Design and Experimental Verification of Vibration Suppression Device on the Lift of Wheelchairaccessible

Transcription

1 Journal o Physics: Conerence Series PAPER OPEN ACCESS Design and Experimental Veriication o Vibration Suppression Device on the Lit o Wheelchairaccessible Vehicles Related content - Structural vibration control using an active resonator absorber Nader Jalili and David W Knowles IV - An experimental comparison o piezoelectric and constrained layer damping Joseph J Hollkamp and Robert W Gordon To cite this article: Yasuyoshi Hatano and Masaki Takahashi 16 J. Phys.: Con. Ser View the article online or updates and enhancements. This content was downloaded rom IP address on 1/1/18 at :9

2 MOVIC16 & RASD16 Journal o Physics: Conerence Series 7 (16) 11 doi:1.188/17-696/7/1/11 Design and Experimental Veriication o Vibration Suppression Device on the Lit o Wheelchair-accessible Vehicles Yasuyoshi Hatano 1, Masaki Takahashi 1 School o science or Open and Environmental Systems, Keio University Hiyoshi, Kohoku-ku, Yokohama 3-8, Japan YasuyoshiHatano@keio.jp Department o System Design Engineering, Keio University Hiyoshi, Kohoku-ku, Yokohama 3-8, Japan takahashi@sd.keio.ac.jp Abstract. In recent years, the number o wheelchair-accessible vehicles has increased with the aging o the population. Such vehicles are eective in reducing the burden on caregivers because the wheelchair user does not have to move rom his/her wheelchair to a seat o the vehicle. Wheelchair-accessible vehicles are expected to be widely used in the uture. However, wheelchair users have reported poor ride comort. It is thus necessary to suppress the vibration o the vehicle considering the wheelchair user. We designed a passive damping device on the lit o wheelchair-accessible vehicles to improve the ride comort or wheelchair users. The vibration due to road disturbances reaches the wheelchair user s body through the vehicle and wheelchair. Our control device decreases the acceleration o the torso and improves the ride comort by ensuring that the requency o the vibration reaching the wheelchair user diers rom the resonance requency band o the acceleration o the torso, which is the body part that eels the most discomort. The eectiveness o the control device is veriied experimentally. 1. Introduction Japan s population has aged in recent years. There are approximately 3 million people who are older than 6 years in Japan, accounting or about.1 percent o the total population [1]. Older people tend to have diiculty in walking because o disabilities associated with exercise unctions and cognitive unctions due to aging. The person who has diiculty walking might use a wheelchair, and the number o wheelchair users is expected to increase with an increase in the number o older people in the uture. The wheelchair is most commonly used as an assistive device or moving a handicapped person. However, the range o motion o a wheelchair user is limited by the excessive eort required to navigate obstacles o the road surace. Welare vehicles have thus been developed or the longrange transport o handicapped people, including wheelchair users. A welare vehicle is easy or a physically disabled person to use. There are dierent types o welare vehicles. As one type o welare vehicle, the wheelchair-accessible vehicle provides high convenience because the wheelchair user does not have to move rom his/her wheelchair to a seat o the vehicle. In addition, it reduces the burden on the caregiver. It is hoped that wheelchair-accessible vehicles will be used widely in the uture []. However, it has been reported that wheelchair users ind wheelchair-accessible vehicles to have poor ride comort [3][][]. An investigation into the ride Content rom this work may be used under the terms o the Creative Commons Attribution 3. licence. Any urther distribution o this work must maintain attribution to the author(s) and the title o the work, journal citation and DOI. Published under licence by Ltd 1

