VB软件_模拟逐点比较法逆圆弧插补的程序设计

XXX学院学生课程设计（论文）题目：逐点比较法圆弧插补的连续轨迹控制设计学生姓名： XXX 学号：2006XXXXXXXX 所在院(系)：机电工程学院专业：机械设计制造及其自动化班级： 06机制6班指导教师： XXX 职称：教授2009年12月8 日XXX学院本科学生课程设计任务书题目逐点比较法插补的连续轨迹控制设计（圆弧插补）1、课程设计的目的专业课程综合训练目的是本使学生通过对所学主要专业课的综合应用，基本掌握一般机电控制系统的设计方法及步骤。

综合运用所学的基础知识和技能，进一步提高学生的设计能力，培养学生创新意识和创新能力，提高控制系统分析设计的总体意识和工程实践能力。

2、课程设计的内容和要求（包括原始数据、技术要求、工作要求等）设计内容要求：（1）铣床CNC系统硬件原理图及其说明；（2）推导完整的插补公式；（3）设计出插补软件流程图；（4）用高级语言编写插补程序清单；（4）画出插补轨迹模拟图形；（5）将上述内容整理成设计说明书及图纸。

设计结束后提交4000字左右的课程设计论文;包含上述全部内容。

3、主要参考文献[1]、张建民等，《机电一体化系统设计》，北京：高等教育出版社，2002年[2]、赵先仲，《机电系统设计》，北京：机械工业出版社，2004年[3]、吴圣庄，《金属切削机床概论》，北京：机械工业出版社，1993[4]、杨有君，《数控技术》，北京：机械工业出版社，20054、课程设计工作进度计划内容学时总体方案设计8CNC系统硬件设计8插补系统原理及公式设计16插补系统软件设计48软件验证 4绘制所需的各类图及编制技术文件20合计3周指导教师（签字）日期2008年12 月1 日教研室意见：年月日学生（签字）：接受任务时间：年月日注：任务书由指导教师填写。

课程设计（论文）指导教师成绩评定表题目名称评分项目分值得分评价内涵工作表现20% 01 学习态度 6 遵守各项纪律，工作刻苦努力，具有良好的科学工作态度。

Private Sub Command1_Click()Const pi = 3.14159265Picture1.ForeColor = vbBlackPicture1.DrawWidth = 2Picture1.Line (50, 500)-(50, 5500)Picture1.Line (50, 5500)-(6500, 5500)Picture1.Line (80, 600)-(50, 500)Picture1.Line (20, 600)-(50, 500)Picture1.Line (6400, 5450)-(6500, 5500) Picture1.Line (6400, 5550)-(6500, 5500) Picture1.ForeColor = vbRedPicture1.DrawWidth = 3If Int(Text1) = 0 ThenPicture1.Circle (50, 5500), Sqr(Int(Text1) *Int(Text1) + Int(Text2) * Int(Text2)) * 400, , Atn(Int(Text4) / Int(Text3)), pi / 2ElsePicture1.Circle (50, 5500), Sqr(Int(Text1) *Int(Text1) + Int(Text2) * Int(Text2)) * 400, , Atn(Int(Text4) / Int(Text3)), Atn(Int(Text2) /Int(Text1))End IfEnd SubPrivate Sub Command2_Click()Dim k, m, j, l, n, F(20) As Integerm = 0l = Text1.Textk = Text2.TextF(m) = 0Picture1.ForeColor = vbGreenPicture1.DrawWidth = 3j = Abs(Int(Text1) - Int(Text3)) + Abs(Int(Text2) - Int(Text4))Form1.CurrentX = 200Form1.CurrentY = 200 Print "初始：进给方向" & "F(m)=0" & " X0=" & Int(Text1) & " Y0=" & Int(Text2) & " ∑= " & jFor n = 1 To jIf F(m) >= 0 And j > 0 Thenm = m + 1k = k - 1F(m) = F(m - 1) - 2 * Abs(k + 1) + 1Picture1.Line (50 + 400 * l, 5500 - k * 400)-(50 + 400 * l, 5500 - (k + 1) * 400)Form1.CurrentX = 200Form1.CurrentY = 200 + m * 300Print "第" & m & "步" & " -△y F(" & m & ")= " & F(m) & " " & "x=" & l & " " & "y="; k & " ∑=" & j - nElsel = l + 1m = m + 1Picture1.Line (50 + 400 * l, 5500 - k * 400)-(50 + 400 * (l - 1), 5500 - k * 400)F(m) = F(m - 1) + 2 * Abs(l - 1) + 1Form1.CurrentX = 200Form1.CurrentY = 200 + m * 300Print "第" & m & "步" & " +△x F(" & m & ")= " & F(m) & " " & "x="; l & " " & "y="; k & " ∑=" & j - nEnd IfNext nEnd SubPrivate Sub Command3_Click()Text1.Text = ""Text3.Text = ""End SubPrivate Sub Command4_Click()EndEnd SubPrivate Sub Command1_Click()Picture1.ForeColor = vbBlackPicture1.DrawWidth = 2Picture1.Line (7500, 8500)-(7500, 500)Picture1.Line (7500, 500)-(500, 500)Picture1.Line (7500, 8500)-(7400, 8400)Picture1.Line (7500, 8500)-(7600, 8400)Picture1.Line (500, 500)-(600, 600)Picture1.Line (500, 500)-(600, 400)Picture1.ForeColor = vbRedPicture1.DrawWidth = 5Picture1.Line (7500, 500)-(7500 + 400 *Int(Text3), 500 - 400 * Int(Text4))End SubPrivate Sub Command2_Click()Form1.ClsDim k, m, j, l, n, F(20) As Integerm = 0l = 0k = 0F(m) = 0Picture1.ForeColor = vbGreenPicture1.DrawWidth = 3j = Abs(Int(Text3)) + Abs(Int(Text4))Form1.CurrentX = 200Form1.CurrentY = 200Print "初始：进给方向" & "F(m)=0" & " Xe=" & Int(Text3) & " Ye=" & Int(Text4) & " ∑= " & jFor n = 1 To jIf F(m) >= 0 And j > 0 Thenm = m + 1l = l - 1F(m) = F(m - 1) - Abs(Int(Text4))Picture1.Line (7500 + 400 * (l + 1), 500 - k * 400)-(7500 + 400 * (l), 500 - k * 400)Form1.CurrentX = 200Form1.CurrentY = 200 + m * 300Print "第" & m & "步" & " △x F(" & m & ")= " & F(m) & " " & "x=" & l & " " & "y="; k & " ∑=" & j - nElsek = k - 1m = m + 1Picture1.Line (7500 + 400 * l, 500 - (k + 1) * 400)-(7500 + 400 * l, 500 - k * 400)F(m) = F(m - 1) + Abs(Int(Text3))Form1.CurrentX = 200Form1.CurrentY = 200 + m * 300Print "第" & m & "步" & " △y F(" & m & ")= " & F(m) & " " & "x="; l & " " & "y="; k & " ∑=" & j - nEnd IfNext nEnd SubPrivate Sub Command3_Click()Text1.Text = ""Text2.Text = ""Picture1.ClsForm1.ClsEnd SubPrivate Sub Command4_Click()EndEnd SubPrivate Sub Form_Load()End SubPrivate Sub Command1_Click()Const pi = 3.14159265Picture1.ForeColor = vbBlackPicture1.DrawWidth = 2Picture1.Line (50, 500)-(50, 5500)Picture1.Line (50, 5500)-(6500, 5500)Picture1.Line (80, 600)-(50, 500)Picture1.Line (20, 600)-(50, 500)Picture1.Line (6400, 5450)-(6500, 5500) Picture1.Line (6400, 5550)-(6500, 5500) Picture1.ForeColor = vbRedPicture1.DrawWidth = 3Picture1.Line (50, 5500)-(50 + 400 * Int(Text3), 5500 - 400 * Int(Text4))End SubPrivate Sub Command2_Click()Dim k, m, j, l, n, F, G As Integerl = 0 k = 0 F = 0 G = 0Picture1.ForeColor = vbGreenPicture1.DrawWidth = 3n = Int(Text5)j = 2 ^ nm = 2 ^ nForm1.CurrentX = 200Form1.CurrentY = 200Print "累加次数" & "F= F + int (text3)" & "+△X " & " G=G +int(text4)" & " +△Y "; ∑ = " & j"Print " n " & " 0 " & " 0 " & " 0 " & " 0 " & jFor n = 1 To mF = F + Int(Text3)G = G + Int(Text4) If F >= m And G >= m Thenl = l + 1 k = k + 1Picture1.Line (50 + 400 * (l - 1), 5500 - (k - 1) * 400)-(50 + 400 * (l), 5500 - k * 400)F = F - mG = G - mPrint " "; n & " " & F & " " & 1 & " " & G & "j - 1" & 1 & " " & ElseIf F >= m And G < m Thenl = l + 1F = F - mPrint " "; n & " " & F & " " & 1 & " " & G & "j - 1" & 0 & " " &Picture1.Line (50 + 400 * (l - 1), 5500 - k * 400)-(50 + 400 * (l), 5500 - k * 400)ElseIf F < m And G >= m Thenk = k + 1 G = G - mPicture1.Line (50 + 400 * l, 5500 - (k - 1) * 400)-(50 + 400 * (l), 5500 - k * 400)Print " "; n & " " & F & " " & 0 & " " & G & " " & 1 & " " & j - 1ElseIf F < m And G < m ThenPrint " "; n & " " & F & " " & 0 & " " & G & " " & 0 & " " & j - 1End Ifj = j - 1Next nEnd SubPrivate Sub Command3_Click()Text1.Text = ""Text2.Text = ""Picture1.ClsForm1.ClsEnd SubPrivate Sub Command4_Click()End End Sub。

