What causes steering wheel vibration at40 mph and below

if the wheel alignment is faulty ( castor wobble ) at 70 mph there is no way that you can describe it as a vibration as it virtually rip the steering wheel out of your hands. If it is a torque converter problem then at around 3850-4025 rpm stationary there will be a vibration of the vehicle and engine The sort of vibration that you are experiencing at 70 mph will come from a drive line problem. If rear wheel drive then it could be faulty "U" joints, worn slip joint or failed rear engine mount
If front wheel drive it may be cv joints or bent drive shafts,wheel bearings or brake callipers not moving freely on the mounting bolts.

were the motor & trans mounts checked?

2 different problems.Vibration when braking would be brake rotors and vibration driving most likely tire balance

sounds like a bent wheel rim

check your engine support, if it is ok check your tie rods and stabilizers or might as well have your wheels aligned...

I don't want to imply you don't have your brakes serviced or your shop is less than competent--But,unless a wheel weight fell off,or you have a really bad CV Joint causing this vibration,along with bad motor mounts,yes you can have a combination of worn items. Then I will bet on the fact that at least 50% of your problem,is worn brake rotors,rusted pad slides,rusted caliper mounting bracket and no one ever lubed a thing during any brake work. So pads grabbing rotors and you got brake chatter. Please don't be offended,but in my world that could have been prevented with semi-annual brake service.

Hi:
Since your BMW 540 series is a rear wheel drive car, a common cause of that sort of vibration is often the U joints on your drive shaft. The vibration often only shows up and certain speeds.

It isn't a particularly expensive repair, but is something to have checked out!

check your upper control arms, does it happen when you step on the brakes or just when driving, you might need a balance of all your wheels or the tires you have could be bad.

if it were the rotors it only happens when braking take in have them turn rotors see what happens good luck

Vibrations while driving like you are describing can come from tires that have defects (internally broken belts) (wheel weights that have fallen off) or a bent rim (perhaps from another driver [not you :-) ] hitting a curb) Are the tires worn? Have they been balanced and rotated regularly? You report no vibration in the steering wheel.
Vibrations during braking can be warped rotors or discs (but this doesn't sound like your problem since these kind are usually felt in the steering wheel during braking).
If and only if you feel like you can do this safely,
you can try getting the car up to 55, placing the car in neutral, then switching the "engine off" but leave the "key on" (be warned the power steering will go out but the vehicle can still be steered though the steering wheel will be much stiffer) if you try this (do it perhaps in a vacant parking lot or on an empty road) and the vibration goes away with the engine off but while the vehicle is still moving, then the vibration is engine or transmission related. If this is the case you might hope for maybe a bad engine mount. Bad engine mounts can be diagnosed with the vehicle stopped as well. However, if the vibration remains with the van moving forward but with the engine off, the vibration is likely a problem with the tires or suspension. Try to provide some more info.
If you don't feel comfortable trying the above suggestion, please take the vehicle in to an ASE certified suspension and steering professional for further diagnosis.

Finally, I had a similar situation happen to me today. I was riding with a friend in their van and the vehicle started vibrating more and more around 55 mph. We stopped and carefully checked the front tires (including the lug nuts for tightness) but
found a tire defect. (it had several broken steel belts that caused a bulge in the tire and thus the vibration) We changed the tire and the vibration was gone. Good luck to you.