Energy 86 (2015) 385e392 Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy Energy harvesting from a vehicle suspension system X.D. Xie b, Q. Wang a, b, * a b Department of Mechanical Engineering, Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates Department of Mechanical Engineering, University of Manitoba, Winnipeg, Canada a r t i c l e i n f o a b s t r a c t Article history: Received 2 February 2015 Received in revised form 16 March 2015 Accepted 10 April 2015 Available online 6 May 2015 A dual-mass piezoelectric bar harvester is developed for energy harvesting from ambient vibrations of a vehicle suspension system subjected to roughness of road surfaces. The harvester is made of a sprung mass (body mass) and an unsprung mass (wheel mass) connected by a piezoelectric bar transducer which is equivalently modeled as a suspension spring and a damper in a mathematics model. The dualmass piezoelectric bar harvester is practically designed in a vehicle suspension system on wheels to generate an electric charge. To describe the energy harvesting process, a mathematics model is developed to calculate the output charge and voltage from the harvester by an iteration method in the temporal domain. The influences of some practical considerations, such as the width of the piezoelectric bar, the speed of vehicles, and the class of the road roughness, on the root mean square of the generated electric power are discussed. Our results show that a power up to 738 W can be realized for a practical design of the harvester with a width and height of the piezoelectric bar of 0.015 m and 0.1 m respectively. This research develops a new design method for efficient and practical energy harvesting from vehicle vibrations. © 2015 Elsevier Ltd. All rights reserved. Keywords: Piezoelectric bar harvester Energy harvesting from vehicle suspension Gauss white noise RMS (Root mean square) 1. Introduction Energy crisis and environmental problems such as oil shortage and atmospheric pollution have brought challenges for new development of an energy saving, efficient and environmentally friendly power transmission system in vehicles. In recent years, electric vehicles play a major role in attaining sustainability and reducing air pollution [1]. The current status of EV (electric vehicle) developments is encouraging. Several countries worldwide have ambitions to electrify their car fleet [2]. In regions such as China, by this year there should be more than 100 000 PHEV (plug-in hybrid electric vehicles) just in Beijing and 150 000 000 all over China according to the “Twelfth Five Year Plan” [3]. EVs have an advantage over conventional internal combustion engine automobiles since they do not emit harmful tailpipe pollutants from the onboard source of power [4]. However, there still remain many challenges and unsolved issues in the development of EVs. The price of EVs is significantly higher than traditional vehicles, even after considering government incentives for EVs available * Corresponding author. Dept of Mechanical Engineering, Khalifa University, Abu Dhabi, United Arab Emirates. Tel.: þ971 (0) 2 501 8437. E-mail address: quan.wang@kustar.ac.ae (Q. Wang). http://dx.doi.org/10.1016/j.energy.2015.04.009 0360-5442/© 2015 Elsevier Ltd. All rights reserved. in several countries. The primary reason for high prices is the high cost of vehicle batteries. The U.S. Department of Energy has set cost targets for its sponsored battery research of US$300 per kilowatt hour in 2015 and US$125 per kilowatt hour by 2022 [5]. In addition, the efficiency of EVs is low because they have a short driving range and a long charging time. Electricity consumption for air conditioning or cabin heating can also shorten the driving range in areas with hot/cold weather [6]. Due to the unsolved problems, research efforts turn to