## 2 Modeling of the Dynamic System  
Figure 1 shows the main structure and components of the yaw system. The conventional medium-sized yaw system was configured and installed with only two yaw drive lead motors that were fixed to the initiative (active) driving unit. The two yaw drive auxiliary motors were specially configured and installed in the present study, which were embedded in the passively driven unit and located between two active motors, as displayed in Figure 1a,b. Figure 1b is the engineering schematic diagram with the auxiliary motor  
embedded in the driven second unit. The first unit includes the rack and its ancillary equipment as well as the engine compartment, while the driven second unit only includes the engine compartment and its sealing components [28]. Figure 1: The main structure and components of the yaw system: (**a**) structural design for the dual-motor system; (**b**) engineering schematic diagram with the auxiliary motor embedded in the driven second unit; (**c**) CLS schematic diagram. In the conventional yaw motion system, the yaw system controller sends a command signal, the two lead motors start synchronously, the yaw gear ring is fixed, and the yaw motors drive the yaw reduction gearbox to drive the main frame and engine room to slowly rotate around the yaw gear ring that is fixed to the tower flange with high-strength bolts. Due to the high mass of parts in the engine room, the yaw speed is extremely low. The yaw action of the megawatt wind turbine is characterized by the typical features of low speed, large load, and friction braking, which lead to LSJ vibrations due to the obvious, uneven speed during the operation, especially when the yaw is initiated and yaw brakes are applied. When the wind speed and direction change dramatically, the LSJ vibration is particularly severe. The LSJ vibration in the yaw system using sliding bearings comes from the crawling phenomenon between the yaw sliding pad (cushion) and the gear ring due to poor lubrication. Therefore, a centralized lubrication system (CLS) was designed in the present study, which was a controlled system that could perform dynamic lubrication. The working process and highlight points of the auxiliary motors were as follows:  
* A CLS schematic diagram was designed (Figure 1c), which was parallel to the auxiliary motor and driven by the same frequency converter. The output voltage of the frequency converter was 220V-690 VAC. The CLS used a complete set of oil supply devices, which could supply oil to multiple lubrication points [29]. It was divided into progressive lubrication systems and single-line lubrication systems. A progressive system generally consists of four basic components: an electric lubrication pump, progressive distributors, pipeline components, and a control system. The single-line lubrication system can be regarded as a safety redundant structure of the progressive lubrication system. The amount of dynamic fuel supply was directly proportional to the voltage of the frequency converter, which also caused dynamic changes in the dynamic friction coefficient. * There were lubricating oil holes on the surface of the sliding pad, which were injected by the lubrication system. Associate the driving voltage of electric lubrication pump with the driving voltage of the frequency converter of the auxiliary motor, and the two are direct proportion to each other. When the wind speed and direction changed dramatically, the proportion coefficient could take a larger value. When the driving voltage of the auxiliary motor was high, it meant an increase in the frictional resistance and an intensification of the LSJ vibration. At this time, an equal proportion of the driving voltage was applied to the electric pump, promoting a more lubricant injection to keep the sliding pad running smoothly and reduce the wear. * During the yaw start phase, the electric lubrication pump was also activated, causing the amount of lubrication received by the sliding cushion to vary with the driving voltage of the auxiliary motor.