3 MOVIC16 & RASD16 Journal o Physics: Conerence Series 7 (16) 11 doi:1.188/17-696/7/1/11 comort o this vehicle revealed that approximately % o wheelchair users were dissatisied with the vibration o the wheelchair [3]. The present study investigates the wheelchair-accessible vehicle shown in Fig. 1 [6]. A previous study revealed that the discomort elt by a wheelchair user is caused by the vertical acceleration o the torso o the user. The resonance requency band o the vertical acceleration o the torso is to 6 Hz, while that o the wheelchair is to 6 Hz [7]. The resonance requency band o the vertical acceleration o the torso thus matches that o the wheelchair, and it is thereore necessary to suppress the vibration o the vehicle considering the vibration characteristic o the wheelchair. One technique o reducing such vibration is to provide suspension between the tires and bodies o vehicle. The suspension is designed according to the size and perormance o the vehicle. For example, the spring and damper o a suspension system are adjusted to reduce vibration at a speciic requency [8]. However, the suspension unctions to support the load, stabilize the operation, and reduce the noise in addition to providing ride comort. The suspension thus cannot be designed with consideration o only the ride comort. It is thus necessary to improve the ride comort o the wheelchair user employing a method that is not based on suspension.. Vibration control device The present study proposes a vibration suppression device on the lit o wheelchair-accessible vehicles so as to improve the ride comort o the wheelchair user. The vibration suppression device is summarized in Fig.. The vibration control device is a passive damping device comprising springs and rubber. The vibration control device has low cost and is compact. We design the springs and rubber o this control device in the present study. The aim is to show the useulness o the vibration control device. NISSAN MOTOR CO. LTD. Fig. 1 Wheelchair-accessible vehicle gum gum spring (side view) (ront view) Fig. Vibration control device

4 MOVIC16 & RASD16 Journal o Physics: Conerence Series 7 (16) 11 doi:1.188/17-696/7/1/11 3. Design o the vibration control device 3.1. Modeling o the wheelchair-accessible vehicle The wheelchair-accessible vehicle model used in this study is shown in Fig. 3. The model is expressed as 1 rigid bodies, namely the ront and rear wheels o the vehicle, the vehicle loor, the vibration suppression device, the wheelchair, and the head, torso, waist, thigh and leg o the human body. The model parameters are given in Table 1 and are set in reerence to CarSim and a previous study []. The model parameters k 1, k 1r, c 1, and c 1r are spring constants and damping coeicients o the suspension. The model parameters K and C are the spring constant and damping coeicient o the control device. The joints o parts o the human user are expressed by a rotary spring and rotary damper. The person s waist and thigh and the point o contact o the torso and waist are connected to the wheelchair with a spring and damper. The oot and the ootrest o wheelchair are ixed. The ront and rear wheels o the wheelchair model are expressed with a spring and damper and are joined to the loor o the vehicle. The generalization coordinate q o the wheelchair-accessible vehicle model is deined as q [ zv zwc v wc z zr, T (1) q ] where z v, zd z, r z, and q respectively denote the vertical displacements o the vehicle loor, the ront wheel, the rear wheel, and the ootrest o the wheelchair and v, d, 9, 1,, 3,, and respectively denote the pitch displacements o the vehicle loor, wheelchair, leg, thigh, waist, torso, and head. The Lagrange equation is L T U, d L L F, () dt q q where F is a general orce that is the orce o vibration input to the vehicle by the road surace in this study. The equation o motion is Mq Cq Kq F, (3) where M, C, and K are matrices. v z w z c 1 V k 1 k m l z v mv J V D B 3 ( c, k) ( i ) 1 I l ( i 3) ( i 1) C F ( i wc) G( c3, k3) H q l 9 A 1 z wc v ( c mwc J ( c 1, k1), k) wc lr ( i ) l t c 1r m r w r ( i ) E V k r k 1r zr v z w z c 1 V k 1 k m l z v mv V D B ( i ) 3 ( c, k) 1 I l ( i 3) ( i 1) C F ( i wc) G( c3, k3) H q l 9 A 1 z wc ( c mwc J ( c 1, k1), k) wc V wc C K J v lr ( i ) l t c 1r m r w r ( i ) E V k r k 1r zr (a) without the control device (b) with the control device Fig. 3 Hal model o the wheelchair-accessible vehicle 3

