The aim of the experiment was to examine the influence of rotational speed and bearing misalignment on value of traction moment in examined bearings.
In the course of the experiment we have used the stand illustrated below. We have attached selected flywheels to the shaft, thus changing its moment of inertia. The bearing on the right with its casing was moved vertically by turning the vertical bolt above it. The displacement was measured, then we applied rotation to the shaft and once the shaft was spinning disengaged the clutch letting the shaft stop on its own. The velocity was measured by an analog photoelectric transducer and a perforated disk attached to the shaft for this purpose, recording was done by a computer linked to the transducer by an Analog-Digital converter and the data was registered in digital, discrete form.
Using PC software at the stand the recorded sets were then best-fit with a polynomial function and the function was differentiated to get values of angular acceleration. Note the printouts contain only raw data sets for angular velocity.
The inaccuracy of the photoelectric transducer is known to be:
δUωU=0.015
The error introduced by AD converter is known to be:
δUczU=0.002
Rotational velocity is measured by transducer with linear characteristic, thus the relative error of measurement of ω is the same as relative error of measurement of voltage U. The total error of measurement of rotational velocity ω is then:δωω+czω=δUU=δUczU+δUωU=0.017
In addition the polynomial regression used also introduces an error. Standard deviation σ of each created curve from the actual vales of measurement. By standard we take the error of this approximation to be:
δωap=3σ
Then the error of values obtained (after polynomial regression) is:
δωω=δωω+czω+δωapω=0.017+3σω
Average torque is calculated using the formulae:
MT=-I∆ω∆t=-Iωk-ωptk-tp
Then using the principle of total differential:
δMT=∂MT∂ωkδωk+∂MT∂ωpδωp=-I1tk-tpδωk+-I-1tk-tpδωp==Itk-tp0.017ωk+3σ+0.017ωp+3σ==-Itk-tpωk-ωpωp-ωk0.017ωk+3σ+0.017ωp+3σ==MT0.017ωp+ωk+6σωp-ωk
The momentary torque is:
MTt=-Idωdt=-Ip
The curve of angular acceleration p is the result of differentiating the polynomial which we used to approximate the values of ω. There was no further error during analytical differentiation of polynomial, thus δp/p = δω/ω. Then using the same rule as before :
δMT=∂MT∂pδp=MTtδpp=0.017+3σωMTt
I =
0,008061
kg*m2
series
D [mm]
s[1/s]
tp [s]
wp [1/s]
tk [s]
wk [1/s]
<MT> [Nm]
d <MT> [Nm]
1
0,0
1,680
4,0
280,0
16,0
5,0
0,185
0,0100
2
0,5
2,693
2,7
334,8
15,0
6,1
0,215
0,0143
3
0,9
1,757
3,5
287,5
14,0
7,5
0,0119
4
1,1
1,688
290,0
13,5
0,230
0,0122
5
1,5
1,637
3,0
300,0
12,0
3,9
0,265
0,0134
6
2,0
1,960
2,6
285,1
9,0
0,353
0,0210
MTω Curve families
MEiL