# Model RS Linear Drives for Positioning & Indexing Applications

## Technical Information

### Design of Series RS

**Contents:**

- Formulae and units used
- Side thrust
- Shaft speed
- Drive torque
- Shaft sag
- Calculation of the operational life of Uhing linear drive nuts

d(mm) | = | shaft diameter |

F(N) | = | side thrust required |

FRS(N) | = | side thrust produced by the linear drive nut |

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 the diagram |

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) | = | drive nut pitch (travel per shaft revolution) |

I(mm) | = | length of shaft between the bearing blocks |

m(kg) | = | total mass to be moved, including the drive nut, connections, etc. |

Md(Ncm) | = | drive torque |

Mo(Ncm) | = | idling torque |

n(rpm) | = | shaft speed |

ncrit(rpm) | = | critical shaft speed |

P(kW) | = | drive power required |

t(s) | = | acceleration or braking time of the drive |

v(m/s) | = | max. traversing speed required |

C(N) | = | dynamic capacity of the rolling rings |

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

The drive nut to be selected must provide a side thrust which is greater than the value calculated.

F < FRS

It is also possible to couple several smaller drive nuts if the space available for installation allows to do so. The total side thrust is the sum of the individual side thrust values.

**3.1. Maximum shaft speed**

RS 3-10-4 =10000 rpm

RS 4-15-4 = 8000 rpm

RS 4-20-4 = 7000 rpm

RS 4-25-4 = 6000 rpm

RS 4-35-4 = 4000 rpm

RS 4-50-3 = 3400 rpm

RS 4-60-3 = 2500 rpm

**3.2. 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 nut.

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.

With double bearing support, the gap between the bearings blocks should be at least 2.5 x the diameter of the shaft.

For Mo, refer to the technical data.

**6. Calculation of the operational life of Uhing linear drive nuts**

1. Determine C

Type | C (N) |

RS 10 | 4 620 |

RS 15 | 5 590 |

RS 20 | 9 360 |

RS 25 | 11 200 |

RS 35 | 15 900 |

RS 50 | 21 600 |

RS 60 | 29 600 |

2. Calculate PR

RS 10 : PR = 5 · FRS*

For RS 15 -60: PR = 2.5 · FRS*

*F = calculated value of the side thrust according to 1.; 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

**Example 1**

RS4-35-4R17.5

Speed = 0.8 m/s

- C = 15900
- PR = 2.5 · 900N = 2250N
- L10h = 2200 operating hours

**Example 2**

RS4-15-4R7.5

**Reduced side thrust of 150 N**

Speed = 0.2 m/s

- C = 5590
- PR = 2.5 · 150N = 375N
- L10h = 35000 operating hours