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Division Ratio for Parameters
Relation between Electronic Gear and Position Resolution or Traveling 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 ∆M per one command pulse) will be described 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)
<Notes>
1) Make a position resolution, ∆M as approx. 1/5 to 1/10 of the machine positioning accuracy, ∆ , consider-
ing a mechanical error.
2) Set up Pr48 and Pr4B to any values between 1 to 10000.
3) You can set up any values to a numerator and denominator, however, action by an extreme division ratio
or multiplication ratio cannot be guaranteed. Recommended range is 1/50 to 20 times.
4)
Pulse train position
command
Travel distance : P1 [P]
Traveling speed : F [PPS]
Electronic gear ratio
Driver
D=
Pr48 x 2
Pr4B
Pr4A
Motor
Encoder
Gear
Machine
Rotational speed : N[r/min]
Reduction ratio : R
Encoder pulse counts : E [P/r]
* 10000 (=A/B-phase 2500 [P/r] x 4)
* 131072 (=17-bit)
Example of ball screw drive
by servo motor
[ ]
+
–
2
n
2
0
2
1
2
2
2
3
2
4
2
5
2
6
2
7
2
8
2
9
2
10
2
11
2
12
2
13
2
14
2
15
2
16
2
17
Decimal
1
2
4
8
16
32
64
128
256
512
1024
2048
4096
8192
16384
32768
65536
131072