Recently, superconductor flywheel energy storage systems (SFESs) have been developed for application to a regenerative power of train, a power quality improvement, the storage of distributed power sources such as solar and wind power, and a load leveling. As the high temperature superconductor (HTS) bearings offer dynamic stability without the use of active control, accurate analysis of the HTS bearing is very important for application to SFESs. Mechanical property of a HTS bearing is the main index for evaluating the capacity of an HTS bearing and is determined by the interaction between the HTS bulks and the permanent magnet (PM) rotor. HTS bearing rotor consists of PM and iron collector and the proper dimension design of them is very important to determine a supporting characteristics. In this study, we have optimized a rotor magnet array, which depends on the limited bulk size and performed various dimension layouts for thickness of the pole pitch and iron collector. HTS bearing rotor was installed into a single axis universal test machine for a stiffness test. A hydraulic pump was used to control the amplitude and frequency of the rotor vibration. As a result, the stiffness result showed a large difference more than 30 % according to the thickness of permanent magnet and iron collector. This is closely related to the bulk stiffness controlled by flux pining area, which is limited by the total bulk dimension. Finally, the optimized HTS bearing rotor was installed into a flywheel system for a dynamic stability test. We discussed the dynamic properties of the superconductor bearing rotor and these results can be used for the optimal design of HTS bearings of the 10kWh SFESs.