锥齿轮的当量齿形与球面渐开线的理论误差
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'"><FONT size=4>锥齿直齿的理论齿形是球面渐开线，但实际生产中，是用当量齿轮来计算的，即以背锥距为分度圆半径所形成的平面齿形，然后滚印在背锥面上所形成的齿形，来近似代替球面渐开线。</FONT></SPAN></P><P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=4><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">笔者出于想知道两者的误差到底有多大的好奇心，对此作了些计算和在</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">CAD</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">中测量。</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman"><FONT size=4> <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p></FONT></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=4><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">样本数据如下：大端模数</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">4</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，压力角</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">20</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">度，轴交角</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">90</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">度，大齿轮齿数</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">29</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，小齿轮齿数</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">14</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">。以大齿轮为测量对象。</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'"><FONT size=4>测量步骤如下：</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=4><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">绘制球面渐开线：球半径为外锥距，基圆半径为模数乘齿数乘压力角的余弦然后除以</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">2</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">。以此可以作出球面渐开线。（渐开线的方程在另一张帖里已说明）</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'"><FONT size=4>绘制当量齿形：通过两次的坐标变换可将平面齿形转换成背锥面上的齿形。再通过两次坐标转换，可与球面渐开线的坐标重合。（坐标转换方法在齿轮手册里有详细说明）</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'"><FONT size=4>再将球面渐开线投影到背锥面上，射点为轴交点。然后对两齿形进行比较。</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman"><FONT size=4> <o:p></o:p></FONT></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=4><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">测量三处，齿顶</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">:</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">分度圆向上一个模数的距离，分度圆，齿根</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">:</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">分度圆向下一个模数的距离。</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=4><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">得到以下三个数据：</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">0.17528</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">0.16533</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">0.15060</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">。</SPAN><FONT face="Times New Roman"> </FONT><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">球面渐开线的投影线在当量齿形的外侧，数据为背锥端面的弧长。</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=4><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">结论：以样本为例，当分度圆处齿形重合，当量齿形在齿顶处齿厚单面减薄了</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">10</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">微米，在齿根处单面增厚了</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">15</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">微米。说明压力角增大了。照数据上来看，啮合时有</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">5</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">个微米的多余材料，如果都换算到基圆弧齿厚，材料的多余量还要增加。更准确的数据还要看配对齿轮的情况。笔者没有作进一步的研究。</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=4><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'"></SPAN></FONT> </P><SPAN style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-size: 12.0pt; mso-font-kerning: 1.0pt; mso-bidi-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><FONT size=4>如果采用当量齿形加工锥齿轮，直齿锥齿轮应比圆柱齿轮有更多的修形量，而且应该在齿根处修形。</FONT></SPAN>
Re: 锥齿轮的当量齿形与球面渐开线的理论误差
楼主你的这个球面渐开线方程在那个贴子里啊,我找不到,还有就是那个坐标变换那里有这方面的资料?谢谢,我急需知道球面渐开线方程的推导过程或者是含意,请赐教,谢谢 看来版主对锥齿轮的参数方程、建模和制造都有很深入的了解，想向你学习、交流一下，加我QQ490155013 作锥齿轮的向你们学习。
页:
[1]