Journal of System Vol. 7, No. 3, 2013 Design and Dynamics Improvement of Riding Comfort by Reduction of Seat Vibration∗

Junji YOSHIDA∗∗, Nobuyuki KAWAGOE∗∗ and Tomohiro KAWAMURA∗∗ **Osaka Institute of Technology, Dept. of Mechanical Engineering 5–16–1 Omiya, Asahi-ku, Osaka-shi, 535-8585, Japan E-: [email protected]

Abstract are popular with the general public because of their low price and easy main- tenance, and they will be an important vehicle in the future because of their low en- vironmental load. Improving the comfort of the ride is one of the important factors that will lead to increased popularity. We attempted to increase comfort by reducing vibration, and evaluated the results with a subjective test. We determined that low fre- quency vibration of the seat greatly affected the comfort of the ride. We then performed a transfer path analysis (TPA) and a hammering test to investigate how the vibration characteristics of the bicycle affected the vibration of the seat. Through TPA, the rear of the was found to have a high influence on the seat vibration, and the vibration behavior was obtained by modal analysis. In order to reduce seat vibration, a spring was inserted in the front of the seat and, to increase the stiffness, a steel plate and bolts were attached to the rear of the frame. As a result, the seat vibration while riding was decreased by about 10 dB, and the comfort of the ride was greatly improved.

Key words : Bicycle, Riding Comfort, Transfer Path Analysis, Modal Analysis, Vibra- tion Control, Human Engineering, Vibration of Moving Body

1. Introduction

Bicycles are popular vehicle alongside automobiles and motorcycles, and they are im- portant in the daily life of many people because of their compact size, light weight, and low price. In addition, bicycles are an ecologically friendly vehicle because they are powered by the rider and do not require fossil fuels. The riding comfort is important for safety and easy handling, but also for good stability and good efficiency. There have been many studies(1) – (12) that have quantified improvements in the comfort of various vehicles, including automobiles, motorcycles, and ships. In these previous stud- ies, it was reported that comfort was related to low-frequency vibration of the seat. Studies investigating the improvement of comfort while riding bicycles, however, have rarely been performed(13), (14). In this study, we investigated the relationship between the comfort of the ride and the vibration of the seat. We measured the vibration and performed a subjective evaluation test of the comfort. We then tried to improve the comfort after obtaining the vibration characteristics from various measurements and analyses. We employed a utility bike, as shown in Fig. 1, as the improvement target because it is one of the most popular bicycles because of its low price.

2. Relationship between Riding Comfort and Seat Vibration

*Received 18 Apr., 2013 (No.T2-2012-JCR-0221) 2.1. Subjective Evaluation Test for Riding Comfort Japanese Original:Trans.Jpn.Soc.Mech.Eng., Vol.78, No.792, C (2012), In this study, a subjective evaluation test was performed with several bicycles to investi- pp.2837-2847 (Received 26 Mar., 2012) gate the relationship between the perceived vibration of the seat and the riding comfort. For [DOI: 10.1299/jsdd.7.293] the evaluation, we used two utility bikes, two mountain bikes (one of which had a suspension Copyright © 2013 by JSME

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Fig. 1 Utility bike used for improvement of the comfort of the ride.

system), and a road bike. We performed subjective evaluation tests of the perceived seat vibration and the riding comfort, and used a paired comparison method for the five bicycles. In the test, a participant first rode utility bike 1, which was set as the standard bicycle for the comparison. The par- ticipant then rode another of the bicycles. After riding the standard and comparison bicycles, the participants evaluated the seat vibration and the riding comfort of the target bicycle by comparing it with the standard bicycle. The riders were then asked to answer the following questions both orally and in writing: “how did the seat vibration of the target bicycle compare with that of the standard bicycle?”, and “how comfortable was the target bicycle compared with the standard bicycle?” In the evaluation of seat vibration, the participant chose from a total of 13 subcategories in which there were seven major categories very large, large, rela- tively large, same, relatively small, small, and very small and six middle categories alternating with the major categories. Numbers from +6 to −6 were applied to the major categories from very large to very small, respectively, for the perceived seat vibration. Hence, when the seat vibration was evaluated as small, the value became negative. In evaluating the riding com- fort, the participant chose one of 13 subcategories, similar to the evaluation of seat vibration, but with the major categories of very comfortable, comfortable, relatively comfortable, same, relatively uncomfortable, uncomfortable, and very uncomfortable. As above, a number from +6 to −6 was applied to the major categories from very comfortable to very uncomfortable, respectively, so that the riding comfort could be analyzed quantitatively. Six males and two fe- males in their 20’s participated. In the test, each participant drove the bicycle at about 10 km/h and the air pressure of the bicycle tires were set at the standard pressure. For the test course, we used a road with a wooden deck so that the participants could more easily evaluate the vibration and comfort in a previous test. The values, averaged among all participants, of the perceived seat vibration and the riding comfort, respectively, are shown for each bicycle in Fig. 2 (a) and Fig. 2 (b).

