1. Structural sketch of the examined shaft-bearing system.

2. Records of measurements and juxtaposition of calculations and plots of measured relationships
for P=const.

a)

Lp.	v[obr/s]	u[mV]	U[V]	∆U[V]	n[obr/min]	2*Mt[N*m]	∆(2Mt)[Nm]	µ srednie	∆µ srednie	błąd +	błąd -
1	10	8,5	0,425	0,0135	600	0,304371	0,009668	0,006442	0,001815	0,008257	0,004627
2	20	9,5	0,475	0,0145	1200	0,340179	0,010384	0,0072	0,00202	0,009219	0,00518
3	30	9	0,45	0,014	1800	0,322275	0,010026	0,006821	0,001917	0,008738	0,004903
4	40	9	0,45	0,014	2400	0,322275	0,010026	0,006821	0,001917	0,008738	0,004903
5	50	9,5	0,475	0,0145	3000	0,340179	0,010384	0,0072	0,00202	0,009219	0,00518

b)

Lp.	v[obr/s]	u[mV]	U[V]	∆U[V]	n[obr/min]	2*Mt[N*m]		µ srednie	∆µ srednie	błąd +	błąd -
1	10	11	0,55	0,016	600	0,393892	0,011459	0,004168	0,000642	0,00481	0,003526
2	20	11,5	0,575	0,0165	1200	0,411796	0,011817	0,004358	0,00067	0,005027	0,003688
3	30	11	0,55	0,016	1800	0,393892	0,011459	0,004168	0,000642	0,00481	0,003526
4	40	11	0,55	0,016	2400	0,393892	0,011459	0,004168	0,000642	0,00481	0,003526
5	50	11,5	0,575	0,0165	3000	0,411796	0,011817	0,004358	0,00067	0,005027	0,003688

c)

Lp.	v[obr/s]	u[mV]	U[V]	∆U[V]	n[obr/min]	2*Mt[N*m]	∆(2Mt)[Nm]	µ srednie	∆µ srednie	błąd +	błąd -
1	10	11,5	0,575	0,0165	600	0,411796	0,011817	0,002905	0,000325	0,003231	0,00258
2	20	11,5	0,575	0,0165	1200	0,411796	0,011817	0,002905	0,000325	0,003231	0,00258
3	30	11,5	0,575	0,0165	1800	0,411796	0,011817	0,002905	0,000325	0,003231	0,00258
4	40	11	0,55	0,016	2400	0,393892	0,011459	0,002779	0,000312	0,003091	0,002466
5	50	12	0,6	0,017	3000	0,4297	0,012175	0,003031	0,000339	0,00337	0,002693

d)

Lp.	v[obr/s]	u[mV]	U[V]	∆U[V]	n[obr/min]	2*Mt[N*m]	∆(2Mt)[Nm]	µ srednie	∆µ srednie	błąd +	błąd -
1	10	12	0,6	0,017	600	0,4297	0,012175	0,002274	0,000207	0,00248	0,002067
2	20	12	0,6	0,017	1200	0,4297	0,012175	0,002274	0,000207	0,00248	0,002067
3	30	11,5	0,575	0,0165	1800	0,411796	0,011817	0,002179	0,000199	0,002378	0,00198
4	40	11,5	0,575	0,0165	2400	0,411796	0,011817	0,002179	0,000199	0,002378	0,00198
5	50	12,5	0,625	0,0175	3000	0,447604	0,012533	0,002368	0,000214	0,002583	0,002154

e)

Lp.	v[obr/s]	u[mV]	U[V]	∆U[V]	n[obr/min]	2*Mt[N*m]	∆(2Mt)[Nm]	µ srednie	∆µ srednie	błąd +	błąd -
1	10	12	0,6	0,017	600	0,4297	0,012175	0,001819	0,000142	0,001961	0,001676
2	20	12	0,6	0,017	1200	0,4297	0,012175	0,001819	0,000142	0,001961	0,001676
3	30	12	0,6	0,017	1800	0,4297	0,012175	0,001819	0,000142	0,001961	0,001676
4	40	11,5	0,575	0,0165	2400	0,411796	0,011817	0,001743	0,000137	0,00188	0,001606
5	50	12,5	0,625	0,0175	3000	0,447604	0,012533	0,001895	0,000148	0,002042	0,001747

3. Derive of formula

4. Plots of measured relationships
for n=const; in the graphs, indicate error intervals.

n=600

n=1200

n=1800

n=2400

n=3000

5. Observations concerning measuring setup structure, measuring methods, and final conclusions.

The preload and the total moment acting on the bearing were measured directly. Knowing appropriate formulas and the parameters of the system we can calculate the friction coefficient in the bearings.

The error of deflection depends mainly on the scaling error (due to inaccuracy of the millimeter scale and hysteresis of the spring) and the read-out error. The voltage measurement error is arising due to nonlinearity and hysteresis of mechanical characteristics of the transducer, as well as instability of amplifier circuits and its reference voltage. Vibrations generated by the rotating shaft also influenced our measurements and caused some errors.

Angular bearings can carry transverse loads only if they are simultaneously subjected to axial (thrust) force. Otherwise they don't work properly and failure can occur.

The value of preload has a big influence on the friction coefficient - contrarily to the value of rotations per minute. With the increase of preload the value of friction coefficient decreases.

Experiment 2 - Support of axles and shafts in angular bearings

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