The present enhanced hair straightening system is directed to enhancing the removal of natural curl from hair having a visibly wavy to tight curly configuration using methods and compositions that provide straightened hair which retains desirable sensory tactile properties and hair sheen. Embodiments further provide for the continuity of experience for devices operating under multiple processors or multiple platforms. With this structure, concentration of stress on the radial direction oil passage can be avoided, and therefore strength of the pulley shaft can be secured. Accordingly, it becomes possible to maintain the performance described above with good accuracy in accordance with the prediction results and also optimize the implementation timing of maintenance and the like.