Speed wobble
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Speed wobble or shimmy is the spontaneous oscillation of the front wheel(s), or "wobbling" of a vehicle, at a set speed or speed range. The oscillations are due to the latent resonant frequency of the steered wheel of the vehicle and are a complex phenomenon. It can occur with motorcycles, skateboards, bicycles or in theory any vehicle with a single steering pivot point and a sufficient amount of freedom of the steered wheel; this does not include most automobiles, however,coil-sprung vehicles with a track bar setup such as the Jeep WJ, XJ, ZJ, and TJ with after-market suspension lifts may have this problem also. While usually easily remedied by adjusting speed or changing position on vehicle, speed wobbles can be fatal, especially at high speeds.
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[edit] Shimmy and Death Wobble
Sustained oscillation has two necessary components: An underdamped second order system and a positive feedback mechanism.
The underdamped second order system is the nutation of the front wheel. An example of an underdamped second order system is a spring and mass system where the mass can bob up and down (oscillate) when hanging from a spring.
The positive feedback mechanism is the bike+rider, approximating a second order damped system. At a critical bike speed, the front wheel nutation frequency matches the bike+rider natural frequency; if the bike+rider side-to-side system is insufficiently damped, the movement provides a positive feedback to the front wheel second order system, amplifying or sustaining the nutation.
[edit] Nutation
Nutation is the torque-free tendency is of a freely spinning rigid body's spin axis to oscillate around the average spin axis. Ideally, it is a second order behaviour with no damping. In real cases, the oscillation will decay due to damping in the system.
Nutation is easily demonstrated by suspending a spinning bicycle wheel by the axle such that the axle hangs vertically. If the rim is given a sharp bump parallel to the spin axis, the spin axis will oscillate in a cone-shaped movement around the average spin axis. This is nutation, not to be confused with precession.
A bicycle or motor bike front wheel has two degrees of freedom in an effective gimbal system. The inner gimbal is the steering fork, free to rotate around the steering axis. The outer gimbal is effectively the entire bike, able to tilt to either side along the longitudinal axis. This gives the front wheel the required two degrees of freedom necessary for nutation to occur.
If a front wheel is disturbed into nutation, the effect on the bike is to rapidly steer from side to side, as well as to tilt the bike from side to side. These 2 motions are rotations around the two degrees of freedom of the effective gymbal system described earlier. The effect is manifested in two fundamentally different modes, depending on how much the rider is a part of the gimbal system:
The first is commonly known as shimmy and can easily occur while riding no hands on a bicycle. It is a relatively harmless side to side shaking of the head tube combined with a side to side steering wobble as the front wheel pivots around the ground contact point. The rider is not a major part of the nutation system. The rider on the saddle provides a firm anchor point for the rest of the frame to pivot around.
The second case is less common and can result in a crash. It is variously called a death wobble or weave. It occurs at a higher speed with a firm grip on the bars. The longitudinal pivot is not near the ground contact patch as in shimmy but closer to the rider's body. In this case the rider is part of the gimbal system due to a firm grip on the handle bars. The effect is that the entire bike+rider weaves rapidly from side to side, as if the riders is riding a mini slalom course, as opposed to shimmy in which mainly the head tube and handlebars are shaking.
[edit] Damping
The damping coefficient (the inverse of Q factor) of the second order nutation system is a function of the angular momentum. The higher the wheel speed, the higher the nutation Q factor (less damping), other factors remaining the same. With a higher Q factor, less positive feedback is needed for instability to occur. This explains why shimmy and death wobble only happens above certain speeds - the Q factor needs to become high enough for steering instability. Motor bikes are often equipped with a steering damper to increase the gimbal damping, lowering the nutation Q factor.
[edit] Gimbal Inertia
The gimbal moment inertia around the steering axis is influenced by how tightly the rider grips the handlebars. No hands on the bars results in the lowest moment of inertia and a higher nutation frequency and a higher Q factor at a given speed. A light grip on the handle bar will have a strong damping effect, lowering the Q factor drastically. However, if the bars are gripped tightly, the rider's body is coupled tighter to the steering gimbal and the arms and upper body become a part of that gimbal, increasing its moment of inertia. The rider's entire body becomes part of the longitudinal gimbal, increasing that moment of inertia as well. The effect is to lower the nutation frequency and nutation Q factor, so a higher speed is required to attain the necessary Q factor for instability as compared to riding no-hands. Because the center of mass for the longitudinal gimbal is higher, the center of rotation is also much higher compared to the no-hands case.
