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

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

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

Only suitable for traversing speeds up to approx. 0.25 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.

* see section 6, Winding applications

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 < F_RG

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 + F_R + F_Z + 1.25 · m · g

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

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

3. Side thrust

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

F < F_RG

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.

Change in the side thrust in relation to the shaft speed

4. Shaft speed

4.1. Calculation

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

nmin	=	10 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

4.2. Critical shaft speed

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

For Mo, refer to the technical data.

5.2. Drive power

6. Winding applications

6.1. Formulae and units used

B(mm) = area of the material deflection

C(mm) = traversing width of the drive

D(mm) = barrel diameter of the bobbin

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

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

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

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

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

6.2. Tension

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

Normally, drives with instantaneous reversal are used for winding applications; therefore, the value calculated for F_K 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

i_opt > 1 = shaft rotates slower
i_opt < 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

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

2. Calculate P_R

Kl and all RG 3 versions: P_R = 5 · F_RG*
All RG 4 versions : P_R = 2.5 · F_RG*
*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.

3. Divide C by P_R

4. Calculate the required shaft speed

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
P_R = 5 · 260 N = 1300 N


L_10h = 16500 operating hours

Nomogram