This has been a problem since I bought the car. The tires have been rotated and balanced since I bought it.

Below 50mph and above 60mph she is nice and smooth. Between 50 and 60 the steering wheels is shaking left to right about an inch and the car is shaking.

I searched and found threads but almost everyone had their problems at higher speeds.

I will be raising the PSI as I saw someone else did since this is a easy try and I can drop the pressure back down if it does not work.

FYI my car is running some gawdy (they were on it when I bought it) 20 inch wheels and I bought hub centric rings figuring that was the issue. The rings did nothing to help.

What do you guys think?

 

I wish I had a good answer, my car did that and I just got new tires and that along with a balance solved it.

 

Just thought about this, have you checked/had checked the suspension bushings up front?

 

+1 on bushings. On a previous car (1986 Olds 442) I had shaking that wouldn't go away..tires rebalanced, alignment done..nothing. Then a tire shop found and replaced the front bushings. Then..smooth as glass well over 100 mph...

 

Any specific bushing?

 

what does it do under braking at those speeds? does it go away under braking around 50-60pm, or get worse?

it very well might be related to the 20" wheels... i'm sure they're not helping matters,

check your alignment and consider roadforce balancing,

i've had a similar problem since I bought my STR, and replaced a lot of parts... still haven't isolated it...

 

Under braking there is still some vibration but not like when cruising at the same speed.

 

Probably the tires. I had the same issue. Had the other tires balanced still had the issue. I bought a set of different used tired and it went away completely.

 

Those hub centric rings may not be perfectly centered or the rims on them may not be perfectly centered on those hub centric rings, or the rims themselves could be bent or warped, or it could be the tires being imperfect, or the bushings, or pick one or all of the above.

I would look to get a set of rims that fit which do not require those hub centric rings. I personally think this advice will resolve your issue. I've experienced that same thing with numerous other cars and aftermarket fancy rims/parts that fit your description to a T.

 

Maybe a nearby member would lend you their wheels for a test drive.

 

try swapping the rear wheels on the front if you want to potentially rule out the wheels as the issue,

 

I think with 20" non-stock wheels I would try to test the car with the correct staggered 18" wheels. Too many problems running 20" wheels for looks.

Just can't rule them out until you try different wheels.
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Spacers on wheels for cars like these Jags or any other high performance vehicles is a NO NO in general. A good friend of mine tore up a Corvette using spacers for some aftermarket cooler rims.

Like Tbird suggested, to baseline the vehicle, you'll need equipment that falls within normal parameters. 18's or 19's manufactured by Jaguar (Or Coventry or HRE or IForGED) to Jaguar Specifications are a sure hit and will not require spacers.

I believe, (based on experience), your root cause is most likely the wheels themselves. What rims do you have on the car? What MFR? What offsets? What tires do you have on the Car? What are their respective sizes including sidewall etc?