Abstract : Taking the servo actuation system of a certain type of aircraft as the research object, this paper analyzes the nonlinear factors affecting its phase characteristics under low-frequency load conditions. Through theoretical analysis and engineering verification, it is concluded that the phase characteristics can be effectively improved by controlling the transmission clearance and reducing the friction torque. This provides theoretical support for the optimization design and performance prediction of the aircraft control system and has high engineering application value.
0 Introduction
Servo mechanisms are the actuators in an aircraft control system. Their function is to control the thrust vector or aerodynamics of the aircraft's engines, control surfaces, or ailerons based on command signals of different amplitudes and polarities input from the control system, thereby achieving stable attitude and directional control. Electro-hydraulic servo mechanisms generally consist of a servo power source and a servo actuator. An ideal aircraft servo actuation system has characteristics such as high structural resonant frequency, low load rotational inertia, small transmission backlash, high transmission accuracy, and high transmission efficiency. In short, it achieves the best dynamic performance and the highest reliability with the simplest structure and the lightest weight.
The phase characteristics of a servo actuation system directly reflect its dynamic characteristics. Determining its key links and sensitive parameters is of great significance for optimizing the design and improving motion accuracy [1]. Taking the engineering application of a servo mechanism配套 with a certain type of aircraft rudder system as an opportunity, this paper analyzes the influence of nonlinear factors on the phase characteristics of the servo actuation system under low-frequency load conditions, and verifies the effectiveness of improving phase characteristics by controlling transmission clearance and reducing friction torque.
1. Servo Mechanism Phase Characteristics
The aircraft's rudder system consists of a servo mechanism and a rudder shaft, as shown in Figure 1. The mathematical model is shown in Figure 2. The servo mechanism is amplified by the servo controller after comparing the command signal input from the control system with the feedback signal output from the feedback potentiometer. This amplifies the signal, drives the servo valve core to move, and converts it into hydraulic pressure to drive the actuator to perform piston-like action. A linear displacement sensor located inside the servo actuator and parallel to the piston's direction of motion is used to realize the closed-loop position control of the servo mechanism. The rudder shaft consists of a rudder surface, rudder shaft, rocker arm, transmission bracket, and support housing. The rocker arm at the end of the transmission chain is fixed to the shaft by a connecting pin and is linked to the servo actuation system, i.e., the external load [2].
Figure 1. Composition diagram of the rudder system
Figure 2. Simplified mathematical model of the rudder system
It should be noted that the control loop actually only controls the servo part. There is a difference between the angle actually reached by the control surface and the angle controlled and realized by the servo. The stiffness and damping of the components such as "rotating shaft + rocker arm + control surface" are simplified by the second-order element in the mathematical model, and are actually expressed as resonant frequency and damping ratio.
The phase characteristics of the servo actuation system are measured by an angular displacement sensor coaxial with the rotating shaft, which is also a traditional method of phase measurement [3]. By inputting a sinusoidal command signal with equal amplitude and equal number of cycles from low frequency to high frequency to the servo, the angle is measured, which is the phase characteristic of the system. The angular displacement sensor does not participate in the control loop. At the same time, the phase characteristics of the no-load part are obtained from the measured linear displacement data participating in the control, and the curve is shown in Figure 3. Among them, the pink curve is the resonance characteristic, the black curve is the linear displacement characteristic, and the red curve is the angular displacement characteristic.
Figure 3 Load characteristic curve
2. Nonlinear factors affecting transmission performance
Based on the structural characteristics of servo actuation systems and combined with engineering experience and literature, the following nonlinear influencing factors are analyzed.
2.1 Frictional Torque
The nonlinear characteristics caused by the static friction torque of the rotating shaft or other relatively moving parts exceeding the dynamic friction torque have the following impacts on performance: increased phase lag, affecting low-speed tracking angular velocity, increased tracking error, and affected cutoff frequency. It also distorts the system's position tracking curve, exhibiting dead-zone characteristics in the input-output signal relationship. Ideally, servo actuation should reduce friction torque while meeting stability margins.
