Götz 1 V 1.0, created: 05/01/2002

ACB

Application fact sheet

Motion drive with drive via wheels

A motion drive is a travelling mechanism on which the wheels are driven directly bythe motor and the gearbox. This application is limited by a maximum lead angle andmaximum acceleration. Alternative drive options would be cable-based or rack-basedmotion drives. Crash motion can be calculated to avoid overloading the gearbox. Youdo this by calculating the torque of the drive shaft when subject to frontal impact.

Inertia J2 represents the types of inertia which do not change during the machiningcycle, e.g. vehicle mass (m2), axes and wheels.

(1)

The useful load mass (m1) must also be taken into account. The value of this massmay change during the machining cycle.

(2)

2

21

12 2000mdJJ ⋅

+=

1

21

2 2000mdJJtot ⋅

+=

Götz 2 V 1.0, created: 05/01/2002

ACB

Application fact sheet

The stationary torque can only be calculated once the train resistance of the vehiclehas been calculated. The train resistance comprises various components: the rollingfriction, the bearing friction and the wheel flange or side friction. It may also comprisetractive and hoisting forces.

(3)

(4)

(5)

(6)

(7)

Alternatively, the train resistance (F'1) can be referenced to earth [N/t]:

(8)

(9)

Special features:A maximum permissible acceleration can be calculated to stop the drive wheels fromslipping. The static friction µ2, the wheel load mass mwheels, the angle of inclination β,the total mass mtot and possibly a countervailing force F2 are required for thiscalculation.

tottot

wheels

mF

mmga 2

2max sincos +

−⋅⋅⋅= ββµ (10)

Crash motion:The angle of inclination and the static friction are amongst the components which arerelevant for crash motion. After overcoming the static friction the torque will bereduced by the slipping wheels.

βµ cos2000

122 ⋅⋅⋅⋅=

dgmM totcrash (11)

321 MMMMstat ++=

20001

22dFM ⋅=

2000sin 1

3dgmM tot ⋅⋅⋅= β

⋅+⋅+⋅⋅⋅= cddfgmM tot 20002000cos

10001

12

1 µβ

1000cos2'1

12

11 ⋅

+⋅+⋅⋅⋅= c

dd

dfgF µβ

20001000'

2000111

11dmFdFM tot ⋅

⋅=⋅=

12 mmm tot +=

Götz 3 V 1.0, created: 05/01/2002

ACB

Application fact sheet

Note: The document "basic calculations.pdf" provides further formulas forcompleting the calculations required for an application.

Key for symbols and arithmetic units:

Symbol Description Unitd1 Wheel diameter mmd2 Bearing diameter mmm1 Useful load mass kgm2 Vehicle mass kg

mwheel Wheel load mass kgmtot Total mass kg

f Rolling friction lever arm mmµ1 Bearing frictionµ2 Static frictionc Wheel flange and side friction

β Angle of inclination °

J1 Additional inertia kgm2

J2 Vehicle inertia kgm2

Jtot Total inertia kgm2

amax Slip acceleration m/s2

Mstat Stationary torque NmM1 Vehicle torque NmM2 Counter torque NmM3 Hoist torque Nm

M2crash Crash torque on gearbox output NmF'1 Train resistance N/tF1 Train resistance NF2 Countervailing force Ng Acceleration due to gravity (9.81) m/s2