There are several methods for braking a hydrogenerator, depending on the type and size of unit. mountk2 has described a very common method for vertically-mounted units, but that design doesn't work well on horizontal units.
All of the hydro units in my system have integral disc brakes. The rotor is installed on the generator shaft near the turbine coupling. Smaller units (<5MW) have one brake caliper. Larger units may have up to 4 calipers. All use high pressure hydraulics to operate the brake.
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Experience: The knowledge you gain just AFTER you needed it.
The disc is mounted on the generator shaft. The caliper is a 2-piece U-shaped steel frame containing a cylinder and brake pads. It is mounted so the disc passes through the open end of the U. When hydraulic pressure is applied to the cylinder, the piston causes the caliper to squeeze the pads against the disc.
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Experience: The knowledge you gain just AFTER you needed it.