SUSPENSION OF A MOUNTAIN BIKE SVOČ FST 211 Bc. Vít Prošek University of West Bohemia Univerzitni 8, 36 14 Pilsen Czech Republic ABSTRACT This work is concerned about suspended mountain bikes, especially about rear suspension. First of all is shown how it is made today. On one hand the kinematics and on the other hand the dampers. Then there are cleared some problems and is suggested how does it should be better. Finally is introduced how is possible to achieve the better behaviour. There are shown some models and cleared the principles. KEYWORDS Mountain bike, suspension, kinematics, damper, inertia valve, velocity sensitive valve INTRODUCTION Suspension takes a big role in mountain bikes, because while riding in rough terrain there are big dynamic forces, which are uncomfortable for the rider. On the other hand, suspension improves handling and adhesion and decreases rolling resistance in terrain. There are two points of view in this work. First one is from the side of kinematics, because there is a good chance to decrease rolling resistance in terrain. The second point of view is from the side of damper, because there is variety of modes of riding on mountain bike. For example pedalling on road or riding through rough terrain down the hill. In each mode rider needs different behaviour of the damper. Also there is a good chance to decrease rolling resistance in terrain. PROBLEM SOLVING In the beginning are done some dynamic simulations to calculate the behaviour of kinematics and damper if the characteristics are done. Then there are shown some alternatives how to achieve these characteristics, especially by dampers.
WHAT IS THAT AND WHY DO WE NEED IT? On one side, suspension decreases terrain induced forces acting on suspended body. It prevents from big stresses in construction of suspended body. On the other side, suspension also decreases the quantity of work needed to get over a bump. Picture 1 Scheme of suspension Picture 2 Czech full-suspension bicycle [1] On the picture 1 is shown scheme of suspension. It represents from the bottom: ground, spring with damper elastic behaviour of a tyre, mass unsprung masses as a wheel, brake, rear derailleur, part of rear linkage etc., spring with damper suspension damper, mass mass of sprung body as a main frame and partially a rider, force with sinus wave rider induced force while pedalling. KINEMATICS There are a lot of types of linkages between rear wheel and main frame. They transfers loads between rear wheel and main frame, guides rear wheel and provides him one degree of freedom. So there is some path for rear wheel s displacement. How does it work now? Picture 3 - Single pivot mechanism with leverage [1] Picture 4 - Virtual pivot mechanism DW link [1] How should it work better and why? Picture 5 - Static forces on the ground and bump caused by spring force On the left image is shown setting with a vertical as a rear wheel path. Spring acts in the direction of the. Forces perpendicular to the spring are acting on guidance of the wheel on sides of, or on bearings if there are some. From static equilibrium are calculated forces from ground or bump. On the right image is shown setting with a sloping as a rear wheel path. All else is the same. In this situation are forces from bump much smaller and forces from ground much bigger. Optimal situation is, when the instantaneous direction of the is in the same direction as the radial force from bump.
Y displacement [mm] Force [N] Force [N] Picture 6 - Simulation of riding across bumps In simulation is involved elastic behaviour of tyre as a bushing in centre of wheel. Wheel axle is guided in three s vertical, curved and sloping. Spring and damper has the same characteristics in all cases. Ground moves under the wheel by velocity of 2 m/s. Measured are forces between tyre and ground in vertical and horizontal direction. The vertical directed force corresponds with comfort and horizontal directed force corresponds with resistance to ride through bumps rolling resistance in terrain. Vertical contact forces Vertical 3 2 curved 1 sloping,,2,4,6,8 1, 1,2 1,4 1,6 Graph 1 Comparison of vertical contact forces Sloping = 7,5% less quantity of work than vertical Curved = 8,31% less quantity of work than vertical vertical Horizontal contact forces 16 12 curved 8 sloping 4-4,,2,4,6,8 1, 1,2 1,4 1,6 Graph 2 - Horizontal contact forces Sloping = 6,69% less quantity of work than vertical Curved = 9,87% less quantity of work than vertical How could we achieve that? 1 Path of rear wheel 8 6 4 2 Real trajectory of single pivot Real trajectory of virtual pivot Optimal trajectory for pedaling Optimal trajectory for bump" -2 32 34 36 38 4 42 44 46 48 5 52-4 X displacement [mm] Graph 3 - Path of the rear wheel The optimal curved path of rear axle is shown in graph as an optimal trajectory for bump. In real situation there is one problem more chain growth. Between the bottom bracket on the main frame and rear axle is chain. And growth of horizontal displacement between bottom bracket and rear axle while compression travel means affecting the pedalling on one hand, or affecting the suspension by pedalling on the other hand. In the graph is represented the optimal path for no chain growth by black colour. There are two alternatives for achieve the optimal path of rear axle single pivot, or virtual pivot. Virtual pivot is more corresponding to optimal path for bump and also has smaller growth of horizontal displacement, so it is the best solution for achieving the bump path and a good compromise for pedalling path.