Private Sub Command1_Click()Const pi = 3.14159265Picture1.ForeColor = vbBlackPicture1.DrawWidth = 2Picture1.Line (50, 500)-(50, 5500)Picture1.Line (50, 5500)-(6500, 5500)Picture1.Line (80, 600)-(50, 500)Picture1.Line (20, 600)-(50, 500)Picture1.Line (6400, 5450)-(6500, 5500) Picture1.Line (6400, 5550)-(6500, 5500) Picture1.ForeColor = vbRedPicture1.DrawWidth = 3If Int(Text1) = 0 ThenPicture1.Circle (50, 5500), Sqr(Int(Text1) *Int(Text1) + Int(Text2) * Int(Text2)) * 400, , Atn(Int(Text4) / Int(Text3)), pi / 2ElsePicture1.Circle (50, 5500), Sqr(Int(Text1) *Int(Text1) + Int(Text2) * Int(Text2)) * 400, , Atn(Int(Text4) / Int(Text3)), Atn(Int(Text2) /Int(Text1))End IfEnd SubPrivate Sub Command2_Click()Dim k, m, j, l, n, F(20) As Integerm = 0l = Text1.Textk = Text2.TextF(m) = 0Picture1.ForeColor = vbGreenPicture1.DrawWidth = 3j = Abs(Int(Text1) - Int(Text3)) + Abs(Int(Text2) - Int(Text4))Form1.CurrentX = 200Form1.CurrentY = 200 Print "初始：进给方向 " & "F(m)=0" & " X0=" & Int(Text1) & " Y0=" & Int(Text2) & " ∑ = " & jFor n = 1 To jIf F(m) >= 0 And j > 0 Thenm = m + 1k = k - 1F(m) = F(m - 1) - 2 * Abs(k + 1) + 1Picture1.Line (50 + 400 * l, 5500 - k * 400)-(50 + 400 * l, 5500 - (k + 1) * 400)Form1.CurrentX = 200Form1.CurrentY = 200 + m * 300Print "第" & m & "步" & " -△y F(" & m & ")= " & F(m) & " " & "x=" & l & " " & "y="; k & " ∑=" & j - nElsel = l + 1m = m + 1Picture1.Line (50 + 400 * l, 5500 - k * 400)-(50 + 400 * (l - 1), 5500 - k * 400)F(m) = F(m - 1) + 2 * Abs(l - 1) + 1Form1.CurrentX = 200Form1.CurrentY = 200 + m * 300Print "第" & m & "步" & " +△x F(" & m & ")= " & F(m) & " " & "x="; l & " " & "y="; k & " ∑=" & j - nEnd IfNext nEnd SubPrivate Sub Command3_Click()Text1.Text = ""Text3.Text = ""End SubPrivate Sub Command4_Click()EndEnd SubPrivate Sub Command1_Click()Picture1.ForeColor = vbBlackPicture1.DrawWidth = 2Picture1.Line (7500, 8500)-(7500, 500)Picture1.Line (7500, 500)-(500, 500)Picture1.Line (7500, 8500)-(7400, 8400)Picture1.Line (7500, 8500)-(7600, 8400)Picture1.Line (500, 500)-(600, 600)Picture1.Line (500, 500)-(600, 400)Picture1.ForeColor = vbRedPicture1.DrawWidth = 5Picture1.Line (7500, 500)-(7500 + 400 *Int(Text3), 500 - 400 * Int(Text4))End SubPrivate Sub Command2_Click()Form1.ClsDim k, m, j, l, n, F(20) As Integerm = 0l = 0k = 0F(m) = 0Picture1.ForeColor = vbGreenPicture1.DrawWidth = 3j = Abs(Int(Text3)) + Abs(Int(Text4))Form1.CurrentX = 200Form1.CurrentY = 200Print "初始：进给方向 " & "F(m)=0" & " Xe=" & Int(Text3) & " Ye=" & Int(Text4) & " ∑ = " & jFor n = 1 To jIf F(m) >= 0 And j > 0 Thenm = m + 1l = l - 1F(m) = F(m - 1) - Abs(Int(Text4)) Picture1.Line (7500 + 400 * (l + 1), 500 - k * 400)-(7500 + 400 * (l), 500 - k * 400)Form1.CurrentX = 200Form1.CurrentY = 200 + m * 300Print "第" & m & "步" & " △x F(" & m & ")= "& F(m) & " " & "x=" & l & " " & "y="; k & " ∑=" & j - nElsek = k - 1m = m + 1Picture1.Line (7500 + 400 * l, 500 - (k + 1) * 400)-(7500 + 400 * l, 500 - k * 400)F(m) = F(m - 1) + Abs(Int(Text3))Form1.CurrentX = 200Form1.CurrentY = 200 + m * 300Print "第" & m & "步" & " △y F(" & m & ")= " & F(m) & " " & "x="; l & " " & "y="; k & " ∑=" & j - nEnd IfNext nEnd SubPrivate Sub Command3_Click()Text1.Text = ""Text2.Text = ""Picture1.ClsForm1.ClsEnd SubPrivate Sub Command4_Click()EndEnd SubPrivate Sub Form_Load()End SubPrivate Sub Command1_Click()Const pi = 3.14159265Picture1.ForeColor = vbBlackPicture1.DrawWidth = 2Picture1.Line (50, 500)-(50, 5500)Picture1.Line (50, 5500)-(6500, 5500)Picture1.Line (80, 600)-(50, 500)Picture1.Line (20, 600)-(50, 500)Picture1.Line (6400, 5450)-(6500, 5500)Picture1.Line (6400, 5550)-(6500, 5500)Picture1.ForeColor = vbRedPicture1.DrawWidth = 3Picture1.Line (50, 5500)-(50 + 400 * Int(Text3), 5500 - 400 * Int(Text4))End SubPrivate Sub Command2_Click()Dim k, m, j, l, n, F, G As Integerl = 0 k = 0 F = 0 G = 0Picture1.ForeColor = vbGreenPicture1.DrawWidth = 3n = Int(Text5)j = 2 ^ nm = 2 ^ nForm1.CurrentX = 200Form1.CurrentY = 200Print "累加次数 " & "F= F + int (text3)" & " +△X " & " G=G +int(text4)" & " +△Y "; ∑ = " & j"Print " n " & " 0 " & " 0 " & " 0 " & " 0 " & jFor n = 1 To mF = F + Int(Text3)G = G + Int(Text4) If F >= m And G >= m Thenl = l + 1 k = k + 1Picture1.Line (50 + 400 * (l - 1), 5500 - (k - 1) * 400)-(50 + 400 * (l), 5500 - k * 400)F = F - mG = G - mPrint " "; n & " " & F & " " & 1 & " " & G & " " & 1 & " " & j - 1ElseIf F >= m And G < m Thenl = l + 1F = F - mPrint " "; n & " " & F & " " & 1 & " " & G & " " & 0 & " " & j - 1Picture1.Line (50 + 400 * (l - 1), 5500 - k * 400)-(50 + 400 * (l), 5500 - k * 400)ElseIf F < m And G >= m Thenk = k + 1 G = G - mPicture1.Line (50 + 400 * l, 5500 - (k - 1) * 400)-(50 + 400 * (l), 5500 - k * 400)Print " "; n & " " & F & " " & 0 & " " & G & " " & 1 & " " & j - 1ElseIf F < m And G < m ThenPrint " "; n & " " & F & " " & 0 & " " & G & " " & 0 & " " & j - 1End Ifj = j - 1Next nEnd SubPrivate Sub Command3_Click()Text1.Text = ""Text2.Text = ""Picture1.ClsForm1.ClsEnd SubPrivate Sub Command4_Click()End End Sub。

