| [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 |