Simulation of an Auto-Tuning Bicycle Suspension Fork with Quick Releasing Valves

Transcription

1 Siulation of an Auto-Tuning Bicycle Suspension Fork with Quick Releasing Valves Y. C. Mao, and G. S. Chen 1 International Science Index, Mechanical and Mechatronics Engineering waset.org/publication/377 Abstract Bicycle configuration is not as large as those of otorcycles or autoobiles, while it indeed coposes a coplicated dynaic syste. People s requireents on cofortability, controllability and safety grow higher as the research and developent technologies iprove. The shock absorber affects the vehicle suspension perforances enorously. The absorber takes the vibration energy and releases it at a suitable tie, keeping the wheel under a proper contact condition with road surface, aintaining the vehicle chassis stability. Suspension design for ountain bicycles is ore difficult than that of city bikes since it encounters dynaic variations on road and loading conditions. Riders need a stiff daper as they exert to tread on the pedals when clibing, while a soft daper when they descend downhill. Various switchable shock absorbers are proposed in arkets, however riders have to anually switch the aong soft, hard and lock positions. This study proposes a novel design of the bicycle shock absorber, which provides autoatic sooth tuning of the daping coefficient, fro a predeterined lower bound to theoretically unliited. An autoatic quick releasing valve is involved in this design so that it can release the peak pressure when the suspension fork runs into a square-wave type obstacle and prevent the chassis fro daage, avoiding the rider skeleton fro injury. This design achieves the autoatic tuning process by innovative plunger valve and fluidic passage arrangeents without any electronic devices. Theoretical odelling of the daper and spring are established in this study. Design paraeters of the valves and fluidic passages are deterined. Relations between design paraeters and shock absorber perforances are discussed in this paper. The analytical results give directions to the shock absorber anufacture. Keywords Modelling, Siulation, Bicycle, Shock Absorber, Daping, Releasing Valve. I. INTRODUCTION A. Background Copared with autoobiles and otorcycles, bicycles construct a saller structure yet coplicated syste with ore than 2 coponents. These coponents can be divided into several subsystes, including the frae, transission, wheel, steering, brake and accessory subsystes. The front suspension fork and rear shock absorber, such as the apparatuses shown in Fig. 1, are Y.C. Mao is with the Departent of Mechanical Design Engineering, National Forosa University, Yun-lin County 632, Taiwan R.O.C. ( ; Fax: ; eail: yjau63@gail.co) G.S. Chen is the Research and Developent Departent Manager, SPINNER Industry Co., Ltd., No.34, Jiahou Rd., Waipu Township, Taichung County 438, Taiwan R.O.C. iportant parts in the frae syste since they significantly affect the riding cofort and safety. Fig. 1 The SPINNER Cargo Air RLC Suspension Fork A feasible suspension syste holds the following capabilities: 1) Vibration isolation. The suspension syste has to isolate disturbances fro the road surface, acceleration and load-transferring effect of the vehicle chassis, thus it can provide a stable operation for drivers. 2) Energy dissipation. The suspension syste stabilizes the vehicle chassis in a short period of tie. The syste conditions the vehicle body controllability and rider safety by keeping the contact forces between wheels and road surface within a feasible range. 3) Coordination aong shock absorbers. The individual shock absorber collaborates with others to adjust the road-wheel contact forces according to the road surface, chassis and loading conditions [1]. B. Technology Classification Vehicle suspension systes can be categorized into three types, naely the passive, sei-active and active suspension systes, as shown in Fig. 2 [1]. The passive suspension syste, as illustrated in Fig. 2a, coposes a constant spring and daper. The spring is utilized to support the vehicle body and store the rebound energy. The daper functions as a dissipater to eliinate the transient energy [2]. The dynaic property of this type is fixed regardless of the road surface and load conditions since it occupies a spring and daper of constant values. The factory setting for this type of suspension syste is a critical issue and can only eet a restricted operation condition range. 661