逐点比较法圆弧插补逐点比较法圆弧插补过程与直线插补过程类似，每进给一步也都要完成四个工作节拍：偏差判别、坐标进给、偏差计算、终点判别。

但是，逐点比较法圆弧插补以加工点距圆心的距离大于还是小于圆弧半径来作为偏差判别的依据。

如图5-7所示的圆弧AB，其圆心位于原点O（0，0），半径为R，令加工点的坐标为P（xi，yj），则逐点比较法圆弧插补的偏差判别函数为当F＝0时，加工点在圆弧上；当F＞0时，加工点在圆弧外；当F＜0时，加工点在圆弧内。

同插补直线时一样，将Fi，j=0同Fi，j＞0归于一类。

下面以第一象限圆弧为例，分别介绍顺时针圆弧和逆时针圆弧插补时的偏差计算和坐标进给情况。

1．插补第一象限逆圆弧1）当Fi，j≥0时，加工点P（xi，yj）在圆弧上或圆弧外，－X方向进给一个脉冲当量，即向趋近圆弧的圆内方向进给，到达新的加工点Pi－1,j，此时xi －1=xi－1，则新加工点Pi－1,j的偏差判别函数Fi－1，j为（2）当Fi，j＜0时，加工点P（xi，yj）在圆弧内，＋Y方向进给一个脉冲当量，即向趋近圆弧的圆外方向进给，到达新的加工点Pi,j＋1，此时yj+1=yj＋1，则新加工点Pi,j＋1的偏差判别函数Fi，j+12．插补第一象限顺圆弧1）当Fi，j≥0时，加工点P（xi，yj）在圆弧上或圆弧外，－Y方向进给一个脉冲当量，即向趋近圆弧的圆内方向进给，到达新的加工点Pi，,j－1，此时yj－1=yj－1，则新加工点Pi，j－1的偏差判别函数Fi，j－1为2）当Fi，j＜0时，加工点P（xi，yj）在圆弧内，＋X方向进给一个脉冲当量，即向趋近圆弧的圆外方向进给，到达新的加工点Pi＋1,j，此时xi＋1=xi ＋1，则新加工点Pi＋1,j的偏差判别函数为Fi+1，j由以上分析可知，新加工点的偏差是由前一个加工点的偏差Fi，j及前一点的坐标值xi、yj递推出来的，如果按式（5-6）、（5-7）、（5-8）、（5-9）计算偏差，则计算大为简化。

大连民族学院本科毕业设计（论文）逐点比较法插补程序程序设计与运行模拟学院（系）：机电信息工程学院_____专业：机械设计制造及其自动化__学生姓名： _________学号： 200902220 _________指导教师： _________评阅教师：_________________________完成日期：_________________________大连民族学院摘要在数控编程时，一般仅提供描述该线形所必须的相关参数，但为了满足几何零件尺寸精度要求，必须在刀具（或工件）运动过程中实时计算出满足线形和进给速度要求的在起点和终点之间的若干中间点，所以就有了插补。

本设计主要阐述了逐点比较法的基本原理，在四个象限直线、圆弧插补的插补原理以及如何实现。

重点研究了逐点比较法的基本算法，控制程序的原理框图，对逐点比较法做了详细的研究，掌握基本的G代码的内容与运用，编写插补程序，并且基于vb平台演示插补过程。

从调试结果来看，本文所提供的运算与编程能够通过简洁的“输入/输出”界面，较好的实现了计算机屏幕模拟。

关键词：简易数控；逐点比较法插补；G代码；VB；计算机屏幕模拟AbstractBy-point comparison interpolation program design and run the simulationprogramIn NC programming, generally only provide a description of the relevant parameters necessary for linear, but in order to meet the accuracy requirements of the geometric part size must be in the tool (or workpiece) during exercise to meet the real-time calculation and linear feed rate required at the start and some intermediate point between the endpoints, so there will be interpolated.The design is mainly explained by-point comparison of the basic principles in the four quadrants linear and circular interpolation interpolation theory and how to implement. Focus on a point by point comparison of the basic algorithm, a block diagram of the control program, right by-point comparison method to do a detailed study and master the basic content and the use of G-code, write interpolation procedures, and is based on interpolation vb platform demo process.From the debugging results, provided herein computing and programming through simple "input / output" interface, to achieve a better simulation of the computer screenKeywords:Simple numerical control; interpolation point by point comparison；G code；VB；Computer simulation on the screen目录摘要 (I)ABSTRACT (II)目录 (III)1 绪论................................................................................................................................ - 1 -1.1课题的背景 (1)1.2课题的主要研究内容 (3)1.3课题的研究方案 (3)2 数控加工基本原理............................................................................................................ - 4 -2.1概述 (4)2.2数控编程内容 (4)2.3逐点比较法直线插补原理 (5)2.3.1偏差计算公式............................................................................................... - 6 -2.3.2插补计算过程............................................................................................... - 6 -2.3.3终点判别....................................................................................................... - 6 -2.3.4不同象限的直线插补计算........................................................................... - 7 -2.4逐点比较法圆弧插补原理 (7)2.4.1偏差计算公式............................................................................................... - 7 -2.4.2终点判别法................................................................................................... - 8 -2.5VB基本原理 (8)3 逐点比较法总体方案设计.............................................................................................. - 10 -3.1程序设计简介 (10)3.2逐点比较法直线插补框图 (11)3.3逐点比较法圆弧插补框图 (12)4 逐点比较法方案的程序设计.......................................................................................... - 14 -4.1逐点比较法直线插补运算 (14)4.2逐点比较法圆弧插补运算 (14)4.3准备功能G代码 (16)4.4插补界面设计 (16)5 VB调试............................................................................................................................. - 17 -5.1直线插补VB调试 (17)5.2圆弧插补VB调试 (17)参考文献.............................................................................................................................. - 20 -附录A 直线和圆弧插补象限区分程序............................................................................. - 21 -致谢.............................................................................................................................. - 28 -1 绪论1.1课题的背景数字控制简称数控，是由数字指令控制对象的一种自动控制技术。

