I think you are feeling the rudder kicking back and forth as it gets more authority as the pilot keeps putting in inputs on takeoff roll while dealing with a crosswind. In strong crosswinds, pilots are often unable to maintain a smooth continuous position of the rudder but rather have to actively modulate rudder position with their pedal input.
One thing that does change when the airplane rotates is that there is no longer a pivot against the gear, so directional control of the rudder will feel a little different and the airplane will start crabbing and using aileron input for directional control. However, I think you are just noticing it more on rotation since the rudder inputs have sharper impacts at higher speed.
|Quoting tdscanuck (Reply 4):|
There's a shift in what's providing directional control at rotation. As long as the nosewheel is down it's providing some lateral control. As speed goes up the vertical fin/rudder do more but it's the sum of nosewheel friction, steering, and aerodynamic force on the vertical fin that's all adding up to the total lateral control force.
Analysis shows that the nose wheel loses effectiveness on steering between 60 and 80 knots. Above 100 knots, full deflection of the nosewheel will have no impact on steering capability since a combination of low forces on the tire and airplane momentum. The nose gear just skids with rudder input. That's why pilot training says stay off the tiller on takeoff since if a pilot needs to start using it, they likely are so out of control that they will end up off the runway regardless.
If you have never designed an airplane part before, let the real designers do the work!