Abstract: This paper briefly introduces the working principle of DC torque motors and discusses in detail the characteristics of DC torque motors and their application in precision tracking radar servo systems. Keywords: radar, DC servo system , torque motors 1 Introduction To date, DC servo systems still dominate in precision tracking radars. Their actuators are either high-speed servo motors or torque motors. The choice of actuator depends primarily on the overall technical and tactical requirements of the radar system for the servo system. A precision tracking radar developed by the author is mainly used for measuring high-altitude satellite orbits and tracking low-altitude fast targets (range testing). The servo system in the radar is responsible for target angle acquisition and tracking. Based on target characteristics, the radar system places high demands on the servo system's speed range, low-speed performance, acceleration, and other performance indicators. For example, the working angular velocity ranges from 0.01 rpm to 50 rpm, and the working angular acceleration is 100 rpm. These indicators all exceed those of similar products we have previously developed. The selection and application of the actuator is a key aspect in achieving these requirements. 2. Brief Description of the Working Principle of a DC Torque Motor The working principle of a DC torque motor is the same as that of a DC servo motor. The torque formula of a DC servo motor is: The speed formula is: From the above formulas, it can be seen that by adopting a special structural design, namely a flat structure with a single-wave winding of winding branch a=1, a can be minimized, and the number of conductors N and pole pairs P can be increased, thus achieving low speed and high torque. Therefore, a DC torque motor is a low-speed, high-torque DC motor. It can operate for extended periods under stall conditions and can directly drive low-speed loads. It has advantages such as small speed and torque fluctuations, good linearity in regulation and mechanical characteristics, and is particularly suitable for high-precision position servo systems and low-speed control systems. [b]3 Characteristics of DC Torque Motors and Their Application in Precision Tracking Radar 3.1 Low-Speed ​​Performance[/b] To achieve the minimum speed requirement of 0.01 rpm, firstly, an actuator with good speed regulation performance must be selected. High-speed servo motors have a rated speed of several thousand revolutions per minute, poor low-speed performance, and cannot operate normally at low speeds, let alone under stall conditions. Their output torque is not very large; therefore, a reducer is needed to drive low-speed and high-torque loads. If the rated speed is 3000 rpm, and the antenna's maximum speed is 50 rpm (8.3 rpm), and the speed ratio i=374, to simultaneously meet the minimum speed requirement of 0.01 rpm, the motor's stable speed must be 0.6 rpm. Such low-speed performance requirements are difficult to achieve using a high-speed motor. The DC torque motor selected by the author has eighteen pairs of magnetic poles with a uniform magnetic field distribution. Therefore, even at low speeds with small signals, the rotational speed remains stable. The motor torque fluctuation is small, and the torque-current characteristic exhibits high linearity. Furthermore, the direct drive of the DC torque motor reduces frictional torque and eliminates backlash dead zones, all of which improve the linearity of the system characteristics, creating conditions for stable low-speed operation. Secondly, the static friction torque of the antenna mount rotating bearing must be strictly controlled within 5% of the motor's rated torque. This is because the ratio of static to dynamic friction torque of the antenna mount rotating bearing is a crucial factor affecting low-speed performance. In a radar I developed, the minimum required speed was 0.01 rpm, but actual testing showed a minimum speed of 0.02 rpm. It was later discovered that a significant reason was that the static friction torque exceeded twice the specified value (calculated as 34 kg·m based on the rated torque, but actual testing showed 80 kg·m). Therefore, measures are taken in the antenna mount structure design and assembly to control the static friction torque within 5% of the motor's rated torque, and the ratio of static to dynamic friction torque can reach 1.1 to 1.25. Secondly, a low-speed DC tachometer with high sensitivity is selected. The introduction of the tachometer enhances the damping of the circuit, overcomes the influence of viscous damping changes caused by motor speed variations on the system, and improves the linearity of the servo system. The low-speed DC tachometer has a multi-pole internal structure with sixteen pairs of magnetic poles. It has high sensitivity, good linearity, and a ripple voltage output of less than 1. The tachometer is coaxially mounted with the torque motor, and there is no backlash in the speed feedback circuit, so sufficient signal output can be obtained even at low speeds. This ensures that the system obtains good low-speed performance. By using a seventeen-bit axial angle encoder (resolution 10 arcseconds) and digital guidance from the radar computer, the minimum speed of the servo system is tested, reaching 0.01 [sup]. [/sup]／s. 3.2 Regarding Acceleration The overall radar acceleration requirement is a maximum angular acceleration of 100 [sup]. [sup]／s, precision angular acceleration 40[sup]. [sup]／s. Using a DC torque motor as the actuator has the following advantages in terms of speed: • High coupling stiffness. The rotor of the torque motor is directly mounted on the antenna mount