In an electric servo system, the reducer plays a crucial role, and its performance significantly affects the overall system. One of the key factors to consider is the selection of the total gear ratio. This choice directly impacts the system's efficiency, response time, and accuracy. The general principle for selecting the gear ratio involves several important considerations. First, it's essential to minimize the moment of inertia of the reducer when converted to the motor shaft. This helps in reducing energy loss and improving system responsiveness. Second, minimizing transmission gaps or errors caused by the reducer ensures smoother operation and higher precision. Finally, the goal is to maximize the acceleration of the motor-driven load. For applications like missile control systems, where rapid response is critical, the gear ratio should be chosen based on the principle of maximum acceleration. When designing for maximum load acceleration, we consider both inertial and frictional forces. Suppose the load has a moment of inertia JL and a frictional torque Mf, while the motor has a rotor inertia Jm and a gear ratio i. The torque balance equation, when converted to the load shaft, becomes: iMm - Mf = (i²Jm + JL) * ωL, where Mm is the motor torque and ωL is the load angular acceleration. By solving this equation, we can determine the optimal gear ratio that maximizes acceleration. If the frictional torque Mf is zero, the formula simplifies to i = √(JL/Jm), which is widely used in practice. This means that the motor’s inertia, when reflected to the load side, matches the load’s inertia, resulting in optimal performance. However, when there is a constant load torque, the gear ratio must be increased to accommodate the additional force. This adjustment ensures that the motor can effectively drive the load under varying conditions. Therefore, during design, the gear ratio should be carefully adjusted based on the actual load characteristics. When the initial speed is not zero, such as in missile maneuvering scenarios, the steering gear must handle two types of control signals: low-frequency, high-amplitude commands from the seeker and high-frequency, small-amplitude signals from the autopilot. These signals are superimposed, leading to non-zero load speeds and hinge moments. In such cases, the gear ratio must be optimized to account for these dynamic conditions. Under non-zero load speeds, the motor’s output torque follows its linear mechanical characteristics, accounting for inertia, viscosity, and constant friction. The force balance equation becomes: i(Mo - Bm * i * ωL) = (i²Jm + JL) * ωL + BL * ωL + ML, where Mo is the motor output, Bm is the motor viscous coefficient, BL is the load viscous coefficient, and ML is the constant load moment. Solving for the optimal gear ratio under these conditions leads to a more complex formula that accounts for multiple variables. When ML = 0 and ωL = 0, the formula reduces to the simpler version seen earlier. However, when loads and initial velocities are present, the gear ratio must be adjusted accordingly. Through normalization and analysis, it becomes clear that the optimal gear ratio increases with the magnitude of the load and angular acceleration. In real-world applications, engineers often choose an intermediate value within the expected range of these parameters to ensure reliable and efficient performance.
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