Uncertainty Analysis and Application of Precision Centrifuge

Xiong Lei, He Rucai, Long Zuhong, Xing Xinting Abstract: The working principle of the centrifuge is introduced. The mathematical model of the centrifuge acceleration is given. The uncertainty of the centripetal acceleration generated by the precision centrifuge is analyzed.
Key words: centrifuge; acceleration; uncertainty
0 Introduction Inertial accelerometers are one of the key components of inertial navigation systems and inertial guidance systems. Their performance indicators directly determine the accuracy of inertial navigation and inertial guidance. The static performance indicators of the inertial accelerometer mainly include: range, bias value, scale factor, second-order nonlinearity, third-order nonlinearity, etc. As a qualified product, the above performance indicators must be tested and can meet the technical indicators. Requirements.
Precision centrifuges are important equipment for full-scale performance testing of 1g and above range accelerometers. The precision centrifugal test is a test that measures the performance parameters of the accelerometer with the centripetal acceleration of the centrifuge as the input. It is one of the basic tests for the accelerometer. Therefore, it is necessary to analyze the uncertainty of the precision centrifuge.
1 Precision centrifuge working principle In order to perform performance test of the full range of 1g or more range accelerometer, the centrifuge is required to provide accurate acceleration value.
According to the mechanics principle, the centripetal acceleration generated by the centrifuge is
a= W2R (1)
Where: a is the centripetal acceleration generated by the centrifuge, m/s2; W is the angular velocity of the centrifuge, rad/s; R is the working radius of the centrifuge, ie the distance from the center of rotation of the centrifuge to the center of mass of the accelerometer, m.
In the centrifugal test, a gravity acceleration component error is introduced due to the installation error of the accelerometer and the change of the dynamic misalignment angle. The dynamic radius change of the centrifuge also causes the centripetal acceleration of the centrifuge to deviate from its theoretical value. In addition, there are interference effects such as celestial gravity, earth rotation, and measurement of the motion noise of the pedestal. In order to eliminate the influence of the above interference on the accuracy of the centrifuge test, it is necessary to take vibration isolation measures to limit the amplitude of the motion noise of the pedestal to the allowable range, and eliminate it by the positive and negative test of the centrifuge. The impact of the Earth's rotation. Other error factors are corrected in equation (2).
When accelerometer calibration is performed, the acceleration acting in the direction of the accelerometer input axis is expressed as
a= W2R co sAco sB+ g sinA+ g sinCsin (Wt) (2)
Where: A is the misalignment angle of the centripetal acceleration and the accelerometer input axis in the vertical direction, that is, the pitch misalignment angle, rad; B is the misalignment angle of the centripetal acceleration and the accelerometer input axis in the horizontal direction, that is, the azimuth loss Quasi-angle, rad; C is the spindle slewing plumbness, rad; g is the local gravity acceleration.
2 Uncertainty analysis of centrifuge acceleration
2.1 The source of uncertainty is known from the working principle of precision centrifuges. When accelerometer calibration, the uncertainty of centrifuge acceleration is mainly derived from the uncertainty of 1 angular velocity; 2 the working radius (static radius and dynamic radius) is not Degree of certainty; 3 Uncertainty of pitch misalignment angle; Uncertainty of 4 azimuth misalignment angle; 5 Uncertainty of spindle pitch sag.
2.2 Synthesis standard uncertainty analysis According to formula (2), the transfer coefficients of each component uncertainty are as follows:
C1= @a/@W= 2WR co sAco sB+ g tsinCco s (Wt) t
C2=@a/@R = W2co sAco sB
C3= @a/@A= g co sA- W2R sinAco sB
C4= @a/@B= - W2R co sAsinB
C5= @a/@C= g co sCsin (Wt)
The gravity field component introduced by the spindle sag plumbness is zero mean per revolution, ie
C5=@a/@C=∫T0g sin (Wt) dt≤-2g/W , take c5= - 2g/W
The synthetic standard uncertainty of centrifuge acceleration is
Uc (a) = (c21u2 (W) + c22u2 (R ) + c23u2 (A) + c24u2 (B) + c25u2 (C)) 1/2 (3)
Therefore, the calibration of the precision centrifuge must take into account the uncertainty of the angular velocity W and the uncertainty of the working radius R, as well as the uncertainty caused by the pitch angle, the azimuth angle, and the spindle sag.
3 Example analysis of uncertainty Based on the above analysis, the uncertainty of a certain type of precision centrifuge is evaluated.
3.1 Source and influence of speed uncertainty The speed uncertainty is mainly from: the following characteristics of the control system, the torque fluctuation of the motor, the error of the speed feedback system and the environmental interference. The uncertainty of the speed affects the uncertainty of the output acceleration of the centrifuge in two times, which is one of the main sources of acceleration uncertainty. This model precision centrifuge angular velocity uncertainty u (W) = 5 × 10 - 6.
3.2 Source and effect of working radius uncertainty The uncertainty of working radius mainly comes from: uncertainty of measurement system, uncertainty of acquisition system and uncertainty caused by temperature influence.
The uncertainty of the working radius is also one of the main sources of acceleration uncertainty for precision centrifuges. This type of centrifuge has a working radius of R = 0.5m and its uncertainty u (R ) = 5 × 10 - 6.
3.3 Uncertainty caused by pitch misalignment angle and influence Pitch misalignment angle refers to the deviation angle of the input shaft of the calibrated accelerometer in the vertical plane from the radius of the centrifuge. The pitch misalignment angle A of this type of precision centrifuge = 10′′, since the pitch misalignment angle is not compensated for acceleration correction, it is directly used as an error term with an uncertainty u (A) = 4.85 × 10 - 5.
3.4 Uncertainty caused by azimuth misalignment angle and influence Azimuth misalignment angle refers to the deviation angle of the input shaft of the calibrated accelerometer in the horizontal plane relative to the radius of the centrifuge. The azimuth misalignment angle of this type of precision centrifuge is B=10 "Because the azimuth misalignment angle is not compensated for acceleration correction, it is directly used as an error term with an uncertainty u (B) = 4.85 × 10 - 5.
3.5 Uncertainty caused by the spindle sag plumbness The component introduced by the spindle centerline and the ground perpendicular is not an alternating component, that is, it is zero-mean at each revolution. The angular deviation of the centerline of the spindle of this type of precision centrifuge from the vertical line of the ground is C= 5′′. Since the spindle sag is not compensated for acceleration correction, it is directly used as the error term, and its uncertainty u (C) = 2.42×10- 5.
3.6 Uncertainty of Acceleration of Precision Centrifuge According to the above conclusions and formula (3), the corresponding acceleration values ​​and synthetic standard uncertainty of precision centrifuges at different speeds are shown in Table 1.
The acceleration measurement of this type of precision centrifuge
a= (W2R/9 18±5×10- 5) g a< 1g (k= 1)
a= W2R/9 18 (1±5×10- 5) g a> 1g (k= 1)

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