Yu et al 2023e - Revision history

Move page script: Move page script moved page Et al 2023a to Yu et al 2023e

2023-12-14T10:09:10Z

Move page script moved page Et al 2023a to Yu et al 2023e

Rimni at 12:25, 15 September 2023

2023-09-15T12:25:21Z

Rimni at 12:23, 15 September 2023

2023-09-15T12:23:17Z

Rimni: /* 3.3 The verification of the contact models */

2023-09-15T12:20:36Z

‎3.3 The verification of the contact models

Rimni at 12:18, 15 September 2023

2023-09-15T12:18:41Z

Rimni: /* 3.2 Particle contact model in shaping process */

2023-09-15T12:12:14Z

‎3.2 Particle contact model in shaping process

Rimni at 12:10, 15 September 2023

2023-09-15T12:10:10Z

Rimni at 12:05, 15 September 2023

2023-09-15T12:05:33Z

Rimni at 11:59, 15 September 2023

2023-09-15T11:59:47Z

Rimni at 11:55, 15 September 2023

2023-09-15T11:55:57Z

@@ Line 424: / Line 424: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>\left\{\begin{array}{c}
+| <math>\left\{\begin{array}{cc}
-M=K_m{\theta }_r=\displaystyle\frac{{\theta }_rK_nB^2}{12}\quad ,\quad {\theta }_r\leq {\theta }_r^0\\
+M=K_m{\theta }_r=\displaystyle\frac{{\theta }_rK_nB^2}{12}\quad ,\quad & {\theta }_r\leq {\theta }_r^0\\
-M=\mbox{0}\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ },{\theta }_r>{\theta }_r^0
+M=\mbox{0} \quad ,\quad & {\theta }_r>{\theta }_r^0
 \end{array}\right\}</math>
 |}
@@ Line 601: / Line 601: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math display="inline">\left\{\begin{array}{ccc}
+| <math display="inline">\left\{\begin{array}{cc}
-M=IK_m{\theta }_r=\displaystyle\frac{{\theta }_rK_nB^2}{12}\quad & ,\quad & {\theta }_r\leq {\theta }_r^0\\
+M=IK_m{\theta }_r=\displaystyle\frac{{\theta }_rK_nB^2}{12}\quad ,\quad & {\theta }_r\leq {\theta }_r^0\\
-M=\mbox{0} \quad & ,\quad & {\theta }_r>{\theta }_r^0
+M=\mbox{0} \quad ,\quad & {\theta }_r>{\theta }_r^0
 \end{array}\right\}</math>
 |}

@@ Line 601: / Line 601: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math display="inline">\left\{\begin{array}{c}
+| <math display="inline">\left\{\begin{array}{ccc}
-M=IK_m{\theta }_r=\displaystyle\frac{{\theta }_rK_nB^2}{12}\quad ,\quad{\theta }_r\leq {\theta }_r^0\\
+M=IK_m{\theta }_r=\displaystyle\frac{{\theta }_rK_nB^2}{12}\quad & ,\quad & {\theta }_r\leq {\theta }_r^0\\
-M=\mbox{0}\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\quad ,\quad{\theta }_r>{\theta }_r^0
+M=\mbox{0} \quad & ,\quad & {\theta }_r>{\theta }_r^0
 \end{array}\right\}</math>
 |}

@@ Line 586: / Line 586: @@
 |-
 | <math>\left\{\begin{array}{c}
-M=IK_m{\theta }_r=\frac{{\theta }_rK_nB^2}{12},{\theta }_r\leq {\theta }_r^0\\
+M=IK_m{\theta }_r=\displaystyle \frac{{\theta }_rK_nB^2}{12}\quad ,\quad {\theta }_r\leq {\theta }_r^0\\
-M=M_0=\frac{1}{6}\left(F_nB\right),{\theta }_r>{\theta }_r^0
+M=M_0=\displaystyle\frac{1}{6}\left(F_nB\right)\quad ,\quad{\theta }_r>{\theta }_r^0
 \end{array}\right\}</math>
 |}
@@ Line 602: / Line 602: @@
 |-
 | <math display="inline">\left\{\begin{array}{c}
-M=IK_m{\theta }_r=\frac{{\theta }_rK_nB^2}{12},{\theta }_r\leq {\theta }_r^0\\
+M=IK_m{\theta }_r=\displaystyle\frac{{\theta }_rK_nB^2}{12}\quad ,\quad{\theta }_r\leq {\theta }_r^0\\
-M=\mbox{0}\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ },{\theta }_r>{\theta }_r^0
+M=\mbox{0}\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\quad ,\quad{\theta }_r>{\theta }_r^0
 \end{array}\right\}</math>
 |}

