Avilble online t www.sciencedirect.com ScienceDirect Procedi Engineering 112 (2015 ) 225 230 7th Asi-Pcific Congress on Sports Technology, APCST 2015 Dynmic clibrtion of n instrumented bike brke hood in mesuring power bsorbed by the hnds Yvn Chmpoux, *, Jochim Vnwllenghem b, Jen-Mrc Drouet Mechnicl Engineering Deprtment, VélUS group, Université de Sherbrooke, 2500, boulevrd de l Université, Sherbrooke (QC) J1K 2R1, Cnd b Mechnics of Mterils nd Structures, Deprtment of Mterils Science nd Engineering, Ghent University, Technologieprk-Zwijnrde 903, 9052 Zwijnrde, Belgium Abstrct One of the most significnt fctors in ride qulity in cycling sports re the vibrtions generted by rod surfce defects pssing through the bicycle nd trnsmitted to the cyclist s hnds nd buttocks. To study comfort, one metric tht hs been put forwrd is the mesurement of the power bsorbed t the cyclist s hnds. Mesuring bsorbed power requires the use of the force nd the velocity t the hnds nd provides n overll energy-bsed quntity. The im of this study is to dynmiclly clibrte n instrumented brke hood trnsducer to mesure the power bsorbed t the cyclist s hnds. Using bse excittion technique involving suspended msses, dynmic clibrtion of the brke hood ws conducted in the 3-100 Hz frequency rnge, nd the force trnsducer sensitivity nd seismic mss were mesured. An ccelerometer ttched to the brke hood enbled mesurements of ccelertion nd clcultion of velocity. A frequency-dependent phse mismtch between the force signl nd the ccelertion ws obtined by mesuring the ccelernce t the hnd-bike interfce. A device clled the Power Clibrtor equipped with n impednce hed ws developed to ssess the ccurcy of the power mesured by the instrumented brke hood. The results show tht the instrumented brke hood cn ccurtely mesure the bsorbed power t the cyclist s hnds. Phse mismtch between the force nd the velocity signls must be corrected to improve the ccurcy of mesurements. To implement the mesurements, it is recommended tht the clcultions be done in the frequency domin. 2015 Published The Authors. by Elsevier Published Ltd. This is by n Elsevier open ccess Ltd. rticle under the CC BY-NC-ND license Peer-review (http://cretivecommons.org/licenses/by-nc-nd/4.0/). under responsibility of the School of Aerospce, Mechnicl nd Mnufcturing Engineering, RMIT University. Peer-review under responsibility of the the School of Aerospce, Mechnicl nd Mnufcturing Engineering, RMIT University Keywords: Absorbed Power; Clibrtion; Dynmics; Trnsducers; Bse Excittion; Hnd Vibrtion * Corresponding uthor. Tel.: +(819) 864-7759. E-mil ddress: Yvn.Chmpoux@usherbrooke.c 1877-7058 2015 Published by Elsevier Ltd. This is n open ccess rticle under the CC BY-NC-ND license (http://cretivecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the the School of Aerospce, Mechnicl nd Mnufcturing Engineering, RMIT University doi:10.1016/j.proeng.2015.07.204
226 Yvn Chmpoux et l. / Procedi Engineering 112 ( 2015 ) 225 230 1. Introduction Rod cycling enthusists ride for periods totlling severl hundred hours per yer. It is therefore not surprising tht they re willing to py extr to obtin comfortble bike tht cn filter the gretest possible mount of rod vibrtions felt t the hnds nd buttocks. In comfort ssessment studies in the trnsport industry, ccelertion is often used to quntify vibrtion. Accelertion is esy to mesure becuse it merely requires ttching smll nd redily vilble trnsducer to the structure. A body prt in contct with vibrting structure dissiptes the energy trnsmitted from the structure in the form of het. For exmple, when cyclist is riding rod bike on rough rod surfce, the hnds nd buttocks bsorb the energy trnsmitted respectively by the hndlebr nd the sddle. Power is the rte of energy trnsferred between two structures. A proposed lterntive metric to ssess comfort is the power bsorbed by the humn body prt t the contct points with the vibrting