Xuegang et al 2023a - Revision history

Zhangxuegang: Add a department to the Acknowledgments section.

2023-10-30T07:45:18Z

Add a department to the Acknowledgments section.

Rimni at 10:34, 7 September 2023

2023-09-07T10:34:19Z

Rimni at 10:32, 7 September 2023

2023-09-07T10:32:05Z

Rimni at 14:09, 6 September 2023

2023-09-06T14:09:58Z

Rimni at 14:06, 6 September 2023

2023-09-06T14:06:34Z

Rimni: /* References */

2023-09-06T13:55:37Z

‎References

Rimni at 13:53, 6 September 2023

2023-09-06T13:53:33Z

Show changes

Rimni: /* References */

2023-09-06T12:44:18Z

‎References

Rimni at 12:17, 6 September 2023

2023-09-06T12:17:14Z

Rimni at 12:16, 6 September 2023

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@@ Line 1,326: / Line 1,326: @@
 ==Acknowledgements==
-<span id='_Hlk49700416'></span><span id='OLE_LINK6'></span><span id='OLE_LINK7'></span>The authors express their deep gratitude to the financial support of Sichuan Provincial Key Lab of Process Equipment and Control (No. GK202211, No. GK201907), Science & Technology Plan Project of Panzhihua City (No. 2021ZD-G-1), Panzhihua Key Laboratory of Advanced Manufacturing Technology (No. 2022XJZD05).
+<span id='_Hlk49700416'></span><span id='OLE_LINK6'></span><span id='OLE_LINK7'></span>The authors express their deep gratitude to the financial support of Sichuan Provincial Key Lab of Process Equipment and Control (No. GK202211, No. GK201907), Science & Technology Plan Project of Panzhihua City (No. 2021ZD-G-1), Panzhihua Key Laboratory of Advanced Manufacturing Technology (No. 2022XJZD05), Sichuan Vanadium and Titanium Materials Engineering Technology Research Center (No. 2021-FTGC-Z-06).
 ==Conflicts of interests==

@@ Line 958: / Line 958: @@
 |-
 | <span id='eq52'></span> <math>\boldsymbol{M}_{l,m}=\left[\begin{array}{cccc}
-cos(\Delta H) & 0 & sin(\Delta H) & 0\\
+\cos (\Delta H) & 0 & \sin (\Delta H) & 0\\
 & 1 & 0 & 0\\
--sin(\Delta H) & 0 & cos(\Delta H) & 0\\
+-\sin (\Delta H) & 0 & \cos (\Delta H) & 0\\
 & 0 & 0 & 1
 \end{array}\right]</math>

@@ Line 410: / Line 410: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <span id='eq19'></span> <math>f(u_g,{\theta }_g,{\psi }_g)=(\frac{\partial \boldsymbol{r}_1^{\left(G\right)}}{\partial {\theta }_g}\times \frac{\partial \boldsymbol{r}_1^{\left(G\right)}}{\partial u_g})\cdot \frac{\partial \boldsymbol{r}_1^{\left(G\right)}}{\partial {\psi }_g} = 0</math>
+| <span id='eq19'></span> <math>f(u_g,{\theta }_g,{\psi }_g)=\left(\frac{\partial \boldsymbol{r}_1^{\left(G\right)}}{\partial {\theta }_g}\times \frac{\partial \boldsymbol{r}_1^{\left(G\right)}}{\partial u_g}\right)\cdot \frac{\partial \boldsymbol{r}_1^{\left(G\right)}}{\partial {\psi }_g} = 0</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (19)