5 MOVIC16 & RASD16 Journal o Physics: Conerence Series 7 (16) 11 doi:1.188/17-696/7/1/11 Mass o vehicle loor Pitch moment o inertia o sprung mass Table 1 Parameters o the wheelchair-accessible vehicle model Parameter Symbol Unit Value Distance between the ront tire center and center o the gravity Distance between the rear tire center and center o the gravity Suspension (ront spring) Suspension (rear spring) Suspension (ront damping) Suspension (rear damping) Mass o ront tire Mass o rear tire Front tire o spring Rear tire o spring Distance between the ront vibration device and center o the gravity m v kg 11 I kgm 97 v l m 1.3 l r m 1. k 1 N/m 6. 1 k 1r N/m 6. 1 c 1 Ns/m 17 c 1r Ns/m 17 m kg m r kg k N/m k r N/m l m 1. Distance between the rear vibration device and center o the gravity l tr m 1. Vibration control device (spring) K N/m - Vibration control device (damping) C Ns/m - t Leg ( i 1) Thigh Body ( i ) Head ( i ) Waist ( i 3 ) ( i ) Mass, m i [kg] Moment o inertia Ii [ Nm / rad ] Length l i [m] Center o gravity l ia [m] Angle w i [rad] Damper c i [ Nms / rad ] Spring k i [ Nm / rad ] Parameter Unit Value Mass o wheelchair, m wc [kg] 18. Moment o inertia o Wheelchair 8.7 I [ Ns / m ] wc Rotational spring constant K i [ Nm / rad ] Rotational damping constant C [ Nms / rad ] i Knee ( i b) Trochanter major ( i c) Lumber ( i d) Cervical vertebra( i e )

6 MOVIC16 & RASD16 Journal o Physics: Conerence Series 7 (16) 11 doi:1.188/17-696/7/1/11 The equation o motion is expressed as q M Cq Kq Yw Z w, 1 r Y k, Z kr, where w and w denote the vibration input to a tire by the road. r The equation o state is thus expressed as I X w 1 1 w X B E r, M K M C q X q, B 1 M Y, E 1 M Z. T T () () 3.. Design o the vibration control device Procedure o the design The vibration characteristic o the vibration control device is determined by simulation. We conirmed the vibration o the wheelchair user when vibration rom the road surace was input to the model o the wheelchair-accessible vehicle in the simulation. The vibration is provided by a class C equivalency o the road surace deined in ISO standards [9]. Simulation is carried out at a sampling interval o 1 ms. It is assumed in the simulation that the vehicle runs at a constant speed o km/h or 1 seconds. The procedure or designing the vibration control device is as ollows. 1. Input the vibration o the road surace to the model o the wheelchair-accessible vehicle.. Calculate the root mean square (RMS) o the acceleration o the torso in the wheelchairaccessible vehicle. 3. Choose the vibration characteristic o the vibration control device when the vertical acceleration o the torso is lowest. The parameters o the wheelchair and human body in the vehicle given in Table 1 are then used as the nominal model Conditions o the design The spring constant K and damping constant C o the vibration control device are calculated rom the composition o the spring and rubber. The spring constant k gum and damping constant c gum o rubber are deined rom dimensions o the rubber as Glh kgum, w (6) cgum gum mkgum, (7) where w, G, l, h, and gum are the width o the rubber, modulus o the transverse elasticity o the rubber, length o adhesion o the rubber, height o adhesion o the rubber, and damping ratio o the rubber. m expresses the load added to the rubber because o the weight o the person and the mass o the vibration control device ( m d ). In addition, the spring constant K and damping constant C o the vibration control device are deined as K kgum ksp, (8) C c gum, (9) where k sp is the spring constant o the spring o the vibration control device.

