Design of the types RG und ARG / KI und AKI

Rolling Ring Drive Design

List of contents:

  1. Formulae and units used
  2. Preselection
  3. Side thrust
  4. Shaft speed
  5. Shaft drive
  6. Winding applications
  7. Calculation of the operational life of Uhing rolling rings

 

1. Formulae and units used

a(m/s2) = acceleration at the reversal point
d(mm) = shaft diameter
F(N) = side thrust required
FRG(N) = side thrust produced by the rolling ring drive
FR(N) = frictional force (FN · µ); only relevant when the payload is mounted on its own carriage
FN(N) = normal force of the total weight of the payload and the carriage
µ = coefficient of friction
FZ(N) = additional force (e.g. component of the cutting force of a separator)
f(mm) = shaft sag from Fig. 1
g(m/s2) = acceleration due to gravity (9.81 m/s2); in the case of horizontal applications, the following applies: m · g = 0
h(mm) = pitch of unit (travel per shaft revolution)
hmax(mm) = maximum pitch from Fig. 3
l(mm) = length of shaft between the centres of the (inner) bearing blocks
m(kg) = total mass to be moved, including the rolling ring drive unit, connections, etc.
Md(Ncm) = drive torque
Mo(Ncm) = idling torque
n(rpm) = shaft speed
ncrit(rpm) = critical shaft speed
P(kW) = drive power required
s(mm) = length of reversal slowdown cam
t(s) = reversal time from Fig. 2
v(m/s) = max. traversing speed required; should always be calculated at the maximum unit pitch (pitch setting 10 from Fig. 3)
C(N) = dynamic capacity of the rolling rings
PR(N) = radial load on the rolling rings

2. Preselection

The drive type should be preselected by estimating the side thrust F required and/or by giving consideration to the permissible shaft sag f for the type of application according to Fig. 1.

Fig. 1
Fig. 1

 

2.1. Rolling ring drives with instantaneous reversal (feature M)

Only suitable for traversing speeds up to approx. 0.25 m/s (Kinemax to appr. 0,4 m/s; RG 3/4-40-2 to appr. 0,6 m/s).

The reversal time of the instantaneous reversal depends on the size of the rolling ring drive and on the pitch selected via the scale (pitch angle). The reversal occurs abruptly.

Formula

* see section 6, Winding applications

Fig. 2
Fig. 2
To determine reversal time t:

Using the pitch selection scale value 10 in Fig. 2, find the curve for the appropriate drive type and read off the corresponding reversal time t.

Note:
The calculated side thrust F must be lower than that of the selected rolling ring drive.

F < FRG

If necessary, select a different drive size and repeat the process.

For winding appications, also refer to section 6.

 

2.2. Rolling ring drives with reversal slowdown (feature V)

Suitable for traversing speeds up to approx. 4.2 m/s.

A reversal with slowdown reduces the forces of gravity on the drive unit at the reversal point.

F = 1.25 · m · a + FR + FZ + 1.25 · m · g

If a maximum acceleration a is specified, the required length s for the deceleration cam is calculated as follows:

Formula

If the length s of the deceleration cam is specified, the acceleration a is calculated as follows:

Formula


 


3. Side thrust

 

The calculated side thrust F must be lower than that of the selected rolling ring drive.

F < FRG

If the side thrust provided by the selected rolling ring drive is too low, either a larger drive or a higher length s for the deceleration cam must be selected.

The side thrust provided by the drives is virtually constant for shaft speeds above 300 rpm. For slower speeds, the side thrust rises slightly above the specified catalogue values as the speed decreases towards zero.

To increase the life of the drives, only the side thrust resulting from 2.1. and 2.2. should be set.

Diagram

Change in the side thrust in relation to the shaft speed
 



4. Shaft

4.1. Calculation

Formula

The speed resulting from this formula must not be exceeded.
Recommended speed range:

nmin = 5 rpm
nmax = 3000 rpm
For speeds outside this range, please consult the supplier.

To obtain pitch h, take pitch selection scale value 10, find the curve for the appropriate drive type and read off the corresponding pitch (Fig. 3).

Minimum reversal distance:
Feature M ~ 1 x d
Feature E + N = 0

 

Fig. 3
Fig. 3

 

4.2. Critical shaft speed

Formula

Note
Depending on its geometry, the shaft can go out of balance already at a speed which is 25 % lower than the value resulting from the formula!
If it is necessary to go through a critical range in order to reach the operating speed, this can lead to short-term shaft vibration. However, this vibration has no effect on the operation of the drive.

If the operating speed is in the critical speed range, this can be rectified as follows:

 

  1. with a double bearing support at one end, increase factor = approx. 1.5.
  2. with double bearing supports at both ends, increase factor = approx. 2.2.

The gap between the bearing blocks should be at least 2.5 x the diameter of the shaft.



5. Shaft drive

5.1. Drive torque

Formula

For Mo, refer to the technical data.

 

5.2. Drive power

Formula

 


6. Winding applications

 

6.1. Formulae and units used

Fig. 5

B(mm) = area of the material deflection

C(mm) = traversing width of the drive

D(mm) = barrel diameter of the bobbin

dmax(mm) = maximum diameter diameter of the material to be wound or maximum pitch

FZug (N) = tension in the material to be wound

FK (N) = tension working against the direction of travel of the drive

Hmax (mm) = maximum pitch of the drive selected, taken from the technical data

vw(m/s) = speed of the material to be wound

 

6.2. Tension

In winding operations, force FK acting on the drive, a component of the tension FZug in the material to be wound, often determines the design of a rolling ring drive.

Formula

Normally, drives with instantaneous reversal are used for winding applications; therefore, the value calculated for FK must be added to the required side thrust determined under 2.1.

 

6.3. Calculation of the traversing speed

 

6.4. Optimum ratio between the bobbin and the shaft speeds

iopt > 1 = shaft rotates slower
iopt < 1 = shaft rotates faster

 

6.5. Special notes

Avoid pitch settings lower than "1". Instead, change the ratio between the bobbin and the shaft speeds (reduce the speed of the shaft).

 


7. Calculation of the operational life of Uhing rolling rings

 

7.1. Determine C

 

Type RG C1(N) C2(N)
15/KI 6050 2800
20/22 11200 5600
30 16800 9300
40 21600 13200
50 29600 18300
60 37700 24500
80 58800 39000

 

C1 = drive operating on the rotating shaft without standstill

C2 = drive operating on the rotating shaft with standstill

 

7.2. Calculate PR

Kl and all RG 3 versions: PR = 5 · FRG*
All RG 4 versions : PR = 2.5 · FRG*

*F = calculated value of the side thrust according to 2.1. and 2.2.; must only be used if required to extend the life of the rolling rings. Must be specified in the order.

 

7.3. Divide C by PR

7.4. Calculate the required shaft speed

Formula

7.5. Determine the life from the nomogram (in hours)

Example 1
ARG3-30-2VCRF
Speed = 0.9 m/s
Side thrust F = 260 N
C1 = 16 800
PR = 5 · 260 N = 1300 N

 

Formula
Formula

L10h = 16500 operating hours

Nomogram

Nomogram

 

If you wish Joachim Uhing KG GmbH & Co. to make the appropriate selection for your application, please fill in our questionnaire.

 


Joachim Uhing GmbH & Co. KG
Konrad-Zuse-Ring 20
24220 Flintbek, Germany

Tel. / Phone +49 (0) 4347 906-0
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