Picture 7 - Supposed kinematic of rear linkage virtual pivot DAMPING How does it work now? A damper exerts two kinds of force. The first one is springing force by coil or air spring, which is dependent on compression travel. This force is in equilibrium with rider s weight when he is sitting on bicycle. The second one is damping force, which is generally dependent on compression velocity. This force is much smaller than springing force and is counteracting to bob unwanted compressing of travel while pedalling. Movement of damper has two directions. When is damper compressed, it is called compression. When is damper expanded, it is called rebound. The damping coefficient is mostly different by compression or rebound. Basically there is a big damping coefficient while rebound to waste the energy accumulated in spring, and mostly no or a little damping coefficient while compression. High-end dampers have a uniform damping force while compression. It is called ProPedal. Also there is an external adjustment for rebound damping coefficient which can be set before ride. Picture 8 Dampers [1] Picture 9 - Function of damper 1 big piston rod; 2 - big piston; 3 positive air chamber; 4 negative air chamber; 5 small piston rod; 6 small piston; 7 oil chamber; 8 unidirectional valve; 9 rebound restriction; 1 rebound adjuster; 11 oil channels; 12 external reservoir; 13 oil chamber; 14 air chamber; 15 separator; 16 air valve; 17 bottom-out adjuster; 18 unidirectional valve; 19 compression restriction; 2 boost valve; 21 ProPedal adjuster; 22 air valve How should it work better and why? There are a lot of modes of using a mountain bike. So the suspension is going to have more characteristics in one package = additional requirements Four basic modes : Pedalling on flat surface (rider needs to get somewhere) o Rider doesn t need to bob (swinging) when pedalling. Pedalling on rough surface (rider needs to get on the hill) o Rider doesn t need to bob when pedalling, but wants a comfort ride and adhesion. Also using the minimum quantity of work to get over the bump is required => it lowers rolling resistance in terrain. Riding in really rough terrain (basically down the hill) o Rider needs to lower the dynamic forces on main frame, respective on him. Also using the minimum quantity of work to get over the bump is required. Jumping and especially landing o Damper needs to absorb a big quantity of work without a bottoming-out. (Getting to the end of travel) Many manufacturers deal with an inertia valve to achieve an automatic lock-out. They ve published many international patents using inertia valve. That is because of fact, that getting over a bump means a vertical displacement of the wheel, which second derivation is acceleration. So if you ride on a flat surface, there is no acceleration and if you ride on rough surface, there is a big acceleration. If it will be possible to adjust the compression restriction by acceleration, it can be dependent only on type of surface on ground and independent on pedalling forces. Another fact is, that while pedalling is frequency of damper s movement low (2-4Hz) and while riding through bumps is much higher (8-2Hz). In cooperation with travel (displacement of damper) is result the velocity. Adjusting the damper by velocity could be very useful it is possible to invert the damping characteristics.