[edit] Case 1: Shimmy, no hands on the handlebars
As there is no contact with the handlebars, the gimbal moment of inertia around the steering axis is the lowest. There is no damping from the rider's hands so the nutation Q factor is high even at modest speed. Most bikes will exhibit shimmy if the speed is sufficient. Damping it is also easy by a light grip on the bars or by touching the top tube with a leg. Both actions add "soft" mass to the gimbal system, lowering the Q factor drastically. Pedalling while riding no-hands also connects "soft" mass more firmly to the front of the bike via the pedal arms, resulting in more stable behaviour.
[edit] Case 2: Death wobble, tightly gripping the bars
The rider's arms and body are a part of the gimbals. The arms' and upper body mass increase the steering gimbal moment of inertia, while the entire body is part of the longitudinal moment of inertia. The nutation frequency is lower. Since the rider's body is a part of the gimbal system inertia, the longitudinal pivot is much higher towards the rider upper body, since the center of mass is now higher. There is less shaking of the head tube and more weaving of the wheels. The rider is shaken from side to side. It is difficult to control the death wobble since the movement occurs too rapidly to impose muscular control, and the involuntary effect of gripping the handlebars tightly only increases the Q factor. A conscious effort to release the tight grip will have a much better effect by increasing damping.
Since the arms and body are not completely rigid, there is still considerable damping provided, so a higher speed is required for the Q factor to be high enough to enable positive feedback.
[edit] Feedback
All 2nd order systems have some amount of damping due to frictional effects. A wheel on its own, if disturbed into nutation, will damp out by itself. To get shimmy or death wobble, a feedback system is required for the nutation to be sustained. The feedback system is provided by the bike+rider.
For positive feedback to exist, there needs to be a system such that nutation is amplified enough for any damping effects to be cancelled. A second order system can provide such feedback at a certain frequency or range of frequencies. If a bike+rider approximates a second order system, then at a certain frequency or range of frequencies, the phase response will be such that positive feedback is established. Since a spinning front wheel is a lightly damped system, only a small amount of positive feedback is required for instability.
[edit] Shimmy
Examination of moving and relatively stationary points on a bike during shimmy reveals:
• The front wheel contact patch is relatively quiet, but the head tube is shaking from side to side. This means the front wheel nutation longitudinal pivot is close to the ground.
• Due to the rider's inertia on the saddle, the saddle is also relatively motionless.
• The back wheel contact patch is also relatively motionless. This implies that there must be flexing motion in the back wheel, the frame, the seat post and the saddle to allow the head tube to move sideways.
• The back wheel will usually be flexing the most since 1) it is not as stiff as the other components; 2) it is under rider load, so the lower vertical spokes' tension is reduced, and with a dished wheel the non-drive side spokes are under even less tension; and 3) it is subject to a lever action. It requires only a small amount of sideways flexing to account for the head tube movement.
All these predict that a stiffer wheel, and an equally dished wheel will be less prone to shimmy. Double-butted spokes should be more prone to shimmy, and likewise heavier riders will reduce bottom spoke tension, increasing shimmy.
• The rear triangle is next in line for doing any flexing. Currently it is not clear if the seat stays or chain stays will flex more.
• The main triangle and seat tube should be flexing very little due to the larger tube diameters.
• The fork should flex very little due to the relatively small bending moment on it. The rear wheel suffers the largest bending moment compared to all other components.
• If the saddle is higher, the downward force through the saddle passes closer to the back axle, and less wheel flexing is required to account for head tube movement. This predicts that taller cases will be more prone to shimmy.
• A loaded rear rack adds a leveraged mass behind the saddle pivot and will amplify any bending moments, increasing shimmy.
The flexing parts provide ample sprung mass to generate the required positive feedback.
[edit] Death wobble
The entire rider is shaken from side to side. Positive feedback is established if the rider is shaken at his/her body natural frequency: At a critical speed the bike+rider is shaken at exactly the frequency itself wobbles at. It is like shaking a jelly: Too slow and you are merely moving the jelly. Too fast and you are just vibrating the jelly. But just right and the jelly will shake violently and may disintegrate. The bike+rider represents the jelly. The "jelly" can be the rider shifting from side to side on the saddle, effectively rolling on the tissue between the pelvis and saddle. The semi-fluid property of the rider's body in the stomach region will amplify the jelly effect. A rider with excess body fat will be less damped than a lean rider. A soft padded saddle which allows the rider to move sideways through the compliance of saddle padding material is yet another possibility.