developments of energy harvesting from the vehicle kinetic energy as a new driving source to increase the efficiency of vehicles and decrease their costs. In fact, only a small part of energy from the onboard source of vehicles is used for driving, while most of the energy dissipating during vibrations and motions [7]. If vibrations of vehicles can be absorbed and reused fully, the utilization efficiency of onboard source could be improved notably. Research efforts on energy recovery from vehicle suspensions, first as an auxiliary power source for active suspension control, and later as energy regenerating devices in their own accord, have been developed during recent years. A research [8] presented a design and analysis of an efficient energy harvesting hydraulic electromagnetic shock absorber with least weight penalty on a vehicle. The conceived shock absorber uses mechanical amplification and linear generator along with a displacement sensitive fluid damper. 386 X.D. Xie, Q. Wang / Energy 86 (2015) 385e392 A HESA (hydraulic electromagnetic shock absorber) was designed [9], which can not only isolate vibration but also recover energy from vibration of vehicles. The damping characteristic of the HESA prototype is tested, and its performance is proven to be good under low cracking pressure and small excitation amplitude without taking into account the requirement that damping force in compression stroke is greater than that in extension stroke. A new kind of semi-active energy-regenerative suspension system was proposed [10] to recover the suspension vibration energy, as well as to reduce the suspension cost and demands for the motor-rated capacity. A design and optimization of tubular LETs (linear electromagnetic transducers) was further presented [11] for vibration energy harvesting from vehicle suspensions, and an average power of 26e33 W was found to be achieved at a RMS (root mean square) of suspension velocity of 0.25 m/s for different LETs of an outer diameter of 300 and a compressed length of 1200 . A design, modeling, bench experiments, and road tests were proposed [12] for a retrofit regenerative shock absorber based on a permanent magnetic generator and a rackepinion mechanism for energy harvesting and vibration damping. A peak power of 68 W and average power of 19 W were attained from one prototype shock absorber when the vehicle is driven at 48 km/h (30 mi/h) on a fairly smooth campus road. Previous studies on regenerative vibration absorbers of vehicles were all designed to generate electric energy from vibrations of vehicles by electromagnetic materials. These absorbers were fixed in parallel with a suspension spring which indispensably dissipates a part of vehicle vibration energy, and hence cannot fully absorb and transfer the kinetic energy from the suspension system. In addition, the conversion efficiency of electromagnetic materials is not very high. Currently, the mostly available vibration-to-electric conversion mechanisms are electromagnetic, electrostatic, and piezoelectric transductions. Among the three types of energy transductions, the efficiency of piezoelectric transductions is preferred and much higher than the other two. It was indicated that the energy density of piezoelectric transduction is three times higher than the other two transductions [13]. Therefore, many research works have been conducted on applications of piezoelectric materials for energy conversion from ambient environmental vibrations. By both numerical simulations and experimental studies, A PEHSA (piezoelectric energy-harvesting shock absorber) system was developed [14] for vehicles to act as an energy harvester that converts vibration energy to electrical energy. Cylindrical piezoelectric transducers are combined with a cylinder of the shock absorber to generate electricity from changes in