2 International Science Index, Mechanical and Mechatronics Engineering waset.org/publication/377 Main structure K s C s Suspension syste Main structure K s C s Suspension syste Main structure K s C s F s Suspension syste K t C t K t C t K t C t (a) Passive suspension (b) Seiactive suspension (c) Active suspension Fig. 2 Schees of vehicle suspension systes Related works proposed the active suspension configurations to overcoe the above-entioned defects, as shown in Fig. 2c. Sensors and actuators with properly developed control algoriths can optiize the vehicle dynaics, restraining wheel bounds and chassis tilts. The Bose Suspension Syste draws the support fro a linear electroagnetic otor to achieve the vehicle stability and cofort [3]. Active suspension systes, however, usually coprise of coplicated costly peripherals, restricting their practical applications. The working frequency is liited to the input power. It is feasible to be equipped with an autoobile syste, applying on the low frequency chassis attitude control. The active suspension syste is not suitable for a low- or huan-powered obile syste, such as the otorcycle or bicycle [4]. Copared with the above two configurations, Fig. 2b represents a sei-active suspension syste which attracts considerable research efforts, since it is capable of tuning the daping coefficient adaptively according to the driving condition [1]. This type of configuration is incapable of balancing the chassis tilts however it can adjust its daping coefficient with liited power consuption [4-5]. The daping force is adjusted in a predeterined range according to different piston velocity, as shown in Fig. 3. Fig. 3 Curves of velocities-forces for passive and sei-active dapers [5] The fluidic circuit inside the shock daper has to involve a sensory echanis to deterine the syste position, velocity or acceleration, thus the sei-active syste can adjust its paraeters by certain eans. There are at least three types of eans that can alter the daping coefficient: 1) Structural friction force. This type eploys an electroagnetic otor or other echanical energy output device to control the noral force between contact coponents, altering the friction force therefore varying the vibration energy dissipation. 2) Fluid viscosity in the daper. These dapers fill at least part of the cylinder chabers with electro- or agneto-rheological fluid. The fluid viscosity is changed as the electric or agnetic field varies, altering the resistant force of the daper. 3) Orifice area control. The orifice area controls the flow rate aong passages and chabers, changing the daping force of the shock absorber. Due to the liited space, power supply deficiency and weight requireent, a great part of daper designs of the bicycle shock absorbers focuses on the orifice area control. C. Related Works Considering the fluid dynaics, Mollica and Youcef-Toui proposed a physical odel for a high pressure onotube shock absorber to analyze the nonlinear dynaic behavior of these dapers [6]. Results explained that the hysteresis frequency dependency is produced by the interaction at higher frequencies that results in added phase loss due to the capacitive eleents. Goncalves evaluated the dynaic response of different sei-active control policies over a agneto-rheological daper as tested on a single suspension quarter-car syste [7]. Bathe et al. presented advances in capabilities for the analysis of fluid flows with structural interactions [8]. An arbitrary Lagrangian-Eulerian forulation is used to solve for the fluid response with structural interface and free surface conditions. Beghi et al. involved a grey-box odeling technique to describe the coplex behavior of otorcycle shock absorbers, exhibiting a significant iproveent in the force prediction capability over traditional linear odels [9]. Yang et al. designed a new shock absorber with Coulob fluid daping through coupling oil, wire gauze, rubber and spring for reinforceent of electronic-inforation equipent in vibration and ipact [1]. The nonlinear dynaic odel for attenuating vibration ode is derived fro coupling physical echanis of fluid and Coulob friction. In the field of vehicle syste dynaics, Wang and Hull proposed a odel for deterining rider induced energy losses in bicycle suspension systes [11]. Ignoring the terrain irregularities, the power dissipated by the stiffness and dissipative characteristics of the suspension eleents was calculated. Pracny et al. perfored a dynaic full vehicle siulation using a thero-echanically coupled hybrid neural network shock absorber odel [12]. In this shock absorber odel, the spline approach is cobined with a teperature-dependent neural network, siulated on a test rig in ADAMS-Car ulti-body siulation software with a displaceent-controlled excitation. As there is currently no infrastructure available to test the shock absorbers perforance, Heritier built a test rig allowing the perforance characteristics of the various daper settings 662

