天津工业大学2014届本科生毕业设计
III.TRAPEZOIDALVELOCITYCOMMANDGENERATIONBASEDONVA
RYINGINTERPOLATION DURATION
An interpolation algorithm in which reference trajectories are generated plays a key role to the performance of the feed drive systems. Generated trajectories must not only describe the desired tool path accurately, but must also smooth kinematical profiles in order to maintain high tracking accuracy. Due to the friction is relating to the feedrate of the servo system, which is strongly influence the performance of designing the controller and machine tools, a novel velocity generation based on the varying interpolation duration is presented.
The feed f is provided by the NC part program, and the minimum interpolation period Tmin is set within the CNC control software. The interpolation step size is calculated as LFT . The step size L is kept constant until Tmin or Fminis changed. When the feed is changed during machining by a feed-override switch or a sensor-based machining process control module, L is kept constant but the interpolation time Ti is updated as [7]
Assuming that the total displacement along an arbitrary path is L, the interpolation task is executed N times at interpolation time intervals of Ti,
N is always rounded to the next higher even integer for computational efficiency. The total number of iterations (N) is divided into a number of stages depending on the type of velocity profile used for trajectory generation. For simplicity, a trapezoidal velocity profile for acceleration and deceleration is presented in this paper, which is simple to implement, computationally advantageous.
The total number of interpolation steps (N) is divided into acceleration (N1), constant velocity (N2) and deceleration (N3) zones shown in Fig. 5, that is. If the 123 initial feed is f0, the tool path length (l1) traveled during the acceleration period is
which leads to
Similarly, if the system decelerates from feed F to fe, thenumber of interpolation periods during deceleration:
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天津工业大学2014届本科生毕业设计
where A is acceleration and D deceleration. The counters N,N1,N2,and N3 are rounded integers. If the desired feed is not reached because of a short tool path, that is N2<0, then N2=0,N1=N3=N/2, assuming A=D.
Since the traveled tool path segment L is kept constant, the following expression can be written between interpolation periods:
By substitutingTk() t t ,t fk()/At, fk( 1)/A, the ikkk 11kinterpolation period during acceleration and deceleration where the velocity changes is found at each increment as
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