@@ Line 222: / Line 222: @@
 |-
 | <span id='eq9'></span><math>\boldsymbol{r}_c^{\left(G\right)}({\theta}_g,u_g)=\boldsymbol{M}_{c,b}({\theta }_g)\boldsymbol{r}_b^{\left(G\right)}(u_g)=\left[\begin{array}{c}
-(\pm  u_g \sin{\alpha }_n-R\, \pm \, \frac{\pi m}{4})\cos{\theta }_g\\
+\left(\pm  u_g \sin{\alpha }_n-R\, \pm \, \frac{\pi m}{4}\right)\cos{\theta }_g\\
 u_g \cos{\alpha }_n\\
-(\pm u_g \sin{\alpha }_n-\, R \pm \frac{\pi m}{4})\sin{\theta }_g\\
+\left(\pm u_g \sin{\alpha }_n-\, R \pm \frac{\pi m}{4}\right)\sin{\theta }_g\\
 \end{array}\right]</math>

@@ Line 52: / Line 52: @@
 ==2. Geometry of curvilinear cylindrical gears==
-===2.1. Generating principle of curvilinear cylindrical gears by face-milling cutters===
+===2.1 Generating principle of curvilinear cylindrical gears by face-milling cutters===
 In order to generate the gear tooth surfaces, the first task is the establishment of the virtual face-milling cutter surfaces. A brief generating mechanism of the gear tooth surfaces is shown in [[#img-1|Figure 1]]. The outer and inner blades of the face-milling cutter are employed for the generation of concave and convex sides of the gear tooth surfaces, respectively. Generating process of the cutter blade surfaces is as follows:
@@ Line 124: / Line 124: @@
 After one tooth space is generated by the face-milling cutter, the gear blank is indexed by one tooth pitch angle, and the generating mechanism of the gear continues to generate the next tooth space, until all tooth spaces have been formed.
-===2.2. Derivation of mathematical model of the wheel tooth surfaces===
+===2.2 Derivation of mathematical model of the wheel tooth surfaces===
 [[#img-1|Figure 1]] (Right) shows the straight-line profiles of the face-milling cutter for the generation of the wheel tooth surfaces. The inner and outer blade profiles are divided into two parts: the straight-line profile, which will be used for generation of the working part of the wheel tooth surfaces, and the circular arc profile, which will be used for generation of the fillet part of the wheel tooth surfaces. The variable <math display="inline"> u_g </math> represents the distance between arbitrary points on the straight-line profile and the origin of coordinate system <math display="inline">S_{ib}</math> or <math display="inline">S_{ob}</math>, and the variable <math display="inline">\lambda_g </math> represents the polar angle of arbitrary points on the circular arc profile.
@@ Line 457: / Line 457: @@
 In Eq. (21), <math display="inline">u_g</math> and <math display="inline">\theta_g</math> are the parameters of the working tooth surfaces. In Eq. (22), <math display="inline">\lambda_g</math> and <math display="inline">\theta_g</math> are the parameters of the fillet surfaces, and <math display="inline">\psi_g</math> is the generalized parameter of movement. Arbitrary point coordinates on the wheel tooth surfaces will be solved by numerical method.
-===2.3. Derivation of mathematical model of pinion tooth surfaces===
+===2.3 Derivation of mathematical model of pinion tooth surfaces===
 The generation of a mathematical model of the pinion tooth surfaces is similar to that of the wheel tooth surfaces. They distinguish only in different cutter blade profiles. Here, the face-milling cutter with the parabolic blade profiles is used to generate the pinion tooth surfaces. [[#img-2|Figure 2]] shows the parabolic profiles of the face-milling cutter. The parabolic profiles of the cutter retain tangent to the standard blade with straight-line profiles. The point of tangency is located at arbitrary positions on the straight-line profiles. The distance between the point of tangency and the cutter pitch plane is <math display="inline">\Delta y_{tp}</math> along the vertical direction. The distance between the center points of circular arc profiles and the origin of the coordinate system <math display="inline">S_b</math> is <math display="inline">x_{fc}</math> along the horizontal direction. The variable <math display="inline"> u_p </math> represents the distance between arbitrary points on the parabolic profile and the origin of the coordinate system <math display="inline">S_{ib}</math> or <math display="inline">S_{ob}</math>. The variable <math display="inline">\lambda_p</math> represents the polar angle of arbitrary points on the circular arc profiles.

