Stepper motors are essential components in mechatronics systems, widely used for precise position control and constant speed regulation. These motors offer advantages such as low inertia, high positioning accuracy, no cumulative error, and straightforward control mechanisms. Their applications span across various electromechanical integration products like CNC machines, packaging equipment, computer peripherals, photocopiers, and fax machines. When selecting a stepper motor, it's crucial to ensure that the motor's output power exceeds the power required by the load. Calculating the load torque of the mechanical system is the first step, followed by verifying that the motor’s torque-frequency characteristics meet or exceed the load requirements with an appropriate safety margin. In practice, the load torque at different frequencies must remain within the motor's torque-frequency curve to guarantee stable operation. The step angle of the motor should be matched with the mechanical system to achieve the desired pulse equivalent. To reduce the pulse equivalent during transmission, you can adjust the screw lead or use a subdivision drive. However, subdivision only increases resolution without affecting the motor’s inherent accuracy, which is determined by its design. When choosing a power stepping motor, it's important to estimate the load inertia and the starting frequency required by the machine tool. The motor’s inertial frequency characteristics should be matched with a certain margin to ensure that the highest continuous operating speed meets the machine's fast movement needs. To select a suitable stepper motor, several calculations are necessary: 1. **Gear Reduction Ratio Calculation**: Based on the required pulse equivalent, the gear reduction ratio $ i $ can be calculated using the formula: $$ i = \frac{\phi \cdot S}{360 \cdot \Delta} $$ where $ \phi $ is the motor’s step angle (degrees per pulse), $ S $ is the screw pitch (in mm), and $ \Delta $ is the pulse equivalent (in mm/pulse). 2. **Inertia Calculation**: Calculate the total inertia $ J_t $ converted to the motor shaft, including the table, screw, and gears: $$ J_t = J_1 + \frac{1}{i^2} \left[ (J_2 + J_s) + \frac{W}{g} \left( \frac{S}{2\pi} \right)^2 \right] $$ where $ J_1 $ and $ J_2 $ are gear inertias, $ J_s $ is the screw inertia, $ W $ is the table weight (in N), and $ g $ is the gravitational acceleration. 3. **Total Motor Torque Calculation**: The total motor output torque $ M $ is the sum of acceleration torque $ Ma $, friction torque $ Mf $, and cutting force torque $ Mt $: $$ M = Ma + Mf + Mt $$ where $ Ma $ is calculated as: $$ Ma = (J_m + J_t) \cdot \frac{n}{T} \times 1.02 \times 10^{-2} $$ and $ Mf $ and $ Mt $ are derived from friction and cutting forces respectively. 4. **Load Start Frequency Estimation**: The start frequency of the CNC control system depends on both the load torque and inertia. An estimation formula is: $$ F_q = f_{q0} \left[ \frac{1 - \frac{M_f + M_t}{M_l}}{1 + \frac{J_t}{J_m}} \right]^{1/2} $$ If exact load parameters are unavailable, an approximate value of $ f_q = \frac{1}{2}f_{q0} $ can be used. 5. **Highest Frequency and Acceleration Time**: As motor torque decreases with increasing frequency, the maximum frequency must be chosen so that the motor has sufficient torque to handle the load. 6. **Load Torque and Maximum Static Torque**: Load torque can be calculated using the formulas for friction and cutting forces. At maximum feed speed, the motor’s output torque should exceed the sum of these torques with a safety margin. Typically, the sum of $ M_f $ and $ Mt $ should not exceed 0.2 to 0.4 times the motor’s maximum static torque $ M_{max} $.
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