3 International Science Index, Mechanical and Mechatronics Engineering waset.org/publication/377 to be explored and vehicle perforance to be optiized [13]. Titlestad et al. built a test rig, siulating regular ipacts of the rear wheel with bups in a rolling road, easuring physiological variables of oxygen consuption and heart rate, together with speeds and forces at various points in that syste. II. THE PROPOSED DESIGN A. Design Goal A significant defect of suspended bicycles is the tendency to dissipate pedaling energy through the spring and shock absorber. As the rider iparts force into the pedals the vertical vector coponent causes the bicycle to bob on its suspension. This undesirable suspension oveent dissipates a significant percentage of the iparted pedaling energy and can reduce the bicycle's overall otive efficiency. A widely adopted solution to this proble is to introduce a lockout eans for riders to anually operate when desired. The ter lockout refers to one or ore of the following eleents in cobination: echanically liiting the aount of suspension travel; increasing the daping response of the shock absorber, ost iportantly in copression; increasing the force-displaceent rate of the suspension; increasing the spring preload of the suspension. Norally the rider would engage the lockout during heavy pedaling as required by hill clibing or acceleration but could disengage it for coasting and downhill operation over bupy terrain. The ost coon for of bicycle suspension lockout consists of a valve that liits the flow of oil past the shock absorber's ain piston. The liitation of the anually activated suspension lockout is that it requires the constant attention of a rider already busy with nuerous other tractive and control functions. This research proposes an innovative self-tuning daper with quick releasing (QR) valve of a suspension fork for bicycles. The fundaental idea of the self-tuning echanis is to set up an orifice with a variable sectional area in the fluid passages inside the daper. This daper autoatically tunes the daping coefficient by altering the oil flow rate through the passages according to the input force or velocity. The QR valve keeps inactive during noral operations, while it sluices the peak fluid pressure when the daper encounters square-edged bups, aintaining the daper softness and preventing the rider libs fro sprained under shock waves. It would therefore be advantageous to autoatically lock out the suspension syste when required, specifically during uphill riding and rapid acceleration when the rider is pedaling hard. This echanis autoatically quickly releases the lockout as well when the suspension syste encounters a downhill operation over bupy terrain. B. Apparatus Configuration and Operations Fig. 4 sketches out the overall configuration of the proposed design, coprising of the key coponents in a daper side of a twin-tube bicycle front fork. The upper fork is slidely connected within the lower fork. The daping stator is fixed at the upper end of the inner tube. The lower end of the inner tube is iobilized with the lower end of the upper fork. The ain piston, synchronally oving with the lower fork, ipels and draws the oil in the lower chaber. The fluid, passing through the orifices inside the daping stator, flows back and forth between the upper and lower chabers. The separation fil keeps the air in the top chaber fro ixing with oil in the upper chaber. Upper fork (toward driver s face) Separation fil Top chaber Upper chaber Inner tube Lower fork (toward ground) Botto chaber Main piston (connected with the lower fork) Lower chaber Daping stator Fig. 4 The overall sectional view of the proposed design The fluid circuit inside the daping stator is shown in Fig. 5. The spool valve CAD odel is shown in Fig. 6, illustrating a double opening design for a wide flowing range. When a certain force drives the ain piston toward the upper side of the daper, high-pressure fluid in the lower chaber is ipelled into the upper chaber, achieving the pressure-release process. Upper chaber Lower chaber Rebound spool valve Contraction spool