Method and system for improved tire uniformity through improved process harmonic resolution
A uniformity and resolution technology that can be used in general control systems, automotive tire testing, control/regulation systems, etc., and can solve problems such as difficulty in candidate process effects
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example 1
[0110] Simulation of uniformity measurements for process harmonics involving five tires. Candidate process harmonics associated with a harmonic number of 0.773 were identified for analysis. The phase angle and point displacement information of the five tires are determined using the waveform alignment method. Table 1 provides a summary of the determined coefficients, phase angles and point displacement information for the five tires:
[0111] Table 1
[0112]
[0113]
[0114] The uniformity measurements for the five tires are re-indexed according to the determined point displacement information, and composite process harmonic samples are generated using the enhanced resolution techniques disclosed herein. Perform regression analysis on a sample of composite process harmonics to identify the magnitude of the process harmonics.
[0115] For comparison purposes, the magnitudes of the process harmonics were also determined using singlet analysis. The single state analys...
example 2
[0120] Process harmonics associated with three different candidate process effects were simulated on five tires, as illustrated in Table 3 below:
[0121] table 3
[0122] Effect number
[0123] Process harmonic magnitudes are estimated for each candidate process effect using a single state method and an enhanced resolution method according to an example aspect of the invention. Table 4 below compares the results of the estimated magnitudes of the singlet method and the enhanced resolution method.
[0124] Table 4
[0125] Effect number
[0126] A near-complete breakdown of the singlet method was noted due to the loss of resolution that occurs when analyzing candidate process effects at the introduced small-spacing rates. However phase angle estimation using singlet methods can be used to align uniformity measurements for enhanced resolution methods. Although the phase angle is not perfectly estimated, the enhanced resolution method still outperforms the...
example 3
[0128] Numerical examples showing homogeneity measurements in the domain of aligned Fourier coefficients are provided below. A single process harmonic with a magnitude of 1 kg and associated with a candidate process effect of 0.877 was simulated on a set of 5 tires with 128 data points per tire. The first four (m=4) Fourier coefficients for the cosine and sine terms of the first four Fourier harmonics for each of the five tires are provided in Table 5 below.
[0129] table 5
[0130] Fourier harmonics
tire
cosine coefficient
Sine coefficient
Amplitude
1
1
0.85852
0.36217
0.93178
2
1
0.05942
0.03660
0.06978
3
1
0.03431
0.03857
0.05162
4
1
0.00968
0.02365
0.02555
1
2
0.39793
0.92768
1.00943
2
2
0.02034
0.13894
0.14043
3
2
0.01856
0.07626
0.07848
4
2
0.02042
0.05854
0.06200
1
3
-0.28186
0.98711
...
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