宿迁学院课程设计说明书设计题目：基于VB数字积分法一、二象限逆圆插补计算与仿真系(部)：机电工程系专业：自动化（数控技术）班级：09数控本（2）姓名：李伟学号：200907052指导老师（签名）：刘萍起止时间：20 12年12月3 日至20 12年12月7 日共 1 周20 12 年12 月6 日正文：数控原理与系统课程设计说明书一、课程设计的目的1）了解连续轨迹控制数控系统的组成原理。

2) 掌握逐点比较法插补的基本原理。

3）握逐点比较法插补的软件实现方法。

二．课程设计的任务逐点比较法插补是最简单的脉冲增量式插补算法之一，其过程清晰，速度平稳，但一般只用于一个平面内两个坐标轴的插补运算。

其基本原理是在刀具按要求轨迹运动加工零件轮廓的过程中，不断比较刀具与被加工零件轮廓之间的相对位置，并根据比较结果决定下一步的进给方向，使刀具向减小偏差的方向进给，且只有一个方向的进给。

也就是说，逐点比较法每一步均要比较加工点瞬时坐标与规定零件轮廓之间的距离，依此决定下一步的走向。

如果加工点走到轮廓外面去了，则下一步要朝着轮廓内部走；如果加工点处在轮廓的内部，则下一步要向轮廓外面走，以缩小偏差，这样周而复始，直至全部结束，从而获得一个非常接近于数控加工程序规定轮廓的轨迹。

逐点比较法插补过程中的每进给一步都要经过偏差判别、坐标进给、偏差计算和终点判别四个节拍的处理，其工作流程图如图所示。

三.逐点比较法基本原理逐点比较法I 象限逆圆插补在加工圆弧过程中，人们很容易联想到使用动点到圆心的距离与该圆弧的名义半径进行比较来反映加工偏差。

假设被加工零件的轮廓为第Ⅰ象限逆走向圆弧SE ，，圆心在O （0，0），半径为R ，起点为S （XS ，YS ），终点为E （Xe ，Ye ），圆弧上任意加工动点为N （Xi ，Yi ）。

当比较该加工动点到圆心的距离ON 与圆弧半径R 的大小时，可获得刀具与圆弧轮廓之间的相对位置关系。

当动点N （Xi ，Yi ）正好落在圆弧上时，则有下式成立22222R Y X Y X e e i i =+=+当动点N （Xi ，Yi ）落在圆弧外侧时，则有下式成立22222R Y X Y X e e i i =+>+当动点N （Xi ，Yi ）落在圆弧内侧时，则有下式成立22222R Y X Y X e e i i =+<+由此可见，取逐点比较法圆弧插补的偏差函数表达式为222R Y X F i i -+=当动点落在圆外时，为了减小加工误差，应向圆内进给，即向(－X)轴方向走一步；当动点落在圆内时，应向圆外进给，即向(＋Y)轴方向走一步。

主界面面板逐点比较圆弧插补程序如下：Private Sub Command1_Click()Xe = Val(Text1.Text)Ye = Val(Text2.Text)Picture1.Scale (-20, 20)-(20, -20)Picture1.ClsPicture1.Line (-20, 0)-(20, 0), vbBluePicture1.Line (19, 1)-(20, 0), vbbiuePicture1.Line -(19, -1), vbBluePicture1.Print "X"Picture1.Line (0, -20)-(0, 20), vbBluePicture1.Line (1, 19)-(0, 20), vbBluePicture1.Line -(-1, 19), vbBluePicture1.Print "Y"Picture1.Line (0, 0)-(Xe, Ye), vbBluePicture1.Print "("; Xe; ","; Ye; ")"If Text1.Text = none Or Text2.Text = none Then MsgBox "请输入加工终点坐标值。

"Text3.Text = 0Text4.Text = 0Text5.Text = 0End SubPrivate Sub Command2_Click()Dim sum As IntegerXe = Val(Text1.Text)Ye = Val(Text2.Text)Xm = Val(Text3.Text)Ym = Val(Text4.Text)m = Val(Text5.Text)sum = Xe * Ym - Xm * Ye'第一象限开始If Xe > 0 And Ye > 0 And sum >= 0 Then Picture1.Line (Xm, Ym)-(Xm + 1, Ym), vbRed: Text3.Text = Xm + 1If Xe > 0 And Ye > 0 And sum < 0 Then Picture1.Line (Xm, Ym)-(Xm, Ym + 1), vbRed: Text4.Text = Ym + 1If Abs(Xm) + Abs(Ym) >= Abs(Xe) + Abs(Ye) - 1 Then MsgBox "加工完毕！"'第二象限开始If Xe < 0 And Ye > 0 And sum >= 0 Then Picture1.Line (Xm, Ym)-(Xm, Ym + 1), vbRed: Text4.Text = Ym + 1If Xe < 0 And Ye > 0 And sum < 0 Then Picture1.Line (Xm, Ym)-(Xm - 1, Ym), vbRed: Text3.Text = Xm - 1If Abs(Xm) + Abs(Ym) >= Abs(Xe) + Abs(Ye) + 1 Then MsgBox "加工完毕！"'第三象限开始If Xe < 0 And Ye < 0 And sum >= 0 Then Picture1.Line (Xm, Ym)-(Xm - 1, Ym), vbRed:Text3.Text = Xm - 1If Xe < 0 And Ye < 0 And sum < 0 Then Picture1.Line (Xm, Ym)-(Xm, Ym - 1), vbRed: Text4.Text = Ym - 1If Abs(Xm) + Abs(Ym) >= Abs(Xe) + Abs(Ye) Then MsgBox "加工完毕！"'第四象限开始If Xe > 0 And Ye < 0 And sum >= 0 Then Picture1.Line (Xm, Ym)-(Xm, Ym - 1), vbRed: Text4.Text = Ym - 1If Xe > 0 And Ye < 0 And sum < 0 Then Picture1.Line (Xm, Ym)-(Xm + 1, Ym), vbRed: Text3.Text = Xm + 1If Abs(Xm) + Abs(Ym) >= Abs(Xe) + Abs(Ye) Then MsgBox "加工完毕！"Text5.Text = Abs(Val(Text3.Text)) + Abs(Val(Text4.Text))End SubPrivate Sub Command3_Click()Form2.HideForm1.ShowEnd Sub数字积分器法圆弧插补程序如下：Private Sub Command1_Click()Xe = Val(Text1.Text)Ye = Val(Text2.Text)Picture1.Scale (-20, 20)-(20, -20)Picture1.ClsPicture1.Line (-20, 0)-(20, 0), vbBluePicture1.Line (19, 1)-(20, 0), vbbiuePicture1.Line -(19, -1), vbBluePicture1.Print "X"Picture1.Line (0, -20)-(0, 20), vbBluePicture1.Line (1, 19)-(0, 20), vbBluePicture1.Line -(-1, 19), vbBluePicture1.Print "Y"Picture1.Line (0, 0)-(Xe, Ye), vbBluePicture1.Print "("; Xe; ","; Ye; ")"Text3.Text = 0Text4.Text = 0Text5.Text = 0Text6.Text = 0Text7.Text = 0End SubPrivate Sub Command2_Click()Xe = Val(Text1.Text)Ye = Val(Text2.Text)ax = V al(Text3.Text)ay = Val(Text4.Text)n = Val(Text7.Text)Xm = Val(Text5.Text)Ym = Val(Text6.Text)If Text1.Text = none Or Text2.Text = none Then MsgBox "请输入加工终点坐标值。

