# Variable Guide Vane Scheduling Method Based on the Kinematic Model and Dual Schedule Curves
## 1 Introduction  
Aerodynamic stability should be assured for the compressor of an aircraft gas-turbine engine, not only at the operating design point, but also at off-design points, due to its wide operating range with frequent acceleration and deceleration. Any mismatch in the angles of inlet air-flow of the compressor and stator vane leads to flow separation and reduces the effective air-flow area. Moreover, aerodynamic instability such as surge or stall might appear, and these could lead to severe structural damage to the engine. Variable guide vanes (VGVs) are therefore generally utilized to obtain stability of the compressor over a wide operating range and the stator vanes of VGVs change their angles according to the inlet air-flow, which varies with the engine RPM [1, 2]. In the case of a centrifugal type compressor, inlet guide vanes (IGV) in front of the impeller and radial gap between impeller blade tip and diffuser leading edge are manipulated by using actuators and variable geometries [3, 4, 5, 6]. In the case of axial type compressors, comparatively large numbers of vanes and multiple vane stages are needed. Thus unique actuation link mechanism is required to manipulate multiple vane stages, simultaneously [7, 8, 9]. The actuation link mechanism generally consists of actuators, links, a unison ring, lever arms, and vanes. The unison ring is connected to links, and rotates vanes about the rotational axis of the vanes via lever arms (shown in Figure 1). The links positioned between the actuators and unison-ring, transform linear extensional and compressional motion of the actuators into the rotational motionof the unison ring. There are a variety of link structures according to engine size, actuator type, and operational range of the vanes. Thus, analysis of the link mechanisms should be performed to define the actuator requirements: such as stroke or load capacity, and the precise vane and actuator control logic should be also needed to obtain exact angles of vanes according to VGV schedule. However, most of studies focused on the effect of the misaligned vane angle on the compressor performance and the fault diagnosis of the compressor [10; 11; 12; 13; 14]. Compared to that, precise control and compensation methods for mechanical drifting or hysteresis of the VGVs link mechanisms have still been rarely studied. Due to the limitations of previous references, this study was performed to obtain solutions for precise VGV control. Link mechanisms are usually designed with redundancy degrees of freedoms (DOFs) in three-dimensional space to produce well, the rotational motion of lever arms from the linear motion of actuators. With this redundancy DOF, manufacturing tolerance, wearing of actuation link mechanism, and loosening of bolts cause drifting from the vane schedule and hysteresis between the actuator strokes and vane angles [10; 12]. To compensate this hysteresis additional mechanical compensations are needed to the VGV link mechanisms such as pre-loading springs or flexible bushings. However, they produce unpredictable friction forces and need a complicated design [15]. In this research, we dealt with a rig-type multiple-stages VGV system which was developed for testing gas-turbine engines. This VGV system has unique link mechanism with three stages of VGV and two hydraulic actuators. For easy instrumentation, it has long vertical link as shown in Figure 1, thus we should investigate the VGV link mechanism to reduce its mechanical hysteresis. Actuator stroke schedule should be presented with considering its coupling linkage motions between two actuators and three stages of VGV. In this respect, we propose novel and simple solution to adjust links and to reduce the hysteresis by analyzing link mechanism and by modifying only control software without mechanical compensations. In Section 2, the link mechanisms of the newly developed VGV system are described, and their coupled kinematics and inevitable hysteresis of the links are explained.