Calculation With Insufficient Numerical Values; Example With Corrected Numerical Values - Danfoss MCO 350 Operating Instructions Manual

Syncronising Controller MCO 350 Operating
Instructions

2.3.3. Calculation with Insufficient Numerical Values

The master/slave gear ratio (numerator to denominator) is now calculated as follows:
Master
1024
Slave side = increments * i1 * power take off
=
This gives a ratio of:
That gives a numerical value of 48,460995 for the numerator and 29,7856 for the denominator.
Note: It is only possible to enter integer values. The most serious error: The master expression
contains the value Pi, an infinite number sequence. Even with small numerical values for master
and slave, the effect would always be that the drives drifted apart, as the Numerator: Denominator
expression can never be an integer.
Another error arises from the gear ratios given, as the master drive was specified with a value of
i = 30.33. The correct ratio is easily found by recalculating the individual numbers of teeth. The
gear is a 2-stage gear; the first stage is formed from two pinions, 126 to 27, and the second stage
from two pinions, 117 to 18.
The ratio is calculated as:
The specified value of 30.33 thus deviates by 0.1 ‰.
This may appear small; if this error is related to the encoder resolution, however, it will be seen
that even this error is serious.
From the example it can be seen that it is important to maintain the exact values of the gear
stages and to ensure that the data include Pi either for both drives or for none of them.

2.3.4. Example with Corrected Numerical Values

Master side: Gear 1st stage 126/27 2nd stage 117/18; belt ratio 40/20; drive shaft 100 mm
Slave side: Gear 1st stage 97/10, 2nd stage 43/11, 3rd stage 27/22; effective diameter of the
sprocket wheel 510mm
Master side:
Slave side:
To remove Pi from the equations, substitute both equations into the combined formula:
M asterside
Slaveside
side = increments
20
incr x x x
30.33
40 102
48, 460995
29, 7856
x
126
x
27
I ncr x x
1024 126
x x x
27 18 40
I ncr x x
1024 97 43
x x x
10 11 22 510
I ncr x
1024
=
x x
27 18
®
MG.33.Q1.02 - VLT is a registered Danfoss trademark
* i1 * i2 *
1
= 48, 460995
mm x
π
incr x
1024
117
= 30, 33
18
x
117 20
x
102 π
x
27
x
π
x x
126 117 20 1024
÷
x x
40 102 π 10
2. Introduction
power take off
1
x
46.54
x mm
8 200
Incr x x x
97 43 27
x x x x
11 22 510 π
2
=
= 29, 7856
13