← Older revision		Revision as of 13:55, 6 September 2023
Line 1,411:		Line 1,411:

	==References==		==References==
		+	<div class="auto" style="text-align: left;width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">

	<span id='ref1'></span>		<span id='ref1'></span>

@@ Line 1,412: / Line 1,412: @@
 ==References==
-<span id='ref1'></span>1. Yang H-C, Tsai P-Y (2021) Mathematical model of S-shaped gear surface. Journal of Mechanical Science and Technology 35(7): 2841-2850. doi:10.1007/s12206-021-0607-z
+<span id='ref1'></span>
-. Arafa HA (2016) C-Gears: Geometry and Machining. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 219 (7):709-726. doi:10.1243/095440605x31481
+[2] Arafa H.A.  C-Gears: Geometry and machining. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 219(7):709-726, 2016. doi:10.1243/095440605x31481
-<span id='ref2'></span>3. Liu S-T (1988) Curvilinear cylindrical gears. Gear Technology 5 (3):8-12
+<span id='ref2'></span>
-<span id='ref3'></span>4. HA A, M B C-gears in rotorcraft transmissions: a novel design paradigm. In: International powered lift conference, Philadelphia, PA, USA, October 5-7, 2010 2010. pp 93-100
+<span id='ref3'></span>
-<span id='ref4'></span>5. HA A, M B Manufacturability and Viability of Different C-Gear Types: A Comparative Study
+<span id='ref4'></span>
 In: ASME (ed) Proceedings of the ASME Design Engineering Technical Conferences, Chicago, IL, USA, August 12-15, 2012 2012. ASME, pp 381-391

@@ Line 1,399: / Line 1,399: @@
 |  style="vertical-align: top;"|Offset distance of the parabolic profile
 |}
 '''Superscripts:'''
-<math display="inline"> p,\,g \qquad </math> Pinion and wheel of gear set
+<math display="inline">p,\,g \quad </math> Pinion and wheel of gear set
 '''Subscripts:'''
-<math display="inline">P_{ib} </math>, <math display="inline">G_{ib} \qquad </math> Convex side of the pinion and wheel<br>
+<math display="inline">P_{ib} </math>, <math display="inline">G_{ib} \quad </math> Convex side of the pinion and wheel<br>
-<math display="inline">P_{ob} </math>, <math display="inline">G_{ob} \qquad </math> Concave side of the pinion and wheel
+<math display="inline">P_{ob} </math>, <math display="inline">G_{ob} \quad </math> Concave side of the pinion and wheel
 ==References==

@@ Line 1,400: / Line 1,400: @@
 |}
-{| style="width: 81%;border-collapse: collapse;"
+'''Superscripts:'''
-|-
-|  style="vertical-align: top;"|'''Superscripts:'''
+<math display="inline"> p,\,g \qquad </math> Pinion and wheel of gear set
-|  style="vertical-align: top;"|
-|-
+'''Subscripts:'''
-|  style="vertical-align: top;"|<math display="inline"> p,\,g </math>
-|  style="vertical-align: top;"|Pinion and wheel of gear set
+<math display="inline">P_{ib} </math>, <math display="inline">G_{ib} \qquad </math> Convex side of the pinion and wheel<br>
-|-
+<math display="inline">P_{ob} </math>, <math display="inline">G_{ob} \qquad </math> Concave side of the pinion and wheel
-|  style="vertical-align: top;"|'''Subscripts:'''
-|  style="vertical-align: top;"|
-|-
-|  style="vertical-align: top;"|<math display="inline">P_{ib} </math>, <math display="inline">G_{ib} </math>
-|  style="vertical-align: top;"|Convex side of the pinion and wheel
-|-
-|  style="vertical-align: top;"|<math display="inline">P_{ob} </math>, <math display="inline">G_{ob} </math>
-|  style="vertical-align: top;"|Concave side of the pinion and wheel
-|}
 ==References==