7 MOVIC16 & RASD16 Journal o Physics: Conerence Series 7 (16) 11 doi:1.188/17-696/7/1/11 The limitations o the vibration control device determined by the dimensions o the lit o the wheelchair accessible vehicle are given in Table. The rubber is then warped by the mass on the vibration control device. Such a phenomenon is expressed as Mg. (1) K It is necessary to limit the spring constant o the device so that the rubber does not undergo plastic deormation by distortion. The limitations o the spring constant and damping constant o the device are thereore expressed as M max g M max g K, limit w wr rate (11) w r sae C gum mk, (1) where r rate, r sae, and M max are respectively the growth rate, actor o saety, and maximum assumed mass. These expressions thereore guarantee a condition that the rubber does not undergo plastic deormation even i there is a maximum mass M max loading the device. Under the conditions w.3, Mmax 13, rrate, and rsae 1., the limitations o the spring constant and damping constant can be expressed as K, (13) C (1) In this case, m in expression (1) is 93 kg; this is the total mass o the person and wheelchair o the nominal model and the mass o the device Design o the device The RMS o vertical acceleration o the torso is calculated by simulation. The relationship between the RMS o vertical acceleration o the torso and the vibration characteristic o the device is shown in Fig.. In the igure, the horizontal axis gives the spring constant K and the vertical axis the damping constant C. The vibration characteristics o the device are set as K and C 6 so that the RMS o vertical acceleration o the torso is lowest within the limitations o the device. Dimensions o the rubber and the size o the spring that match the vibration characteristic are given in Table 3. Table Constraint ranges Parameter Symbol Unit Constraints range Width o gum w m w.3 Height o gum h m. h.1 Adhesion length o gum l m h 3.6 Maximum growth rate o gum r m wr r rate r sae Maximum strain amount o gum limit m limit wr rate r sae w r rate : Growth rate r sae : Saety actor 6

8 MOVIC16 & RASD16 Journal o Physics: Conerence Series 7 (16) 11 doi:1.188/17-696/7/1/11 Table 3 Parameters o the vibration control device Symbol Width o gum [m] w.3 Height o gum [m] h.6 Adhesion length o gum [m] l 3.1 Spring [N/m] k 1387 C [Ns/m] K [N/m] x 1 Fig. RMS o the vertical acceleration o the torso sp Analysis and inspection.1. Results o analysis This section presents results obtained or the perormance o the device designed in the previous section. The dierence in the vibration behavior o the wheelchair user with the device and without the device is derived by simulation analysis. The analysis condition is that the vehicle travel across a road surace o class C at km/h, in the same way as in the design o the control device. The simulated vertical acceleration and displacement o the torso are shown in Fig.. The igure conirms that the control device reduces the vertical acceleration o the torso. Moreover, the vertical displacement is not worse when using the control device. The vibration characteristic o the device is shown in Fig. 6. The device reduces vibration in the requency range o to 6 Hz as designed. The power spectral density (PSD) o the vertical acceleration o the installation surace o the wheelchair is shown in Fig. 6. It is seen in the igure that the acceleration and displacement o the installation surace o the wheelchair are reduced because o the reduction o vibration in the requency range o to 6 Hz by the control device. w/o control device w/ control device Acceleration [m/s ] Displacement [m] (a) acceleration (b) displacement Fig. Vertical vibration behavior o the torso 7

9 MOVIC16 & RASD16 Journal o Physics: Conerence Series 7 (16) 11 doi:1.188/17-696/7/1/11 w/o control device w/ control device PSD [(m/s ) /Hz] 1 x (a) vibration characteristic o device (b) PSD o installation surace o wheelchair Fig. 6 Perormance o the control device w/o control device w/ control device Acceleration [rad/s ] (a) acceleration (b) displacement Fig. 7 Pitch behaviors o the user s head In addition, pitch acceleration, and pitch displacement o the user s head are shown in Fig. 7. This quantity is also reduced by the control device. Displacement [rad]... Veriication o robustness Further simulation is carried out using model parameters or a large male subject [] and small emale subject []. The relationship between the RMS o vertical acceleration o the torso o the large male and the speed o the vehicle is shown in Fig. 8, while that between the RMS o vertical acceleration o the torso o the small emale and the speed o the vehicle is shown in Fig. 8. We conirm that the control device perorms well or both human models. rms [m/s ].6. w/o control device. 6 8 v [km/h] rms [m/s ].6. w/ control device. 6 8 v [km/h] (a) Male (b) Female Fig. 8 Relationships between the velocity and acceleration o the torso 8