structure [1]. No filter is required when using the bsorbed power [2-3]. Since power is sclr quntity, it cn be clculted when deling with complex multi-degree of freedom system to determine humn response. Absorbed power hs previously been mesured on rod bike using n instrumented hndlebr [4-5]. In this pper, n instrumented brke hood previously developed to mesure cyclist hnd force [6] is used. To obtin ccurte mesurements, the dynmic behvior of the trnsducer must be tken into ccount. A direct technique tht obtins the mplitude nd phse reltionship between the force nd the ccelertion is described. A comprtive technique using n impednce hed nd llowing n in-situ clibrtion is lso presented. A typicl bsorbed power mesurement exmple is provided. The dvntges of clculting the power in the frequency domin re lso underlined. 2. The bsic principles of power mesurement The time domin verge mechnicl bsorbed power cn be mesured using the following eqution T 1 P () t v() t dt (1) T 0 where T is the integrtion time, () t nd vt () the respective instntneous force nd velocity. In prctice, n ccelerometer is used to provide the velocity following time integrtion of the ccelerometer signl. In the frequency domin nd for frequency spn f to f min mx, the power is clculted s follows: fmx fmin P Re G ( f) df (2) where Re G ( f) v is the rel prt of the cross-spectrum G ( f) v v between the force nd the velocity. The velocity is clculted in the frequency domin by dividing the ccelertion spectrum by j. 3. Brke hood force trnsducer An instrumented brke hood mounted on rod bike ws originlly designed [6] to mesure the verticl trnsmitted force t the hnd of cyclist. As shown in Fig. 1, the trnsducer consists of 2 prts bolted together: hnd rest in contct with one of the cyclist s hnds, nd n luminum instrumented body ttched to the hndlebr. The hnd rest is connected (bolted) t the right hnd side of the instrumented body only. The functioning principle of the trnsducer is equivlent to cntilever bem force trnsducer. The left side of the instrumented body is clmped to the hndlebr. The rod vibrtion is trnsmitted to the hndlebr which in turn trnsmits its motion to the trnsducer. The verticl force 2 t the right hnd side of the instrumented body pushes on the hnd rest. The instrumented zone section hs rectngulr shpe. A full WhetStone bridge using 1000 strin guges mesures the deformtion of the instrumented body due to the force loding. The bipolr bridge voltge supply is ± 15 V. A PCB unixil ccelerometer model 352C65 secured to the hnd rest provides the ccelertion tht will be used to clculte the velocity.
Yvn Chmpoux et l. / Procedi Engineering 112 ( 2015 ) 225 230 227 The time vrying force tht cyclist must pply on the brke hood to steer nd ccelerte the bike hs frequency content below 2 Hz. This force cnnot be distinguished in the time domin from the force interction between the brke hood nd the hnd resulting from the vibrtion cused by the rod surfce. Note in pssing tht high pedling cdence of 120 RPM corresponds to 2 Hz. In this study, it is ssumed tht the cyclist is lening on the brke hood (not grsping it) nd tht the steering forces re smll enough to be considered negligible for the purposes of this study. The frequency spn considered in this study for ll mesurements is 3 100 Hz. b Fig. 1. () Brke hood force trnsducer; (b) one degree of freedom bse excittion model for representing the dynmic behvior of the instrumented brke hood. It is importnt to stress tht the dynmic system studied is excited by the motion of the bse z 0(t) which corresponds to the motion of the ttchment point of the instrumented brke hood to the hndlebr. All mesurements were mde using LMS SCADAS recorder (model SCR01-08B) driven by LMS Test.Lb softwre. Ded weights hve been used to stticlly clibrte the force trnsducer nd lso to evlute its crosssensitivity. The nominl z-xis sensitivity ws determined to be equl to 12.3 V/N. 