Hi, what has happened is the steel belts in your radials have let go! You have one of two options to fix this problem! Buy new tires which cost lots of money, or else have a few drinks before you go that speed!!
Did you say the BRAKES are ok? Fine but b r a k e s have nothing to do with shaking at 70 unless you are stopping at 70m.p.h. Try jacking your car two inches off the ground and check your tie rod ends for minor looseness. Any is bad. Also check the steering rack for looseness to the frame. I hope your front wheels are computer balanced. Other wise all bets are off! It took me years to get a smooth 90m.p.h. so I offer these solutions. Also don't forget to hit the front end alignment shop, they have a $50,000 front end rack to check the ole' caster camber and toe-in. GOOD LUCK JIM!
Your post made me laugh, because it is very similatr to what I am workign on at work. I am currently working to resolve customer issues with very similar problems on new cars. The common cause in new cars is imbalances in the wheel/tire assembly. I would recommend that you first check for anything loose in the front end as the other responses have suggested (SAFETY FIRST), and then get your wheels and tires spin balanced. This may cure your problem. If a new car with power steering and wheels that are presumably balanced has steering vibration, I can only imagine how much vibration could exist in a Z if it lost a balance weight from one of the front wheels or something.
Thanks for all the good post. I took the car to a Big-O-Tire place and they ruled out the wheels and tire. Normaly I don't trust tire shops but these guys race cars on weekend so they know thier stuff.
Well at this point I'm going to add that PST kit I got that came with new tie-rod ends and new ball-joints and see if that helps. Next will be the rack bushing, it looks in bad shape.
Have fought this problem for years. Here are some other culprits.
Bad struts (yes, this can be a problem)
Severly warped rotors CAN cause a shimmy problem. Normally only felt under braking, can be felt at high speed if bad enough.
Incorrect air pressure.
T/C arm malfunction (missing hardware/nut at the end).
Faulty tires. I had tires that would balance fine, but produced a shake. After several attempts to have them balanced, I finally convinced the tire manufacturer they were bad. They replaced them, and the shake was gone. They were as amazed as I was.
Slightly imperfect rims, combined with slightly imperfect tires, combined with slightly bad rack bushings pushing slightly bad inner tie rod ends. Looked at individually, each of these may not be bad enough to cause the problem. Together they are a nightmare.
Tires that balance fine at 60, and somehow pick up a harmonic at 70 causing the shakes.
Seems our cars are very sensitive to vibration. Everything must be right to fix this issue.