[edit] System excitation
[edit] Shimmy
Since the front wheel is a poorly damped second order system, any amount of disturbance will cause nutation. This will happen at all speeds except zero speed and on all bicycles, essentially continuously because there is always wind and road vibrations and rider movement. Below a certain speed the disturbance is continuously and immediately damped so is not noticed. Above this speed, the nutation frequency matches the natural frequency of any springiness on the bike. As the nutation causes a slight sideways movement of the bike, it pulls along the springy mass. The nutation causes the movement to reverse and the mass is pulled along in the opposite direction. At a critical speed the springy mass is shaken at its natural frequency and positive feedback is established.
To check stability, ride fairly low speed with no hands and give the bars a slight steering bump. You should see nutation which damps out quickly. Increase speed and repeat the experiment. The nutation will take longer to dissipate. At a certain speed it will not dissipate. Press a knee against the top tube or a hand lightly on the bars for damping.
[edit] Death wobble
Initiation of death wobble requires a sudden steering movement such that inertia causes a relative sideways movement of mass. The jelly effect will provide feedback to the steering mechanism; if the bike speed is sufficient such that the nutation matches the jelly frequency, death wobble may ensue providing the positive feedback is more than the minimum amount to cancel any nutation damping effects.
It is not advisable to experiment with death wobble except perhaps on a roller system.
[edit] Observations explained
[edit] Shimmy
Pressing a knee against the top tube dampens it out: Effectively, a mass is added to the top tube. Since shimmy is manifested as a side to side shaking of the head tube, adding mass to the top tube will increase the moment of inertia around the longitudinal axis. In addition, the leg's added mass is connected to the top tube via the muscle tissue and not rigidly fixed, so acts like a powerful damping mass. The combined effect is to lower nutation frequency, shifting it away from the frequency of sufficient positive feedback, and damping the nutation system, such that the positive feedback provided by rider+bike is no longer sufficient to sustain the nutation and it damps out. The damping effect is the most important of the two.
It doesn't happen on xyz bike: Not all bikes have enough springiness to provide the necessary feedback for nutation to be amplified, which explains why many riders have never experienced it; Or they have not reached that critical speed where the nutation Q factor is high enough, or where the nutation frequency matches the natural frequency of any springy mass.
Loaded bike: The inertia of the rider on the saddle in combination with the back wheel contact patch creates a pivot; any mass behind this pivot will have a sling-shot effect and powerfully increase positive feedback to the shaking head tube. An otherwise stable bike will worsen drastically with a loaded rack on the back, more so if the load is not rigidly fixed. A lot of mass shaking sideways near the back of the bike will make any bike shimmy at fairly modest speeds, regardless of how stable it was before.
Slowing down or speeding up: Either case will change the nutation frequency and pull it away from the jelly frequency, eliminating the positive feedback. Speeding up often does not work on bicycles due to the wide range of frequencies in the feedback system where positive feedback is sufficient to sustain shimmy.
Frame stiffness: May play a small part, flexible frames may exhibit some flex during shimmy, decreasing the damping of the system. However, frame flexibility is not required for shimmy.
Different wheels: Changing the front wheel for one with different mass will affect the angular momentum will therefore change the nutation frequency. This may eliminate the effect or introduce it, depending on the critical frequencies. Usually it will change the speed where shimmy is observed. A wheel with more flexibility in it will add tendency to shimmy to a bike.
[edit] Death Wobble
It doesn't happen on xyz bike: Not all bike+rider systems provide the necessary feedback for nutation to be amplified, which explains why many riders have never experienced it. Or they have not reached that critical speed where the positive feedback is more than the critical amount, or where the nutation frequency matches the "jelly frequency".
Lifting body off the saddle: Lifting the body up from the saddle completely alters the dynamics of the feedback system and the moments of inertia. In particular, lifting yourself off the saddle eliminates the jelly effect.
Releasing handle bars stops it: releasing the handle bars decouples the rider from the steering gimbal and alters the moment of inertia. Nutation frequency shifts away from the jelly frequency and so positive feedback is eliminated.
[edit] Mathematical description
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