4. Dynmic clibrtion of the power trnsducer 4.1. Dynmic brke hood clibrtion The force trnsducer dynmic clibrtion technique used in this study is described in n ISO 2631-1 [7]. Note tht both the clibrtion technique setup nd the brke hood re bse excited systems. A simplified equivlent representtion of the instrumented brke hood is shown in Fig. 1b. A free-sliding bem equipped with strin guges is set in motion by imposing verticl displcement z 0(t) t the left hnd side of the bem. The numbers 0, 1 nd 2 in Fig. 1b indicte the contct point loctions between structures. The bse excittion corresponds to the movement of the hndlebr t the brke hood ttchment point. The suspended mss m c used for the dynmic clibrtion is entrined by the bem pplying verticl force 2 t point 2. The mss m c mimics the mss of the hnd. It is the rection of the suspended mss being set in vibrtion tht cuses the force 2. An ccelerometer mesures the ccelertion of the mss m c. A one degree of freedom model of the instrumented brke hood is shown in Fig. 1b. Both the bem nd the instrumented hood hve stiffness k nd dmping coefficient c. The mss m s represents the seismic mss of the trnsducer which corresponds to portion of the bem s mss t the right hnd side of the strin guges. It hs been noted [6] tht the stiffness of the instrumented hood must be s close s possible to the stiffness of commercil brke hood to prevent ny chnge to its dynmic behvior, even though the first nturl frequency of the brke hood is close to or within the frequency rnge of interest. Note tht if we were to mnufcture stiff trnsducer to push wy the first bending mode frequency from the frequency zone of interest, this would constitute design misconception for bse excittion system [8]. To chieve dynmic clibrtion, the instrumented brke hood is ttched to rigid support on top of
228 Yvn Chmpoux et l. / Procedi Engineering 112 ( 2015 ) 225 230 shker tble imposing verticl sinusoidl oscilltion s shown in Fig. 1b. Known msses m c re ttched in sequence on top of the hnd rest. The voltge output V, provided by the strin guges of the force trnsducer, is V S ( ms mc) z2 (3) where S (V/N) is the brke hood force sensitivity. The voltge output V of the ccelerometer is V S z (4) 2 where S (mv/ms -2 ) is the ccelerometer sensitivity. A clibrted ccelerometer with n ccurte nd known sensitivity must be used here becuse it will constitute the reference of the clibrtion process. Note tht both the force nd the ccelertion will be used subsequently to determine the bsorbed power. The rtio of Eqs. (3) nd (4) provides the following expression: V S ( ms mc) (5) V S Using sinusoidl signl to excite the brke hood, the Frequency Response Function (FRF) V V cn be mesured t specific frequencies between 3-100 Hz for different clibrtion msses m c. Amplitudes nd phses re mesured. A totl of 9 msses re used, rnging from 0.09 kg to 0.67 kg. At ech frequency, plot between V V vs m c cn be obtined. The slope s of the stright line is equl to S S. The force trnsducer sensitivity S cn be clculted. According to Eq. (6), the horizontl xis intercept point provides the seismic mss m s. the following results re obtined for the brke hood force sensitivity nd seismic mss: S = 11.92 V/N nd m s = 0.198 kg. 4.2. Phse correction between the mesured force nd ccelertion To ccurtely mesure the verge bsorbed power, both the mplitude nd the phse ccurcy between the force nd the velocity signls must be verified. According to Eq. (1), ny extrneous time dely between the force nd the velocity tht is not ssocited with the physicl phenomenon being studied will bis the power mesurement. Time dely is ssocited in the frequency domin to phse error in the cross-spectrum of Eq. (2). The source of phse errors cn be ssocited with signl conditioning or with the A/D process. The dynmic clibrtion procedure of the force trnsducer described in section 4.1 enbles us to mesure mplitude rtios between the force nd the ccelertion but lso provides phse reltionships. After hving determined the force trnsducer sensitivity, corrected the phse mismtch nd dequtely clculted the velocity, n ccurte estimtion of bsorbed power is expected to be obtined using Eq. (2). 