Radial Ball Bearings Research Articles

ラジアル玉軸受の取付けと測定に関する二, 三の問題

ラジアル玉軸受の取付けと測定に関する二, 三の問題

On the inclined Radial Ball Bearing (III)

When a radial ball bearing is mounted with a inclination by mistake, the bearing, if rotating under a axial load, brings about a radial runout of the shaft. Denoting the inclined angle of the bearing by α, the ball diameter by d and the radial clearance of the bearing by Cr, the amount of the induced radial runout ε is given approximately by the following equation for the ordinary deep groove ball bearings.[numeical formula] The above theoretical equation has been certified by some experiments.

On Critical Speeds Induced by Ball Bearings at Lower Rotating Speeds

When single-row radial ball bearings are used, several critical speeds take place in a vertical shaft at certain rotating speeds lower than the major critical speed. When the bearing center line of both bearing pedestals is not in alignment and the shaft is not in a perfectly straight line, there is the possibility that these critical speeds occur. The frequencies of vibrations of these critical speeds are represented by zω1, zω1+1 and zω1-1, where ω1 is the precessional rotating speed of balls in bearing and z is the number of balls. The whirling motions of these critical speeds are those of both forward and backward precessions. When self-aligning double-row ball bearings are used, these critical speeds do not occur ; they occur only in the shaft supported by single-row radial ball bearings.

On Critical Speeds Induced by Ball Bearings in Lower Rotating Speeds

When single-row radial ball bearings are used, several critical speeds take place in a vertical shaft at certain rotating speeds lower than the major critical speed. When the bearing center lime of both bearing pedestals is not in alignment and the shafe is not in a perfectly straight line, there is the possibility that these critical speeds occur. The frequencies of vibrations of these critical speeds are representea by zω1, zω1+1 and zω1-1, where ω1 is the precessional rotating speed of balls in bearing and z is the number of balls. The whirling motions of these critical speeds are those of both forward and backward precessions. When self-aligning double-row ball bearings are used, these critical speebs do not occur ; they occur only in the shaft supported by single-row radial ball bearings.

On the inclined Radial Ball Bearing

On the inclined Radial Ball Bearing

The Oil Bath Lubrication of Ball and Roller Bearings at High Speed

In pursuit of information concerning the performances of the high speed rolling bearings operating under oil bath 1ubrication and light load, measurements of bearing temperature rise and friction coefficient have been made using radial ball and roller bearings of 40mm bore with pressed cages. As the lubricant, spindle oil or turbine oil is applied and the level of oil bath is always kept in somewhat lower than the centre of rolling element which is placed at the lowest position in the bearing. The experimental results of bearings, operated at a rotating speed up to 24, 000 rpm for the ball bearing and 16, 000 rpm for the roller bearing, indicate that the bearing temperature rise and friction coefficient increase proportionally to the rotating speed of bearing. From the fact that bearings had been operated securely under such high speed, it may be convinced that, under light load, the oil bath lubrication can be applied for a speed far higher than the speed which is adopted customarily under the limitation of dn-value of 250, 000. Furthermore, at such a high speed, the friction coefficients of bearings under oil bath lubrication take the values nearly twice as the values lubricated with minimum oil, and such differences depend on the hydrodynamic friction losses owing to churning oil.

On the Critical Speed of a Shaft at Lower Rotating Speeds

Since single-row radial ball bearings have small clearance, the statical deflection of shaft varies with angular position of shaft provided that bearing center lines of both bearing pedestals are not in alignment and the shaft is not in a perfectly straight line. Obviously the statical deflection fluctuates with period 2π/ω and this fluctuation has components of sin nωt and cos nωt, in which n is any integer and ω is rotating speed of the shaft. Under such conditions, the periodic disturbing forces having frequencies nω are applied to the disc supported by this shaft and the forced vibrations with frequencies 2ω, 3ω, 4ω etc. are induced. In the system in which the disc is not located at mid-point of shaft, gyroscopic action is applied to the disc. Consequently such a system has natural frequencies of modes of vibrations of forward and backward precession and both kinds of critical speeds of nω can appear.

On the Critical Speeds of Synchronous Backward Precession

Although, as has already been reported, the resonance of synchronous backward precession can occur when the bearing pedestals deflect, this resonance can also appear when the pedestals have no flexibility and there is a loose fit of ball bearing in pedestal. Since there are errors in machining the outer ring of ball bearing as well as the inner surface of bearing box where neither are made exact circle, the degree of flt is not equal in all directions and the shaft has an unequal flexibility. Consequently the critical speeds of synchronous backward precession do occur. Similarly these critical speeds appear in the shaft supported by single-row radial ball bearings, because such a shaft has non-symmetrical, non-linear characteristics and unequal flexibility. Because the phenomenon of shaft whipping induced by dry friction takes place, it is undesirable to equip a gard ring to check an increase of deflection of the shaft at the critical speeds of synchronous backward precession.

On the Critical Speeds with Peculiar Modes of Vibration

When single-row radial ball bearings are used the stiffness of a shaft has non-symmetrical, non-linear spring charactristics. In experiments using such a shaft mounting one disc, several critical speeds of peculiar modes of vibration occurred with a critical speed of sub-harmonic oscillation of order 1/2. These critical speeds consist of two vibrations having the same frequencies pi and pj as the natural frequencies of this system. It is remarkable that the absolute value of sum of or difference in two frequencies pi and pj is equal to the rotating speed of the shaft. In numerous experiments with several kinds of shafts, this relation between pi and pj always held at these critical speeds. For a system having linear spring characteristics or a system with one degree of freedom, this type of critical speed does not appear ; it occurs only in the system with multiple degrees of freedom and non-linearity.

On the Critical Speed of a Shaft of Sub-harmonic Oscillation

Since single-row radial ball bearings have angular a shaft supported by them has a non-linear and non-symmetrical spring characteristic provided the bearing center lines of both bearing pedestals are not in alignment. In a small angular clearance, a shaft is freely supported, and the inclination angle of the deflection curve of the end of the shaft grows larger than a small angular clearance, then the shaft is not freely supported. When bearing center lines of both pedestals are not in alignment, the equilibrium position of a shaft is not located at the middle position of a small angular clearance, then the shaft has a non-symmetrical non-linearity. Therefore, sub-harmonic oscillation of order 1/2 can occur. In fact, the whirl of shaft with the mode of sub-harmonic oscillation of 1/2 appears at a rotating speed higher than the major critical speed.

ころがり軸受の壽命に及ぼす遊隙の影響

Since the bearing clearance has a great influence on the performance and life of bearings, the selection of it becomes a very important problem, and it is necessary to know the suitable value of the clearance under operation.Then, in this paper, basing upon the Lundberg-Palmgren Theory, the influence of the clearance of bearings under operation on the life is studied in the case of radial bearings under pure radial load.According to this consideration, the influence in the case of cylindrical roller bearings is greater than in radial ball bearings and in both cases there are particular values of the clearance with which bearing life becomes maximum.