@@ Line 409: / Line 409: @@
 |-
 | <math>\left\{\begin{array}{c}
-M=K_m{\theta }_r=\frac{{\theta }_rK_nB^2}{12}\quad ,\quad {\theta }_r\leq {\theta }_r^0\\
+M=K_m{\theta }_r=\displaystyle\frac{{\theta }_rK_nB^2}{12}\quad ,\quad {\theta }_r\leq {\theta }_r^0\\
-M=M_0=\frac{1}{6}\left(F_nB\right)\quad ,\quad {\theta }_r>{\theta }_r^0
+M=M_0=\displaystyle\frac{1}{6}\left(F_nB\right)\quad ,\quad {\theta }_r>{\theta }_r^0
 \end{array}\right\}</math>
 |}

@@ Line 409: / Line 409: @@
 |-
 | <math>\left\{\begin{array}{c}
-M=K_m{\theta }_r=\frac{{\theta }_rK_nB^2}{12},{\theta }_r\leq {\theta }_r^0\\
+M=K_m{\theta }_r=\frac{{\theta }_rK_nB^2}{12}\quad ,\quad {\theta }_r\leq {\theta }_r^0\\
-M=M_0=\frac{1}{6}\left(F_nB\right),{\theta }_r>{\theta }_r^0
+M=M_0=\frac{1}{6}\left(F_nB\right)\quad ,\quad {\theta }_r>{\theta }_r^0
 \end{array}\right\}</math>
 |}
@@ Line 425: / Line 425: @@
 |-
 | <math>\left\{\begin{array}{c}
-M=K_m{\theta }_r=\frac{{\theta }_rK_nB^2}{12},{\theta }_r\leq {\theta }_r^0\\
+M=K_m{\theta }_r=\displaystyle\frac{{\theta }_rK_nB^2}{12}\quad ,\quad {\theta }_r\leq {\theta }_r^0\\
 M=\mbox{0}\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ },{\theta }_r>{\theta }_r^0
 \end{array}\right\}</math>

← Older revision	Revision as of 10:09, 14 December 2023
(No difference)

@@ Line 233: / Line 233: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>K_n=k_n B, \quad K_s=k_sB, \quad {\mu }_n={\eta }_n B</math>
+| <math>K_n=k_n B, \quad K_s=k_sB\qquad , \qquad {\mu }_n={\eta }_n B</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (2)
@@ Line 250: / Line 250: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>p^l=\overline{p}+\frac{{\theta }_rK_n}{2}, \qquad p^r=\overline{p}-\frac{{\theta }_rK_n}{2}</math>
+| <math>p^l=\overline{p}+\frac{{\theta }_rK_n}{2}\qquad , \qquad p^r=\overline{p}-\frac{{\theta }_rK_n}{2}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (3)
@@ Line 321: / Line 321: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>p_{\min}=0, \qquad p_{\max}=\frac{{\theta }_rK_nl^2}{B}</math>
+| <math>p_{\min}=0\qquad , \qquad p_{\max}=\frac{{\theta }_rK_nl^2}{B}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (7)
@@ Line 334: / Line 334: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>M=\frac{{\theta }_rK_nl^2}{2B}\left(\frac{B}{2}-\frac{l}{3}\right), \qquad F_n=\frac{{\theta }_rK_nl^2}{2B}</math>
+| <math>M=\frac{{\theta }_rK_nl^2}{2B}\left(\frac{B}{2}-\frac{l}{3}\right)\qquad , \qquad F_n=\frac{{\theta }_rK_nl^2}{2B}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (8)
@@ Line 344: / Line 344: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>M=\left(F_nB\right)\left(\frac{1}{2}-\frac{l}{3B}\right),\qquad l={\left(\frac{2F_nB}{K_n{\theta }_r}\right)}^{0.5}</math>
+| <math>M=\left(F_nB\right)\left(\frac{1}{2}-\frac{l}{3B}\right)\qquad ,\qquad l={\left(\frac{2F_nB}{K_n{\theta }_r}\right)}^{0.5}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (9)
@@ Line 381: / Line 381: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>M_0=\frac{1}{6}\left(F_nB\right),{\theta }_{r}^{0}\mbox{=}\frac{{2}F_{n}}{K_{n}B}</math>
+| <math>M_0=\frac{1}{6}\left(F_nB\right)\qquad ,\qquad {\theta }_{r}^{0}=\frac{{2}F_{n}}{K_{n}B}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (10)

@@ Line 827: / Line 827: @@
 |  style="text-align: center;vertical-align: bottom;"|
 |  style="text-align: center;vertical-align: bottom;"|
 |-
 |  style="text-align: center;vertical-align: bottom;"|Error  <math display="inline">e\Delta </math>
 |  style="text-align: center;vertical-align: bottom;"|0.0170
 |  style="text-align: center;vertical-align: bottom;"|4
@@ Line 917: / Line 913: @@
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