shaft, and its stator is integrated with the antenna mount, eliminating the need for a transmission gearbox. This eliminates errors caused by backlash dead zones and elastic deformation, improving transmission accuracy; it also enhances mechanical coupling stiffness, increasing the resonant frequency of the entire transmission device's mechanical structure. • High torque-inertia ratio on the load shaft, resulting in fast response speed. As shown in Figure 1, if the reduction ratio (motor speed/load speed) is i, and the same electromagnetic torque and speed are required at the load, i.e., T[sub]L[/sub]=iT[sub]1[/sub]=T[sub]2[/sub], when indirectly driven, the system rotational inertia referred to the load shaft is i[sup]2[/sup]j[sub]1[/sub]+j[sub]L[/sub]. The theoretical acceleration of the system should be: For direct drive, the theoretical acceleration of the system should be: Generally, J2 is much smaller than i2j1, and in indirect drive, the reduced inertia of the reducer must also be added. Therefore, when using a torque motor, the torque-inertia ratio at the load is large, and the theoretical acceleration is large. Compared with a common servo motor with the same inertia, the electromechanical time constant is smaller. In addition, the torque motor is designed with multiple pole pairs and a high armature core magnetic flux density, resulting in very small inductance, and thus a very small electromagnetic time constant. Therefore, the speed in the transition process is very good. [align=center]Figure 1[/align] After selecting a torque motor with good speed performance, the following two points should be noted for system application: First, determine the appropriate motor torque according to the load conditions. The torque motor should have a sufficiently large driving torque to have acceleration capability. Usually, the torque motor parameters listed in the product catalog include: maximum no-load speed n. (r/mln), peak stall torque Tfd (N•m), continuous stall torque TLd (N•m), armature voltage Um during peak stall, and armature voltage U during continuous stall, etc., based on these parameters, the mechanical characteristic diagram of the motor can be determined as shown in Figure 2. From the target trajectory, calculate the angular velocity corresponding to the maximum angular acceleration, find the corresponding torque Td in Figure 2, and when it is in the figure, it indicates that the selection is qualified. Secondly, the speed loop bandwidth should be wide enough. A certain radar that I once developed has a precision acceleration requirement of 40sup/s. During open-loop testing, the angular acceleration is 40sup/s, indicating that the drive motor has this acceleration capability. However, after the speed loop is closed, the angular acceleration cannot reach 40sup/s, mainly because it is limited by the speed loop bandwidth. The bandwidth of the speed loop is often limited by the resonant frequency of the mechanical structure. Therefore, it is necessary to increase the natural frequency of the structure. This can be achieved by increasing the structural stiffness K and reducing the load inertia J. As can be seen from the characteristics of torque motors, using a torque motor can significantly increase the natural frequency of the structure. However, measures still need to be taken to reduce the load inertia to meet the system's requirements for the resonant frequency of the mechanical structure. 3.3 Wind Resistance Performance The biggest drawback of torque motors is their soft load characteristics; the output torque decreases as the motor speed increases. When the speed is below 6 rpm, the motor output torque is provided according to the rated torque; when the speed is above 6 rpm, the motor output torque is provided according to the torque at the corresponding speed. For every 1 rpm increase in average speed, the output torque decreases by 50 kg•m. When the motor speed is 8 rpm, the motor output torque is: 300 kg•m - 2 × 50 kg•m = 200 kg•m. At this point, if acceleration or exposure to sudden gusts of wind is required, the system error may increase. It is evident that torque motors have poor overload capacity, meaning they are poor at resisting instantaneous wind torque. Since torque motors are directly driven, wind torque acts directly on them, making them highly susceptible to its influence. In applications, improving the wind resistance of torque motor drive systems primarily involves enhancing the system's wind stiffness and reducing speed errors through the speed loop. Two measures can be taken: first, increasing the speed loop gain to reduce steady-state wind torque error; second, designing the speed loop as a Type I system to eliminate errors caused by gust torque. 4 Conclusion The radar servo system constructed using a DC torque motor has been successfully delivered to the user after several months of subsystem debugging and full radar system integration testing. The servo system design has been successful, and user testing has shown that all performance indicators have met or exceeded overall requirements. In particular, the superiority of the torque motor servo system is fully demonstrated in terms of acceleration, low-speed performance, and speed range. References 1 Zhao Wenchang, Hou Rongen, Zhou Hongyu. Automatic Control Components. Harbin: Harbin Shipbuilding Engineering Institute Press, 1986. 2 Mei Xiaoguan. Lan Pusen, Bai Guizhen. Automatic Control Components and Circuits. Harbin: Harbin Institute of Technology Press, 1993. Zhang Yanshen, Yuan Zengren. Design and Practice of Control Systems. Beijing: Tsinghua University Press, 1992. Application of DC Torque Motors in Precision Tracking Radar: PDF