12 8 4 Parameters when riding across the bump velocity y'[cm/s] acceleration y' [m/s^2] displacement real y'2[mm] deformation of tyre y'[mm] 15 2 25 3 35 4 45 5-4 -8 displacement x [mm] Graph 4 - Parameters while riding across the bump - 8 kph, 3mm bump, 35 stiffness of tire While the wheel is getting onto the bump, there is a positive velocity damper makes compression. Since that time, when the wheel just on the bump is, is the velocity negative damper makes rebound. In the beginning of compression there is a positive acceleration, but it becomes negative, when the velocity reaches the maximum. While is the damper adjusted by acceleration, there are two problems negative acceleration and very short duration of positive acceleration. Last patents deals with it by hydraulic timing circuit, which holds the valve open for some unspecified time. Much better solution is, using the velocity as a delay. Acceleration opens the damper and velocity holds it open until the velocity drops under some value. So right before the wheel reaches the top of the bump, the damper becomes closed. To verification the behaviour of damper, which is adjusted by velocity in real time, are done simulations of three modes of using a mountain bike riding across bumps, pedalling on flat surface and pedalling on rough surface, with three alternatives of damper classic, damper with ProPedal, and velocity sensitive damper. Classic damper has a linear characteristic passing through zero. The steepness of this characteristic is characterised by damping coefficient. In simulations is the same as the rebound coefficient in other two alternatives. Picture 1 - ProPedal damper characteristics Picture 11 - Velocity sensitive damper characteristics First quadrant is rebound and third quadrant is compression behaviour of damper. Important is, that the independent variable is velocity and dependent is force. Only in this setup could excel the behaviour of velocity sensitive damper. But while pedalling is input to the simulation force of the rider on the frame, so the solver must be iterative. Picture 12 Simulation of riding across bumps with velocity sensitive damper Picture 13 Simulation of pedalling on flat surface with velocity sensitive damper Picture 14 Simulation of pedalling on rough surface with velocity sensitive damper Simulation of riding across bumps with velocity sensitive damper: Ground is moving under the frame with rear linkage by velocity of 2 m/s and bumps are 7mm high. Picture 15 - v and F classic d. Picture 16 - v and F ProPedal d. Picture 17 - v and F vel. Sensitive d. In classic damper is the force linear dependent on velocity, in ProPedal damper is the force uniform and velocity sensitive damper has low force by high velocity and bigger force by lower velocity. It has inverted characteristic than classic damper.
Vertical displacement [mm] Vertical displacenemt [mm] Force [N] Force [N] 1 5 Vertical contact forces in bumps classic damper ProPedal damper velocity sensitive damper,,1,2,3,4,5,6,7,8,9 Graph 5 - Vertical contact forces ProPedal = 4,46% more quantity of work than classic Vel.sens. =,27% less quantity of work than classic Horizontal contact forces in bumps 4 2 velocity sensitive damper,,1,2,3,4,5,6,7,8,9-2 classic damper ProPedal damper Graph 6 - Horizontal contact forces ProPedal = 5,16% more quantity of work than classic Vel.sens. = 9,89% less quantity of work than classic Simulation of pedalling on flat surface with velocity sensitive damper: Pedalling is represented by sinus wave of 4N force on main frame, which has one DOF - vertical displacement. Vertical displacement of frame while pedalling on flat surface,,2,4,6,8 1, 1,2 1,4-25 -5 classic damper ProPedal damper -75 velocity sensitive damper Graph 7 Vertical displacement of frame while pedalling on a flat surface ProPedal = 24,63% less bob than classic Vel.sens. = 23,18% less bob than classic Simulation of pedalling on rough surface with velocity sensitive damper: Pedalling is represented by sinus wave of 4N force on main frame, which has one DOF - vertical displacement. Ground is moving under the frame with rear linkage by velocity of 2 m/s and bumps are 1mm high. Vertical displacement of frame while pedalling in rough terrain,,2,4,6,8 1, 1,2 1,4-25 -5 classic damper ProPedal damper -75 velocity sensitive damper Graph 8 Vertical displacement of frame while pedalling in rough terrain ProPedal = 2,97% less bob than classic Vel.sens. = 14,52% less bob than classic How could we achieve that? Acceleration sensitive damping delayed by velocity sensitive damping, which lowers quantity of work needed to get over a bump and helps with rebounding in big speeds, so it improves adhesion. Maximal force constrained, travel sensitive damping against bottoming-out.
