Thank you for your comments.
I tested and the pulsating grinding noise has no relations with braking. When it happens, during that few minutes, the noise is increased and decreased by the rotation of the steering wheel only. Going straight creates a dull pulsating noise. It starts a few seconds after the cold car starts moving and hits twenty mph. Speeding up over thirty five mph or slowing down under fifteen mph causes the noise to go away.
Steering counter-clockwise (left) increases the loudness and steering clockwise (right) decreases the loudness.
The pulsating grinding noise is similar to beetle larva eating wood type noise, there is about half-second interval between pulses.
People told me to re-rotate the tires again just in case it is bad cupped tire issue. It is zero degrees outside. I will either rotate it myself when it is a bit warmer outside or take the car to a tire store to have them rotate and update this thread.
Regarding the transmission fluid, eighteen months ago I removed three quarts and added 3.75 quarts of total of AT fluid because I thought the fluid level was low. I used Valvoline MaxLife Multi-Vehicle Automatic Transmission. According to Valvoline, it is compatible with SP-II, SP-III and SP-IV which is used by Hyundai. I checked the fluid level two months ago and found the AT fluid level was actually too high. I removed 1.75 quarts and added one quart new AT fluid two months ago. The fluid level was in between the lines on the dipstick two months ago and I don't have a AT fluid leak. The fluid is very dark brown. Experts told me the fluid gets dark after several months on Hyundai and that is Okay.
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Monday, December 25th, 2017 AT 12:16 PM