and the nominal current into account in the generator selection. In this prototype, we select a dc motor (Maxon Motor, model 218010) as a generator. The parameters are shown in Table II. Plugging the motor parameters into (4) and (5), we see that the output voltage at the rated rotational speed and rated current will be 38.9 V, and the output power is only 41.1 W, much smaller than the rated power 48 V × 1.38 A = 66 W as a motor. One may think that the maximal output power happens when the external resistor is the same as the internal resistor: (48 V/2)2 /6.6 Ω = 87.3 W. However, a simple calculation indicates that the current in the electrical machine in such a case will be 3.6 A = 48 V/(2 × 6.6 Ω), which is much larger than the rated current 1.38 A, which is
The analysis in Section III-A is the capacity of steady power generation when an electrical motor is used as a generator. To model the dynamics of the system, we have to consider the inertia and inductance of the electrical generator. Fig. 7 shows the dynamic modeling of a dc generator. Electric current i in the generator coil will produce torque τi following the relationship τi = kt i
(6)
where kt represents the torque constant. Based on Newton’s second law, we can get τm − τi = J m
d2 θ dt2
(7)
where τm is the input mechanical torque on the generator, and Jm is the inertia of the rotor. Based on Kirchhoff’s voltage laws, we have Uemf − L
di − iR = 0 dt
(8)
where back EMF voltage Uemf = ke (dθ/dt), L represents the generator’s internal inductance, and R is the sum of generator internal resistance ri and electric load resistance Re . Take (6)–(8) into consideration, the overall expression of the generator’s dynamics can be written as L d dθ d2 θ d2 θ R = ke τm − Jm 2 . (9) τm − J m 2 + dt kt dt dt kt dt This equation can be written in the Laplace domain with Laplace operators, i.e., kt ke s Tm = + Jm s2 . Θ R + Ls
(10)
If we express the torque in mass–spring-damping form, i.e., Tm = Jm Θs2 + cm Θs + km Θ
(11)
then we can obtain the equivalent torsional damping of coefficient cm (frequency dependent), i.e., cm =
kt ke R R 2 + L2 ω 2
(12)
and the equivalent torsional stiffness km , i.e., km =
kt kt Lω 2 . R 2 + L2 ω 2
(13)
Equations (12) and (13) indicate that the coil resistance contributes to torsional damping, and the coil inductor appears to be a stiffness. Considering that the vibration induced by road irregularities is usually in the frequency range 1–10 Hz, and the inductance
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TABLE II PARAMETERS OF THE DC “MOTOR” USED IN THE PROTOTYPE
where kg , ηg , and Jg are the overall transmission ratio, efficiency, and rotation inertia of the gear transmission system from the pinion gear to the generator rotor, as explained in Section III-C; r is the radius of pinion gears; mr and mc are the masses of the rack and the moving casing; ke and kt are the voltage and torque constants of the generator; R is the electrical loop resistance; and kv is the viscous damping between the inner and outer cylinders. Therefore, the equivalent can be obtained as Fig. 7. Dynamics modeling of the electromagnetic generator, where Re can be the equivalent resistance of the power charge circuit.
of the generator (motor) is very small compared with the resistance (Lω R), the influence of the generator’s inner inductance can be neglected. Therefore, the generator can be simplified as a torsional damper: cm ≈ ke kt /R and km ≈ 0. The inertia of the motor will be considered together with the gear transmission as an equivalent mass. C. Gear Transmission The gear transmissions in our prototype system include planetary gears in the gearbox, bevel gears, and rack–pinion gears, as shown in Fig. 4. Considering that friction and backlash are comparatively small, the gears’ large stiffness and small damping effect, the whole transmission gears can be modeled together as one transmission system with an overall transmission ratio kg = kp · kb /r, efficiency ηg = ηp · ηb · ηr , and rotation inertia Jg = Jp · kp2 kb2 + Jb · kb2 + Jr , where Jp , kp , and ηp represent the rotation inertia, transmission ratio, and efficiency of the planetary gears; Jb , kb , and ηb represent the rotation inertia, transmission ratio, and efficiency of the bevel gears; and Jr , r, and ηb represent the rotation inertia, pinion radius, and efficiency of the rack and pinion. D. Linear Model Under Sinusoidal Vibration The backlash and Coulomb friction in this design are much smaller than those in the previous prototype [16]. Therefore, a linear model can be obtained with the equivalent mass, stiffness, and damping coefficient. Based on the models of the generator and gear transmission, we can obtain the relationship between the driving force and the motion displacement, i.e., ⎤ ⎡ J k2 Jg + mηg g + (mr + mc )⎦ F =⎣ r2 d2 x · 2 + dt
kg2 ke kt + kv r 2 ηg R
dx · dt
meq =
Jm kg2 ηg r2
Jg +
+ (mr + mc ).
