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#1
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Angular acceleration and rolling resistance
I'm trying to understand the resulting torques that act back on the
axle. For a free rolling wheel travelling purely in the longitudinal direction and with a slip ratio > 0, it will output a force of say 100N. As well as pushing the vehicle forward it also creates a torque on the axle which is then used to calculate the angular acceleration. The forward velocity also creates a rolling resistance moment as a function of vertical load and forward rolling speed. There is also a moment produced by the internal bearing friction trying to slow it down. I understand this, however if the vehicle were to rotate instantaneously such that the the longitudinal velocity = 0, the longitudinal slip ratio = 0, the angular velocity > 0, and the lateral velocity was 10mts/s and hence the lateral slip ratio > 0, the tyre is not outputting any force in the longitudinal direction thus meaning the only forces acting against the angular velocity of the wheel are the internal bearing friction and rolling resistance moment. However the rolling resistance moment is a function of forward rolling speed which if equal to 0 there is no moment produced. Thus in the simulation if travelling purely in a lateral direction in the tyre's frame of reference, the only force acting against the angular velocity of the wheel is internal bearing friction, however this is wrong as it is not the only force acting on it. The wheel would only slow down as a result of the bearing friction which is not correct There must be another additional force derived from lateral slip that adds to the rolling resistance moment. In real life if a vehicle were to instantaneously rotate and travel in a purely lateral direction, the wheels would stop rolling from the lateral slip. I'm trying to work out what that force is. I hope this post is clear. Any help is much appreciated! |
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#2
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Angular acceleration and rolling resistance
"Zach" > wrote in message ... > I'm trying to understand the resulting torques that act back on the > axle. For a free rolling wheel travelling purely in the longitudinal > direction and with a slip ratio > 0, it will output a force of say > 100N. As well as pushing the vehicle forward it also creates a torque > on the axle which is then used to calculate the angular acceleration. > The forward velocity also creates a rolling resistance moment as a > function of vertical load and forward rolling speed. There is also a > moment produced by the internal bearing friction trying to slow it > down. > > I understand this, however if the vehicle were to rotate > instantaneously such that the the longitudinal velocity = 0, the > longitudinal slip ratio = 0, the angular velocity > 0, and the lateral > velocity was 10mts/s and hence the lateral slip ratio > 0, the tyre is > not outputting any force in the longitudinal direction thus meaning > the only forces acting against the angular velocity of the wheel are > the internal bearing friction and rolling resistance moment. However > the rolling resistance moment is a function of forward rolling speed > which if equal to 0 there is no moment produced. Thus in the > simulation if travelling purely in a lateral direction in the tyre's > frame of reference, the only force acting against the angular velocity > of the wheel is internal bearing friction, however this is wrong as it > is not the only force acting on it. The wheel would only slow down as > a result of the bearing friction which is not correct There must be > another additional force derived from lateral slip that adds to the > rolling resistance moment. > > In real life if a vehicle were to instantaneously rotate and travel in > a purely lateral direction, the wheels would stop rolling from the > lateral slip. I'm trying to work out what that force is. I hope this > post is clear. Any help is much appreciated! Tire friction with the road surface? Higher vehicle weight = more road friction and bearing friction. Drivetrain friction? Even air resistance to a minimal degree. A good example of decreasing rolling resistance is when Nascar crews pry the brake pads 1/2" away from the rotors before qualification at Daytona and Talledega and the driver is always reminded not to touch the brake pedal. Higher tech F1 braking systems keep the pads a good distance from the rotors when not braking and even take into consideration slight warping of the rotors over the course of a race. Taking into consideration your slip ratios, your main consideration is forward rolling resistance and there are many factors to consider. Even the viscosity of lubrication fluids is a factor. Ed |
#3
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Angular acceleration and rolling resistance
On Jan 19, 12:45*am, "Ed Medlin" > wrote:
> "Zach" > wrote in message > > ... > > > > > I'm trying to understand the resulting torques that act back on the > > axle. For a free rolling wheel travelling purely in the longitudinal > > direction and with a slip ratio > 0, it will output a force of say > > 100N. As well as pushing the vehicle forward it also creates a torque > > on the axle which is then used to calculate the angular acceleration. > > The forward velocity also creates a rolling resistance moment as a > > function of vertical load and forward rolling speed. There is also a > > moment produced by the internal bearing friction trying to slow it > > down. > > > I understand this, however if the vehicle were to rotate > > instantaneously such that the the longitudinal velocity = 0, the > > longitudinal slip ratio = 0, the angular velocity > 0, and the lateral > > velocity was 10mts/s and hence the lateral slip ratio > 0, the tyre is > > not outputting any force in the longitudinal direction thus meaning > > the only forces acting against the angular velocity of the wheel are > > the internal bearing friction and rolling resistance moment. However > > the rolling resistance moment is a function of forward rolling speed > > which if equal to 0 there is no moment produced. Thus in the > > simulation if travelling purely in a lateral direction in the tyre's > > frame of reference, the only force acting against the angular velocity > > of the wheel is internal bearing friction, however this is wrong as it > > is not the only force acting on it. The wheel would only slow down as > > a result of the bearing friction which is not correct There must be > > another additional force derived from lateral slip that adds to the > > rolling resistance moment. > > > In real life if a vehicle were to instantaneously rotate and travel in > > a purely lateral direction, the wheels would stop rolling from the > > lateral slip. I'm trying to work out what that force is. I hope this > > post is clear. Any help is much appreciated! > > Tire friction with the road surface? Higher vehicle weight = more road > friction and bearing friction. Drivetrain friction? Even air resistance to a > minimal degree. A good example of decreasing rolling resistance is when > Nascar crews pry the brake pads 1/2" away from the rotors before > qualification at Daytona and Talledega and the driver is always reminded not > to touch the brake pedal. Higher tech F1 braking systems keep the pads a > good distance from the rotors when not braking and even take into > consideration slight warping of the rotors over the course of a race. Taking > into consideration your slip ratios, your main consideration is forward > rolling resistance and there are many factors to consider. Even the > viscosity of lubrication fluids is a factor. > > Ed Right. The bearing friction I'm modelling as a function of radial load and coefficients for viscosity/friction etc. I would have thought that the rolling resistance would be increased dramatically if there was any degree of lateral slip or is it totally independent of it? The equation for rolling resistance taken from Pacejka's Tyre & Vehicle Dynamics is: My = -Vertical Load * Unloaded Tyre Radius * (scalar value * arctan (Forward Rolling Speed / Reference Velocity) + scalar value * Fx / Adapted Vertical Load) * scalar value which would suggest that it is independent of lateral slip Thanks for you help Ed |
#4
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Angular acceleration and rolling resistance
"Zach" > wrote in message ... On Jan 19, 12:45 am, "Ed Medlin" > wrote: > "Zach" > wrote in message > > ... > > > > > I'm trying to understand the resulting torques that act back on the > > axle. For a free rolling wheel travelling purely in the longitudinal > > direction and with a slip ratio > 0, it will output a force of say > > 100N. As well as pushing the vehicle forward it also creates a torque > > on the axle which is then used to calculate the angular acceleration. > > The forward velocity also creates a rolling resistance moment as a > > function of vertical load and forward rolling speed. There is also a > > moment produced by the internal bearing friction trying to slow it > > down. > > > I understand this, however if the vehicle were to rotate > > instantaneously such that the the longitudinal velocity = 0, the > > longitudinal slip ratio = 0, the angular velocity > 0, and the lateral > > velocity was 10mts/s and hence the lateral slip ratio > 0, the tyre is > > not outputting any force in the longitudinal direction thus meaning > > the only forces acting against the angular velocity of the wheel are > > the internal bearing friction and rolling resistance moment. However > > the rolling resistance moment is a function of forward rolling speed > > which if equal to 0 there is no moment produced. Thus in the > > simulation if travelling purely in a lateral direction in the tyre's > > frame of reference, the only force acting against the angular velocity > > of the wheel is internal bearing friction, however this is wrong as it > > is not the only force acting on it. The wheel would only slow down as > > a result of the bearing friction which is not correct There must be > > another additional force derived from lateral slip that adds to the > > rolling resistance moment. > > > In real life if a vehicle were to instantaneously rotate and travel in > > a purely lateral direction, the wheels would stop rolling from the > > lateral slip. I'm trying