4.3. Clibrtion vlidity check using the Power Clibrtor In order to scertin the ccurcy of the mesured bsorbed power using the instrumented brke hood, device herein referred to s the Power Clibrtor ws developed to impose lod tht cn dissipte energy s well s mesure the bsorbed power using its own independent trnsducer. Fig. 2 shows the Power Clibrtor mde of wood hndle equipped with piezoelectric PCB hed impednce model 288D01 providing force nd ccelertion signls. Only xil forces cn be pplied to piezoelectric force trnsducer to ccurtely mesure the force. A shrp contct pin is fixed t the free end of the impednce hed to prevent ny ppliction of cross lods. To use the Power Clibrtor, full bike is first instlled on rod simultor [9]. Two hydrulic shkers impose verticl displcement under ech wheel. The bike is held in verticl position with the help of horizontl bungee cords ttched to the set tube. A 0-100 Hz rndom signl is use to drive the shkers. While the bike is being excited nd s shown in Fig. 2, the Power Clibrtor is positioned over the brke hood to impose downwrd DC force. The Power Clibrtor is set in motion by the brke hood vibrtion with the vibrting hnd bsorbing energy. The impednce trnsducer provides the signls to mesure the bsorbed power. The sme filters, signls tretment, phse correction nd numericl clcultion steps described previously re used with the impednce hed signls to clculte the power using Eq. (2). Fig. 2b llows the power mesured by the brke hood trnsducer nd the Power Clibrtor to be compred. The level of correspondence is excellent. The discrepncy between the totl power of ech is 0.02 W or 3%.
Yvn Chmpoux et l. / Procedi Engineering 112 ( 2015 ) 225 230 229 b 0.05 0.045 0.04 Brke Hood 0.68 W Power Clibrtor 0.66 W 0.035 Power (W) 0.03 0.025 0.02 0.015 0.01 0.005 0 20 40 60 80 100 Frequency (Hz) Fig. 2.() Power clibrtor for loding structure nd mesuring the bsorbed power t the contct point. (b) Power mesurement comprison between the instrumented hood nd the Power Clibrtor. 4.4. Power mesurement on the rod In order to provide in-situ mesurement of the power bsorbed t one of the cyclist s hnds, the instrumented brke hood ws instlled on rod bike. A corse grnulr rod ws selected for the test nd the bike speed ws kept constnt t speed of 26 km/h. The solid line of Fig. 3 shows typicl mesured verge frequency spectrum which totl bsorbed power mesure by the brke hood of 0.99 W. 0 0.08 0.07 Phse mismtch corrected P = 0.99 W Phse mismtch not corrected P = 1.05 W Power (W) 0.06 0.05 0.04 0.03 0.02 0.01 0 0 20 40 60 80 100 Frequency (Hz) Fig. 3.Power mesurement on grnulr rod t the cyclist s hnd (right hnd only). Comprison of power spectr with nd without correction for the phse mismtch. 5. Discussion Clculting the bsorbed power in both the time nd frequency domins ccording to Eq. (1) nd Eq. (2), respectively, should provide the sme results. However, the difficulty in obtining the numericl velocity from the ccelertion in the time domin must not be underestimted. A simple detrending of the time signl is not sufficient in some cses, especilly for non-sttionry signls. The in-situ mesurement spectrum of Fig. 3 shows tht in the cse of the cyclist s hnd, the bsorbed power is t reltively low frequency. To illustrte the importnce of correcting for the phse mismtch, the phse mismtch correction ws eliminted in the power clcultion. The spectr re compred in Fig. 3. A 6% vrition between the
