The aim of the exercise is to learn about the principles of applying bearing systems to shafts and axles with the use of angular roller bearings and to examine the influence of preload in a system of cone bearings on the resistance to rotational motion. For better understanding the problem we need to determine experimentally the characteristics (P) for different speeds of rotation .

Angular bearings can carry transverse loads only if they are simultaneously subjected to axial (thrust) forces. This is a fundamental feature of angular bearings. The axial force, in the form of a preload, is intentionally introduced during assembling of the bearing system. For this reason, single-row angular bearings must always be applied in pairs. In our experiment we use the divergent, "O", bearings setup.

On the beginning we became familiar with the setup structure. During the exercise we were applying preload by tightening the spanners on the shaft. Then we were measuring how the speed of rotation influences the bearing. we subjected different angular velocity to the shaft and measured indications of two tensometers connected in bridge. We managed to examine 5 different preloads (for each preload 5 speeds of rotation).

We were able to measure 2 values - rotational speed of the shaft and indication of tensometer. Rest of the necessary values were calculated from the formulas given in the instruction to the laboratory.

Given value x is the displacement of the nut, which causes the preload P.

Case 1:

x1= [mm]	2			P=	280	N
		U	n[rev/min]	2Mt[N*m]	u	delta u	lower band	upper band
1	10	0,35	600	0,250658	0,005304941	0,000266573	0,005038367	0,005571514
2	20	0,375	1200	0,268563	0,005683865	0,000285614	0,005398251	0,005969479
3	30	0,375	1800	0,268563	0,005683865	0,000285614	0,005398251	0,005969479
4	40	0,375	2400	0,268563	0,005683865	0,000285614	0,005398251	0,005969479
5	50	0,4	3000	0,286467	0,006062789	0,000304655	0,005758134	0,006367445

Graph 1.1 Relation between friction coefficient and number of revolutions

Graph 1.2 Relation between friction coefficient and axial load

Case 2:

x2= [mm]	4			P=	560	N
		U	n[rev/min]	2Mt[N*m]	u	delta u	lower band	upper band
1	10	0,45	600	0,322275	0,003410319	0,000170942	0,003239377	0,003581261
2	20	0,425	1200	0,304371	0,003220857	0,000161445	0,003059411	0,003382302
3	30	0,4	1800	0,286467	0,003031395	0,000151949	0,002879446	0,003183343
4	40	0,375	2400	0,268563	0,002841933	0,000142452	0,002699481	0,002984384
5	50	0,375	3000	0,268563	0,002841933	0,000142452	0,002699481	0,002984384

Graph 2.1 Relation between friction coefficient and number of revolutions

Graph 2.2 Relation between friction coefficient and axial load

Case 3:

x3= [mm]	6			P=	840	N
		U	n[rev/min]	2Mt[N*m]	u	delta u	lower band	upper band
1	10	0,625	600	0,447604	0,003157703	0,000158148	0,002999555	0,003315851
2	20	0,625	1200	0,447604	0,003157703	0,000158148	0,002999555	0,003315851
3	30	0,575	1800	0,411796	0,002905087	0,000145496	0,00275959	0,003050583
4	40	0,55	2400	0,393892	0,002778778	0,00013917	0,002639608	0,002917949
5	50	0,55	3000	0,393892	0,002778778	0,00013917	0,002639608	0,002917949

Graph 3.1 Relation between friction coefficient and number of revolutions

Graph 3.2 Relation between friction coefficient and axial load

Case 4:

x4= [mm]	8			P=	1120	N
		U	n[rev/min]	2Mt[N*m]	u	delta u	lower band	upper band
1	10	0,75	600	0,537125	0,002841933	0,000142274	0,002699658	0,002984207
2	20	0,725	1200	0,519221	0,002747201	0,000137532	0,00260967	0,002884733
3	30	0,675	1800	0,483413	0,002557739	0,000128047	0,002429692	0,002685786
4	40	0,65	2400	0,465509	0,002463008	0,000123304	0,002339704	0,002586313
5	50	0,675	3000	0,483413	0,002557739	0,000128047	0,002429692	0,002685786

Graph 4.1 Relation between friction coefficient and number of revolutions

Graph 4.2 Relation between friction coefficient and axial load

Case 5:

x5= [mm]	10			P=	1400	N
		U	n[rev/min]	2Mt[N*m]	u	delta u	lower band	upper band
1	10	0,875	600	0,626646	0,00265247	0,000132756	0,002519714	0,002785227
2	20	0,8	1200	0,572934	0,002425116	0,000121377	0,002303739	0,002546493
3	30	0,775	1800	0,555029	0,002349331	0,000117584	0,002231747	0,002466915
4	40	0,75	2400	0,537125	0,002273546	0,000113791	0,002159755	0,002387337
5	50	0,75	3000	0,537125	0,002273546	0,000113791	0,002159755	0,002387337

Graph 5.1 Relation between friction coefficient and number of revolutions

Graph 5.2 Relation between friction coefficient and axial load

Final remarks:

The error of deflection depends mainly on the scaling error (due to inaccuracy of the millimeter scale) and the read-out error. We may assume that the overall deflection error does not exceed Dx = 0.5mm. The voltage measurement error, arising due to nonlinearity of characteristics of the transducer, as well as instability of amplifier circuits and its voltage, can be estimated as DUw/U = 0.025. The read-out error should be assumed not less then DUcz/U = 0.025. The total error of voltage measurement is then DU/U=0.05.

From the obtained graphs we can conclude that the friction coefficient does not depend on the rotational velocity of the shaft. The graphs are not perfectly constant, but this is due to the inaccuracies of measurements and vibrations of the whole system. The second family of graphs shows that the coefficient of friction decreases with increasing preload in the shaft.

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