fluid pressure produced by piston vibrations. A design and testing of a vibration energy harvester [15] was proposed with tunable resonance frequency, wherein the tuning is accomplished by changing the attraction force between two permanent magnets by adjusting the distance between the magnets. An optimal design of a piezoelectric coupled cantilever structure attached by a mass subjected to vibrations was introduced [16] to achieve a higher efficient energy harvesting. Sea wave piezoelectric energy harvesters from longitudinal/transversal wave motion of water particles were introduced later [17,18]. The results show that the harvesters can generate power up to 55 W/ 30 W for a practical longitudinal/transversal wave motion. A ring piezoelectric energy harvester excited by magnetic forces was developed [19] and it was found that a power up to 5274.8 W can be realized for a practical design of the harvester with a radius around 0.5 m. The above references show that the piezoelectric technology has the ability of generating up to thousands of watts of electric power through absorbing ambient vibration energy. It is expected that the piezoelectric harvesting energy technology may also be used in absorbing kinetic energy from vehicles as a new driving source to increase the efficiency of vehicles and decrease their costs. To achieve a new effective design of energy harvesting for driving vehicles with piezoelectric technology, a dual-mass piezoelectric bar harvester for absorbing energy from vibrations and motions of a suspension system under random excitations from road roughness is developed. A mathematical model of the dualmass piezoelectric bar harvester is established and studied by an iteration method in temporal domain. Some key considerations for the developed harvester are hence discussed for achieving a high efficiency of energy harvesting. 2. Design and methods Design of a dual-mass piezoelectric bar harvester is depicted in Fig. 1(aec). The piezoelectric bar transducer model is schematically illustrated in Fig. 1a which consists of a spring with a stiffness coefficient of k, a lever AB consisting of a long moment arm of AC with a length of L1 and a short moment arm of BC with a length of L2, a fixedhinge for restricting linear displacements of the lever at point C, and a piezoelectric bar with a Yong's modulus, a width and height of Ep, a, and h respectively. The equivalent stiffness coefficient of the device assembled by the lever and the piezoelectric bar is k’ ¼ Epa2/n2h (n ¼ L1/L2). Therefore, the total stiffness coefficient of the piezoelectric bar transducer is equal to kk’/(k þ k’). A typical quarter car model is shown in Fig. 1b which includes a chassis and a wheel connected by a spring and damper which can replace the piezoelectric bar transducer as an equivalence in the model. Because the wheel can be modeled by a mass and a spring moving on a random rough road with a motion function of q(t), the quarter car model can be furthermore modeled by a dual-mass piezoelectric bar harvester model shown in Fig. 1c for the convenience of analysis. The dualmass piezoelectric bar harvester consists of a sprung mass of m2, an unsprung mass of m1, namely the mass of the wheel with a spring stiffness coefficient of k1. Two masses are connected in series by a suspension spring with stiffness of k2 ¼ kk'/(k þ k') and a damper with an equivalent damping coefficient of c2. Based on the model in Fig. 1c,a mathematical model for the dual-mass piezoelectric bar harvester is developed and solved by an iteration method. According to the principle that the dissipation energy of a damper is equal to the electric energy generated by the piezoelectric bar harvester, the damping coefficient c2 can be derived as below: c2 ¼ n2 d233 k22 . p2 cv f ; (1) where n ¼ L1/L2 is a ratio of the moment arms