Utility bike 1 Utility bike 2 1 Mountain bike 2 Road bike

6 543 2 1 0−1−2−3 −4−5 −6 −6 −5−4−3−2 −1 0 1 2 3 4 5 6 (a) Perceived seat vibration (b) Riding comfort High Low Bad Good

Fig. 2 Relationship between the perceived seat vibration and the riding comfort.

As shown in the figure, mountain bike 2, which has a suspension system, had the smallest perceived seat vibration and the best riding comfort among all the bicycles. Note that for the

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, both the perceived seat vibration and the riding comfort were zero because it was set as the standard bicycle against which the others were compared. The results also show that when the perceived seat vibration was smaller, the riding comfort was considered to be better, and vice versa. This tendency was identical to what was found in previous studies that considered the riding comfort of other vehicles(1) – (12).

2.2. Relationship between Vibration Acceleration Level of Seat and Riding Comfort The vibration acceleration of the seat of each bicycle was measured in order to inves- tigate which frequency band had the highest influence on riding comfort. The measurement was performed on the same running course and under the same conditions as the subjective evaluation test, and measured vibration acceleration along the vertical axis at the seat. For mountain bike 2 (most comfortable) and utility bike 1 (standard bicycle), Fig.3 com-

pares the acceleration level at each frequency (LVa: Eq. (1)).

−6 2 2 LVa = 20log(a/a0), a0 = 10 [m/s ], a : Vibration acceleration [m/s ] (1)

120 (dB) Va

L 110

100

90 Mountain bike 2 Utility bike 1 80 Acceleration level: 0 5 10 15 20 25 30 35 40 45 50 Frequency (Hz)

Fig. 3 Comparison of acceleration level at running condition between mountain bike 2 and utility bike 1.

The horizontal and vertical axes show the frequency and vibration acceleration level(LVa), respectively, and the solid and dotted lines indicate the acceleration levels of mountain bike 2 and utility bike 1. As shown in the above figure, the vibration acceleration level of mountain bike 2, which was evaluated as the most comfortable, was not the smallest for all frequency bands, but it was smaller than that of the standard bicycle at frequencies of less than 30 Hz. This tendency was also observed with the other bicycles. From these results, it was found that the seat vibration is related to the riding comfort; in particular, when the seat vibration was small at low frequencies (less than 30 Hz), the bicycle was evaluated as more comfortable. Similar tendencies were reported by studies investigating the riding comfort of automobiles and motorcycles(1) – (12). 3. Vibration Characteristics of the Bicycles 3.1. Vibration Characteristics During Running Test As a first step to improve the riding comfort, we obtained the vibration characteristics of utility bike 1. We measured the vibration acceleration of the seat along the vertical axis while the bicycle was moving, and the results are shown in Fig. 4. The measurement conditions were identical to those for the vibration acceleration measurements in the previous section, and the vibration of utility bike 1 is shown as dotted line in Fig. 3. The results show that utility bike 1 has several vibration peaks at frequencies less than 30 Hz, and it is necessary to reduce these high vibration peaks in order to reduce the seat vibration.

3.2. Contribution Analysis Using Transfer Path Analysis In order to determine effective countermeasures for the seat vibrations, transfer path anal- ysis (TPA)(15) – (18) was performed to obtain the contributions from the front and rear wheels.

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120 (dB) Va L 110

100

90

Acceleration level: 80 0 5 10 15 20 25 30 35 40 45 50 Frequency (Hz)

Fig. 4 Acceleration level of utility bike 1 while running.

