The first thing is to drive carefully to a tire and alignment shop to have the steering and suspension systems inspected. Vibrations and shaking are caused by something that is rotating, in this case the parts you already replaced. They can still cause minor shaking that would go unnoticed except when suspension parts are worn, and Ford has had a lot more trouble with that, especially on their front-whee-drive vehicles, than all other manufacturers combined. In particular, the ball joints, tie rod ends, and control arm bushings are the best suspects.
What were the comments about this from the people who worked on the car? If a mechanic test-drove it, he must have noticed your complaint wasn't solved.
Every once in a while someone doesn't recognize the vibration caused by anti-lock brakes, especially when they develop a "false activation" problem where they activate and pulse the brakes when that isn't needed. This happens more often at lower speeds.
Some of the less-common causes include grease or other contaminants getting on the brake rotors. That can even include greasy fingerprints from handling the new rotors improperly. Those rotors can be left in service as long as all the grease is washed off before they go through a warm-up cycle. At the first drive cycle, the grease will soak into the porous linings and cast iron rotors, then they must be replaced again to solve that pulsing.
There's also things we can do to accidentally cause that shaking. When we machine old rotors for reuse, if they aren't mounted on the brake lathe correctly, they can wobble, then we'll machine that corresponding wobble into them. That can be identified by removing the wheel, reinstalling the lug nuts, then using a dial indicator to measure "lateral run out".
Related to that lateral run out, it can also be caused by a chip of scale or debris becoming lodged between the rotor and hub. In that case it will also cause the wheel to wobble. That can be identified by running the dial indicator along the outer lip of the wheel.
A less-known but real common cause involves two things, either by themselves, but more so together. One is caused by using Chinese rotors. There is nothing wrong with their quality, but when we make parts out of cast iron, we set them aside for 90 days to "age" before they get their final machining. When the Chinese make them, they cast 'em, machine 'em, pack 'em, ship 'em, and then they age on your car. It is real common for them to warp within the first month or two, but it's important to understand when the owner angrily demands new rotors under warranty, he is likely going to have the same problem with the replacements. The proper fix is take a light cut on the brake lathe to true-up the rotors, then that problem is very unlikely to occur again.
The second part of that issue with Chinese rotors can affect any rotor, new or used, regardless where it was made. That has to do with tightening the lug nuts. They must be tightened with a click-type torque wrench to specifications. That insures the clamping forces will be equal all the way around, the threads won't be peeled, or damaged, the nuts won't work loose, and a small person can get them off to change a flat tire.
When lug nuts are tightened without the torque wrench, or with air tools, the rotor will be clamped too tightly or unevenly. The heating and cooling cycles will lead to them warping, and that can occur faster when a hot rotor is splashed with water. The need for the torque wrench became well-known by the late 1980's, but there are still a lot of do-it-yourselfers and untrained mechanics who don't understand that need.
You can find more information in this article too:
https://www.2carpros.com/articles/steering-wheel-shakes-when-accelerating-or-braking
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Saturday, January 18th, 2020 AT 1:25 PM