Since you're talking "3D", I assume you're not trying to make a black and white logo.
I would suggest creating a blend between 2 instances of your tread symbol. Set one of the symbols to "0%" opaque (transparent). The resulting blend will give a blur effect (you can play with the number of steps in the blend).
Now make this blend into a symbol and map it to your 3D cylinder.
There are many other ways to approach a "motion" effect. Among them are:
1. Creating a gradient from solid to transparent and filling some "swooshes" over the tire tread.
2. Using a raster blur effect. AI does not have a motion blur, per se, but you can mimic it using the radial blur and offsetting the blur center to a corner.
Someone else may have a better idea.
Hope these help.
Ok, I played around a bit. Here is one way to make a motion blur in AI (since there is not "motion blur" filter).
Please note the single anchor point near the top. This is required, to force the Radial blur filter to work more like a motion blur.
Here's another approach:
The blur effect is created by building an art brush created by blending 2 rectangles together. The bottom rectangles is set to transparent, giving the brush more versatility.
This is another Illustrator "work-around" because gradients cannot be used in a brush. I suggest keeping your original brush artwork in a "Symbol" so you can edit the brush using the original blends. If you simply drag the brush onto the artboard, you'll find the blend has been expanded into multiple rectangles.
The other option is to take that portion of the artwork into Photohsop (as a smart object) and assign a motion blur there, then place the PSD in AI.
The 2nd option is actually much more editable within AI. you would need to build the right brush to accomplish the effect. Here's a link to a few custom brushes that might help you.
Here is a custom brush file that might be helpful: