数控机床圆弧的计算方法是什么？

 
圆上任意两点间的部分叫做圆弧
<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>弧长的计算公式L＝的推导过程：

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>因为360°的圆心角所对的弧长就是圆周长C＝2πR（R为圆的半径）

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>所以1°的圆心角所对的弧长是2πR/360，即。

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>这样n°的圆心角所对的弧长的计算公式是L＝n*2πR/360

<p style="margin: 26px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>举个例子：

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>已知圆弧两点直线间距为5285MM,圆半径R=3359MM,求弧长？

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>两点间连线，长度5285，一半是2642.5

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>取连线中点，该中点，圆心，和任意端点构成直角三角形。

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>圆心所在角为圆弧所对角的一半，

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>该角的sin值是2642.5/3359=0.7867

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>该角度数为arcsin0.7867=51.88度

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>所以圆弧所对角为51.87*2=103.76度

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>弧长=2派r×103.76/360

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>=2*3.14*103.76/360

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>=6083MM

<p style="margin: 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-family: -apple-system-font, BlinkMacSystemFont, "Helvetica Neue", "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei UI", "Microsoft YaHei", Arial, sans-serif; font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; box-sizing: border-box !important; overflow-wrap: break-word !important;”> 

<p style="margin: 26px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>R是图纸上半径值.

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>指令格式：<span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>G02/G03 X(U)___Z(W)___I___K___F___；

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>G02/G03 X(U)___Z(W)___R___F___；

<p style="margin: 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-family: -apple-system-font, BlinkMacSystemFont, "Helvetica Neue", "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei UI", "Microsoft YaHei", Arial, sans-serif; font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; box-sizing: border-box !important; overflow-wrap: break-word !important;”> 

<p style="margin: 26px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>1.圆弧顺逆的判断

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>圆弧插补指令分为顺时针圆弧插补指令G02和逆时针圆弧插补指令G03。

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>数控车床是两坐标的机床，只有X轴和Z轴，按右手定则的方法将Y轴也加上去来考虑。<span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>观察者让Y轴的正向指向自己(即沿Y轴的负方向看去)，站在这样的位置上就可正确判断X-Z平面上圆弧的顺逆时针了。

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>圆弧顺逆的判断

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>①采用绝对值编程时，圆弧终点坐标为圆弧终点在工件坐标系中的坐标值，用X、Z表示。<span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>当采用增量值编程时；<span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>圆弧终点坐标为圆弧终点相对于圆弧起点的增量值，用U、W表示。

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>②圆心坐标I、K为圆弧起点到圆弧中心所作矢量分别在X、Z坐标轴方向上的分矢量(矢量方向指向圆心)。<span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>本系统I、K为增量值，并带有“±”号，当分矢量的方向与坐标轴的方向不一致时取“－”号。

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>③当用半径只指定圆心位置时，由于在同一半径只的情况下，从圆弧的起点到终点有两个圆弧的可能性，为区别二者，规定圆心角≤180°时，用“＋R”表示。<span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>若圆弧圆心角>180°时，用“－R”表示。

<p style="margin: 22px 0px 0px; padding: 0px; max-width: 100%; clear: both; min-height: 1em; color: rgb(51, 51, 51); font-size: 16px; letter-spacing: 0.544px; text-align: justify; text-indent: 0px; line-height: 24px; font-family: arial; box-sizing: border-box !important; overflow-wrap: break-word !important;”><span style="margin: 0px; padding: 0px; max-width: 100%; box-sizing: border-box !important; word-wrap: break-word !important; font-size: 15px;”>④用半径只指定圆心位置时，不能描述整圆