valve Spool valve spring Stopper Contraction quick releasing valve Rebound quick releasing valve Fig. 5 Fluid circuits inside the daping stator Take the contraction valves for illustration. The fluid pushes the contraction spool valve against the spring at this oent. The valve keeps closed before the lower chaber pressure rises up to a certain level, functioning as an autoatic locking-out capability. The valve together with the tunnel inside the stator open an equivalent orifice and allow the fluid flow through the orifice if the pressure is high enough to balance or surpass the spring force. The daping coefficient is decreased as the equivalent orifice area is increased, achieving an autoatic tuning function. If the daper encounters a square-edged bup, the QR valve opens, allowing the peak fluid pressure in the lower chaber to drop down rapidly. The operation anner of the rebound ode is siilar to that of the contraction ode. Hence the proposed design autoatically adjusts the daping ratio according to a wide road surface 663

4 condition. Opening 2 pressures in the botto and lower chabers, pushes the ain piston upward to a certain position x. ɺɺ x + C xɺ + k x = F P A + P A + P A g l 1 b 2 a 3 International Science Index, Mechanical and Mechatronics Engineering waset.org/publication/377 Opening 1 Fig. 6 CAD odel and diensions of the spool valve III. MODELLING THE SYSTEM DYNAMICS The frictional forces between pistons and cylinder walls are neglected in this study. Daping coefficient due to the friction is odeled but set to be zero in this study. A. Syste Overview The physical and atheatical paraeters are defined in Fig. 7. Initial volue of the top, upper, lower and botto chabers are V t, V u, V l and V b, respectively. Top chaber, V t, P t Upper chaber, V u, P u Lower chaber, V l, P l Botto chaber, V b, P b Force Upside piston area A 1 Underside piston area A 2 Mass of piston and lower fork s s s Piston rod sectional area A 3 Fig. 7 Matheatical odel of the entire daper B. The Driving Force The force F is odeled as a sinusoid wave with the aplitude of F : ( ) F = F Sin wt+ φ where w is a constant angular velocity, φ denotes the initial angular position of the driving force. The tie-derivative is: Fɺ = F Cos wt+ φ C. Main Piston ( ) The resultant force, derived fro the driving force and where C is the daping coefficient caused by friction; k denotes the ain spring in the shock absorber, which is installed in the other side of the fork and not shown in this study; P a is the atosphere of 1.134e5 Pa; g represents the gravity. D. Daping Stator, Spool Valves and QR Valves The valve oveents induce the daping characteristics of the proposed design, as defined in Fig. 8, which shows the contraction spool and QR valves only. Rebound valves work at the opposite sides in the daping stator, and have siilar operating conditions. They slide in the valve tunnels according to the pressures in the lower and upper chabers. For the contraction spool valve: ɺɺ x + C xɺ + k x = P A P A g cn cn cn cn cn cn l cn u cn cn while the rebound spool valve s dynaics is: ɺɺ x + C xɺ + k x = P A + P A + g rn rn rn rn rn rn l rn u rn rn For the contraction QR valve: ɺɺ x + C xɺ + k x = P A P A + g cb cb cb cb cb cb l cb u cb cb and the rebound QR valve s dynaics can be described as: ɺɺ x + C xɺ + k x = P A + P A g rb rb rb rb rb rb l rb u rb rb where the positive directions of x rn and x rb are toward the ground. QR valve spring, k cb cb cb cb Mass of the QR valve, cb Upper chaber Lower chaber Daping stator Spool valve spring, k cn cn cn cn Spool valve effective area, A cn Mass of the spool valve, cn Fig. 8 Model of the contraction valves in the daping stator E. Separation Fil The separation fil is odeled as a piston with an extreely sall ass, and frictionless with the cylinder wall. The pressure difference between the upper and top chabers ipels its oveent: ɺɺ x + C xɺ = P A P A g s s s s u s t s s where s represents the ass of the fil. F. Pressure in the Botto Chaber The botto chaber is initially filled with air of 1 at. The pressure change rate varies with the ain piston position and velocity: 664

