# Model RG Linear Drives for Reciprocating Motion Applications

## Technical Information

### Design of Series RG and ARG / KI and AKI

**Contents:**

- Formulae and units used
- Preselection
- Side thrust
- Shaft speed
- Shaft drive
- Winding applications
- Calculation of the operational life of Uhing rolling rings

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 |

I(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 |

I 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 |

Pp(N) | = | radial load on the rolling rings |

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 < 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:

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

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.

Change in the side thrust in relation to the shaft speed

**4.1. Calculation**

The speed resulting from this formula must not be exceeded.

Recommended speed range:

nmin | = | 10 rpm |

nmax | = | 3000 rpm |

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.

**5.1. Drive torque**

For Mo, refer to the technical data.

**5.2. Drive power**

**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

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.

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**

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 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.

3. Divide C by PR

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

PR = 5 · 260 N = 1300 N

L10h = 16500 operating hours

Nomogram