Picture 18 Alternatives 1 and 2 Picture 19 used damper [1] With using an existing damper and getting over a loss of acceleration sensitive damping could be solution really simply. Aqua coloured parts external reservoir of used damper Yellow coloured parts new parts and new internals To take advantage of acceleration sensitive damping is necessary to place the compression valve near the rear wheel axle. Best solution is placing the external expansion reservoir with compression valve there, using a connecting hydraulic hose and fittings. (1),(4) (2) (3) Picture 2 Alternatives 3 and 4 Picture 21 External reservoir placed near rear wheel axle [2] Pressure sensor pressure on the small face up on the element (1) downward force Velocity sensor small resistance besides cylindrical faces of element (2) thanks to dynamic viscosity of oil pressure drop difference of pressure on the same area up and down of element downward force Acceleration sensor relative inertia of element s mass with upwards acceleration downward force Adjustable (not really programmable) logic controller spring below the element (3) compares if the downward forces are bigger then adjusted preload or not typical boolean operation Actuator spring acting on element which is closing the restriction (4) (big resistance up) (3) (1) (2) Picture 22 - Alternatives 5 and 6 Picture 23 - Options of 6th alternative There is a negative air chamber (1) and a negative coil spring instead of positive coil spring and actuator is inner pressure in damper s hydraulic system Negative influence of negative acceleration is solved with separating of mass element (2) and actuator element (3) Total pressure in hydraulic system must be bigger than dynamic pressure in the place of biggest velocity of oil to prevent before cavitations
(1) (2) Picture 24 - Cutaways of 6th alternative On the picture 24 is shown the movement of T-shaped element (1), which is closing the compression restriction (2). Damper behaviour 8 -,3 -,2 -,1-2,,1 Force,2 on wheel [N],3 damper velocity [mm/s] -4 wheel acceleration [m/s^2] -6 time [s] wheel displacement [mm*1] Graph 9 - alter. 6, opt. 1 behaviour 1 Hz, 6% of travel In the beginning of the bump is damper opened and closes while the wheel is getting on top prevents from unnecessarily large vertical movement of the wheel so it touches ground earlier improves adhesion. Force on wheel [N] Damper behaviour 6 damper velocity [mm/s] wheel acceleration [m/s^2] 4 wheel displacement [mm*1] 2 -,3 -,2 -,1-2,,1,2,3-4 time [s] Graph 1 - alter. 6, opt. 1 behaviour 4 Hz, 6% of travel In slow movement while pedalling on a flat surface is the damper closed the same as the ProPedal damper is. WHERE CAN WE USE IT ALSO? In automobile industry and also in all transportation vehicles as a trolley buses etc. 6 4 2 Picture 25 Cutaways of automobile damper with inertia and velocity sensitive valve Very simple and robust solution is done by inserting a compression valve into body of a conventional damper. CONCLUSION AND RECOMMENDATION There are shown some great improvements in mountain bike suspension. The virtual pivot rear linkage can save o lot of rider s energy and makes him faster. The damper with inertia and velocity sensitive valve can prevent from bob while pedalling, improves adhesion and handling, and also decreases rolling resistance, respective saves rider s energy and makes him faster as well. ACKNOWLEDGMENTS Doc. Ing. Jaromír Horák, CSc. leader of diploma work Ing. Vladimír Navara, PhD. alias It must be simple as a hammer! Milan Duchek, Duratec s.r.o., Město Touškov consultant of diploma work REFERENCES [1] Google. Google. [Online] [Cited: 3 2, 211.] http://www.google.cz. [2] Fox, Robert, C. Inertia Valve Shock Absorber. WO32113A1 US/US, 3 13, 23.