13.Setup of command division and multiplication ratio — Relation between Electronic Gear and Position Resolution or Travelling Speed

Abstract

The setting of the command division and multiplication ratio is the promise of an efficient automation system driven by a Panassonic A6 series of AC servo motor and driver. Here in this chapter we're discussing the relation between Electronic Gear and Position Resolution or Travelling Speed.

Here we take a ball screw drive as an example of machine.

A travel distance of a ball screw M[mm] corresponding to travel command P1[P], can be described by the following formula (1) by making the lead of ball screw as L[mm]

M=P1 x (D/E) x (1/R) x L ……………(1)

therefore, position resolution (travel distance ΔM per one command pulse) will be described by the formula(2)

ΔM = (D/E) x (1/R) x L ……………(2)

modifying the above formular (2), electronic gear ratio can be found in the formula (3).

D=(ΔM x E x R) x L ……………(3)

Actual travelling velocity of ball screw, V[mm/s] can be described by the formula (4) and the motor rotational speed, N at that time can be described by the formula (5).

V=F x (D/E) x (1/R) x L ……………(4)
N=F x (D/E)/(F x 60) ……………(5)

modifying the above formula (5), electronic gear ratio can be found in the formula (6).

D=(N x E)/(F x 60) ……………(6)

Note →

1. Make a position resolution, ΔM as approx, 1/5 to 1/10 of the machine positioning accuracy, Δε, considering a mechanical error.
2. Set up Pr0.09 and Pr0.10 to any values between 1 to 2³⁰.
3. The desired setting can be determined by selecting value of numberator and denominator of electronic gear. However, an excessively high division or multiplication ration cannot guarantee the operation. The ratio should be in a range between 1/1000 and 1000. Excessively high multiplication ratio will cause Err27.2 (command pulse multiplication error protection) due to varying command pulse input or noises, even if the other settings are within the specified range.

4. 2n	Decimal
   20	1
   21	2
   22	4
   23	8
   24	16
   25	32
   26	64
   27	128
   28	256
   29	512
   210	1024
   211	2048

   2n	Decimal
   212	4096
   213	8192
   214	16384
   215	32768
   216	65536
   217	131072
   218	262144
   219	524288
   220	1048576
   221	2097152
   222	4194304
   223	8388608

	Electronic gear ratio D=ΔM x E x R/L	D=Pr0.09/Pr0.10
Lead of ball screw, L=10mm Gear reduction ratio, R=1 Position resolution, ΔM = 0.005mm Encoder, 23-bit (E=223P/r)	0.0005 x 223 x 1/10 = 5 x 223/10 x 104 = 41943040/100000	Pr0.09 = 41943040 Pr0.10 = 100000

	Motor rotational speed (r/min), N = F x D/E x 60
Lead of all screw, L=20 mm Gear reduction ration, R=1 Position resolution, ΔM = 0.0005mm Line driver pulse input, 500 kpps Encoder, 23-bit	500000 x 0.0005 x 223 x 1/20 x 1/223 x 60 = 750
Ditto To make it to 2000 r/min	Electronic gear ratio D = N x E/F x 60	D = Pr0.09/Pr0.10
	D = 2000 x 223/500000 x 60 = 2000 x 223/2000 x 500 x 30 = 8388608/15000	Pr0.09 = 8388608 Pr0.10 = 15000
	Travel distance per command pulse (mm) (Position resolution) ΔM = D/E x 1/R x L
	2000 x 223/500000 x 60 x 1/223 x 1/1 x 20 = 0.00133 mm

---

Related page → • P.4-10 "Details of Parameter"