Relationship between steering torque and ease of driving with bar type steering in high speed range

Bulletin of the JSME Journal of Advanced Mechanical Design, Systems, and Manufacturing Vol., No., 7 Relationship between steering torque and ease of driving with bar type steering in high speed range Shun TAMAKAWA*, Hisaya TANABE* and Hiroshi MOURI* *Tokyo Univ. of Agriculture and Technology Dept. of Mechanical Systems Engineering -- Nakacho, Koganei-shi, Tokyo -5, Japan E-mail: s5x@st.go.tuat.ac.jp Received: March 7; Accepted: 9 May 7 Abstract In previous study it was confirmed that changing of grip position counteracts drivers' maintenance of appropriate steering angle. Therefore, we developed the bar type steering system with low steering gear ratio. In high-speed driving, the range of steering angles used is smaller than in low-speed driving. with a steering system with a low gear ratio, further delicate steering is required. Human operation resolving ability is insufficient for such operation, it is expected that high-speed driving at a low gear ratio will become difficult. Motorcycles enable high-speed driving even at a low gear ratio. In motorcycles, a sufficiently large torque occurs during high-speed driving. Referring to this, we developed a steering system that enables easy high-speed operation at a low gear ratio from the viewpoint of vehicle behavior including both steering angle and steering torque. As the result, the difficulty of steering operation with low steering gear ratio at high speed was improved by adjusting steering reaction torque of bar type steering. Furthermore, the dynamic characteristics from the steering torque to the vehicle was examined. As result, where a large steering torque is required, the driver drives mainly based on the steering torque. Therefore, the ease of driving does not change if the phase of steering torque is delayed from the steering angle. On the other hand, the experiment confirmed that driving becomes difficult if the yaw rate is delayed from the steering torque that the driver relies on. We designed reactive torque control system to improve maneuverability and verify performance of the system by using driving simulator. Here, we report the maneuverability of bar type steering in high speed range. Key words : Automobile, Steering system, Human-machine-interface, Steering torque, Driving simulator. Introduction A driver is required to perform some complex operations simultaneously and it makes driving difficult. Therefore, a beginner is required to learn driving at a driver s school for safety. Furthermore, an experienced driver must continue driving to maintain their driving skill for executing such complex operations without awareness. Among driving skills, changing of steering grip position, which occurs while driving at a low speed, is said to be a particularly difficult skill. (Kitahara et al., ) In the initial stage of developing the steering wheel, the steering torque during low-speed driving was reduced by a large steering gear ratio. Therefore, the driver was required to operate the steering wheel at large angles at low speeds. Today, however, the steering torque can be set arbitrarily using electric power steering or steer-by-wire technology. Therefore, the steering gear ratio also can be set freely. A steering system with a low gear ratio is desirable to eliminate the need for changing of steering grip position. However, it is reported that if a low gear ratio is set while using a steering wheel, the driver cannot drive well, and, as a result, the vehicle meanders. (Kitahara et al., ) For such reasons, we have proposed a bar-type steering system to enable easy driving at a low gear ratio. (Tamakawa et al., 5) By using this steering system, even a driver with little driving experience is able to steer intuitively and therefore drive the vehicle just as he or she wants. In high-speed driving, the range of steering angles used is smaller than in low-speed driving. Even at an ordinary Paper No.7- [DOI:.99/jamdsm.7jamdsm] 7 The Japan Society of Mechanical Engineers

Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol., No. (7) steering gear ratio, the driver is required to perform delicate steering to drive within a small range of steering angles. In a steering system with a low gear ratio, in particular, the vehicle response to the steering angle becomes larger than in an ordinary steering gear ratio. Therefore, further delicate steering is required. In this case, the driver must perform the abovementioned delicate steering exactly. Human operation resolving ability is insufficient for such operation, so it is expected that high-speed driving at a low gear ratio will become difficult. Motorcycles enable high-speed driving even at a low gear ratio. In motorcycles, a sufficiently large torque occurs during high-speed driving. Referring to this, we sought to develop a steering system that enables easy high-speed operation at a low gear ratio from the viewpoint of vehicle behavior including both steering angle and steering torque.. Discussion of steering torque As shown in Table and Figure, the steering torque was set while changing the elastic coefficient for the steering angle. Figure shows the experiment course. The lateral position of the vehicle driving on the target course was moved instantly on the screen while screen was being blacked out. The driver s steering operation to return to the target course was then observed. In this case, the timing of moving the lateral position was varied randomly.the vehicle speed is kept constant at km/h automatically without the driver s maneuver. The subjects consisted of three males in their twenties, and each subject steered only.figure shows the configuration of the simulator used for the experiment. A system controller (AD55 made by A&D Co.) was used for signal processing and vehicle behavior controlling, and a CarSim (made by Virtual Mechanics Co.) was employed for drawing the experiment course. The experiment in this study was implemented in accordance with the rules of the Study Ethical Review Board of Tokyo University of Agriculture and Technology and after obtaining the informed consent of each subject. Table. Steering System Specifications Bar-type steering system Steering gear ratio Elastic coefficient [N m/deg] k k. k. k. k. Viscosity coefficient [N m s/deg]. Friction coefficient [N m]. [N m/deg].... k k k k k Fig. This figure shows setting elastic coefficients of steering torque. Screen Projector.5m Reaction motor.5m DSP PC Fig. This figure shows experiment course. The lateral position of the vehicle driving on the target course was moved instantly on the screen. The driver s steering operation to return to the target course was observed. Fig. This figure shows configuration of the driving simulator. Steering torque was generated by reaction motor. [DOI:.99/jamdsm.7jamdsm] 7 The Japan Society of Mechanical Engineers

Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol., No. (7). Experiment results The experiment result for Subject A is shown below as an example. The steering angle is depicted in Figure (a), and the yaw angle, in Figure (b). - - - k = k =. k =. Elastic coefficient - Increased Yaw angle [deg] - - - k = k =. k =. Elastic coefficient - Increased (a) Time-series data of steering angle (b) Time-series data of yaw angle Fig. These figure show time-series data of steering angle and yaw rate. Correction steering and meandering increased at smaller elastic coefficients. However, when the elastic coefficient increased, they converged faster. As depicted in Figure (a), correction steering increased at smaller elastic coefficients. However, when the elastic coefficient increased, the steering angle converged faster. Also from Figure (b), it can be seen that meandering decreases when the elastic coefficient increases. Information of steering torque cannot be obtained with a small elastic coefficient, so the driver drives by inputting the angle. At high speed, the required steering angle is small, and the driver is urged to perform driving within a minute range of steering angle as described in Section, particularly at a low gear ratio. In this case, exact steering is difficult with the limited angle-resolving ability of the driver.when the elastic coefficient is increased, the required steering torque increases, and the driver becomes able to drive by inputting both the angle and the torque. Furthermore, as the elastic coefficient is increased, the torque that the driver should input increases. In this case, the resolving ability improved substantially because it becomes possible to adjust the torque over a wider range. Based on this result, high-speed driving using a bar-type steering system has become possible.. Experiment of varying damping oscillation properties The previous section discussed the result of lowering the steady state gain of vehicle behavior for the steering torque. This section examines the dynamic characteristics from the steering torque to the vehicle. Therefore, we changed the dynamic characteristics of yaw rate of the vehicle when inputting the steering torque with the steady state gain decreased as described in the previous section and observed the changes in steering operation when changing lanes. The driving simulator calculated vehicle behavior from the vehicle models expressed by equations () and () using steering angle as input. G( B( g ng kg s s () ng ng kbnb () s bnbs nb [DOI:.99/jamdsm.7jamdsm] 7 The Japan Society of Mechanical Engineers

Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol., No. (7) where, k g.9 kb. ng nb.5 g b. Transfer function F( from the steering torque to the yaw rate of the vehicle was defined as a second order delay system expressed by equation (). To realize this, transfer function H( from the steering angle to steering torque was defined by equation (). n k F( T s ns T G( H ( F( () n () Experiments were conducted by setting steady state gain to k=. deg/s/nm in equation () and by varying natural frequency n and damping ratio. Various specifications ( to 5) are shown in Figure 5. Experiments were conducted while changing the damping ratio (specifications,, and ) and while changing natural frequency n (specifications,, and 5). Figures and 7 depict the respective frequency characteristics. Eight males in their twenties participated as subjects, and each experiment was conducted four times. As the experiment course, a lane change course as depicted in Figure was used. Each subject performed only steering while vehicle speed was adjusted to constant km/h by the simulator....5 5 (Natural frequency and damping coefficient ofeq. () ) was changed.5 n n was changed Phase [deg] Gain [/sec] - - - - Fig. 5 This figure shows Specification of natural frequency and damping ratio using in experiment. Experiments were conducted while changing the damping ratio and while changing natural frequency n. Fig. This figure shows frequency characteristic of vehicle model G(. damping ratio g and natural frequency ng ware set. and.5hz. [DOI:.99/jamdsm.7jamdsm] 7 The Japan Society of Mechanical Engineers

Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol., No. (7) Phase [deg] Gain [deg/s/nm] Phase [deg] Gain [deg/s/nm] increased - - increased - -.5 5 n increased.5-5 - n increased - - (a) Frequency Characteristics of Transfer Function F( (b) Frequency Characteristics of Transfer Function H( Fig. 7 These figure show frequency characteristics of transfer function F( and H( while changing the damping ratio and while changing natural frequency n..5m.5m Phase [deg] Gain [deg/s/nm] Phase [deg] Gain [deg/s/nm] increased - - increased - n increased 5 - - n increased - 5 - - m 7m m 7m m Fig. This figure shows experiment course. This course was set twice single lane change. 5. Experiment results The averaged result of four experiments on Subject A is shown as an example. Figure 9(a) depicts time-series data of yaw rate to the steering torque while changing damping ratio, and Figure 9(b), the same data obtained while changing natural frequency n. Under these experiment conditions, the second peak ( in Figure 9(a)) becomes larger and the overshoot of correction steering after the lane change ( in Figure 9(a)) also increased when damping ratio is increased ( ). From Figure 9, it can be seen that the main frequency component of steering is about.5 Hz. Extra steering wheel operation increased because the phase delay became larger in the low-frequency area around.5 Hz (one-dot broken line in Figs. 7) when damping ratio was increased. Also from the subjective evaluation, delay becomes [DOI:.99/jamdsm.7jamdsm] 7 The Japan Society of Mechanical Engineers 5

Tamakawa, Tanabe and Mouri, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol., No. (7) ① Larger ② - ③ - ③ ② Larger ① Reaction toque [N m] - - 9 Yaw rate [deg/s] - - -9 ③ ② Larger ① n Larger ③ ④ ⑤ - - n Larger - ⑤ ④ ③ 9 - Yaw rate [deg/s] Reaction toque [N m] remarkable and driving becomes more difficult when damping ratio was increased and the subject felt fatigue when extra steering wheel operation increased. Other subjects exhibited roughly the same trend. - - -9 n Larger ⑤ ④ ③ (a) Time-series Data when Is Changed (b) Time-series Data when n Is Changed Fig. 9 This figure shows time series data while and n were changed. When damping ratio is increased, the second peak () becomes larger and the overshoot of correction steering after the lane change () also increased. On the other hand, when natural frequency n was increased, they were decreased. The second peak ( in Figure 9(b)) and the overshoot of correction steering after the lane change ( in Figure 9(b)) decreased when natural frequency n was increased (③ ④ ⑤). Also, subjective evaluation, indicated that response is good and the subject can perform steering just as he wanted when natural frequency n was increased. Other subjects showed roughly the same trend.. Driving method and phase delay The vehicle characteristic G( is constant, so a relationship exists between phase delay of F( and the phase delay of steering torque characteristic H( such that if one increases, the other decreases (Figure ). The experiment result shows that a smaller phase delay of F( makes driving easier. At this time, the phase delay of H( has become large. As described in Section, this experiment was conducted while the steady state gain of the yaw rate to steering torque was lowered. In other words, a small steering angle occurs if a large steering torque is input. As a result, the driver mainly used steering torque T as the manipulated variable rather than steering angle. Therefore, the driver uses the responsiveness of yaw rate from steering torque T and feels driving is easier if the phase delay of steering torque from steering angle θ is large. [DOI:.99/jamdsm.7jamdsm] 7 The Japan Society of Mechanical Engineers

Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol., No. (7) Steering angle Vehicle (Angle input) G( yaw late Steering H ( Steering toque T Vehicle (Torque input) F( yaw late Phase delay : Large Phase delay : Small Phase delay : Small Phase delay : Large Phase delay : Fixed Fig. This figure shows Phase delay of each characteristic. The angle input vehicle characteristic G( is constant, so a relationship exists between phase delay of The torque input vehicle characteristic F( and the phase delay of steering torque characteristic H( such that if one increases, the other decreases. The experiment result shows that a smaller phase delay of F( makes driving easier. At this time, the phase delay of H( has become large. We conducted experiments by preparing two specifications in which the steady state gain of the steering torque to the steering angle differs from each other. In one specification, reducing the steering gear ratio increased steady state gain. In this specification, a large steering torque is required for lane changing. In the other specification, the gear ratio was increased so that lane changing can be made with a small steering torque. In the abovementioned two specifications, we investigated the relationship between the phase delay of yaw rate to the steering torque and the ease of driving. We call the specification where a large steering torque is required torque-input driving because the driver drives mainly based on the steering torque. We call the other specification angle-input driving because the driver drives based on the steering angle. 7. Experiment method Table lists the specifications of the steering system of each driving method. In torque-input driving, a low gear ratio was adopted to increase the steering torque. In angle-input driving, on the other hand, a high gear ratio was adopted to reduce the steering torque. As in the case of the previously conducted experiment, the vehicle changed lanes while driving on the course shown in Figure at a speed of km/h. We conducted experiments while changing the natural frequency n of yaw rate to the steering torque. Each specification (,) is shown in Figure. The subjects were five males in their twenties, and each experiment was conducted times. Table. Steering System Specifications Steering gear ratio Steady gain Steeringangle ( ) angle Front wheel. Torque-input Driving Angle-input driving [Nm/deg] 5 [Nm/deg].5.5 n Fig. This figure shows natural frequency of yaw rate to the steering torque. [DOI:.99/jamdsm.7jamdsm] 7 The Japan Society of Mechanical Engineers 7

Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol., No. (7). Experiment result The experiment result for Subject A is shown as an example. The solid line represents the average, and the widths above and below painted portion represent the standard deviation of trials. Figure (a) plots the time-series data in torque-input driving, and Figure (b) plots time-series data in angle-input driving. In torque-input driving, the second peak ( in Figure (a)) and the overshoot of correction steering ( in Figure (a)) decreased as the natural frequency of yaw rate to the torque increased. Furthermore, standard deviations (standard deviation.5, in Figure (a)) also decreased, so the course traceability improved. In angle-input driving, on the other hand, no change occurs in time-series data if the natural frequency of yaw rate to the steering torque changed ( and in Figure (b)). Furthermore, the differences in standard deviation also are very small. Other subjects exhibited roughly the same trend. From the above, in torque-input driving, driving becomes easier when the delay in yaw rate from steering torque is reduced. In angle-input driving, on the other hand, confirmed that the influence of the delay in yaw rate on the ease of driving is small. In other words, the same result as predicted in Section 5 was obtained. Steering torque [N m].5 - n - n.5 - n.5 n -.5 - Steering torque [N m] - - - - n n.5 n.5 n - Yaw rate [deg/s]. -. n.5 n.5 Yaw rate [deg/s]. -. n n.5 (a) Time-series Data of torque-input driving (b) Time-series Data of angle input driving Fig. This figure shows time series data of torque-input driving and angle input driving. The solid line represents the average, and the widths above and below the painted portion represent the standard deviation of trials. In torque-input driving, the peaks ( and in (a)) decreased as the natural frequency of yaw rate to the torque increased. Furthermore, standard deviations (standard deviation.5, in (a)) also decreased. In angle-input driving, on the other hand, no change occurs in time-series data if the natural frequency of yaw rate to the steering torque changed ( and in (b)). Furthermore, the differences in standard deviation also are very small. [DOI:.99/jamdsm.7jamdsm] 7 The Japan Society of Mechanical Engineers

Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol., No. (7) 9. Conclusion We investigated the ease of driving with a bar-type steering system while driving at a high speed and obtained the following findings. When the steering torque is increased, convergence becomes faster resulting in less meandering. In the area of low natural frequency n of yaw rate to the steering torque, extra steering decreases when damping ratio is small, resulting in easier driving. When n is large, damping ratio has little influence on the ease of driving. When the natural frequency n of yaw rate to the steering torque is large, extra steering wheel decreases, resulting in easier driving. When a large steering torque is required, the driver drives using steering-torque information. Therefore, the ease of driving does not change if the phase of steering torque is delayed from the steering angle. On the other hand, the experiment confirmed that driving becomes difficult if the yaw rate is delayed from the steering torque that the driver relies on. When little steering torque occurs during driving, the driver drives using the steering angle as input. Therefore, the experiment has confirmed that the steering torque has little influence on the ease of driving if it is delayed from the steering angle. References Horiguchi, N., Mouri, H., Kubota, M. and Furushou, H., Investigation on Relationship between Steering Effort and Performance of Driver Vehicle Closed Loop System Forcus on the Dumping Feature (nd report), Proceedings of JSAE. No.- (), pp.7- (in Japanese). Kitahara, K., Haramiishi, Y. and Mouri, H., Proposal of New Steering System Considering the Direction of Upper Limb Motion, Transactions of JSME Series C Vol. 79 No. (), pp. (in Japanese). Kitahara, K., Tamakawa, S., Yoshida, H., Raksincharoensak, P. and Mouri, H., Development of new steering system for resolution of steering operation problems during low speed driving, Transactions of JSME Vol. No. (), pp.- (in Japanese). Kubota, M., Mouri, H. and Horiguchi, N., An investigation on the effect of transient assistant torque input on steering effort, Proceedings of JSAE No.75-5 (5), pp.9- (in Japanese). Kushiro, I. and Yamamoto, M., Vehicle Steering Behavior by Low Frequency Sinusoidal Torque Input, Proceedings of JSAE No.- (), pp.- (in Japanese). Kushiro, I., Yamazaki, I. and Kunihiro, Y., A New Electronic Power Steering Control to Compensate for Steering Torque under Influence of Vehicle Dynamics, Transactions of JSAE Vol. No. (9), pp.5- (in Japanese). Nagae, N., Mouri, H., Kubota, M. and Furushou, H., Investigation of the effect of Steering Effort on the Performance of Driver-Vehicle Closed Loop System, Proceedings of annual convention of JSME No- (), (in Japanese). Tajima, T., Sato, K., Tada, Y., Fujita, H., Nakasato, Y. and Noguchi, W., Study of the Next-generation Steering System Study of the Twin Lever Steering System, Proceedings of JSAE No.75- (), pp.7- (in Japanese). Tamakawa, S., Kitahara, K., Mouri, H., Sato, K. and Yoshida, H., Proposal new steering system to improve maneuverability under the low speed drive, Proceedings of annual convention of JSME No5- (5), (in Japanese). Tamakawa, S., Mouri, H., Kazama, K. and Sato, K., Study on maneuverability of bar type steering in high speed range, Proceedings of Kanto branch nd convention of JSME No.- (), (in Japanese). Yamazaki, I. and Kamata, M., A Study of Driving with Control Stick - Report : Considering the Lateral and the Longitudinal Motion Control Simultaneously -, Transactions of JSAE Vol. No. (), pp.75- (in Japanese). [DOI:.99/jamdsm.7jamdsm] 7 The Japan Society of Mechanical Engineers 9