TPA was originally developed to quantitatively determine the contributions from each part (such as the engine) to the interior noise and vibrations of an automobile. In this study, op- erational TPA, which can quickly obtain accurate contributions, was applied in some TPA methods(15) – (18). In operational TPA, the contribution is calculated from vibration accelera- tion signals at a reference point near the input point and at a response point. The seat vibration along the vertical axis was set as the response signal, and the vibrations at the center of the front and rear wheels (vertical axis) were set as the reference point signals. This was done because the main sources of seat vibrations for a moving bicycle are considered to be the front and rear wheels. In operational TPA, the reference and response data, measured while the bicycle is mov- ing, are transformed to the frequency domain using the fast Fourier transform (FFT). The

relationship between the multiple reference-point data matrix [Ain] and the response-point data matrix [Aout] can be expressed by the transfer matrix [H] for each frequency, as follows:

[ ] [ ][ ] Aout = Ain H (2)

The (i, j)-th element in the reference matrix [Ain] is the data at the j-th reference point in the i-th fast Fourier transform (FFT), and the (i, k)-th element in the response matrix [Aout] is the data at the k-th response point in the i-th FFT. The ( j, k)-th element in the transfer matrix [H] is the transfer function from the j-th reference point to the k-th response point. Following

singular value decomposition (SVD), the reference matrix [Ain] can be expressed as follows: [ ] [ ][ ][ ] T Ain = U S V (3)

The principal component (PC) matrix [T] is then obtained using the results of SVD: principal component analysis (PCA):

[ ] [ ][ ] [ ][ ] T = Ain V = U S (4)

Here, [V] is the coefficient matrix for transposing the reference matrix [Ain] to the PC matrix [T], and the (i, m)-th element of [T] is the m-th PC in the i-th FFT. Next, multiple regression

analysis (MRA) from the PC matrix [T] to the response matrix [Aout] was performed, and the regression coefficient matrix [B] was obtained as follows:

[ ] [ ][ ] Aout = T B (5)

[ ] ([ ] [ ])− [ ] [ ] T 1 T B = T T T Aout (6)

Here, [B] is the coefficient matrix used to transpose the PC matrix [T] to the response matrix

[Aout], and the (m, k)-th element of [B] is the regression coefficient from the m-th PC to the

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k-th response point. The acceleration transfer function [H] is obtained by multiplying the coefficient matrix [V] with the coefficient matrix [B] (Eq. (7),(8)). [ ] [ ] ([ ] [ ])− [ ] [ ] T 1 T H = V T T T Aout (7)

[ ] [ ][ ] [ ] [ ] −1 T H = V S U Aout (8)

Finally, the contribution of the response signal [Aout cont] can be obtained by multiplying the reference signal [Ain cont] by the calculated acceleration transfer function [H] in each fre- quency, as follows:

[ ] [ ][ ] Aout cont = Ain cont H (9)

Here, (i, j)-th element of [Ain cont] is the reference point signal at the j-th reference point in the i-th FFT, and the (i, k)-th element of [Aout cont] is the contribution of the k-th response point in the i-th FFT. This is the general procedure for the operational TPA. In addition, it has been reported that it is necessary to measure both the reference and response signals at various running conditions in order to obtain an accurate transfer function(17), (18). The reference point vibrations at the front and rear wheel centers and the response point vibrations at the seat were measured at speeds from 5 km/h to 15 km/h to calculate the transfer function, and the vibrations at 10 km/h were used for the contribution separation, which were identical to the conditions of the subjective evaluation test and vibration measurements. Figure 5 (a) shows the measured vibration acceleration level at each reference point (front and rear wheel centers), and Fig. 5 (b) shows the calculated acceleration transfer functions (TFL: Eq. (10)).from the front and rear wheel centers to the seat. Figure 5 (c) shows the contributions to the vibration of the seat from the front and rear wheels.

TFL = 20logha, ha : Acceleration transfer function (10)

The results of the analysis show that, while the bicycle is moving, the acceleration level of

130 120

(dB) Front 0 (dB) Front

Va Rear Va Rear L 120 L 110 −10 110 100 −20 TFL (dB) 100 Front 90 −30 Rear 90 80 Acceleration level: 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Acceleration level: 0 5 10 15 20 25 30 35 40 45 50 Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) Source (b) Transfer function (c) Contribution

Fig. 5 Result of transfer path analysis.

the rear wheel center is smaller than that of front wheel center, but its contribution is much greater. In particular, the contribution from the rear wheel is about 15 dB higher than that from front wheel when the frequency is less than 30 Hz, precisely where the seat vibration has a high influence on riding comfort. From the results, we found that, to improve the riding comfort of utility bike 1, it was necessary to institute intensive countermeasures to reduce the vibrations from the rear wheel.