The most important parameter of this energy-harvesting absorber is the equivalent of the damping ratio. Thus Ceq =
kg2 ke kt + kv . r 2 ηg R
(16)
We see that the equivalent damping coefficient is mainly determined by generator constants ke and kt , transmission ratio kg from the pinion gear to the generator rotor, loop resistance R = ri + Re , and viscous friction coefficient kv between the inner and outer cylinders. Equation (16) can be used to guide the selection of the generator, gearbox ratio, and pinion gear diameter. Equation (16) also indicates that electrical resistance R = ri + Re is important to the damping coefficient. As a result, the damping coefficient can be controlled with resistance Re of external load or charging circuit. It should be noted that an electrical charging circuit is very important for energyharvesting suspension, which is out of the scope of this paper. However, it is useful to note that the charging circuit with a dc/dc converter can be modeled as a pure resistor Re controlled with pulsewidth modulation under moderate assumption [22], [23]. Although the equivalent stiffness of the electrical generator due to inductor L [see (13)] is negligible, the equivalent mass meq will appear to have a negative slope in the force–displacement loops under sinusoidal vibration input, which we will see in the bench tests. Thus x = A cos(ω0 t + ϕ0 ) + x0 2
d x = −Aω02 cos(ω0 t + ϕ0 ) = ω02 x. dt2
(17)
Hence, the force can be expressed as ⎡ ⎤ J k2 Jg + mηg g F = −⎣ + (mr + mc )⎦ r2
(14)
(15)
·
ω02 x
+
kg2 ke kt + kv r 2 ηg R
·
dx . dt
(18)
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Fig. 10. Force–displacement loop for different frequencies with 30-Ω external load and 30-mm displacement input, where the negative slope is due to the effect of mass inertias. Fig. 8. Equivalent dynamic model of the shock absorber. (a) For general input excitation. (b) For harmonic excitation.
Fig. 11. Force–displacement loops for different electrical loads at displacement input of 0.1-Hz frequency and 30-mm amplitude.
Fig. 9. Bench test setup for the regenerative shock absorber.
The coefficient of x is a negative stiffness. Thus ⎡
⎤ J k2 Jg + mηg g Keq = −meq ω02 = −⎣ +(mr +mc )⎦ ω02 . r2
(19)
We will see this phenomenon as a negative slope in the force–displacement loops in Section IV-A. Hence, the whole system can be viewed as mass meq and damper Ceq in series or a negative spring element Keq and damper Ceq in parallel, as shown in Fig. 8. IV. B ENCH T ESTS The experiment setup for the laboratory test of the energy harvester prototype is shown in Fig. 9. The bench tests are conducted on an 858 Mini Bionix II material testing system from MTS. A dynamic signal analyzer HP 3567A is used to record the voltage signal from the generator. Force and displacement signals are measured with a displacement sensor and a load cell (integrated in the 858 Mini Bionix II testing system). A. Symmetric Test of the Damping and Harvesting The prototype was first tested with sinusoidal displacement input. Power resistors were used as the external electrical load.
The force–displacement damping loops are shown in Figs. 10 and 11 at different frequencies and external electrical loads. It is shown in Fig. 10 that the orientation of the loop is not horizontal, and the slope changes when the frequencies increase. This can be explained using (19). The slope is mainly caused by the inertia of moving parts, and the orientation represents the negative stiffness Keq of the system, where Keq = −meq ω02 . In Figs. 10 and 11, the area of the loop means the mechanical work input of the shock absorber ΔW in one cycle; hence, the mechanical power input can be calculated as Pin = ΔW · ω0 /2π. Moreover, the equivalent damping coefficient can be calculated as Ceq =
ΔW πω0 X 2
(20)
where ω0 means the input frequency, and X means the displacement magnitude. The force–displacement loops in Figs. 10 and 11 are not smooth. The fluctuating waves on the force–displacement loops are due to the imperfect engagement of the gear teeth of bevel gears and rack–pinion gears. This problem may be taken care of by more precise machining and tolerance control. Fig. 12 shows the relationship between force and velocity. We can see that the relationship is almost linear, and the slopes correspond to the damping coefficients. In addition, the slopes increase when the electrical load decreases, which means we attend larger damping.