第24卷第4期2006年7月北京工商大学学报(自然科学版)Journal of Beijing Techno logy and Business U niversity (N atural Science Editi on )V o l 124N o 14Ju l .2006 文章编号:167121513(2006)0420019204数控插补的VB 实现聂学俊,　高　峰(北京工商大学机械自动化学院,北京　100037)摘　要:插补算法是数控系统控制软件的核心Λ介绍了利用V isual B asic 610编程,对插补算法执行结果进行动态仿真的方法Λ关键词:插补;V isual B asic 610;仿真中图分类号:TH 164;T P 273 文献标识码:A 收稿日期:20060328作者简介:聂学俊(1965-),女,湖南湘乡人,副教授,硕士,主要从事CAD CAM 的教学和研究工作Ζ 在数控系统中,插补的任务是根据数控机床进给速度的要求,在被加工零件轮廓的起点和终点之间计算出若干个中间点的坐标值Ζ由于每个中间点计算所需的时间直接影响数控系统的控制速度,而插补中间点的计算精度又影响到整个数控系统的精度,所以插补算法对整个数控系统的性能指标至关重要,可以说插补是整个数控系统控制软件的核心[1]Ζ目前常用的插补算法有脉冲增量插补和数据采样插补Ζ为了分析各种插补方法的性能好坏,本文以脉冲增量插补中的算法之一——逐点比较法为例,利用可视化对象语言V isual B asic 610进行编程,将插补执行结果在屏幕上动态仿真显示出来,直接观察插补结果Ζ1　插补方法——逐点比较法简介逐点比较法的基本思想是被控制对象在数控系统的控制下,按要求的轨迹运动时,每走一步都要和规定的轨迹比较,根据比较的结果决定下一步移动的方向Ζ其插补步骤分为4步:偏差判别、坐标进给、偏差计算和终点判别Ζ111　逐点比较法直线插补的偏差计算如图1,被加工直线轮廓为OA ,P 点代表加工过程中的动点Ζ根据P 点与被加工直线轮廓OA 的位置关系,得到偏差函数为:F =X e Y i -X i Y e(1)式(1)中,X e 、Y e 为被加工轮廓的终点坐标;X i 、Y i 为加工动点P 的坐标,F 为偏差Ζ图1　逐点比较法直线一象限插补112　逐点比较法圆弧插补的偏差计算如图2,被加工逆圆弧轮廓为A B ,P 点代表加工过程中的动点Ζ根据P 点与被加工逆圆弧轮廓A B 的位置关系,得到偏差函数为:F =X 2i +Y 2i -R 2(2)式(2)中,X i 、Y i 为加工动点坐标,R 为被加工轮廓A B 的半径,F 为偏差Ζ图2　逐点比较法逆圆弧一象限插补将上述一象限直线和逆圆弧的插补方法推广至914个象限,得到直线和圆弧在不同象限的进给方向和偏差的关系分别如图3和图4Ζ图中,X -Y 为计算机屏幕坐标系,X ′-Y ′为工件坐标系,L 1到L 4和C 1到C 4分别为被加工直线和圆弧的理想轮廓,各箭头方向表示对应的坐标轴插补进给方向Ζ图3　逐点比较法直线插补进给方向和偏差的关系图4　逐点比较法逆圆弧插补进给方向和偏差的关系2　插补算法的VB 实现211　V isua l Ba sic 简介M icro soft V isual B asic 是可视化的、面向对象的、采用事件驱动方式的结构化高级程序设计语言,是一套完全独立的开发系统,它提供了开发M i 2cro soft W indow s 应用程序的最迅速、最简捷的方法[2]Λ在本程序实现中,应用了V isual B asic 提供的如下对象:fo rm (窗体)、comm and (命令按钮)、tex t (文本框)、p ictu re (图像对象)、label (标签)等及它们的属性和方法Λ212　插补算法的流程图根据图3和图4,可以方便地得到直线和逆圆弧的逐点比较法四象限插补流程图分别如图5和图6Λ图中,x 0、y 0和x e 、y e 分别为被加工轮廓的起点和终点坐标,n 为插补总步数Λ图5　逐点比较法直线四象限插补流程图6　逐点比较法逆圆弧四象限插补流程213　插补算法的VB 实现应用VB 编程,逐点比较法直线插补的程序如下Λ逐点比较法圆弧插补程序的编写与直线插补的程序类似,不再赘述ΛP rivate Sub Comm and 1-C lick ()　’逐点比较法直线插补D i m x e ,y e ,n ,i A s In teger D i m f ,q ,x ,y A s In tegerCall Comm and 3-C lick ’画坐标系x e =In t (V al (T ex t 1.T ex t ))　’输入直线的终点坐标,画直线y e =In t (V al (T ex t 2.T ex t ))2北京工商大学学报(自然科学版)2006年7月　P ictu re1.D rawW idth=1P ictu re1.L ine(0,0)-(x e,y e),vbR edP ictu re1.Cu rren tX=0P ictu re1.Cu rren tY=0If(x e>=0)A nd(y e>=0)T hen　’判断象限　q=1E lse If(x e<0)A nd(y e>=0)T hen　q=2E lse If(x e<=0)A nd(y e<0)T hen　q=3E lse　q=4End Ifn=In t(A b s(x e)+A b s(y e))　’确定插补次数f=0Fo r i=1To n　’插补开始’　If f>=0T hen　’X方向进给 select case q case1 x=x+1 P ictu re1.L ine-(x,y),vbB lack Call arrow E(x,y) case2 x=x-1 P ictu re1.L ine-(x,y),vbB lack Call arrow W(x,y) case3 x=x-1 P ictu re1.L ine-(x,y),vbB lack Call arrow W(x,y) case4 x=x+1 P ictu re1.L ine-(x,y),vbB lack Call arrow E(x,y) End select f=f-ab s(y e)　else　’Y方向进给 select case q case1 y=y+1 P ictu re1.L ine-(x,y),vbB lack Call arrow N(x,y) case2 y=y+1 P ictu re1.L ine-(x,y),vbB lack Call arrow N(x,y) case3 y=y-1 P ictu re1.L ine-(x,y),vbB lack Call arrow S(x,y) case4 y=y-1 P ictu re1.L ine-(x,y),vbB lack Call arrow S(x,y) End select f=f+ab s(x e) End If N ex t i End Sub逐点比较法直线插补和逆圆弧插补的执行结果分别如图7和图8Λ图7　逐点比较法直线四象限插补结果图8　逐点比较法圆弧四象限插补结果在编写程序时,必须注意几个问题:1)由于计算12　第24卷第4期聂学俊等:数控插补的VB实现机屏幕坐标系和工件坐标系不相一致,故在屏幕上显示插补轨迹时,应注意进给方向和屏幕坐标的转换;2)对于跨越不同象限的圆弧,应考虑插补自动过象限问题Λ3　结论数控插补方法有多种,通过在屏幕上动态显示插补轨迹,可以对比各种插补方法的优劣,对已有的插补方法进行改进和创新,有利于数控插补技术的提高Λ参考文献:[1]　任玉田,焦振学,王宏甫.机床计算机数控技术[M].北京:北京理工大学出版社,1996.[2]　希望图书创作室.V isual Basic610教程[M].北京:北京希望电子出版社,1999.VB REAL IZ ING OF INTERPOLATI ONAL G OR ITH M IN NU M ER I CAL CONTROL S Y STE MN IE Xue2jun,　GAO Feng(Colleg e of M echan ica l E ng ineering and A u to m a tion,B eij ing T echnology andB usiness U n iversity,B eij ing100037,Ch ina)Abstract:In terpo lati on algo rithm is a co re of the con tro l softw are in num erical con tro l system.A m ethod si m u lating the in terpo lati on resu lt th rough p rogramm ing u sing the V isual B asic610is in2 troduced.Key words:in terpo lati on;V isual B asic610;si m u lating(责任编辑:檀彩莲) (上接第18页)ANALY SE AND OPTI M U M ON THE STRUCTUREOF TESTING SUPPORT PLATFOR MON ANTENNA PREC ISI ON M EASURE M ENTJ I AO Hong2jie1,　ZHAN G Y i2du1,　X I AN G H u i2yu2,　YAN G Zhao1,　RON G Zh i2yang1(11R esea rch Cen ter of P recision T rans m ission T echnology,B eij ing U n iversity of A eronau tics andA stronau tics,B eij ing100083,Ch ina;21Colleg e of M echan ica l E ng ineering and A u to m a tion,B eij ing T echnology and B usiness U n iversity,B eij ing100037,Ch ina)Abstract:It is very i m po rtan t that an tenna target suppo rt structu re and rigidity du ring an tenna p recisi on is m easu red in com p act testing fields.B ased on the p recisi on requ irem en t,u sing sub sec2 ti on design,a novel testing suppo rt p latfo rm w h ich satisfies RCS m easu rem en t requ irem en ts is designed.B esides,structu re disto rti on analysis is carried ou t in detail.F inal,structu re di m en2 si on is calcu lated acco rding to target rigidity w eigh t rati o and to tal m ass m in i m izing m ethod.Key words:an tenna;m easu rem en t;suppo rt p latfo rm;p recisi on(责任编辑:檀彩莲) 22北京工商大学学报(自然科学版)2006年7月　。

