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Explanation of Acceleration of Stepping Motors
 
Type of Load
Generally speaking, motor load
consists of torque and inertia load
A.Torque load (Tf)

Tf=G*r
G: weight
r: radius
B.Inertia load (TJ)

TJ:=J*dw/dt
J=M*(D12+D22)/8*(Kg* cm)
M:mass
D1:outside radius
D2:inside radius
dw/dt:angle acceleration
Explanation of the Dynamic Torque Curve
The dynamic torque curve is an important aspect of stepping motor's output performance.
The followings are some keyword explanations.
Keyword Explanation
1.Working Frequency Point: express the stepping motor's rotational speed value at this point. Units: Hz
n=0*Hz/(360*D)
n:rev/sec
Hz:the frequency value at this point
D:the subdividing value of motor driver
0:the step angle of stepping motor
E.g.: 1.8 stepping motor, in the condition of 1/2 subdividing (each step 0.9) runs at 500Hz, its speed is 1.25r/s.

2.Start/Stop Region: the region in which a stepping motor can be directly started or stopped.

3.Slew Range: the motor cannot be started directly in this area. It must be started in the start/stop region first, and then accelerated to this area. In this area, the motor cannot be directly stopped, either. Otherwise this will lead to losing-step. The motor must be decelerated back to the start/stop region before it can be stopped.

4.Maximum starting frequency point: at this point, the stepping motor can reach its maximum starting speed under unloaded condition.

5.Maximum running frequency point: at this point, the stepping motor can reach its maximum running speed under an unloaded condition.

6.Pull-in Torque: the maximum dynamic torque value that a stepping motor can load directly at the particular operating frequency point.

7.Pull-out Torque: the maximum dynamic torque value that a stepping motor can load at the particular operating frequency point when the motor has been started. Because of the inertia of rotation, the Pull-Out Torque is always larger than the Pull-In Torque.
Control of Acceleration and Deceleration
How to accelerate or decelerate in the shortest time is most important when the system's operating frequency point is in the slew range of the dynamic torque curve graph.

It is shown by the following graph: the dynamic torque's performance of stepping motor will always keep a horizontal straight line in low speed. But in high speed, the curve will slope down quickly influenced by the inductance.
(1)Accelerated Motion of Straight Line
Motor's load value is known as TL, it has to be accelerated from F0 to F1 in the shortest time(tr), what is the value of tr? What is the value of pulse frequency of the acceleration F(t)?
A. Generally TJ=70% Tm
B. tr=1.8*10-5*J*0* (F1-F0)/(TJ-TL)
C. F (t)=(F1-F0)*t/tr+F0, 0<t<tr

(2)Exponential Acceleration
A. Generally TJ0=10%Tm0, TJ1=70%Tm1,
TL = 60%Tm1
B. tr=F4*ln[(TJ0-TL)/(TJ1-TL)]
C. F(t)=F2*[1-e^(-t/F4)]+F0, 0<t<tr
F2=(TL-TJ0)* F1-F0)/(FJ1-TJ0)
F4=1.8*105*J*0*F2/(TJ0-TL)
Note: J is the torque inertia of motor rotor plus its load.
0 is the angle of each step, it equals to the step angle of stepping motor when motor runs in full step. As for the control of deceleration, it can be realized by turning the accelerate pulse frequency above-mentioned.
 
Reduction of Vibration and Noise
In a non-loading condition, stepping motors may appear to have vibration or even lose steps when the motor is running at or close to resonant frequency.
Solutions for These Conditions
A. Having the motor operate outside of this range.
B. By adopting the micro-step driving method, you can divide one step into multiple steps thereby reducing the vibration. Micro-step is used for increasing a motor's step resolution. This is accomplished by controlling the motor's phase current ratio. Micro-step does not increase step accuracy. However, it will allow a motor to run more smoothly and with less noise. When the motor runs in half step mode, the motor torque will be 15% less than running in full step mode. If the motor is controlled by sine wave current, the motor torque will be reduced by 30%.