LI et al.: ENERGY-HARVESTING SHOCK ABSORBERS: DESIGN, MODELING, AND ROAD TESTS
Fig. 12. Force–velocity relationship for different electrical loads at displacement input of 0.5-Hz frequency and 30-mm amplitude.
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Fig. 14. Output electrical power for different resistors at displacement input of 0.5-Hz frequency and 30-mm vibration amplitude.
Fig. 13. Damping coefficients with different electrical loads.
Equation (16) predicts that the damping coefficient of the regenerative shock absorber depends on the electrical loads: Ceq = (kh2 ke kt /r2 ηg R) + kv . Such a prediction very well matches with the experiment, as shown in Fig. 13. Therefore, the shock absorber can be controlled in a large range by controlling the external resistances or the PMW of the circuit circuitry [22], [23]. In this prototype, a 30-Ω electrical load corresponds to a damping coefficient of around 5000 Ns/m, which is close to the value of the commercial shock absorber used in the test SUV. In addition, a 94-Ω electrical load corresponds to a damping coefficient of 1800 Ns/m, which is good for a typical passenger car. We also recorded the voltage of the external load. The instant output electrical power is calculated based on the recorded voltage and resistor value Pout = V 2 /Re , as shown in Fig. 14. The peak output power attains 22 and 12 W, respectively, on 42- and 94-Ω external loads and at 0.5-Hz and 30-mm vibration amplitude. It should be noted that the energy-converting efficiency is an important index of the harvester performance. However, we have rarely seen such a number in the published papers. After we obtain the input mechanical power and output electrical power, we can then calculate the total efficiency of the regenerative shock absorbers. The total efficiency is further
Fig. 15. Mechanical efficiency under different vibration frequencies with 94-Ω resistive load, where the vibration amplitude is 10 mm.
deconvoluted into mechanical and electrical efficiencies. The electrical efficiency is the ratio of the external resistance and the loop resistance (sum of the external resistance and the generator internal resistance, 6.6 Ω in the prototype). The mechanical efficiency ranges from 33% to 63% with different vibration frequencies (see Fig. 15) and different electrical loads (see Fig. 16). It is shown that the mechanical efficiency achieves the maximum at around 1-Hz frequency input, and the efficiency decreases at high frequency. The mechanical efficiency at 0.5 Hz increases from 47% to 60% when the vibration amplitude increases from 10 to 30 mm. In addition, the mechanical efficiency also varies with the change in electrical load, as shown in Fig. 16. B. Asymmetry in the Jounce and Rebound Asymmetric damping coefficients are essential for the vehicle suspension system because they can help vehicles keep good contact with roads and reduce shock to the vehicle body. The regenerative shock absorber is symmetrically designed; however, the asymmetric characteristics can be achieved by shunting the regenerative shock absorber with different electric loads during the jounce and rebound motions. Considering
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Fig. 18.
Force–velocity relationship of the regenerative shock absorber.
Fig. 16. Mechanical efficiency for different external resistances under harmonic vibration of 30-mm amplitude.
Fig. 17. Control circuit for asymmetric characteristics.
that the upward and downward motions will generate voltages with opposite polarities in the dc generator (i.e., positive and negative voltages), a simple circuit can be built to achieve the asymmetry, as shown in Fig. 17. Such a circuit connects R2 in positive voltage direction and R1 in negative voltage direction. Hence, the damping coefficient of the regenerative shock absorber is ⎧ 2 ⎨ k2g ke kt + kv , positive voltage direction r ηg R 2 (21) Casym = 2 ⎩ k2g ke kt + kv , negative voltage direction.