230 Yvn Chmpoux et l. / Procedi Engineering 112 ( 2015 ) 225 230 totl power of ech curve is noticed. To obtin ccurte mesurements if the bsorbed power is t low frequencies, phse mismtch correction is recommended. Implementing phse correction in the time domin is complex tsk. In the frequency domin, correcting the phse is strightforwrd nd simply requires subtrcting the phse mplitudes from the ccelertion phse (reltive to the force). Integrting the ccelertion to get the velocity is lso strightforwrd nd requires only dividing the complex ccelertion spectrum by j. An verge cross-spectrum clculted over severl time segments llows the non-correlted noise between the force nd the velocity to be eliminted. This is n dvntge of using the power s metric rther thn ccelertion, becuse verging the signl does not eliminte the noise in the ccelertion signl. Moreover, in the frequency domin, the coherence function between the force nd the ccelertion is esily clculted. The coherence provides vluble informtion on the qulity of the signls nd on the number of verges required to eliminte the noise in the power mesurement. For ll these resons, we strongly recommend clculting the power in the frequency domin. 6. Conclusion The objective of this study ws to obtin dynmic clibrtion of n instrumented brke hood trnsducer to mesure the power bsorbed t one of the cyclist s hnds. A clibrtion technique using suspended msses nd bse excittion ws used to obtin the sensitivity of the force trnsducer s function of the frequency s well s to obtin the phse mismtch between the ccelertion nd force signls. The force trnsducer s seismic mss ws lso mesured. Its sensitivity did not show ny strong frequency dependence. The phse mismtch is prevlent minly t low frequencies. Becuse the energy dissipted t the cyclist s hnds is lso t low frequency, phse correction is used to mximize mesurement ccurcy. A Power Clibrtor ws introduced nd ws used to ssess the ccurcy of the power mesurement provided by the instrumented brke hood. Similr to commercil clibrtion pprtus such s n ccelerometer or microphone clibrtor, the Power Clibrtor is n esy to use device tht verifies the proper functioning of the instrumented brke hood for power mesurements. The dvntges of using the frequency domin rther thn the time domin for processing nd clculting the power were presented nd discussed. Acknowledgements The uthors grtefully cknowledge finncil support from the Ntionl Science nd Engineering Council of Cnd (NSERC) nd the prticiption of Cervélo nd Vroomen-White Design. References [1] F. Prdko, R.A. Lee, Vibrtion Comfort Criteri, PA Wrrendle: SAE Interntionl, doi:10.4271/660139 (1966). [2] R. Lundström, P. Holmlund, L. Lindberg, Absorption of energy during verticl whole-body vibrtion exposure, Journl of Biomechnics 31(4), (1998) 317326. [3] N.J. Mnsfield, M.J. Griffin, Effect of Mgnitude of Verticl Whole-Body Vibrtion on Absorbed Power for the Seted Humn Body, Journl of Sound nd Vibrtion 215(4) (1998) 813825. [4] J. Vnwlleghem, F. Mortier, I. De Bere, M. Loccufier, W. Vn Pepegem, Design of n instrumented bicycle for the evlution of bicycle dynmics nd its reltion with the cyclist s comfort, Procedi Engineering 34 (2012) 485490. [5] J. Vnwlleghem, I. De Bere, M. Loccufier, W. Vn Pepegem, W.V., Sensor design for outdoor rcing bicycle field testing for humn vibrtion comfort evlution, Mesurement Science nd Technology 24(9): (2013). [6] A. Cy, Y. Chmpoux, J.-M. Drouet, Dynmic behviour nd mesurement ccurcy of bicycle brke hood force trnsducer, Procedi Engineering, 34 (2012) 526-531. [7] ISO 7626-1:2011(E), Mechnicl vibrtion nd shock Experimentl determintion of mechnicl mobility Prt 1: Bsic terms nd definitions, nd trnsducer specifictions (2011). [8] J.M. Drouet, Y. Chmpoux, Designing Strin Guge Trnsducer for Dynmic Lod Mesurement in Cycling, Proceeding of the conference The Engineering of sport10, Interntionl sports Engineering Assocition, Sheffield, Procedi Engineering 72 (2014) 304-309. [9] J. Lépine, Y. Chmpoux, J.-M. Drouet, A Lbortory Excittion Technique to Test Rod Bike Vibrtion Trnsmission, IMAC XXIX Jcksonville, Florid USA, Conference of SEM (2011) 35-43.