to work out what that force is. I hope this > > post is clear. Any help is much appreciated! > > Tire friction with the road surface? Higher vehicle weight = more road > friction and bearing friction. Drivetrain friction? Even air resistance to > a > minimal degree. A good example of decreasing rolling resistance is when > Nascar crews pry the brake pads 1/2" away from the rotors before > qualification at Daytona and Talledega and the driver is always reminded > not > to touch the brake pedal. Higher tech F1 braking systems keep the pads a > good distance from the rotors when not braking and even take into > consideration slight warping of the rotors over the course of a race. > Taking > into consideration your slip ratios, your main consideration is forward > rolling resistance and there are many factors to consider. Even the > viscosity of lubrication fluids is a factor. > > Ed Right. The bearing friction I'm modelling as a function of radial load and coefficients for viscosity/friction etc. I would have thought that the rolling resistance would be increased dramatically if there was any degree of lateral slip or is it totally independent of it? The equation for rolling resistance taken from Pacejka's Tyre & Vehicle Dynamics is: My = -Vertical Load * Unloaded Tyre Radius * (scalar value * arctan (Forward Rolling Speed / Reference Velocity) + scalar value * Fx / Adapted Vertical Load) * scalar value which would suggest that it is independent of lateral slip Thanks for you help Ed I think they would be totally independent of each other. Both would affect momentum, but in entirely different directions.....I guess that is the correct word.....:-). I hope you get my drift.... Ed |
#5
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Angular acceleration and rolling resistance
>rolling resistance
>which would suggest that it is independent of lateral slip In real life it isn't. Most of rolling resistance is due to deformation at the contact patch, combined with the fact that hysteresis is involved when rubber is compressed or stretched and then returns to it's former state. The force during the deformation is greater than the force during the recovery, which is why rubber is good for reducing vibration. Lateral slip increases the rubber deformation, and it's enough to slow down a race car pulling a high g turn. In the case of a Formula 1 car, top speed at full throttle might be around 190+ mph on a straight, but this gets reduced to about 160mph in a 4 g turn. |
#6
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Angular acceleration and rolling resistance
"jeffareid" > wrote in message ... > >rolling resistance >>which would suggest that it is independent of lateral slip > > In real life it isn't. Most of rolling resistance is due to > deformation at the contact patch, combined with the fact that > hysteresis is involved when rubber is compressed or stretched > and then returns to it's former state. The force during the > deformation is greater than the force during the recovery, > which is why rubber is good for reducing vibration. > > Lateral slip increases the rubber deformation, and it's enough > to slow down a race car pulling a high g turn. In the case > of a Formula 1 car, top speed at full throttle might be around > 190+ mph on a straight, but this gets reduced to about 160mph > in a 4 g turn. > Yea, I was kind of "toungue in cheek" on that one.....:-). Where you can really see these effects is at Indy where the IRL cars are flat out all the time and the lateral force slows them in the four corners. They do a lot with camber where on the straights, there is a much smaller contact patch from the tires and thus causing less friction there. The by product of this is more wear and heat on the inside of the right tires and outsides of the lefts. This causes a much larger contact patch in the corners due to the distortions from the lateral Gs which will place the entire tire into contact with the track surface. There is also the effect of the extra Gs causing compression and therefore more friction. How to determine and calculate the extent of both the Gs and added tire friction have with forward rolling resistance is a tough one. I am sure the F1 and IRL (and even Nascar today) engineers have some sort of formula for this. Ed |
#7
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Angular acceleration and rolling resistance
> Lateral slip increases the rubber deformation, and it's enough
> to slow down a race car pulling a high g turn. In the case > of a Formula 1 car, top speed at full throttle might be around > 190+ mph on a straight, but this gets reduced to about 160mph > in a 4 g turn. Correction, the speed loss is there, but it's not 30mph, more like in the range 10 mph to 20 mph (perhaps some CART cars back in the 1990's that went over 255 mph on the straights). The 160mph 4 g turn was a comment in this video, but the driver slowed before entering "pouen": David Coulthard in F1 McLaren, 2002 (remember automatic shifters?): http://jeffareid.net/real/spaf1.wmv Onboard lap from 1998 CART car, you can hear the engine rpms drop, but it isn't a lot. http://www.youtube.com/watch?v=T_kt2T6HM3A&fmt=18 |
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