Calcultation of the necessary torque to enable a rotation of the whole assembly takes into account :
• loads on the machine,
• rotating masses,
• distance of these masses to the rotation axis,
• speeds and accelerations,
• resisting torques.
Two types of torque are distinguished :
Start up slewing torque : Cd=Crv+Crc
Acceleration slewing torque : Cg=Crv+Crc+Ca
Crv = Friction torque of unloaded bearing
Crc = Rotating torque due to loads
Ca = Accélération torque
Cd = Starting torque
All these torques are expressed in kNm
Crc : ROTATING TORQUE DUE TO LOADS
The starting torque required takes into consideration loads on the bearing and friction of the components.
Balls type slewing ring :
Crc = [ (13,11 MT / Ø m ) + 3 FA + 11,34 FR ] Ø m . 10 -3
Crossed rollers type slewing ring :
Crc = [ ( 15,3 MT / Ø m ) + 3,75 FA + 8,19 FR ] Ø m . 10 -3
MT = Resulting moment in kNm
Ø m = Raceway mean Ø in meters
FA = Axial load in kN
FR = Radial load kN
Ca : ACCELERATION TORQUE
The torque needed to accelerate the loads from the initial speed up to the final speed, during time (t) is defined by :
Ca = [ ( (PI)*n*l) / 30 . t ] . 10 -3
t = Acceleration time in sec.
n = Speed variation in RPM
(Final speed - Initial speed)
l = Moment of inertia of the machine in Kg . m²
l = l1 + l2 + l3 + ..... ln
where l1 to ln = moments of inertia of the moving loads with regard to rotation axis expressed in Kg . m²
Generally, we have :
l1 = G1 * r1²
ln = Gn * rn²
G1 to Gn = Mass of various rotating components expressed in Kg.
r1 to rn = Distances between the loads centre of gravity and the ring rotation axis expressed in meters.
Note : the resisting torque depends on the support surface flatness and lubrication.
The friction torque of standard slewing ring is defined in the following graph. ROLLIX, upon request, can supply slewing ring with lower or higher torque values.
LOAD APPLIED ON THE RING :
Axial FA : 68 kN + 5 kN = 73 kN
Radial FR : 0,29 kN, negligible
Moment MT : 5kN * 1,5 m = 7,5 kNm
SLEWING TORQUE : Raceway mean ø = 2 meters
Crv : according to the graph : 1 kNm
Crc=[( 13,11 * 7,5 / 2 ) + (73*3) + (11,34 * 0)] 2.10-3
Crc = 0,536 kNm
Slewing torque at start up :
Cd = 1 + 0,536 = 1,536 kNm
Platform moment of inertia :
MR²/2 = ( 6800 / 2² ) / 2 = 13600 Kg.m²
Cube moment of inertia :
Mr² = 500 * 1,5² = 1125 kg.m²
Total moment of inertia :
13600 + 1125 = 14725 Kg.m²
Acceleration torque :
n= 6 - 2 = 4 RPM
Acceleration time : 20 sec
Ca = (14725 * π * 4 ) / (20 * 30) 10-3 = 0,3084 kNm
Slewing torque during acceleration
Cg = 1 + 0,536 + 0,3084 = 1,845 kNm
Platform diameter : 4 m.
Platform mass: 6800 kg
Cube mass : 500 kg
Ball type slewing ring raceway mean Ø : 2 m.
Distance from the cube to the rotation axis : 1,5 m.
Initial speed : 2 RPM
Final speed : 6 RMP
Acceleration time : 20 sec.