# Design of the Uhing®-linear drive nuts List of contents:

Formulae and units used
 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

1.
Side thrust 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.

2. Shaft Speed 2.1. Max. 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

2.2. 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.

3. Drive torque For Mo, refer to the technical data.

4. Shaft sag 5. 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

1. C = 15900
2. PR = 2,5 · 900N = 2250N
3. 4. 5. LR10h = 2200 operating hours

Example 2

RS4-15-4R7,5

Reduced side thrust of 150 N
Speed = 0,2 m/s

1. C = 5590
2. PR = 2,5 · 150N = 375N
3. 4. 5. L10h = 35000 operating hours

Nomogramm Joachim Uhing GmbH & Co. KG