3.3. Vibration Characteristics of the Bicycle Frames From operational TPA, we found that the rear wheel made the largest contributions to the seat vibration. An impact hammering test was performed to obtain the vibration characteristics

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from the rear wheel to the seat. To carry out the impact hammering test, the impact point was set at the bottom of the rear tire, which was considered to be the actual input point while the bicycle was moving, and the response point was set at the back of the seat, where the seat vibrations were measured, also while the bicycle was moving. To measure the transfer function during actual riding conditions, the bicycle was hung by the frame using a thin cable, the rider sat on the seat as normal, and a hammer was placed to impact beneath the rear tire, as shown in Fig. 6.

Fig. 6 Impact hammering test to obtain the transfer functions.

In this way, the transfer function from the rear tire to the seat was measured with a free- free boundary condition. The transfer functions were measured with the rider sitting on the seat (standard riding condition) and the rider standing on the pedals (rider’s weight was not added to the seat). The measured transfer functions (INL: Eq. (11)) for each condition are shown in Fig. 7.

2 INL = 20logh f , h f : Transfer function [m/s N] (11)

The results show that the transfer function when the rider is sitting on the seat is much smaller

0 −10 −20 −30

INL (dB) −40 −50 Sitting Standing −60 0 5 10 15 20 25 30 35 40 45 50 Frequency (Hz)

Fig. 7 Transfer functions obtained by impact hammering test with sitting and standing conditions.

than when the rider is standing. The transfer function with the rider on the seat has a vibration peak at 4 Hz, and it is larger than that without the rider. This peak level is considered to be the result of a resonance of rider’s weight with the seat spring. This resonance was observed at a similar frequency in the measured acceleration level while moving, as shown in Fig. 4. From these results, the resonance peak at 4 Hz observed in the measured transfer function is considered to be generated mainly by the seat spring and the other resonances at 15 and 32 Hz are considered to be generated by the vibration of the rear part of the frame. Hence, the seat

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vibration could be improved by the modification of the seat spring and the rear part of the frame structure.

3.4. Modal Analysis for Countermeasure Modal analysis was performed to determine the vibration behavior of the rear part of the frame and to carry out an effective countermeasure. In our analysis, we focused on the vibration mode at 15 Hz, where the transfer function had a resonance peak and the vibration while moving had a high influence on riding comfort. Figure 8 shows the modal vibration behavior from the side view, and Fig. 9 shows the modal vibration from the back view. The dotted lines in these figures show the original shape of the frame.

Fig. 8 Modal behavior at 15 Hz from side view.

Fig. 9 Modal behavior at 15 Hz from back view.

The results show the vibration mode at 15 Hz is a combination of a wave-shaped mode along the vertical axis (Fig. 8) and an open-close mode along the horizontal axis (Fig. 9). We also note that the vibration mode at 32 Hz is the second mode of the vibration at 15 Hz. From the results of this analysis, the vibration of the seat and the riding comfort are improved by modification to the part of the rear frame that has the highest amplitude of vibration. 4. Reduction of Seat Vibration

4.1. Modification of Bicycle Structure The results of the analysis in the previous section revealed that the low-frequency seat vibration of utility bike 1 was increased by the resonance of the seat spring and the rider’s weight at the frequency of 4 Hz, and the resonance of the vibration mode at the rear part of the frame at frequencies around 15 Hz. In this section, we discuss the results of the modification of the structure of utility bike 1, which was done to reduce the seat vibration. The intent was to reduce the seat vibration not only at 4 and 15 Hz where the resonance occurred, but also in the remainder of the low-frequency band, since low-frequency vibrations strongly affect riding comfort. The stiffness of the seat springs was decreased to reduce the vibration at 4 Hz, and the stiffness of the rear frame was increased to reduce the seat vibration at frequencies less than 15 Hz. The seat was initially supported by two springs (combination spring rate of 20 N/mm) at the rear and fixed by a metal bar at the front, as shown in Fig. 10 (a). In order to reduce the

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stiffness, it was floated by inserting a spring at the front (spring rate of 12 N/mm), as shown in Fig. 10 (b).

Fig. 10 Spring inserted for floating seat.

Next, a steel plate (4.6 mm thick) was attached between the seat stay and the chain stay, as shown in Fig. 11. This was done to increase the stiffness of the rear frame, which had a wave-shaped vibration mode, as shown in Fig. 8. In addition, a bolt (φ4 mm) was inserted between the left and right seat stays, and another bolt (φ10 mm) was inserted between the left and right chain stays, as shown in Fig. 11 (b). This was done to constrain the open-close vibration mode of the rear frame, as shown in Fig. 9.