of the lever; d33 is the piezoelectric constant in the polling direction; cv is the electrical capacity of the piezoelectric bar; f is the first natural vibration frequency of the vehicle suspension. The governing differential equations of the dual-mass piezoelectric bar harvester system in Fig. 1c are expressed below according to Newton second law: m1 €z1 c2 ðz_2 z_1 Þ k2 ðz2 z1 Þ þ k1 ðz1 qðtÞÞ ¼ 0 ; m2 €z2 þ c2 ðz_2 z_1 Þ þ k2 ðz2 z1 Þ ¼ 0 (2) where z1 and z2 denote displacements of the unsprung mass and sprung mass with respect to their respective equilibrium positions; q(t) is the transverse motions function of road surface, which can be obtained by the equation: _ þ 2pf0 qðtÞ ¼ 2pn0 qðtÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Gq ðn0 ÞvðtÞwðtÞ; (3) where Gq ðn0 Þ is the roughness coefficient of the road surface in m3; n0 is a reference spatial frequency with a value of 0.1 m1; f0 is a X.D. Xie, Q. Wang / Energy 86 (2015) 385e392 387 Fig. 1. Sketch of the dual-mass piezoelectric bar harvester of a quarter-car. (a) A piezoelectric bar transducer, (b) The Quarter-car model, and (c) The qual-mass piezoelectric energy harvester. Table 1 Material properties and dimensions of a dual-mass piezoelectric bar harvester. Dual-mass piezoelectric energy harvester Lever(hardened steel) and piezoelectric bar (PZT4) m1(kg) m2(kg) a(m) 24 Cv0 (nF))) 350 85 270 60 000 0.015e0.025 0.1 5e9 6.4e-10 0.375 for the piezoelectric patch with the geometry of 0.01, 0.01, 0.0001 m k1(N/m) k(N/m) h(m) n(L1/L2) d33(C/N) Table 2 Road-roughness coefficients Gq(n0) (m3) classified by ISO/TC108/SC2N67. Road class A B C D E F G H Gq(n0)(106) 16 64 256 1024 4096 16 384 65 536 262 144 minimal boundary frequency with a value of 0.0628 Hz; v(t) is the vehicle velocity in m/s; w(t) is a zero-mean (temporal) white noise process [20]. The natural frequencies, ɷ1, ɷ2, and mode shapes, {f}1,2, of the 2 DOF (degree-of-freedom) dual-mass piezoelectric bar harvester system are therefore listed below [21]: 8 0 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi311=2 > > > 1 k þ k k k1 þ k2 k2 2 k k > 1 2 2 4 @ > ¼ þ þ 4 1 2 5A u > 1 > > 2 m1 m2 m1 m2 m1 m2 < 0 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi311=2 ; > > > > 1 k þ k2 k2 k1 þ k2 k2 2 k k > > > u2 ¼ @ 4 1 þ þ þ 4 1 2 5A > : 2 m1 m2 m1 m2 m1 m2 (4) Fig. 2. Displacements and RMS of electric power versus ratio of L1/L2 based on a certain Gauss white noise. (a) Gauss white noise with zero mean value, (b) Transverse displacement of road surface, (c) Relative displacement of sprung mass and unsprung mass, and (d) RMS of electric power versus ratio of L1/L2. 388 X.D. Xie, Q. Wang / Energy 86 (2015) 385e392 Table 3 Dimensions and harvesting capacity of two different vehicle suspension harvesters. Type of harvester Dimension Linear electromagnetic transducers(LETs) Piezoelectric bar harvester Out diameter: 300 (7.62 cm) Width:1.5 cm ffg1;2 k2 ¼ : ðk1 þ k2 Þ m1 u21;2 Compressed length:1200 (30.48 cm) Height:10 cm (5) Eq. (2) is re-arranged as €z1 0 c k þ k2 z_1 þ 2 þ 1 €z2 0 c2 k2 z_2 0 c2 k1 qðtÞ z_1 ¼ þ ; c2 0 z_2 0 m1 0 0 m2 k2 k2 z1 z2 (6) or simply written as n o n o n o € þ ½C Z_ þ ½KfZg ¼ fPg þ ½C 0 Z_ : ½M Z (7) According to the modal analysis methods, we write fZg ¼ ½4fYg ¼ f4g1 Y1 þ f4g2 Y2 ; (8) RMS of suspension velocity Average power 0.25 cm/s 0.29 cm/s 26e33 W 738 W where [f] is a mode matrix; {Y} is a vector of the generated coordinates. Substituting Eq. (8) into Eq. (7) and multiplying it by f4gT1 and f4gT2 respectively lead to € þ C C 0 Y_ þ K Y ¼ P þ C 0 Y_ ¼ P ; M1 Y 1 1 1 1 1 11 1 11 12 2 (9) € þ C C 0 Y_ þ K Y ¼ P þ C 0 Y_ ¼ P ; M2 Y 2 2 2 2 2 22 2 22 21 1 (10) in which M1 ¼ f4gT1 ½Mf4g1 , M2 ¼ f4gT2 ½Mf4g2 , C1 ¼ f4gT1 ½Cf4g1 , C2 ¼ f4gT2 ½Cf4g2 , K1 ¼ f4gT1 ½Kf4g1 , K2 ¼ f4gT2 ½Kf4g2 , 0 ¼ f4gT ½C 0 f4g , P11 ¼ f4gT1 fPg, P22 ¼ f4gT2 fPg, C11 1 1 T 0 T 0 0 0 0 C12 ¼ f4g1 ½C f4g2 , C22 ¼ f4g2 ½C f4g2 , C 21 ¼ f4gT2 ½C 0 f4g1 . The generalized coordinates, Y1 and Y2, can be obtained by an iteration method. In order to ensure the constringency of the iteration, the forces of P1 and P2 are separated into small incremental segments in time domain and are supposed to be linear with time at each time interval. The governing differential equations at each time interval are thus given as: Fig. 3. Displacements and RMS of electric power versus width of the piezoelectric bar based on a certain Gauss white noise. (a) Gauss white noise with zero mean value, (b) Transverse displacement of road surface, (c) Relative displacement of sprung mass and unsprung mass, and (d) RMS of electric power versus width. X.D. Xie, Q. Wang / Energy 86 (2015) 385e392 € ðtÞ þ C C 0 Y_ ðtÞ þ K Y ðtÞ ¼ P ðtÞ þ C 0 Y_ ðtÞ M1 Y 1 1 1 1 1 11 11 12 2 ¼ P1 ðtÞ ¼ P1i þ a1i t; (11) € ðtÞ þ C C 0 Y_ ðtÞ þ K Y ðtÞ ¼ P ðtÞ þ C 0 Y_ ðtÞ M2 Y 2 2 2 2 2 22 22 21 1 h ¼ 0.0001 m [22]. The force applied to the piezoelectric bar in its poling direction at time ti is a random excitation at the end of the lever from the driving vehicle. Hence the RMS of the generated power from 0 to t from the piezoelectric bar can be obtained as: Perms ¼ P2 ðtÞ ¼ P2i þ a2i t; 389 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u Zt u u1 ¼t ½Pe ðtÞ2 dt; t (16) 0 (12) Where ti t tiþ1 , tiþ1 ¼ ti þ Dt, 0 Y_ ðt Þ; i ¼ 0; 1; 2; /∞ , P1i ¼ P11 ðti Þ þ C12 a1i ¼ ðP1ðiþ1Þ P1i Þ=Dt, 2 i 0 Y_ ðt Þ; i ¼ 0; 1; 2; /∞ , a ¼ ðP P2i ¼ P22 ðti Þ þ C21 1 i 2i 2ðiþ1Þ P2i Þ=Dt. Consequently, we can obtain the displacements, z1, z2 and velocities, z_ 1, z_ 2 at each time point of the unsprung mass and sprung mass at their respective equilibrium positions. The relative displacements, z21 ¼ z2z1, and velocities, z_ 21 ¼ z_ 2z_ 1, of the sprung mass and the unsprung mass can also be obtained. Then the generated charge, Qg(ti), and voltage, Vg(ti), from the piezoelectric bar at time ti can be solved by equations below: Qg ðti Þ ¼ d33 nk2 z21 ðti Þ; (13) Vg ðti Þ ¼ d33 nk2 z21 ðti Þ=Cv ; (14) Ig ðti Þ ¼ d33 nk2 z_21 ðti Þ; (15) where Cv ¼ Cv0 a a 0:0001=ð0:01 0:01 hÞ is the electric capacity of the piezoelectric bar in nF;Cv0 is the unit capacitance of the piezoelectric patch with an geometry of a ¼ 0.01 m, b ¼ 0.01 m, where Pe ðtÞ ¼ d233 n2 k22 z21 ðtÞz_21 ðtÞ=Cv is the generated power of the piezoelectric bar at time t (0 < t < t). To estimate the RMS of the generated power, the period, t, can be separated into j time steps with a sufficiently short time interval Dt. As a result, the expression in Eq. (16) can be rewritten in a discrete form below: Perms vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u j u X Dt ½Pe ðti Þ2 þ ½Pe ðti1 Þ2 : ¼t 2ðt DtÞ i¼2 (17) 3. Results In the following simulations, some important factors in designs, such as the ratio of the moment arms of the lever, the width of the piezoelectric bar, the velocity of vehicles, and the road roughness coefficient, that influence the RMS (root mean square) of the generated power are investigated for the proposed harvester. The dimensions and material properties of the energy harvester are Fig. 4. Displacements and RMS of electric power on a road of class B based on a certain Gauss white noise. (a) Gauss white noise with zero mean value, (b) Transverse displacement of road surface, (c) Relative displacement of sprung mass and unsprung mass, and (d) RMS of electric power versus speed of vehicle. 