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. 2023 Mar 15;16(6):2351. doi: 10.3390/ma16062351
[Op Xd Yd Zd] Fixed coordinate system
[Op Xz Yz Zz] Rotary coordinate system
[Oz, Xs Ys Zs] Rotation coordinate system of ceramic ball
δ Rotation angle of ceramic ball
[Oz, Xs, Ys, Zs] The coordinate system in the state of spin angle change
P N Initial matrix
tran(u, δ) Coordinate change matrix of ceramic ball
ω1, ω2, ω3 Angular velocity of contact point
ωz Rotational angular velocity of ceramic balls
ω b Projection of angular velocity on x axis
ω c Projection of angular velocity on y axis
RB, RC The distance from the contact point to the radius of rotation of the sphere
r The radius value of ceramic ball
η Groove angle
ΔF Rotation amplitude matrix
Δt The unit sampling time of the trajectory points on the sphere surface
C Real-time state matrix of sphere rotation angle in grinding process
PN(i + 1) The trajectory coordinates of the ceramic ball obtained after turning any angle during the grinding process
δ(i)/Δδ The variation range of rotation angle in unit time
m 1 Upper envelope line
m 2 Lower envelope line
D The difference between the time series signal and the mean value
L Stopping function
Pj (t) Data set from initial high-frequency IMF to minimum low-frequency IMF
Pj (t) IMF classification
Qm (t) Residual error
Zj(t) Zero-frequency component
IMF Intrinsic Mode Functions
K c Number of waveforms
O L The center of the least squares circle
C i The actual measured contour points
ΔEmin The roundness deviation of the sphere obtained by the least square method
e The distance from the center of Rotation O to the circle OL
rp The distance from any point on the actual contour line to the center OL
β The initial angle between rp and polar axis
Δrp The distance deviation value in the model
R Approximation region radius of the algorithm
O x Highly fine points
R max The maximum radius in each minimum partition region
R min The minimum radius in each minimum partition region
ΔR The radius range in each minimum partition area
MZM Minimum zone method
LSM Least square method
MCM Minimum circumcircle method
MIC Maximum inscribed circle method
E C1 The algorithm is based on the MCM to evaluate the roundness deviation obtained by the standard
E C2 The algorithm is based on the MIM to evaluate the roundness deviation obtained by the standard
E C3 The algorithm is based on the MIC to evaluate the roundness deviation obtained by the standard
E c Roundness deviation value detected by instrument
E a1 The roundness deviation calculated by the MCM
E a2 The roundness deviation calculated by the LSM
E a3 The roundness deviation calculated by the MIC method
E a4 The roundness deviation calculated by the MZM