5 International Science Index, Mechanical and Mechatronics Engineering waset.org/publication/377 Pb A 2x Pɺ b =γ ɺ V + A x b 2 where γ is the specific heat ratio for air, and is selected as 1.4 in this siulation [18]. G. Lower and Upper Chaber Pressures Pressure derivatives relate to the lower and upper chaber volues, and the fluid flow rates between these chabers: A xɺ Q + Q pɺ l = β Vl A 1x A xɺ + Q Q pɺ = β s s 1 3 u Vu + As xs where β denotes the bulk odulus of the daping fluid, and has a value of about N/ 2 for petroleu fluids [17]; Q 1, Q 3 are the flow rate fro lower to upper chaber, and that fro upper to lower chaber, respectively: Q = C A Q = C A 1 d1 1 3 d1 3 2 ( p p ) 2 l ρ u ( p p ) u ρ l where C d1 is the discharge coefficient of.7 in this study, which is sufficient for design purpose [16]. H. Top Chaber (Air Reservoir) Pressure change rate in the top chaber can be defined as: pt As xɺ s pɺ t =γ V A x t s s I. The Entire Syste The entire odel can be expressed using the previous derivations. These forulae represent a 15 th order dynaic syste. We are interested in the syste outputs, position and velocity of the ain piston. IV. SIMULATION AND DISCUSSION A. Conditions The diensions and asses involved in this siulation are evaluated fro the CAD syste. The coplete paraeter list is collected in TABLE. The Runge-Kutta ethod is eployed to solve these ODEs [19]. Sapling tie during the siulation is 3.737e-4s, attentively tracking the dynaics with 72 data points per round in the 225rp cycles. Deforation of structures and frictional forces between the pistons and cylinders are not considered in this odel. B. Results The siulation result is shown in Fig. 9. Various quantities are noralized and cobined in the sae plot for the convenience of coparison. Refer to subplot (a), F indicates the sinusoidal driving force to ipel the ain piston, having the axiu value N. The ain piston starts to oscillate with the input force after a.5s delay, caused by the throttling effect of the spool valves. The axiu value of the ain piston displaceent is 66.41e-3. The separation fil coincides with ain piston s noralized oscillation approxiately with a displaceent of 43.32e-3. TABLE I PARAMETERS AND VALUE EMPLOYED IN THIS STUDY Category Object Noen. Value Mass of (kg) Sectional area of ( 2 ) Initial volue of ( 3 ) Initial pressure in (Pa) Spring constant of (N/) ain piston.2363 separation fil s 1.e-3 contraction spool valve cn rebound spool valve rn 1.22e-4 contraction QR valve cb rebound QR valve rb 2.546e-4 upside ain piston A e-4 downside ain piston A e-4 ain piston rod A e-5 contraction spool valve (effective) A cn rebound spool valve (effective) A rn 1.179e-5 separation fil A s e-4 contraction QR valve (effective) A cb rebound QR valve (effective) A rb e-6 botto chaber V b e-5 lower chaber V l 3.878e-5 upper chaber V u top chaber V t e-5 botto chaber P b lower chaber P l upper chaber P u 1.134e5 top chaber P t contraction spool valve k cn rebound spool valve k rn.9555 contraction QR valve k cb rebound QR valve Bulk odulus (N/ 2 ) β e9 Specific heat ratio γ 1.4 Rotational speed of driving force (rad/s) w Driving force aplitude (N) F Discharge coefficient of spool valves C d1.7 The force(f ) to ain piston displaceent(d)/velocity(v) plot is given in subplot (b). The F -D curve can be ignored since the proposed echanical design is a velocity-sensitive fluid structure and irrelevant to the piston displaceent. The axial absolute value of force occurs when displaceent is zero, since the piston reaches its axial velocity when it passes the neutral position. The top-right corner of the F -V curve represents this phenoneon, saying the axiu velocity is.85/s. The daper shows a rigid-style fork when the noralized velocity is about.1, while it shifts to a soft-style suspension when velocity is about This curve is ore preferable for riders because it reveals a lower speed daping for a good yet fir controlled feeling, and less high-speed daping for a ore cofortable ride on square-edged bups. Subplot (c) is generated fro piston velocity with respect to F / xɺ, which represents the equivalent daping coefficient. k rb 665

6 International Science Index, Mechanical and Mechatronics Engineering waset.org/publication/377 Data points nearby zero velocity iply the atheatical transient state of the dynaic syste, feasible to be disregarded in this study. However, the reaining portion of the curve shows a downside tendency approaching to zero coefficients as the piston velocity increases, achieving a different style against the constant value of a traditional daper. V. CONCLUSION This research proposed an innovative fluid daper design utilized in a suspension fork and odeled the high-order syste dynaics. The siulation result explains that the proposed daper appears to be firer when it run into a sooth road surface, the bicycle rider is pedaling hard or the autoobile driver is steering, because the input force or velocity of the force is relative sall. On the other hand, the daper becoes softer when the rider enters to a terrain route. More iportant, the switching processes are autoatically achieved without any anual or electric operation. Force (N) Coefficient (Ns/) (a) Force/Displaceent F, ax= n x,...