390 X.D. Xie, Q. Wang / Energy 86 (2015) 385e392 provided in Table 1. The road roughness adopts the first three classes, namely classes of B, C, and D, which are given in Table 2. The piezoelectric bar and lever are made of PZT4 (lead zirconate titanate) and hardened steel, respectively. The effect of the ratio of the moment arms of the lever on the RMS of the electric power generated by the dual-mass piezoelectric bar harvester is studies in Fig. 2(aed). A random Gauss white noise with a zero mean value is shown in Fig. 2a, and the transversal motions in 30 s of the car with a velocity of 35 m/s on a road of class D is shown in Fig. 2b. The motions are with a maximum amplitude of 0.097 m based on the white noise shown in Fig. 2a. The relative displacement, with the maximum amplitude of 0.094 m, of sprung mass and unsprung mass excited by the random road transversal motions in Fig. 2b is shown in Fig. 2c. A nonlinear increase of the RMS with an increase in the ratio of the moment arms of the lever is shown in Fig. 2d. The results shown by the solid curve in Fig. 2d are calculated based on the white noise excitation shown in Fig. 2a. The results by the solid line show that the highest RMS of the generated power is 714 W with a width and height of the piezoelectric bar, the vehicle speed, the road roughness coefficient, and the ratio of moment arms of the lever being a ¼ 0.015 m, h ¼ 0.1 m, v ¼ 35 m/s, Gq(n0) ¼ 1024e-6 m3, and L1/L2 ¼ 9, respectively. The results indicate that the RMS can be in a range of 457 We714 W when the ratio of the moment arms of the lever changes from 5 to 9. It is concluded that the novel dual-mass piezoelectric bar harvester is very efficient compared to the developed electromagnetic harvesters. For example, as indicated in Table 3, an average power of 33 W can only be achieved from vibrations of a vehicle suspension by an optimal tubular LETs (linear electromagnetic transducers) of an outer diameter of 300 and a compressed length of 1200 [11]. In addition to the fact that the piezoelectric technology has higher transduction efficiency than that by the electro-magnetic technology, a piezoelectric bar harvester can fully harvest the energy induced by the suspension system of vehicles. The results by dashed curves in Fig. 2d are obtained based on random white noise excitations 2 and 3 that are with a same intensity of that shown in Fig. 2a, but are chosen randomly in calculations. It is clearly seen that although a difference in the obtained RMS can be identified, the variations of the generated power remain same when white noises with a same mean value are used in evaluating the power by the model. The results show that the difference is within 10% only. The above analysis indicates that the model of the dual-mass piezoelectric bar harvester is robust since it is relatively insensitive to the environmental factors such as various white noise excitations. The effect of the width of the piezoelectric bar on the RMS of electric power generated by the dual-mass piezoelectric bar harvester is shown in Fig. 3(aed). A random Gauss white noise excitation with a zero mean value is given in Fig. 3a. The transversal motions in 30 s of the car with a velocity of 35 m/s on a road of class D are provided in Fig. 3b. The motions are with a maximum amplitude of 0.106 m. The relative displacement, with a maximum amplitude of 0.106 m, of the sprung mass and the unsprung mass excited by the random road transversal motions given in Fig. 3b is shown in Fig. 3c. The variations of the RMS versus the width of the piezoelectric bar is provided in Fig. 3d. The geometry and material parameters of the dual-mass piezoelectric bar harvester in this simulation are set to be: L1/L2 ¼ 9, h ¼ 0.1 m, m1 ¼ 24 kg, m2 ¼ 350 kg, k1 ¼ 85 270 N/m, k ¼ 60 000 N/m, f0 ¼ 0.0628 Hz, v ¼ 35 m/s and Gq(n0) ¼ 1024e-6 m3. It can be found that the RMS nonlinearly decreases with an increase in the width of the Fig. 5. Displacements and RMS of electric power on a road of class C based on a certain Gauss white noise. (a) Gauss white noise with zero mean value, (b) Transverse displacement of road surface, (c) Relative displacement of sprung mass and