Table of Contents
2
Preparation
Pulse train position
command
[
Travel distance : P1 [P]
Traveling speed : F [PPS]
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 ∆M per one command pulse) will be de-
scribed by the formula (2)
∆M = (D/E) x (1/R) x L ........................ (2)
modifying the above formula (2), electronic gear ratio can be found in the formula (3).
D = (∆M x E x R) x L ........................... (3)
Actual traveling 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) 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, ∆ M as approx. 1/5 to 1/10 of the machine positioning ac-
curacy, ∆ ε , considering a mechanical error.
2) Set up Pr0.09 and Pr0.10 to any values between 1 to 2
3) You can set up any values to a numerator and denominator, however, action by an ex-
treme division ratio or multiplication ratio cannot be guaranteed. Recommended range
is 1/1000 to 1000 times.
4)
2-50
14.
Setup of command division and
multiplication ratio (electronic gear ratio)
Relation between Electronic Gear and Position Resolution or Traveling Speed
Electronic gear ratio
Pr0.09
D=
]
Pr0.10
Example of ball screw drive by servo motor
2
Decimal
n
2
1
0
2
2
1
2
4
2
2
8
3
2
16
4
2
32
5
2
64
6
2
128
7
2
256
8
2
512
9
2
1024
10
Driver
Rotational speed : N[r/min]
+
–
2
Decimal
n
2
2048
11
2
4096
12
2
8192
13
2
16384
14
2
32768
15
2
65536
16
2
131072
17
2
262144
18
2
524288
19
2
1048576
20
Motor
Gear
Machine
Reduction ratio : R
Encoder
Encoder pulse counts : E [P/r]
* 1,048,576 (=20bit)
* 131,072 (=17bit)
.
30
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