=.6645 x s,...= Tie (s) (b) F -D/F -V Diagra Displaceent, ax=.6645 Velocity,...=.8513/s Noralized ain piston displaceent/velocity x 14 (c) Equivalent Dap. Coeff Main piston velocity (/s) Fig. 9 Siulation results of the daper syste The proposed design can reduce the cost by eliinating the lockout-related coponents. Furtherore, it can iprove the rider convenience and safety since the frequently operations are oitted. This design consues no electric power to operate, feasible to be equipped on low-powered or powerless vehicles such as bicycles. Further works cover (1) coposing a ore coprehensive syste odel for the cavitation occurring during heavy load and rapid piston oveents; (2) foring a coputational fluidic dynaic analysis odel to virtually confir the proposed theoretical odel; and (3) constructing a daper prototype and a dynaic test rig to experientally verify the atheatical odel. ACKNOWLEDGMENT This work was supported by (1) National Science Council in Taiwan R.O.C. under the project nuber NSC E-15-3 and (2) Industry-Education Collaborative Project with SPINNER Industry Co., Ltd. REFERENCES [1] J. Y. Wong, Theory of ground vehicles, 2nd Ed., John Wiley & Sons Inc., 21. [2] T. D. Gillespie, Fundaentals of vehicle dynaics Society of Autootive Engineers Inc., [3] The Bose Suspension Syste resolving the conflict between cofort and control, Bose Learning Center, 28. Available: T&url=/learning/project_sound/suspension_coponents.jsp [4] Y. Shen, M. F. Golnaraghi and G. R. Heppler, Load-leveling suspension syste with a agnetorheological daper, Vehicle Syste Dynaics, Vol. 45 No. 4, 27, pp [5] A. Mehdi, Seiactive fuzzy logic control for heavy truck priary suspensions: Is it effective? SAE Transactions, Vol. 114 No. 2, 25, pp [6] R. Mollica and K. Youcef-Toui, A nonlinear dynaic odel of a onotube shock absorber, Proceedings of Aerican Control Conference, Albuquerque, NM, USA, 1997, pp [7] F. D. Goncalves, Dynaic analysis of sei-active control techniques for vehicle applications, Master of Science in Mechanical Engineering, Virginia Polytechnic Institute and State University, 21. [8] K. J. Bathe, H. Zhang and S. Ji, Finite eleent analysis of fluid flows fully coupled with structural interactions, Coputers and Structures, Vol. 72, 1999, pp [9] A. Beghi, M. Liberati, S. Mezzalira and S. Peron, Grey-box odeling of a otorcycle shock absorber for virtual prototyping applications, Siulation Modelling Practice and Theory, Vol. 15 No. 8, 27, pp [1] P. Yang, Y. H. Tan, J. M. Yang and N. Sun, Measureent, siulation on dynaic characteristics of a wire gauze-fluid daping shock absorber, Mechanical Systes and Signal Processing, Vol. 2 No. 3, 26, pp [11] E. L. Wang and M. L. Hull, A odel for deterining rider induced energy losses in bicycle suspension systes, Vehicle Syste Dynaics, Vol. 25 No. 3, 1996, pp [12] V. Pracny, M. Meywerk and A. Lion, Full vehicle siulation using theroechanically coupled hybrid neural network shock absorber odel, Vehicle Syste Dynaics, Vol. 46 No. 3, 28, pp [13] C. Heritier, Design of shock absorber test rig for UNSW@ADFA Forula SAE car, Initial Thesis Report, School of Aerospace Civil and Mechanical Engineering, Australian Defense Force Acadey University of New South Wales, 28. [14] J. Titlestad, T. Fairlie-Clarke, M. Davie, A. Whittaker and S. Grant, Experiental evaluation of ountain bike suspension systes, ACTA Polytechnica, Vol. 43 No. 5, 23. [15] D. H. Wang and W. H. Liao, Sei-active suspension systes for railway vehicles based on agnetorheological fluid dapers, 666

7 Proceedings of the ASME 27 International Design Engineering Technical Conferences and Coputers and Inforation in Engineering Conference, DETC , 27. [16] H. E. Merritt, Hydraulic control systes, New York: John Wiley & Sons Inc., [17] R. H. Warring, Hydraulic handbook, Surrey, England: Trade and Technical Press Ltd., [18] E. C. Yeh, S. H. Lu, T. W. Yang and S. S. Hwang, Dynaic analysis of a double tube shock absorber for robust design, JSME International Journal Series C., Vol. 4 No. 2, 1997, pp [19] G. Lindfield and J. Penny, Nuerical ethods using MATLAB, Prentice Hall International, 21. International Science Index, Mechanical and Mechatronics Engineering waset.org/publication/