Air carrier flight crew reported a brake malfunction causing the aircraft to abruptly yaw to the right and skid to a stop while taxing to the gate.
Synopsis
Air carrier flight crew reported a brake malfunction causing the aircraft to abruptly yaw to the right and skid to a stop while taxing to the gate.
Narrative
After a normal landing utilizing normal light braking after landing. We respected the required cool down time before I called for the shut down of the #2 engine for a single engine taxi to the gate.As soon as the First Officer (FO) placed the master switch to off we heard the normal click of the generator then experienced a sudden violent and continued yaw to the right. I used left tiller and left brake to to stay on the taxi way and the airplane came to an abrupt stop. Ground controllers called and ask if we were OK and if we needed assistance. They later told me they observed the airplane yaw hard and smoke billow from under the airplane. (Assuming from sliding tires)After we stopped I released all manual brake pressure in an urge to return to center-line and the airplane did not move. I set the parking brake. Resetting the A/SKID / N/W STRG switch and then releasing the parking brake and the aircraft began to roll with noticeable thumping of flat spots during taxi in.Maintenance was called and jacked up the right side and spun the tires; finding both mains with relatively new tires significantly flat spotted. #3 brake was found dragging and maintenance mentioned deferring it for 5 landings. I communicated that it's a solution that doesn't address the fact that #4 tire was also flat spotted. After several more hours Maintenance deactivated the #3 brake completely and proffered a ferry flight to ZZZ1. A solution that again doesn't address why the #4 tire was flat spotted.After 5+ hours on the ground and at XA:00 I received an unsolicited call from the flight manager. The flight manager mentioned his [decades long career] and how hard it would be for the company to address fixing the airplane in ZZZ.My safety concerns can be divided into three main areas of concern:If this airplane goes back in service without a concrete reason or problem that can be mitigated. What if a generator trips for an unrelated reason? What should be a flicker of screens at V1 could instead be a violent uncontrolled total lockup of two main tires. Previously we carefully controlled the moment of power transfer; is this un-commanded and uncontrolled application of brakes a specific failure mode of a component? Should we be trained to expect this as a possibility on power transfers? This certainly will factor into my decision whether or not to single engine taxi. If the problem happened on taxi out with the flight attendants up doing a demonstration my in-flight team could have been gravely hurt.Maintenance repeatedly ignoring the inconvenient fact that both #3 AND #4 were involved as indicated by the continual work on #3 while ignoring the evidence of #4s involvement. The nature of a complete and total lockup of both main tires and inability of the airplane to roll forward until the A/S NWS (Nose Wheel Steering) reset indicated that the physical components of the wheel Assembly/brakes worked fine. A reset of that switch clearly points to a brake valve or other electronic component that would be reset or changed by the movement of that switch. Fishing for a ferry-able solution in the face of un-ferry-able reality is a setup for tragedy. As the timeline between indoc. and upgrading to narrow body Captain becomes shorter; are we expecting relatively new and inexperienced Captains to be a backstop against a poor decision to ferry without a real diagnosis?My most pressing concern is reserved for the usage of the flight manager as a lever to push an unsafe solution. He specifically mentioned that ZZZ was a challenging place to work on an airplane and it would be advantageous to have the airplane at a maintenance base.In it's most mild interpretation it could be considered an incredibly stupid thing to say from someone with manager in the title to a safety sensitive employee evaluating a safety decision. The economic inconvenience of where an airplane is should have no weight on the evaluation of it's safety to operate. A Captain should know better. In a more malicious interpretation and what I believe is closer to the truth: this is a clear case of 'pilot pushing.' The fact that maintenance skipped right over calling me and instead had the flight manager call made the intention crystal clear. When I call a flight manager I get help. When they call me it's to push. Continued tolerance for this behavior from someone not legally responsible for a flight will have future unintended consequences. As our indoctrination; mentoring and education period before upgrade shortens; a flight manager applying pressure might get what they wish for: The ability to influence a safety decision....not with new and pertinent operational information but with inappropriate consideration of a number on a balance sheet with possible tragic results.
Second reporter narrative
During taxiing in and cool-down requirements are met. After shutting down engine 2; we felt a large yaw to the right while taxiing in a straight line. It is unclear what caused the yaw. ATC asked if we required any assistance; which we declined as we continued to taxi to the gate with no issues.
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Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.