2.2 Transmission clearance
Transmission clearance is a common nonlinear factor affecting transmission performance. Due to limitations in machining accuracy and assembly process, clearance between moving parts in a servo actuation system cannot be avoided. Its impact on performance includes: increased phase lag, decreased positioning accuracy, decreased system stability, and potential self-oscillation static error [5]. Ideally, servo actuation should reduce transmission clearance while satisfying motion lubrication requirements.
3. Simulation and Analysis
Ignoring the influence of the servo loop, the phase lag of the first-order torsion of the rudder system can be expressed as:
(1)
In the formula, f is the operating frequency of the rudder system, and fc is the first-order torsional natural frequency of the rudder system (the first-order torsional natural frequency reflects the stiffness of the system).
The relationship between the first-order torsional natural frequency and phase characteristics can be obtained through simulation based on the simplified mathematical model, as shown in Figure 4. The low-frequency phase lag of the rudder system under ideal conditions with no backlash is extremely small [6]. It can be seen that transmission backlash and friction torque play a key role.
Figure 4. Relationship between torsional frequency and phase hysteresis curve
The rudder system structure of this type of aircraft is shown in Figure 5. The upper support lug of the servo actuator is connected to the bulkhead via a pin, and the lower support lug is connected to the rotating shaft via a pin. Based on literature, engineering experience, and performance data, the dimensions and tolerances of the upper mounting hole are designed as follows: [details omitted]. The dimensions and tolerances of the upper rudder pin are designed as follows: [details omitted]. The dimensions and tolerances of the lower rudder pin are designed as follows: [details omitted].
Figure 5. Steering system structure diagram
Excessive backlash directly affects the system's response speed. When the servo actuator receives a command signal, it performs a piston-like extension and retraction action according to the command, causing the rudder shaft to swing. When there is excessive backlash, the backlash must be eliminated before the rudder shaft swings, a process that will cause a partial lag in the phase response.
If the transmission clearance is too small, the frictional torque will increase accordingly. Although a certain frictional torque will provide stability to the system, the process of overcoming friction before the servo actuation system makes the rudder shaft swing will also cause a partial lag in the phase response.
The impact of clearance on the rudder system can be indirectly measured by the angular displacement loop width, which is obtained through position characteristic testing. The testing method involves inputting two sinusoidal signals with a period of 50 seconds and the largest amplitude, and obtaining the loop width value by comparing the input and output relationship curves. In the figure, points A and C indicate that the output signal follows the input signal only after overcoming the effect of clearance, while points B and D indicate that the output signal immediately reverses due to clearance, as shown in Figure 6.
Figure 6 Comparison curves of input and output signals
3.3 Analysis of the Influence of Friction on Low-Frequency Phase
For the entire rudder system, the frictional torque can be divided into two parts: the friction of the rudder shaft and the friction of the servo mechanism. The friction of the servo mechanism is mainly the friction at the actuator rod [7]. The frictional torque of the rudder system can be indirectly determined by the differential pressure loop width in the position characteristic test.
The relationship between the frictional torque width and the pressure difference is:
In the formula, k is the conversion factor; is the differential pressure loop width, which can be calculated from the test curve (Figure 7); As is the nominal effective area of the piston; and Rmax is the maximum force arm of the actuator.
Figure 7. Calculation diagram of differential pressure loop width
The differential pressure loop width measured by the servo mechanism under no-load conditions can be used to determine the frictional torque of the servo mechanism itself. The differential pressure loop width measured by the servo mechanism under load conditions of the air rudder system is the sum of the frictional torque of the servo mechanism itself and the frictional torque of the rudder shaft. In other words, the frictional torque of the rudder shaft can be obtained by subtracting the two types of frictional torques.
4 Comparison Experiment
Four servo mechanisms were installed in four workstations (quadrants) respectively, and position characteristic tests were performed in no-load/load conditions to measure the angular displacement loop width and differential pressure loop width . The phase lag was measured by the flatness characteristic test at a rudder deflection of 1.0° and an angular frequency of 2 rad/s, as shown in Table 1.
The phase lag of the servo mechanism with angular frequency in the low-frequency range was tested under the condition that the friction torque is 11 Nm and the rudder deflection is 1.0° . The results are shown in Figure 8.