Fig. 11 Addition of bolt and steel plate for increasing stiffness.

4.2. Effect of Structure Modification An impact hammering test and a moving test were performed to measure the vibration characteristics of the modified bicycle. The experimental conditions were identical to those for the previous tests on the original bicycle (utility bike 1). Figure 12 (a) shows the transfer function level (INL) from the center of the rear wheel to the seat, as measured by the impact

hammering test. Figure 12 (b) shows the acceleration level of the seat (LVa) of the modified bicycle while it is moving. The dotted and solid lines indicate the levels of the original and modified bicycles, respectively. From the results of the impact hammering test (Fig. 12 (a)), the resonance frequency at 4 Hz was decreased by the floating of the seat, and the response level at frequencies around 15 Hz was observed to be much reduced by the stiffening of the rear frame. The resonance frequency at 15 Hz was not much changed, even though the stiffness of the rear frame was increased. This is because adding the steel plate and bolts increases not only the stiffness but also the weight. While moving, the low frequency vibrations were reduced by almost 10 dB by the modification, as shown in Fig. 12 (b). The transfer function level for frequencies less than 4 Hz was increased by the seat floating, as shown in 12 (a). However, at this frequency range, the increase of the seat acceleration while moving was negligible compared with the reduction

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−20 120 (dB) Va −30 L 110

−40 100 INL (dB) −50 Base 90 Base Modified Modified

−60 Acceleration level: 80 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Frequency (Hz) Frequency (Hz) (a) Transfer function (b) Acceleration at running

Fig. 12 Comparison of transfer functions and acceleration levels while moving, between original and modified utility bike 1.

level of over 4 Hz, as shown in Fig. 12 (b). The differences in the frequency characteristics between the transfer function and the acceleration level while moving depend on the frequency characteristics of the input at the rear tire. As described above, the seat vibration at low frequency, which had high influence on riding comfort, was decreased by the modification. Subjective evaluation tests for the seat vi- bration and riding comfort were repeated in order to check if the riding comfort was improved by the modification. In the verification test, utility bike 1 was used, and the modification parts (steel plate and two bolts) were attached to the bicycle to evaluate the effect of the modifica- tion. The evaluation was performed both before (original) and after making the modifications. Six males participated in this test (four males participated in the first subjective test). Fig- ure 13 shows the perceived seat vibrations and the riding comfort averaged among all the participants.

Base

Modified

6543 2 1 0−1−2−3 −4 −5 −6−6−5−4−3−2 −1 0 1 2 3 4 5 6 (a) Perceived seat vibration (b) Riding comfort High Low Bad Good

Fig. 13 Comparison of perceived seat vibration and riding comfort between the original and modified utility bike 1.

Figure 13 (a) compares the perceived seat vibrations, and Fig. 13 (b) compares the riding comfort. In the figure, a small vibration score means a small perceived vibration, and a large riding comfort score indicates a comfortable ride. Compared to the original bicycle, the mod- ified bicycle, in which both the seat springs and the rear frame were modified, resulted in less perceived seat vibration and more riding comfort. 5. Summary

In this study, subjective evaluation and vibration measurement tests were performed to improve the riding comfort of a bicycle. In the subjective evaluation tests, participants rode several bicycles and evaluated the perceived seat vibration and the riding comfort. We found that when the seat vibration was perceived as small, the ride was comfortable. Measurement of seat vibrations while the bicycle was moving showed that low-frequency vibrations (less than 30 Hz) had a high impact on the riding comfort. Next, we measured the transfer function and performed TPA and modal analysis to de- termine how to reduce the seat vibrations at low frequencies. Our results clarified that seat vibrations at low frequencies were increased by a resonance generated by the seat spring at 4 Hz and a resonance at the rear frame at around 15 Hz.

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To reduce the low-frequency seat vibrations, a spring was added to the seat for floating, and a steel plate and bolts were attached to constrain the vibration mode of the rear frame at 15 Hz. As a result, the transfer function from the center of the rear wheel to the seat and the seat vibrations when the bicycle was moving were reduced by about 10 dB. We also verified through subjective evaluation that the riding comfort was improved by the modifications. We were able to improve the riding comfort of the utility bicycle, which is one of the most popular bicycles, and we proposed a method that uses various measurements and analysis in order to improve the comfort of bicycle riding. In future work, it will be necessary to determine the influence of these additional parts on other performance aspects of a bicycle, such as operability, and to determine a suitable balance between riding comfort and the weight of a bicycle.