Fig. 19. Asymmetric forces of the regenerative shock absorber in jounce and rebound motions. TABLE III VEHICLE INFORMATION
r ηg R 1
Figs. 18 and 19 show the regenerative shock absorber with asymmetric damping coefficients. We can see that the regenerative shock absorber can act similarly as the traditional hydraulic shock absorber for the asymmetric characteristics. Hence, the regenerative shock absorber can replace traditional shock absorbers for its complete function while harvesting energy from vehicle vibration. In addition, if the external load resistor can be controlled with semiactive control laws, it can further improve the vehicle dynamics and harvest energy at the same time. V. ROAD T ESTS To validate the given analysis and demonstrate energy harvesting from the shock absorbers, we carried out road tests us-
ing a Chevrolet Surburban SUV (2002 model). Its information is shown in Table III. The experiment setup is shown in Fig. 20. The displacement of the rear shock absorber was recorded by a laser displacement sensor from Micro-Epsilon with a sampling rate of 1000 points/s. The output voltage is recorded with a digital signal analyzer HP 35670A. The road tests were conducted on the campus road of Stony Brook University, Stony Brook, NY, at different speeds, including 30 and 20 mi/h (or 48 and 32 km/h). The recorded voltages on an external electrical load of 30 Ω generated from the energy-harvesting shock absorber at these two vehicle speeds are shown in Figs. 21 and 22, respectively. It is shown that the peak voltages were over 40 V. Correspondingly, the peak
LI et al.: ENERGY-HARVESTING SHOCK ABSORBERS: DESIGN, MODELING, AND ROAD TESTS
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powers are 67.5–58.2 W. The average power values are 4.8 and 3.3 W, respectively, at 48 and 32 km/h (30 and 20 mi/h), or 19.2 and 13.2 W can be harvested on four shock absorbers at 48 and 32 km/h. Recall in Table I, we estimate 54.1- and 13.5-W energy dissipation on a local road at 48 and 32 km/h. The results from the road tests are encouraging, although the harvesting efficiency in road tests cannot be drawn from these values since the suspension vibration highly depends on the road conditions. VI. C ONCLUSION
Fig. 20. Setup of the road tests. (Top) Vehicle. (Bottom left) Instruments. (Bottom right) Mounting of sensors and the regenerative shock absorber.
A retrofit rack–pinion-based electromagnetic regenerative shock absorber is developed and tested, which can generate electric power from the road-induced suspension vibration of vehicles. The working principle and design are presented. A dynamic modeling for a rack–pinion-type shock absorber system has been derived and analyzed. The prototype is evaluated on a testing machine with sinusoidal displacement input. The results show that the equivalent damping coefficient depends on the external electrical resistances. As a result, the regenerative shock absorber can be used as a controllable damper, and the damping coefficient can be handled by controlling equivalent external electrical load. A total energy conversion efficiency of up to 56% is achieved under +/−30-mm 0.5-Hz vibration and 94-Ω external load. We also demonstrated the asymmetric characteristics of the regenerative shock absorber in jounce and rebound motions by connecting it with asymmetric electrical loads. Road tests were carried out to verify the performance of the new designed regenerative shock absorber. The experiment results indicate that the generated voltage reflects the road irregularities well. A peak power of 67.5 W and an average power of 19.2 W can be obtained from four energy-harvesting shock absorbers when the vehicle travels at 48 km/h (30 mi/h) on a fairly smooth campus road. ACKNOWLEDGMENT
Fig. 21. Displacement and voltage measured at 48 km/h (30 mi/h) on a paved campus road.
The authors would like to thank the people who helped greatly with this project, including Mr. D. McAvoy and J. T. O’Connor of the Stony Brook University Transportation Department, for providing the test vehicles, and X. Tang, P. Li, T. Lin, and W. Zhou, for assistance with the road test. R EFERENCES
Fig. 22. Displacement and voltage measured at 32 km/h (20 mi/h) on a paved campus road.
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Zhongjie Li was born in China in 1988. He received the B.S. degree in mechanical engineering from Harbin Institute of Technology, Harbin, China, in 2010. He is currently working toward the M.S. degree with the Department of Mechanical Engineering, State University of New York at Stony Brook. His current research is in the areas of design, modeling, and testing of regenerative shock absorbers.
Lei Zuo received the B.S. degree in automotive engineering from Tsinghua University, Beijing, China, in 1997 and two M.S. degrees in electrical and mechanical engineering and the Ph.D. degree in mechanical engineering from Massachusetts Institute of Technology, Cambridge, in 2005. In 2008, after working four years in industry, he joined the State University of New York at Stony Brook as an Assistant Professor and founded the Energy Harvesting and Mechatronics Research Laboratory. His research is currently supported by the U.S. National Science Foundation, the U.S. Department of Energy, the U.S. Department of Transportation, the New York Energy Research and Development Authority, and industry. His research interests include vibration and thermoelectric energy harvesting, mechatronics design, control systems, smart structures, and biosensors. Dr. Zuo received an R&D 100 Award by R&D 100 Magazine for his work on energy-harvesting shock absorbers.
George Luhrs, photograph and biography not available at the time of publication.
Liangjun Lin, photograph and biography not available at the time of publication.
Yi-xian Qin, photograph and biography not available at the time of publication.
