If the oil leakage is found on it, replace the steering damper with a new one (see Steering Damper Removal/ Installation in the Steering chapter).

ZX1000JD/KD [B]

Steering Stem Bearing LubricationPiston Wear Inspection
Measure the outside diameter [A] of each piston 5 mm
(0.20 in.) [B] up from the bottom of the piston at a right
angle to the direction of the piston pin.
If the measurement is under service limit, replace the piston.
Piston Diameter
Standard: 75.959 75.974 mm
(2.9905 2.9911 in.)
...
How Do I Get Warranty Service?
If there is a problem with your vehicle within the limited warranty period,
you will
need to schedule a service appointment and provide any maintenance records to
an authorized Kawasaki dealer for inspection and diagnosis. You can go to any
Kawasaki dealer for warranty repairs. Your Kawasaki de ...
Technical Information - Electronic Steering Damper (ESD/ZX1000JD/KD models)
1) Overview
This model has an Electronic Steering Damper (ESD)
[A]. Unlike conventional manual adjustment method of
Kawasaki, damping characteristics are adjusted by the
electronic control unit.
2) Purpose
Designed to offer increased stability at high speed without interfering with
light ...