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( 1 ) Ikeda, Y. and Shigehiro, R., Seasickness and boarding comfort. Evaluation method for boarding comfort, Bulletin of The Kansai Society of Naval Architects, Vol.20, (1933), pp.17-22. (In Japanese) ( 2 ) Corbridge, C., and Griffin, M. J., Vibration and comfort: vertical and lateral motion in the range 0.5 – 5.0 Hz, Ergonomics, Vol.29, No.2, (1986), pp.249-272. ( 3 ) Cucuz, S., Evaluation of ride comfort, International Journal of Vehicle Design, Vol.15, No.3,4,5, (1994), pp.318-325. ( 4 ) Akatsu, Y. C., An Evaluation Method of Improving Ride Comfort, JIDOSHA-GIJUTSU, Vol.52, No.3, (1998), pp.47-52. (In Japanese) ( 5 ) Nishiyama, S., and Uesugi, N., Research on vibration characteristics between human body and seat, steering wheel, and pedals, Journal of Sound and Vibration, Vol.236, No.1, (2000), pp.1-21. ( 6 ) Demic, M., Lukic, J., and Milic, Z., Some aspects of the investigation of random vibra- tion influence on ride comfort, Journal of Sound and Vibration, Vol.253, No.1 (2002), pp.109-129. ( 7 ) Koizumi, T., Tsujiuchi, N., and Tanaka, A., Investigation on Riding Comfort and Stabil- ity Analysis on Vibration Input for Motorcycles, Proceedings of JSME Symposium on Sports Engineering and Human Dynamics 2004, (2004), pp.236-241.(In Japanese) ( 8 ) Els, P. S., The applicability of ride comfort standards to off-road vehicles, Journal of Terramechanics, Vol.42, No.1, (2005), pp.47-64. ( 9 ) Arima, M, Tamura, Y., and Yoshihira, M., Evaluation of ride comfort of passenger craft, 2006 IEEE International Conference on Systems, Man, and Cybernetics, Vol.1, (2006), pp.802-807. (10) Koyano, M., Takeuchi, T., Ohara, T., and Yokoi, M., Establishment of Evaluation Method for Riding Comfort of Motorcycle Seats Honda R&D Technical Review, Vol.19, No.2, (2007), pp.117-122. (In Japanese) (11) Koizumi, T., Tsujiuchi, and Yamazaki, K., Establishment of Evaluation Method for Im- proving Ride Quality Based on Human Dynamics, Proceedings of JSME Dynamics & Design Conference 2007, No.149, (2007), pp.1-5.(In Japanese) (12) Koizumi, T., Tsujiuchi, Okumura, S., Ninomiya, J., and Yamada, S., Suggestion for Evaluation Methods of Ride Comfort at low frequencies Proceedings of JSME Dynamics & Design Conference 2009, No.419, (2009), pp.1-5.(In Japanese) (13) Kawagoe, N., and Yoshida, J., Consideration of hammering test condition for reduc- tion of bicycle vibration, Proceedings of JSME Dynamics & Design Conference 2010, No.208, (2010), pp.1-5.(In Japanese) (14) Kawagoe, N., Kawamura, T., and Yoshida, J., Quantification of Bicycle Ride Comfort, Proceedings of Korea-Japan Joint Symposium on Dynamics and Control (K-J Sympo- sium 2011, (2011), pp.1-3. (15) Van der Auweraer, H., Wyckaert, K., Hendricx, W., and Van Der Linden, P., Noise and Vibration Transfer Path Analysis, Lecture series - van Kareman Institute for fluid dynamics (1979), van Kareman Institute, Rhode-Saint-Genese. (16) Van der Auweraer, H., Mas, P., Dom, S., Vecchio, A., Janssens, K., and Van de Pon- seele, P., Transfer Path Analysis in the Critical Path of Vehicle Refinement: The Role of Fast, Hybrid and Operational Path Analysis, Proceedings SAE Noise and Vibration Conference, AE 2007-01-2352, (2007), pp.15-17. (17) Noumura, K., Yoshida, J., Method of Transfer Path Analysis for Vehicle Interior Sound with No Excitation Experiment, FISITA2006 Proceedings, F2006D183, (2006), pp.1-10. (18) Yoshida, J. and Noumura, K., Noise Reduction Method for Running TPA Using Sig- nificance Probability, Journal of System Design and Dynamics, Vol.5, No.8, (2011), pp.1572-1581.

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