unsprung mass, and (d) RMS of electric power versus speed of vehicle. X.D. Xie, Q. Wang / Energy 86 (2015) 385e392 391 Fig. 6. Displacements and RMS of electric power on a road of class D based on a certain Gauss white noise. (a) Gauss white noise with zero mean value, (b) Transverse displacement of road surface, (c) Relative displacement of sprung mass and unsprung mass, and (d) RMS of electric power versus speed of vehicle. piezoelectric bar. The observation is interpreted that an increase in the width of the piezoelectric bar would lead to an increase in the electric capacity of Cv, and in turn a decrease in the electric voltage, i.e. a decreased generated power (see Eqs. (14) and (16)). It can be seen from Fig. 3d that the RMS decreases from 738 W to 340 W when the width of the piezoelectric bar changes from 0.015 m to 0.025 m. The effects of velocities of vehicles on the RMS of the electric power generated by cars on road classes of B, C, and D are revealed in Figs. 4e6. Three different random Gauss white noises are provided in Figs. 4ae6a with a zero mean value. The transversal motions in 30 s of the car are provided in Figs. 4ae6b with a velocity of 35 m/s on a road of classes B, C, and D. The motions are with a maximum amplitude of 0.02 m, 0.05 m and 0.107 m, respectively. Accordingly, three relative displacements, with maximum amplitudes of 0.032 m, 0.052 m, and 0.099 m, of the sprung mass and unsprung mass excited by the random road transversal motions in Figs. 4be6b are provided in Figs. 4ce6c, respectively. The relationship between the RMS and velocities of vehicles in a range of 10 m/s to 35 m/s on a road of classes B, C, and D, is demonstrated in Figs. 4e6d respectively. These simulations adopt the same geometry and material parameters with previous simulations. It is found in Figs. 4de6d that the RMS linearly increases with an increase in the velocity of vehicles. The observation is interpreted by the fact that the transversal motions and velocities of the road surface and the relative displacements and velocities of the sprung mass and unsprung mass are all proportional to the square root of the velocity of vehicles shown as Eq. (3). It can be seen from Figs. 4e6d that the RMS increase from 18 W to 40 W, 70 W to 162 W and 281 W to 652 W, respectively, when the velocity of vehicle changes from 10 m/s to 35 m/s. Thus it is obvious that a slight increase of velocity of vehicles would lead to a remarkable augment of the RMS. 4. Conclusions A novel efficient dual-mass piezoelectric bar harvester is developed for energy harvesting from ambient vibrations of a vehicle suspension system subjected to roughness of road surfaces. A mathematics model is developed to calculate the output charge, voltage, and electric power from the harvester by an iteration method in temporal domain. The computation results show that the RMS increases with an increase in the velocity of vehicles and the class of road surface, an increase in the ratio of the moment arms of the lever, and a decrease in the width of the piezoelectric bar. For an energy harvester structure with geometry and material parameters of a ¼ 0.015 m, L1/L2 ¼ 9, h ¼ 0.1 m, m1 ¼ 24 kg, m2 ¼ 350 kg, k1 ¼ 85 270 N/m, k ¼ 60 000 N/m, f0 ¼ 0.0628 Hz, v ¼ 35 m/s and Gq(n0) ¼ 1024e-6 m3, a value of RMS about 738 W can be achieved. It is expected that in practice four or more of the novel piezoelectric bar energy harvesters could be installed on a vehicle and provide more efficient energy harvesting as an auxiliary energy of vehicles. The research develops a new design method for an efficient and practical energy harvesting from vehicle vibrations, and hence would have a significant impact on automobile industry. References [1] Karsten Hedegaard, Hans Ravn, Nina Juul, Peter Meibom. 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