10 MOVIC16 & RASD16 Journal o Physics: Conerence Series 7 (16) 11 doi:1.188/17-696/7/1/11. Experiment using a traveling wheelchair-accessible vehicle.1. Purpose and method o the experiment We constructed the vibration control device designed in the previous section. The vibration control device is shown in Fig. 9. The control device uses six coil springs[1] with a combined spring actor o,93 N/m. Chloroprene rubber was used in the device. We measured the acceleration o a person and a wheelchair in an experiment using the vibration control device. In the experiment, the wheelchair-accessible vehicle travelled at a constant speed along a straight road, and acceleration meters were attached to the person and wheelchair. We measured acceleration with and without the vibration control device... Conditions o the experiment The experiment conditions are shown below. In the experiment, the wheelchair-accessible vehicle travelled at km/h or 1 seconds along a private road o a university. Then, the wheelchairaccessible vehicle was used the SERENA o Nissan. Wherein the running speed, which were designed with km/h in the analysis, set km/h in the experiment because the speed limit is km/h in experimental environment. The acceleration meters were set at the user s head and torso, the wheelchair, the ront wheel o the wheelchair, the rear wheel o the wheelchair and under the wheelchair. We examined it on such an experiment condition and measured the acceleration or three people; photographs o the experiment are shown in Fig. 1. The heights and weights o the subjects are given in Table. Table Characteristics o subjects participating in the experiment Sex Weight [kg] Height [cm] Classiication Subject 1 emale 1 small Subject male 17 normal Subject 3 male large (a) Computer-aided design o the vibration control (b) Real equipment device Fig. 9 Computer-aided design and actual equipment o the vibration control device Fig. 1 Conditions o the experiment 9

11 MOVIC16 & RASD16 Journal o Physics: Conerence Series 7 (16) 11 doi:1.188/17-696/7/1/11.3. Results and considerations o the experiment.3.1. Results Figures present time histories o the acceleration and transmissibility o vibration rom the vehicle loor or three people (subjects 1,, and 3 in the experiment). When the weight was normal or light, we ind that the acceleration o the torso was ampliied by the control device. Meanwhile, the acceleration o the torso o a heavy person was reduced by the control device. In Fig. 11 Fig. 13, each case has a speciic requency o high vibration transmissibility; i.e.,,, or 3. Hz. This tendency was ound in all results..3.. Considerations The previous section conirmed that the acceleration o the torso was ampliied in the case o a light person or person o normal weight. The relationship between the loading mass o the control device and the distortion o the control device is presented in Table 6. Table 6 shows that, when the loading mass is light, the control device has a desired spring constant. However, when the loading mass is heavy, the spring constant is larger than that desired. It is thought that we have exceeded the linear domain o the spring and rubber by the loading mass. The relationship between the spring constant and resonant requency is then deined as K. m (1) It is thought that the resonance requency increases with the spring constant. According to expression (1), or a light person, a person o normal weight, and a heavy person, the resonance requency o the control device is.,., and 3.9 Hz respectively. In the case o a light person or person o normal weight, the resonance requency o the control device matches the resonance requency o the acceleration o the torso. Meanwhile, or a heavy person, the resonance requency o the control device does not match the resonance requency o the acceleration o the torso. It was thereore possible to reduce the acceleration o the torso o the wheelchair user using the control device in the case o a heavy person. It is thus necessary to design the control device again to obtain a desired spring constant. Table RMS o acceleration o the torso in the experiment the irst experiment the second experiment w/o device w/ device w/o device w/ device Subject (Fig. 11) 1.77 (Fig. 11) Subject (Fig. 1) 1.6 (Fig. 1) Subject 3 1. (Fig. 13).73 (Fig. 13) Table 6 Relation o the loading mass and the distortion o the control device Loading mass [kg] Distortion [mm] Spring constant [N/m]

