I. PLC controller frequency, servo driver, and load speed
Given that our servo drive has a Pm = 10000 Pulse/r and the PLC controller outputs a frequency f (puls/s), how do we calculate the load axis rotational speed n (r/s)?
1. When the servo motor is directly connected to the shaft, let the numerator of the electronic gear ratio be N compared to the denominator.
n = (f*N)/Pm........ This formula calculates the number of pulses in r/s. The number of pulses generated in 1 second divided by the number of pulses required for one revolution = the number of revolutions in 1 second.
n: Load speed, unit: r/s.
f: Frequency emitted by the controller, unit: pls/s.
N: Drive electronic gear ratio.
Pm: Servo driver resolution, unit: Pulse/r.
2. With equation 1, we can deduce that when the load shaft carries a turntable or pulley, we can calculate the linear velocity V of the belt.
V=r*ω=r*2πn
Substitute equation 1 into:
V = πd ((f*N)/Pm)
d: Diameter of the pulley and load shaft, unit: mm.
n: Load speed, unit: r/s.
f: Frequency emitted by the controller, unit: pls/s.
N: Drive electronic gear ratio.
Pm: Servo driver resolution, unit: Pulse/r.
3. On-site situations may encounter insufficient output torque, requiring the addition of a speed reducer. Let the reduction ratio be K.
From equation 1, we already know the output speed n of the motor shaft, so we can calculate the output speed n1 after passing through the reducer.
n1=n/k=（f*N）/(Pm*K).............r/s
n1=n/k=（f*N*60）/(Pm*K)............r/min
Assuming axis n1 carries the slider, we can also calculate the slider's speed V.
V=n1*D=（f*N*D）/(Pm*K)……mm/s
Similarly, we can deduce that f = (V * Pm * K) / (N * D)
n: Motor direct shaft speed, unit: r/s.
n1: Output speed after the reducer, unit: r/s.
K: Gearbox reduction ratio.
V: Speed of slider movement, unit: mm/s.
D: Lead screw pitch, unit: mm
II. Relationship between Pulses Output by the PLC Controller and Displacement
With the above introduction, let's discuss the following:
As shown in the figure below, our servo driver has a value of Pm = 10000 Pulse/r, the lead of the lead screw (thread pitch, which can be understood as the lead screw moving one lead per revolution of the motor) is D, the number of pulses issued by the PLC controller is P, and the electronic gear ratio is assumed to be 1.
How do I calculate the distance S that the corresponding workbench moves?
4. S = (D/Pm) * P... First, calculate the displacement of one pulse, then multiply by the number of pulses to get the distance traveled. If an electronic gear ratio N is set, then S = (D/Pm) * P * N... because P * N is the actual pulse sent to the motor by the servo drive.
D: Lead screw pitch, unit: mm
P: Number of pulses sent by the controller, unit: pulses
How would you calculate the distance traveled in the following system? The mechanical part of the system has a speed reducer with a reduction ratio of K.
5. S = (D/(Pm*K))*P*N... Similarly, in step 4, we can calculate the displacement of one pulse. Due to the addition of a speed reducer, the displacement of one pulse reflected on the load shaft is smaller than that in step 4. It can be seen that the displacement is inversely proportional to the gear structure of the system speed reducer and directly proportional to the electronic gear ratio of the servo drive.
Based on the above formula, it can be deduced similarly that for a disk-based structure, the number of pulses corresponds to the angle of disk rotation, which is equivalent to D = 360 degrees.
The phrase mentioned in points 4 and 5 above, "first calculate the displacement of one pulse," is actually the legendary pulse equivalent δ.
III. A Brief Discussion on Pulse Equivalent δ
From 4 and 5, we know that (D/Pm) is the pulse equivalent without a speed reducer, and D/(Pm*K) is the pulse equivalent of the system with a speed reducer. It can be seen that if the mechanical structure is determined, this value is also determined; the displacement corresponding to one pulse is determined, meaning the system's accuracy is determined. For example, a 5mm lead screw directly connected to an EVE servo drive has an accuracy of 5/10000mm. If an external speed reducer with a reduction ratio of 40 is used, the pulse equivalent of this system is 5/(10000*40)mm. The parameters determined above are called the inherent pulse equivalent of the system.
Suppose we need to adjust the system accuracy to 1µm/pls. What do we do then? This is where the electronic gear ratio of the servo drive comes in handy.
The following formula can be used to calculate it:
1:5*1000/(10000*40)=1:1/80=80:1, which means setting the numerator P1-00 of the electronic gear ratio of the Yiwei US100 servo driver to 80 and the denominator P1-01 to 1.