五、算法程序Private Sub Command1_Click()Picture1.ForeColor = vbBlackPicture1.DrawWidth = 2Picture1.Line (0, 4000)-(9000, 4000)Picture1.Line (4500, 0)-(4500, 8000)End SubPrivate Sub Command2_Click()Picture1.ForeColor = vbBluePicture1.DrawWidth = 2If Val(Text1.Text) * Val(Text1.Text) + Val(Text2.Text) * Val(Text2.Text) <> Val(Text3.Text) * Val(Text3.Text) + Val(Text4.Text) * Val(Text4.Text) Thenans = MsgBox("出错了，该象限所绘圆弧不以原点为圆心", 48, "提示信息")Text1.Text = ""Text2.Text = ""Text3.Text = ""Text4.Text = ""Text5.Text = ""Text6.Text = ""ElseIf Option1.Value = True ThenIf Val(Text1) >= 0 And Val(Text2) >= 0 And Val(Text3) >= 0 And Val(Text4) >= 0 And Val(Text1) >= Val(Text3) Then If Int(Text2) = 0 ThenIf Int(Text3) = 0 ThenPicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , 0, 3.14159 / 2Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))ElsePicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , Atn(Val(Text2) / Val(Text1)), 3.14159 / 2Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))End IfElseIf Int(Text4) = 0 ThenPicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , 0, Atn(Val(Text2) / Val(Text1))ElsePicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , Atn(Val(Text2) / Val(Text1)), Atn(Val(Text4) / Val(Text3))Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))End IfElseans = MsgBox("坐标象限错误或预定圆弧将为顺时针", 48, "提示信息")Text1.Text = ""Text2.Text = ""Text3.Text = ""Text4.Text = ""Text5.Text = ""Text6.Text = ""End IfElseIf Option4.Value = True ThenIf Val(Text1) >= 0 And Val(Text2) <= 0 And Val(Text3) >= 0 And Val(Text4) <= 0 And Val(Text1) <= Val(Text3) Then If Int(Text2) = 0 ThenIf Val(Text3) = 0 ThenPicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , 3 * 3.14159 / 2, 0Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))ElsePicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , Atn(Val(Text4) / Val(Text3)) + 3.14159 * 2, 0Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))End IfElseIf Val(Text3) <> 0 ThenPicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , Atn(Val(Text2) / Val(Text1)) + 3.14159 * 2, Atn(Val(Text4) / Val(Text3)) + 3.14159 * 2Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))ElsePicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , 3 * 3.14159 / 2, Atn(Val(Text2) / Val(Text1)) + 3.14159 * 2Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))End IfElseans = MsgBox("坐标象限错误或预定圆弧将为顺时针", 48, "提示信息")Text1.Text = ""Text2.Text = ""Text3.Text = ""Text4.Text = ""Text5.Text = ""Text6.Text = ""End IfElseIf Option2.Value = True ThenIf Val(Text1) <= 0 And Val(Text2) >= 0 And Val(Text3) <= 0 And Val(Text4) >= 0 And Val(Text1) >= Val(Text3) Then If Int(Text2) = 0 ThenIf Val(Text3) = 0 ThenPicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , 3.14159 / 2, 3.14159Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))ElsePicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , Atn(Val(Text4) / Val(Text3)) + 3.14159, 3.14159Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))End IfElseIf Val(Text3) = 0 ThenPicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , 3.14159 / 2, Atn(Val(Text4) / Val(Text3)) + 3.14159Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))ElsePicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , Atn(Val(Text2) / Val(Text1)) + 3.14159, Atn(Val(Text4) / Val(Text3)) + 3.14159Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))End IfElseans = MsgBox("坐标象限错误或预定圆弧将为顺时针", 48, "提示信息")Text1.Text = ""Text2.Text = ""Text3.Text = ""Text4.Text = ""Text5.Text = ""Text6.Text = ""End IfElseIf Option3.Value = True ThenIf Val(Text1) <= 0 And Val(Text2) <= 0 And Val(Text3) <= 0 And Val(Text4) <= 0 And Val(Text1) <= Val(Text3) ThenIf Int(Text1) = 0 ThenIf Int(Text4) = 0 ThenPicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , 3.14159, 3 * 3.14159 / 2Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))ElsePicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , Atn(Int(Text4) / Int(Text3)) + 3.14159, 3 * 3.14159 / 2Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))End IfElseIf Int(Text4) = 0 ThenPicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , 3.14159, Atn(Int(Text2) / Int(Text1)) + 3.14159Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))ElsePicture1.Circle (4500, 4000), Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2)) * Int(Text6), , Atn(Int(Text2) / Int(Text1)) + 3.14159, Atn(Int(Text4) / Int(Text3)) + 3.14159Text5.Text = Sqr(Val(Text1) * Val(Text1) + Val(Text2) * Val(Text2))End IfElseans = MsgBox("坐标象限错误或预定圆弧将为顺时针", 48, "提示信息")Text1.Text = ""Text2.Text = ""Text3.Text = ""Text4.Text = ""Text5.Text = ""Text6.Text = ""End IfEnd IfEnd IfEnd SubPrivate Sub Command3_Click()If Val(Text1.Text) * Val(Text1.Text) + Val(Text2.Text) * Val(Text2.Text) <> Val(Text3.Text) * Val(Text3.Text) + Val(Text4.Text) * Val(Text4.Text) Thenans = MsgBox("出错了", 48, "提示信息")Text1.Text = ""Text2.Text = ""Text3.Text = ""Text4.Text = ""Text5.Text = ""Text6.Text = ""ElseDim k, m, j, l, n, F(20) As IntegerDim a, b, c, d, e As Integerm = 0l = 0k = 0F(m) = 0a = Int(Text1)b = Int(Text2)c = Int(Text3)d = Int(Text4)e = Int(Text6)Picture1.ForeColor = vbGreenPicture1.DrawWidth = 3j = Abs(c - a) + Abs(d - b)Form1.CurrentX = 15000Form1.CurrentY = 200If Option1.Value = True ThenIf Val(Text1) >= 0 And Val(Text2) >= 0 And Val(Text3) >= 0 And Val(Text4) >= 0 And Option1.Value = True ThenPrint "初始：进给方向 " & "F(m)=0" & " X0=" & Int(Text1) & " Y0=" & Int(Text2) & " ∑ = " & jFor n = 1 To jIf F(m) >= 0 Thenm = m + 1k = k + 1F(m) = F(m - 1) - 2 * a + 1Picture1.Line (4500 + Int(Text1) * e - e * (k - 1), 4000 - Int(Text2) * e - l * e)-(4500 + Int(Text1) * e - e * k, 4000 - Int(Text2) * e - l * e)a = a - 1Form1.CurrentX = 15000Form1.CurrentY = 200 + n * 300Print "第" & m & "步" & " -△x F(" & m & ")= " & F(m) & " " & "x=" & a & " " & "y="; b & " ∑=" & j - nElsel = l + 1m = m + 1Picture1.Line (4500 + Int(Text1) * e - e * k, 4000 - Int(Text2) * e - (l - 1) * e)-(4500 + Int(Text1) * e - e * k, 4000 - Int(Text2) * e - l * e)F(m) = F(m - 1) + 2 * b + 1b = b + 1Form1.CurrentX = 15000Form1.CurrentY = 200 + n * 300Print "第" & m & "步" & " +△y F(" & m & ")= " & F(m) & " " & "x=" & a & " " & "y="; b & " ∑=" & j - nEnd IfNext nElseans = MsgBox("出错", 48, "提示信息")Text1.Text = ""Text2.Text = ""Text3.Text = ""Text4.Text = ""Text5.Text = ""Text6.Text = ""Form1.ClsEnd IfElseIf Option4.Value = True ThenIf Val(Text1) >= 0 And Val(Text2) <= 0 And Val(Text3) >= 0 And Val(Text4) <= 0 And Option4.Value = True ThenPrint "初始：进给方向 " & "F(m)=0" & " X0=" & Int(Text1) & " Y0=" & Int(Text2) & " ∑ = " & jFor n = 1 To jIf F(m) >= 0 Thenm = m + 1l = l + 1F(m) = F(m - 1) - 2 * Abs(b) + 1Picture1.Line (4500 + Int(Text1) * e + e * k, 4000 - Int(Text2) * e - (l - 1) * e)-(4500 + Int(Text1) * e + e * k, 4000 - Int(Text2) * e - l * e)b = b + 1Form1.CurrentX = 15000Form1.CurrentY = 200 + n * 300Print "第" & m & "步" & " +△y F(" & m & ")= " & F(m) & " " & "x=" & a & " " & "y="; b & " ∑=" & j - nElsek = k + 1m = m + 1Picture1.Line (4500 + Int(Text1) * e + e * (k - 1), 4000 - Int(Text2) * e - l * e)-(4500 + Int(Text1) * e + e * k, 4000 - Int(Text2) * e - l * e)F(m) = F(m - 1) + 2 * Abs(a) + 1a = a + 1Form1.CurrentX = 15000Form1.CurrentY = 200 + n * 300Print "第" & m & "步" & " +△x F(" & m & ")= " & F(m) & " " & "x=" & a & " " & "y="; b & " ∑=" & j - nEnd IfNext nElseans = MsgBox("出错", 48, "提示信息")Text1.Text = ""Text2.Text = ""Text3.Text = ""Text4.Text = ""Text5.Text = ""Text6.Text = ""Form1.ClsEnd IfElseIf Option2.Value = True ThenIf Val(Text1) <= 0 And Val(Text2) >= 0 And Val(Text3) <= 0 And Val(Text4) >= 0 And Option2.Value = True ThenPrint "初始：进给方向 " & "F(m)=0" & " X0=" & Int(Text1) & " Y0=" & Int(Text2) & " ∑ = " & jFor n = 1 To jIf F(m) >= 0 Thenm = m + 1l = l + 1F(m) = F(m - 1) - 2 * Abs(b) + 1Picture1.Line (4500 + Int(Text1) * e - e * k, 4000 - Int(Text2) * e + (l - 1) * e)-(4500 + Int(Text1) * e - e * k, 4000 - Int(Text2) * e + l * e)b = b - 1Form1.CurrentX = 15000Form1.CurrentY = 200 + n * 300Print "第" & m & "步" & " -△y F(" & m & ")= " & F(m) & " " & "x=" & a & " " & "y="; b & " ∑=" & j - nElsek = k + 1m = m + 1Picture1.Line (4500 + Int(Text1) * e - e * (k - 1), 4000 - Int(Text2) * e + l * e)-(4500 + Int(Text1) * e - e * k, 4000 - Int(Text2) * e + l * e)F(m) = F(m - 1) + 2 * Abs(a) + 1a = a - 1Form1.CurrentX = 15000Form1.CurrentY = 200 + n * 300Print "第" & m & "步" & " -△x F(" & m & ")= " & F(m) & " " & "x=" & a & " " & "y="; b & " ∑=" & j - nEnd IfNext nElseans = MsgBox("出错", 48, "提示信息")Text1.Text = ""Text2.Text = ""Text3.Text = ""Text4.Text = ""Text5.Text = ""Text6.Text = ""Form1.ClsEnd IfElseIf Option3.Value = True ThenIf Val(Text1) <= 0 And Val(Text2) <= 0 And Val(Text3) <= 0 And Val(Text4) <= 0 And Option3.Value = True ThenPrint "初始：进给方向 " & "F(m)=0" & " X0=" & Int(Text1) & " Y0=" & Int(Text2) & " ∑ = " & jFor n = 1 To jIf F(m) >= 0 Thenm = m + 1k = k + 1F(m) = F(m - 1) - 2 * Abs(a) + 1Picture1.Line (4500 + Int(Text1) * e + e * (k - 1), 4000 - Int(Text2) * e + l * e)-(4500 + Int(Text1) * e + e * k, 4000 - Int(Text2) * e + l * e)a = a + 1Form1.CurrentX = 15000Form1.CurrentY = 200 + n * 300Print "第" & m & "步" & " +△x F(" & m & ")= " & F(m) & " " & "x=" & a & " " & "y="; b & " ∑=" & j - n Elsel = l + 1m = m + 1F(m) = F(m - 1) + 2 * Abs(b) + 1Picture1.Line (4500 + Int(Text1) * e + e * k, 4000 - Int(Text2) * e + (l - 1) * e)-(4500 + Int(Text1) * e + e * k, 4000 - Int(Text2) * e + l * e)b = b - 1Form1.CurrentX = 15000Form1.CurrentY = 200 + n * 300Print "第" & m & "步" & " -△y F(" & m & ")= " & F(m) & " " & "x=" & a & " " & "y="; b & " ∑=" & j - nEnd IfNext nElseans = MsgBox("出错", 48, "提示信息")Text1.Text = ""Text2.Text = ""Text3.Text = ""Text4.Text = ""Text5.Text = ""Text6.Text = ""Form1.ClsEnd IfEnd IfEnd IfEnd SubPrivate Sub Command4_Click()Text1.Text = ""Text2.Text = ""Text3.Text = ""Text4.Text = ""Text5.Text = ""Text6.Text = ""Picture1.ClsForm1.ClsPicture1.ForeColor = vbBlackPicture1.DrawWidth = 2Picture1.Line (0, 4000)-(9000, 4000)Picture1.Line (4500, 0)-(4500, 8000)End SubPrivate Sub Command5_Click()Text1.Text = ""Text2.Text = ""Text3.Text = ""Text4.Text = ""Text5.Text = ""Text6.Text = ""Picture1.ClsForm1.ClsEnd SubPrivate Sub Command6_Click()EndEnd SubPrivate Sub Command7_Click()End Sub。