The calculation shows that the phase lag is of the same magnitude as the actual phase lag and the overall trend is consistent. The phase lag test results of the rudder system in each state have a large dispersion. The phase lag test results of the same servo mechanism will also differ due to the difference in the amount of clearance. However, the smaller the clearance, the smaller the phase lag angle. Under the same clearance, the larger the friction torque, the more severe the phase lag [8].
The low-frequency phase lag of linear displacement is consistent and small, and the frictional torque of the servo mechanism is consistent and small. That is, the main factors affecting the phase lag of the rudder system are not in the servo mechanism (including the connection joint between the actuator and the rocker arm, the servo mechanism itself, the servo circuit, etc.). The frictional torque of the rudder system is directly related to the low-frequency phase lag of angular displacement, and the degree is corresponding.
Table 1. Servo Actuator No-load and Load Test Results
Figure 8 shows the relationship between phase lag angle and frequency.
5. Improvement Plan and Verification
To facilitate the analysis of its influence on phase lag, a second-order linear element is used to convert the nonlinearity into linearity between linear displacement and angular displacement, and a simulation model is established [9].
Figure 9 Simulation model of the transfer link
Where ωL is the undamped resonant frequency, which is the structural resonant frequency of this type of rudder system, i.e., 500 rad/s, and is the damping ratio, i.e., the friction force.
Given a sinusoidal wave with input ω = 2 rad/s, output waveforms with different hysteresis angles are obtained by adjusting the damping ratio. The data shows that the damping ratio can be expressed as a linear relationship:
In the formula, θ is the angle difference between the linear displacement and the angular displacement that lags behind the linear displacement.
Therefore, measures to improve low-frequency phase lag mainly focus on controlling the rudder shaft fit clearance and reducing the frictional torque of the rudder shaft. To verify the effectiveness of the measures, the same rudder system was disassembled, reassembled, and retested twice. The local structure of the shaft is shown in Figure 10 below.
Figure 10 Partial structural diagram of the rudder shaft
When disassembling and reassembling the rudder shaft, leave a 0.3mm compression allowance when installing the sealing packing ring and sealing ring. Use a special tool to firmly tap the packing ring and sealing ring, and then tighten the cap into place. At this point, turning the rocker arm is relatively difficult . Then, select a sealing gasket according to the 0.3mm compression allowance and place it under the heat shield. At this point, the graphite gasket is prone to slight wrinkles, making it difficult for the rudder to turn. The frictional torque and low-frequency phase lag measured under this condition are shown in Table 2 below.
The rudder was disassembled and reassembled. This time, when installing the sealing packing ring and sealing ring, no compression was allowed, and no special tooling was used to firmly tighten the packing ring and sealing ring. At this point, the rocker arm rotated more freely . Then, a sealing gasket was selected with a compression of 0.3 mm, placed under the heat shield, and the rudder shaft was inserted into place. The tapered pin was not locked, and the rudder rotation was more difficult at this point. Subsequently, one sealing gasket was removed, and the rudder still rotated freely. The frictional torque and low-frequency phase lag measured under these conditions are shown in Table 2 below.
Table 2 Data before and after the modal test chamber repair
The above experiments show that the phase lag of the rudder system is sensitive to friction control during the assembly process. Increasing the friction torque of the rudder system will significantly aggravate the phase lag. Appropriately reducing the sealing gasket during rudder shaft installation, increasing its fitting clearance, and studying and optimizing assembly process parameters such as sealing gaskets can effectively improve the problem of low-frequency phase lag while ensuring system stability.
6. Conclusion
Low-frequency phase lag is a common problem in servo mechanism applications. Besides commonly used methods such as dynamic pressure feedback adjustment and adding filters, the impact of nonlinear load factors on the system should be fully considered. This paper verifies the correctness of the analysis method for the low-frequency phase lag problem presented. Further research can address the nonlinear dynamics of similar structures by adjusting the rudder shaft clearance and reducing frictional torque. Optimizing assembly process parameters such as sealing gaskets will further improve the overall performance and control accuracy of the air rudder system.
