Nomenclature

 

,,,: lengths of crank, follower, coupler and fixed link

: creep rate

,: direction vectors of contact point at the driving and driven part

,,: direction vectors of rotating axis of the driving, driven rotor and the coupler

,: normal and shear pressure vectors at the infinitesimal area

,: radii of driving and driven rotor

,: angles of fixed link and coupler

: overall speed ratio(OSR)

 

: energy efficiency

,: angles of crank and follower

: traction coefficient

: local position vector of the infinitesimal area

,: rotating speeds of the driving, driven, and                 counter rotor

1.        Introduction

Since the CVT is more drivable and controlable than gear transmissions, many researches in and developments for vehicle usage of CVT have been gradually increasing. The typical bicycle transmission is a chain sprocket type. When the chain is shifted to the neighboring sprocket during drive, it frequently derails. A few researchers have developed CVTs for bicycles but have not obtained significant results yet because the installation¡¯s narrowness and compactness required high power efficiency for the rider¡¯s comfort, and large torque capacity due to slow pedal speed (about 6 rad/s at rated power of 100 W). For the same reason, there are few published papers referencing CVT development. Recently, J. Kim, et al. have proposed a spherical type of CVT connecting a sphere with four discs (1). A conceptual model having very small torque capacity (about 0.1 Nm) is investigated numerically and experimentally and it may be impossible to apply this model to the bicycle.

However many investigations into automobile CVTs with belts and toroidal types have been published (2). These research works have mainly focused on improving power density for fuel economy. But in the bicycle CVT design, the most significant design concepts is maintaining the comfort of the rider through narrow-compact packageability and high power efficiency.

To develop a bicycle CVT satisfying the required design specifications in this paper, a new inner spherical type of CVT (ISCVT) is proposed. The driving and driven rotors are kinematically connected by using a four bar linkage as a relay to the counter rotor assembly which is the position device. Each pair of rotors consists of two partially prepared spherical rotors of which the inner and outer surfaces are contacted at a point.

The proposed mechanism has three merits, compared to the toroidal one. Firstly, in the aspect of power transmissibility, the concave-convex contacting is superior to the convex-convex one because the former has larger contact area than the latter under the same maximum contact pressures. Secondly, the shape of the contact area of the ISCVT is always circular, compared to the one of the elliptical toroidal CVT. When the contact area is circular, the power loss due to the spin rotation is less than in case of the elliptical contact area. Lastly, the four bar linkage removes the counter rotor assembly at the desired position which means that there are two centers of the four spherical traction drives, the driving, driven, and conjugated counter rotor surfaces. This mechanism was introduced in the papers of Park, N.G. With this mechanism, it is possible to design an infinitely variable transmission (IVT). The coverage of overall speed ratio of the CVT can be expanded infinitively according to the crank and follower locations, respectively.

These three merits (high power transmissibility, low spin loss, and large coverage of overall speed ratio) make it possible to obtain several feasible solutions to satisfying the aforementioned design specifications for bicycle usage. The object of this study is to design the ISCVT for a manually powered bicycle. The kinematical analysis was completed to evaluate the design specifications such as the range of overall speed ratio and interferences among the components of the mechanism. The kinetic analysis also calculated the overall power efficiency under the condition of dry contact with the steel and steel bodies. Several transmission performances were examined numerically during the simulations. The best solution was selected and the associated prototype was manufactured for laboratory performance tests in order to verify the mathematical model for the kinematical and kinetical calculations.

2.        Proposed Mechanism for CVT

                     Fig. 1    Schematic diagram of CVT

 

A pairing of spherical CVTs at the inner and outer surfaces is proposed for bicycle use. The schematic diagram is shown in Fig. 1. It consists of three parts,  which are two set of traction rotors, a 4-bar linkage and two pressure devices. In the traction rotors, the inner surface of driving rotor is adjacent to the outer surface of the counter rotor. Similarly, the inner surface of the driven rotor comes in to contact with the outer surface of the counter rotor. The counter rotors to the driving and driven rotors are connected within a body. The 4-bar linkage controls the location of the counter rotor assembly by continuously changing the speed by using the control lever to transform the crank angle. In order to supply normal force to the friction surface, pressure devices using bolt-nut were considered. Pressure is applied by the tightening of screws.

 

3.        Design for bicycle CVT

Fig. 1 shows the layout of the bicycle CVT (BCVT). Power is supplied by a rider or electrical motor. BCVT has a front belt system connecting the pedals and the input pulley of the CVU. CVU is installed on the bicycle frame. It also has a rear belt system connecting the output pulley of CVU and the rear wheel. The speed controller is kinematically designed to change the crank angle by controlling the handlebars. Crank torque must be so small that the speed controller can be operated easily by hand.

For bicycle use, the range of overall speed ratio, input power and regular input speed are given as 1.0~4.5, 100 Watt and 6 rad/s respectively.

  Fig. 2    Average energy efficiency under dry friction with respect to torque and speed (=0.25, =450N, =250N)

 

Overall size capable of installation at the front part is within 244¢¥125¢¥160 mm³.

The kinetic analysis for the given power and speed is simulated in order to avoid occurrence of the excessive crank torque and contact stress, to satisfy the size constraints and to maximize the average energy efficiency in the operating speed range, dimensions of CVU and thrust forces of pressure devices.

The range of input torque and speed for a primary bicycle operating line is assumed to be 6~20 Nm and 3~9 rad/s, respectively. The optimal efficiency is at thrust forces of 450N and 250N.

When optimal thrust force is applied, the contour diagram of average energy efficiency by speed range is as shown in Fig. 2.  In the neighborhood of rated speed and torque, energy efficiency is 0.78~0.89.

     Fig. 3    Energy efficiency of CVT(=13Nm, =6)

   Fig. 4    Crank torque

 

The energy efficiency of CVT with respect to the overall speed ratio varied slightly more than 0.9 as shown in Fig. 3. The maximum reactive force and moment at the two pivot joints are 725 N and 1.6 Nm, respectively throughout the range of the crank angle. The maximum shear stress of the driving rotor pair is 469 MPa, so with a safety factor of 1.0 AISI 4140H is a suitable material. Fig. 4 shows crank torque of 4.1~4.3 Nm. Life time is infinite.

3.        Summery

In this brief investigation, we have presented the analysis of the newly developed ISCVT for a manual powered bicycle. The ISCVT is intended to overcome some of the limitations of existing CVTs for bicycles, e.g. difficulty in the narrow-compact installation, and the necessity of a large torque capacity and high power efficiency.  Moreover, the ISCVT, as compared to toroidal CVT, has high power transmissibility, low spin loss and large coverage of overall speed ratio. We performed a numerical study on the overall energy efficieny and transmission performances of ISCVT. For the validation of our theoretical investigations of the ISCVT, we will build a prototype and present the experimental results of the power efficiency

References

(1)     Jungyun Kim, F. C. Park, Yeongil Park, Mishima Shizuo, 2002, Design and analysis of a spherical continuously variable transmission, Transactions of ASME, Journal of Mechanical Design, Vol. 124, pp. 21-29

(2)     H. Tanaka, H. Machida, 1996, Half-toroidal traction-drive continuously variable power transmission, Proceedings of the Institution of Mechanical Engineers Part J, Journal of engineering tribology, Vol. 210 No. 3, pp. 205-212