12 MOVIC16 & RASD16 Journal o Physics: Conerence Series 7 (16) 11 doi:1.188/17-696/7/1/11 Acc. [m/s ] power [-] torso device loor (a) without the control device (b) with the control device Fig. 11 Time history and transmissibility o vibration rom the vehicle loor (subject ) Acc. [m/s ] power [-] 1 1 Acc. [m/s ] power [-] (a) without the control device (b) with the control device Fig. 1 Time history and transmissibility o vibration rom the vehicle loor (subject ) Acc. [m/s ] power [-] 1 1 Acc. [m/s ] power [-] (a) without the control device (b) with the control device Fig. 13 Time history and transmissibility o vibration rom the vehicle loor (subject 6) Acc. [m/s ] power [-]

13 MOVIC16 & RASD16 Journal o Physics: Conerence Series 7 (16) 11 doi:1.188/17-696/7/1/11 6. Conclusion This study presented a vibration suppression device on the lit o wheelchair-accessible vehicles. The proposed device attempts to improve the ride comort or wheelchair users by reducing vibration in the resonance requency band. Analysis revealed that the proposed device suppressed the vertical acceleration o the torso o the wheelchair user. In addition, we produced the designed vibration control device and experimentally demonstrated its potential in reducing the acceleration o the torso o the wheelchair user. In the experiment, we conirmed that the acceleration o the torso o a heavy person was reduced by the control device. However, it is necessary to design the control device again to obtain a desired spring constant. And it is necessary to experiment with more running speed and more subjects. Thereore, we would like to urther experimentally again and veriy the useulness o the proposed device. Acknowledgements This work was supported by JKA (7-16) and its promotion unds rom Auto Race. Reerences [1] Ministry o internal aairs andcommunications, Population o the elderly person, stat.go.jp/data/topics/topi631.htm (as o Jun.1). [] Japan Automobile Industry Association (JAMA), Market trend o the welare vehicle o the 13, (as o Jun.1). [3] Kentaro S., Emiko K., Takashi K., A study on saely and comortableness about utilization o the wheelchair transportation behicle, The Journal o Hapan Academy o Health Sciences, Vol.1, (7), pp [] Yoshiyuki M., Kohei K., and Ryo S., Vibration Simulation Model o Passenger-Wheelchair System in Wheelchair-Accessible Vehicle, Journal o Mechanical Design, Vol.1, (3), pp [] Ministry o Land, Inrastructure, Transport and Tourism (MLIT), About the ixed method o the crew o the wheelchair and the wheelchair, o July 1). [6] SUZUKI MOTOR CORPORATION, Welare vehicle o SUZUKI, wagon R wheelchair -acce ssible vehicle, (as o Jun.1). [7] Matsuoka Yoshiyuki, Experimental Vibration Model Analysis o the Wheelchair Transporting Apparatus : Design Support Methods or Riding Comort o Vehicles or Wheelchair Users (1), Japanese Society or the Science o Design, Vol. 7, No. 1 (), pp.3-8. [8] Liu, C., Gazis, D. C. and Kennedy, T. W.: Human judgment and analytical derivation o ride quality, journal o Transportation Science, Vol. 33, No. 3 (1999), pp [9] ISO-631: Guide or the Evaluation o Human Exposure to Whole body Vibration, International Organization or Standardization, (198). [1] MiSUMi-VONA, Coil spring or more than lexibility MISUMI, (as o Nov.1). 1