The multi-axis linear interpolation and its acceleration and deceleration algorithms are fundamental to high-end numerical control (NC) systems. These techniques ensure smooth and precise motion control, which is crucial for advanced manufacturing applications. Acceleration and deceleration processes are typically divided into two main stages: pre-acceleration/deceleration and post-acceleration/deceleration.
Pre-acceleration and deceleration occur before the actual interpolation process. This method allows for better control of the synthesized speed and ensures that position accuracy is not compromised. However, it requires accurate prediction of the deceleration point. Typically, this stage involves linear acceleration and deceleration. In contrast, post-acceleration and deceleration involve individual axis control, which can lead to inaccuracies in the overall path due to lack of coordination between axes. To address this, S-curve acceleration and deceleration are commonly used in post-processing, as they provide smoother transitions and reduce mechanical stress.
When developing a multi-axis fiber winding machine based on an open CNC system, we applied pre-acceleration and deceleration using S-curve planning, achieving excellent results in terms of precision and performance.
In multi-axis linear interpolation, S-curve acceleration and deceleration involve controlling the jerk (the rate of change of acceleration) to be constant during acceleration and deceleration phases. This approach minimizes mechanical shocks and enhances system stability. By adjusting parameters such as acceleration and jerk, the system can adapt to different machine tool conditions, offering greater flexibility in motion control.
In an n-dimensional linear interpolation NC program, each interpolation segment is represented as |P1, P2, ..., Pn, F|, where F is the synthesized speed and Pi represents the displacement of each axis. According to the principle of linear interpolation, the velocity ratio of each axis is proportional to their respective displacements. This leads to the calculation of sub-velocities for each axis, ensuring synchronized motion across all axes.
An S-curve acceleration and deceleration plan divides the motion into several zones, including acceleration, constant velocity, and deceleration sections. Each section has specific acceleration and jerk values, allowing for smooth transitions between different motion states. The motion parameters of each axis are derived from the planned synthesized velocity, ensuring consistent and controlled movement.
The recurrence formulas for S-curve acceleration and deceleration interpolation allow for efficient computation of displacement increments during each interpolation cycle. These formulas take into account the time intervals, acceleration, and jerk values, enabling real-time adjustments and maintaining synchronization across all axes.
During the interpolation process, the algorithm checks the velocity, acceleration, and jerk limits for each axis, ensuring safe and stable operation. The displacement increments for each axis are calculated based on the proportionality factor derived from the synthesized displacement.
This approach is particularly useful in applications where precise motion control is required, such as in fiber winding machines or other high-precision CNC systems. The algorithm's simplicity and adaptability make it suitable for various types of machine tools, enhancing their performance and reliability.
Overall, the S-curve acceleration and deceleration method provides a robust solution for multi-axis interpolation, improving both efficiency and accuracy in modern CNC systems.
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