Centrifugal forces increase with speed squared. The material of the coupling and the permissible peripheral velocities must be calculated. The maximum peripheral velocity for grey iron, for example, is 35 m/sec. To avoid vibrational damage it is necessary, for couplings which are not fully machined, to carry out both static and dynamic balancing at much lower speeds than those which are fully machined.
The mass of the coupling is often quite small in relation to the rotating masses in the driving and driven machines. For a fan unit the relationship of coupling/total rotor weight may be as low as 0.02. It therefore follows that out-of-balance in the coupling normally has less effect on bearings and vibration than out-of-balance in the actual main components. Howeverthe actual position of the coupling relative to the bearings may change this.
The following relationship applies:
F = meco2-10~3 Equ 12.2
F = out-of-balance force (N)
M = out-of-balance mass (kg)
E = distance from centre of rotation to centre of
Gravity of out-of-balance mass (mm)
Co = angular velocity (rad/s)
For highly resilient rubber element couplings with a spacer, the out-of-balance can be further increased by whirling. It is also important that balancing is carried out using whole keys, half keys or without keys, depending upon the method of balancing the attached component.
A fully-machined coupling can be assumed to have an inherent degree of balancing, without dynamic balancing, equivalent to G16toG40, i. e. approximately 0.08 mm permissible centreline deviation at 3000 rev/min.
If the concentricity tolerance for the shaft bore in the hub is 0.05 mm, the maximum centreline deviation can therefore be 0.13 mm. This is not abnormal. In many cases the tolerance alone reaches this value. This centreline deviation generates an out-of-balance force of about 12 N per kg coupling weight at 3000 rev/min. Acoupling for 50 kW can weigh 10 to 15 kg, which thus generates a rotational out-of-balance force of 120 to 180 N.
Most couplings have no components which can move radially to create out-of-balance forces. The gear coupling is different.
The teeth on the hubs and the spacer must have clearance at the top and bottom; this allows the spacer to move radially. In theory, the angle of the teeth flanks should provide a centralising force to counteract any tendency for the spacer to run eccentrically. Problems have been experienced with gear couplings and special attention should be paid to radial clearances and spacer weight.
The flexible spring coupling has a spring which could move and run eccentrically. These couplings are usually used on fans running at speeds which are low enough not to have balance problems.
The importance of small size and low weight to achieve as little a moment of inertia as possible, as well as reducing the out-of-balance forces, has been mentioned previously.
In certain extreme cases light-alloy metal spacers and diaphragms are used to reduce weight. Apart from the need to maintain a small size/transmitted torque ratio, it is also important, from the cost and standardisation point of view that the coupling should be able to accommodate large variations in shaft diameter. Figure 12.8 shows the normal range of shaft diameters possible.
Figure 12.8 Non-sparking diaphragm coupling
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