(二)逐点比较法圆弧插补
逐点比较法圆弧插补是数控加工中常用的一种圆弧插补方法，其原理是通过逐点比较给定的圆弧路径与机床实际移动轨迹的差异，不断调整目标点的加工速度和轨迹实现精细的加工。

1.将给定的圆弧路径分割成若干个目标点，通常每隔一定距离取一个目标点。

2.根据目标点之间的距离和已知的转速，计算每个目标点的加工速度。

3.将目标点逐个输入数控系统，根据当前位置和目标点的位置计算运动轨迹和加工速度。

4.在运动过程中不断比较实际轨迹和目标轨迹之间的误差，根据误差大小调整加工速度，保证加工精度。

5.重复步骤3和4，直到完成整个圆弧的加工。

逐点比较法圆弧插补的优点是在加工过程中能够动态地调整加工速度，避免加工误差的累积。

同时，它对系统精度要求不高，能够适应各种数控系统。

不过，逐点比较法圆弧插补的缺点也是比较明显的。

由于每个目标点的加工速度独立计算，导致加工过程中产生了较大的速度变化，容易引起加工表面的纹路和不良的表面质量。

因此，在实际应用中，需要根据加工要求和机床精度选择合适的加工方法，并进行适当的加工优化。

逐点比较法第一象限直线，圆弧插补编程逐点比较法是以折线来逼近给定的轨迹，就是每走一步控制系统都要将加工点与给定的图形轨迹相比较，以决定下一步进给的方向，使之逼近加工轨迹。

