# Analysis of the Influencing Factors of Grinding Uniformity under Three-Body Coupling Grinding Mode
## 5 Effects of Mechanism Error on the Rotating Angular Velocity of the Ball
### Establishing the ADAMS Numerical Simulation Model  
In this study, a numerical model of a three-body coupling grinding mode was constructed on the basis of the Automatic Dynamic Analysis of Mechanical System (ADAMS) developed by MSC. This software can easily conduct nonlinear kinetic analysis, and it has an advanced numerical analytical technology. It is convenient for the parameter analysis of mechanical system performance, and it meets the requirements of the simulation analysis of the three-body coupling grinding process [30,48]. Hence, the optimal mixing ratio between the mechanical parameters of grinding discs and the diameter of the processing ball was determined on the basis of this numerical model. Moreover, the relationship between various motion states and the grinding uniformity of the ball during the grinding process was analyzed. The 3B-CGM numerical model is established, and the ADAMS numerical simulation model is shown in Figure 11. The variables of parameterized points are shown in Table 3.  
To make the simulation analysis results of the ADAMS numerical model of the three-body coupling grinding agree with practical processing results as much as possible, the balling geometry and motion states under the three-body coupling grinding mode were analyzed. Moreover, the grinding was in the finish machining stage, when the material removal and geometric shape of the ball changed slightly. Hence, the following simulation conditions were made to model the three-body coupling grinding mode [30,48,49]:  
Figure 11: Numerical simulation model of three-body coupling grinding. \begin{table}
\begin{tabular}{c c} \hline \hline
**Name of Design Variables** & **Meanings** \\ \hline TC & Period of rotating speed \\ \hline DV\_QIU & Radius of the ball \\ \hline DV\_RA & Distance from the ball center to the spin axis of the grinding disc \\ \hline DV\_H & Height position of the upper grinding disc \\ \hline DV\_A & Lateral angle of the V-shaped groove \\ \hline DV\_B & Inner angle of the V-shaped groove \\ \hline DV\_WAIPAN1 & Design variables of the outer disc shape \\ DV\_WAIPAN2 & Design variables of the inner disc shape \\ \hline DV\_NEIPAN1 & Design variables of the inner disc shape \\ DV\_NEIPAN2 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Meaning and values of design variables. Ignore the corrosion of the grinding fluid or chemical reactions caused by friction during grinding;
* Ignore the material removal effect;
* A single ideal real ball is used as the analysis object;
* Rigid contact occurs between the ball and grinding discs without relative slippage. Additionally, the revolving and rotating states of the ball center in the ground coordinate system were calculated by using the system measuring function in the ADAMS software. Meanwhile, the revolute pairs and driving were added to the reference ball in the model to solve the problem in the motion state measurement at contact points. Data of the revolving angular speed of the ball center was input into the driving. Finally, the coordinates of the reference points were transformed into the coordinate system of the ball center from the ground coordinate system, thus enabling the plotting of the grinding tracks of the ball [30,48,49]. To study whether grinding tracks cover the spherical surface uniformly, a triangular meshing technique was applied (Figure 12) to divide the spherical surface into several triangular zones with the same shape and area. In accordance with the simulation results of grinding tracks, the grinding track points were sampled regularly. Then, a statistical analysis of the quantity of grinding track points in each triangular zone was conducted. The standard deviation (S) of the quantity of grinding track points in each region was calculated to characterize grinding uniformity. The higher S value indicates the poorer distribution uniformity of the grinding track points. In this model, the single-factor analysis method was applied.