Advanced Kaizen
6.1 Group 214: bearing’s overheating
6.1.1 Load case determination
Firstly it has to be identified the type of loads acting on the bearings: the Gr. 214 under investigation is still and the only motion the primary shaft experiences is the rotation determined by the belt-pulley transmission, so that no radial nor axial forces are present, except the ones eventually produced by the motion transmission system.
The belt used is a poly-V type from POGGI, an Italian maker whose catalogue [20] has been used to verify the transmission system and to compute the reaction forces. The belt mounted on Gr. 214 is identified as 11L2020-12, meaning that it has a length of 2020 mm and 12 ribs. In Figure 6.6 is reported a sketch of the transmission and in Table 6.1 are collected its main geometrical and physical data.
Figure 6.6: Transmis-sion system sketch
Feature Symbol Value Unit
driving pulley pitch circle diameter d1 157 mm
wrap angle α1 180 ◦
driven pulley pitch circle diameter d2 157 mm
wrap angle α2 180 ◦
interaxis c 763 mm
belt length L 2020 mm
transmission ratio i 1 /
belt mass per
meter of single rib ml 0.032 kg/m/rib
number of ribs nn 12 /
Table 6.1: Transmission system geometrical and phys-ical data
Assuming that type and size of the belt chosen by the designer are the correct ones for the application and receiving the confirmation of that from the machine maker, following the POGGI catalogue [20] the belt mounting frequency is checked and consequently the reaction forces are evaluated.
The mounting frequency is the frequency of vibration the belt shows while excited by an impulse, usually a small hammer hit on the free portion of the belt between the two pulleys; it can be evaluated through a digital tensiometer, helping the maintainers to impress the right tension to the belt while positioning it. The frequency can be regulated by tightening the bolts holding the driving pulley group (Gr. 204 with respect to Table 5.1).
To verify the correctness of belt tension imposed by the maintainers, which is of 37 Hz, this value is compared with the theoretical one, related to the maximum power the transmission should be able to deliver. To be on the safety side, the following three powers are computed and the maximum between them is considered for the verification.
Mt,N = 60 N m
nN = 3000 N m ⇒ PN = 18.8 kW (6.1)
Mt,A= 84.8 N m
nA = 1805 N m ⇒ PA= 16.0 kW (6.2)
Mt,B = 2.4 N m
nB = 4285 N m ⇒ PB = 1.1 kW (6.3)
The nominal power (6.1) comes from the electric motor tag of Gr. 204, while the load cases A and B (6.2 and 6.3) are deduced by the cyclogram depicted in Figure 6.7, taking the points at maximum torque and maximum speed respectively.
It emerged that actually, the maximum power transmitted by the system is around 16 kW, corresponding to the instant during which the shaft undergoes a maximum torque of 84.8 Nm, but having an electric motor which has a nominal power set on around 19 kW, it is reasonable and safe to verify the belt tension using the highest value of power: Pmax = PN.
Following the procedure reported in POGGI catalogue [20] step by step, here are the quantities and the corresponding formulas, useful to determine the fre-quency of the belt and to check if the theoretical one matches with the actual frequency imposed on the test bench Thyssen5.
• Design Power: it is the maximum transmitted power the belt-pulley system should ensure to the machine, and it is computed starting from the maximum power previously evaluated, corrected by the coefficient Cc, accounting for the specific operating conditions of test bench:
Pc = P · Cc [kW ] (6.4)
Figure 6.7: Primary shaft excitation from cyclogram
• Belt Linear Speed: value obtainable from the rotational speed of the pulley:
V = π · d1 · n
60000 [m/s] (6.5)
• Static Tension: it expresses the belt tension deriving from its operating conditions and the specific belt type chosen (mass and number of ribs); also in this case the power value is increased by the corrective factor C1y, depending on the wrap angle:
Tst = 500 · C1y· Pc
V + ml · nn · V2 [N ] (6.6)
• Static Axial Load: derived from the static tension of the belt, it is strictly related to the belt pull of the system; having in this case a wrap angle of 180◦, it is just the double of the static tension value:
Fa = 2 · Tst· sin
Aα 2
B
[N ] (6.7)
• Frequency of Vibration: it depends on the belt type (mass and number of ribs), to the mounting conditions through the inter-axis c and to the static tension computed before:
f r = 1 2 · c ·
ó Tst
ml · nn [Hz] (6.8)
The results of the computations described above are reported in Table 6.2.
The actual mounting frequency of 37 Hz slightly differs from the theoretical one, but the two are still comparable: it is reasonable, since real mounting conditions could affect the belt tension, making necessary to perform some adjustments to the system and producing a small difference between real and theoretical mounting parameters.
Table 6.2: Belt excitation from POGGI catalogue Feature Symbol Value Unit
design power Pc 24.5 kW
belt linear speed V 24.66 m/s static tension Tst 979 N static axial load Fa 1958 N
frequency f r 33 Hz
Figure 6.8: Loads on bearings according to POGGI catalogue
Having checked the belt installation tension, POGGI catalogue provides the formulas to compute the loads on the bearings, starting from the belt pull: indi-cations are reported in the catalogue’s extract of Figure 6.8.
Note that the primary shaft changes speed and transmitted torque as the check-ing cycle goes on, thus implycheck-ing that bearcheck-ings undergo variable loadcheck-ing conditions:
the formulas circled in Figure 6.8 will be applied in the next paragraphs for all operating conditions, in order to proceed with the bearings verification according to the SKF catalogue [17]. Computational details and results are reported in the next paragraphs.