逐点比较法以折线来逼近直线或圆弧，其最大的偏差不超过一个最小设定单位。

只要将脉冲当量取得足够小，就可以达到精度要求。

逐点比较插补法在脉冲当量为0.01mm，系统进给速度小于3000mm/min时，能很好的满足要求。

一、逐点比较法直线插补如下图所示设直线 oA 为第一象限的直线，起点为坐标原点o (0 ， 0) ，终点坐标为， A( ) ， P() 为加工点。

若 P 点正好处在直线 oA 上，由相似三角形关系则有即点在直线 oA 上方 ( 严格为直线 oA 与 y 轴正向所包围的区域 ) ，则有即若 P 点在直线 oA 下方 ( 严格为直线 oA 与 x 轴正向所包围的区域 ) ，则有图 3 — 1 逐点比较法第一象限直线插补即令则有：①如，则点 P 在直线 oA 上，既可向 +x 方向进给一步，也可向 +y 方向进给一步；②如，则点 P 在直线 oA 上方，应向 +x 方向进给一步，以逼近oA 直线；③如，则点 P 在直线 oA 下方，应向 +y 方向进给一步，以逼近 oA 直线一般将及视为一类情况，即时，都向 +x 方向进给一步。

当两方向所走的步数与终点坐标相等时，停止插补。

这即逐点比较法直线插补的原理。

对第一象限直线 oA 从起点 ( 即坐标原点 ) 出发，当 F 时， +x 向走一步；当 F<0 时，y 向走一步。

特点：每一步都需计算偏差，这样的计算比较麻烦。

递推的方法计算偏差：每走一步后新的加工点的偏差用前一点的加工偏差递推出来。

采用递推方法，必须知道开始加工点的偏差，而开始加工点正是直线的起点，故。

下面推导其递推公式。

设在加工点 P( ) 处，，则应沿 +x 方向进给一步，此时新加工点的坐标值为新加工点的偏差为即若在加工点 P( ) 处，，则应沿 +y 方向进给一步，此时新加工点的坐标值为，新加工点的偏差为即综上所述，逐点比较法直线插补每走一步都要完成四个步骤 ( 节拍 ) ，即：(1) 位置判别根据偏差值大于零、等于零、小于零确定当前加工点的位置。

四、调试分析1.缩短型2.伸长型3.插入型附录：程序如下：Option ExplicitDim X0 As Single '圆弧三点坐标Dim Y0 As SingleDim X1 As SingleDim Y1 As SingleDim X2 As SingleDim Y2 As SingleDim I1 As Single ' 两个圆心相对圆弧起点坐标Dim J1 As SingleDim I2 As SingleDim J2 As SingleDim R1 As Single '两个圆弧半径Dim R2 As SingleDim r As Single '刀具半径Dim OX1 As Single '两圆心实际坐标Dim OY1 As SingleDim OX2 As SingleDim OY2 As SingleDim Xx1 As SingleDim Yy1 As SingleDim Start1 As Single '第一段圆弧起始弧度Dim End1 As Single '第一段圆弧结束弧度Dim Start2 As Single '第二段圆弧起始弧度Dim End2 As Single '第二段圆弧结束弧度Const Pi = 3.1415926Private Sub Command1_Click()Picture1.Cls '清除picturebox控件中的内容Picture1.DrawWidth = 1X0 = Val(Split(Text1.Text, ",")(0)) '将文本框中的文本从逗号分离并转化成数值Y0 = Val(Split(Text1.Text, ",")(1))X1 = Val(Split(Text2.Text, ",")(0))Y1 = Val(Split(Text2.Text, ",")(1))X2 = Val(Split(Text3.Text, ",")(0))Y2 = Val(Split(Text3.Text, ",")(1))I1 = Val(Itext1.Text) '取圆心相对圆弧起点坐标J1 = Val(Jtext1.Text)I2 = Val(Itext2.Text)J2 = Val(Jtext2.Text)R1 = Sqr(I1 * I1 + J1 * J1) '计算第一段圆弧半径If Not Option1.Value Then R1 = -R1 '通过确定顺圆逆圆判断半径符号R2 = Sqr(I2 * I2 + J2 * J2) '计算第二段圆弧半径If Not Option3.Value Then R2 = -R2 '通过确定顺圆逆圆判断半径符号r = Val(rText.Text) '取刀具半径If Not Option5.Value Then r = -r '通过确定左刀补右刀补判断刀具半径符号'=======================画动态坐标系====================== Dim t1 As Single '取出X最大值Dim t2 As Single '取出X最小值Dim t3 As Single '取出Y最大值Dim t4 As Single '取出Y最小值t1 = X0t2 = X0t3 = Y0t4 = Y0If t1 < X1 Then t1 = X1 '求坐标中最大值与最小值If t1 < X2 Then t1 = X2If t2 > X1 Then t2 = X1If t2 > X2 Then t2 = X2If t3 < Y1 Then t3 = Y1If t3 < Y2 Then t3 = Y2If t4 > Y1 Then t4 = Y1If t4 > Y2 Then t4 = Y2If t1 < t3 Then t1 = t3If t2 > t4 Then t2 = t4Dim m As SingleIf Abs(R1) < Abs(R2) Thenm = Abs(R2)Elsem = Abs(R1)End Ift1 = t1 + Abs(r) + m '坐标轴对圆弧和刀补轨迹留有余量t2 = t2 - Abs(r) - mPicture1.Scale (t2, t1)-(t1, t2) '设定picturebox左上角右下角坐标值Picture1.Line (t2, 0)-(t1, 0), vbRed '画X轴Picture1.Line (0, t2)-(0, t1), vbRed '画Y轴Dim I As IntegerDim Ts1 As IntegerDim Ts2 As IntegerTs1 = Fix(t2)Ts2 = Fix(t1)For I = Ts1 To Ts2 Step 1Picture1.Line (I, -0.2)-(I, 0.2), vbRed '画X轴竖线Picture1.CurrentY = -0.2Picture1.Print I '打印刻度值Picture1.Line (-0.2, I)-(0.2, I), vbRed '画Y轴横线Picture1.CurrentX = -0.5Picture1.Print I '打印刻度值Next IPicture1.CurrentX = Ts2 - 1Picture1.CurrentY = -1Picture1.Print "X" '标上XPicture1.CurrentX = -1Picture1.CurrentY = Ts2 - 1Picture1.Print "Y" '标上YPicture1.Line (t1 - 0.3, -0.3)-(t1, 0), vbRed '画箭头Picture1.Line (t1 - 0.3, 0.3)-(t1, 0), vbRedPicture1.Line (-0.3, t1 - 0.3)-(0, t1), vbRedPicture1.Line (0.3, t1 - 0.3)-(0, t1), vbRed'================================================ End SubPrivate Sub Command2_Click()Picture1.DrawWidth = 2 '线宽OX1 = I1 + X0 '圆心实际坐标OY1 = J1 + Y0OX2 = I2 + X1OY2 = J2 + Y1Dim tt As SingleXx1 = -I1 '圆弧起点相对圆心坐标Yy1 = -J1Start1 = hudu(Xx1, Yy1) '第一段圆弧起点对应弧度Xx1 = X1 - OX1 '圆弧终点相对圆心坐标Yy1 = Y1 - OY1End1 = hudu(Xx1, Yy1) '第一段圆弧终点对应弧度If Option1.Value Then '画图时如果是顺圆，起点与终点弧度调换tt = Start1Start1 = End1End1 = ttEnd IfIf End1 < Start1 Then '圆弧经过X轴正方向Picture1.Circle (OX1, OY1), Abs(R1), , Start1, 2 * Pi, 624 / 697 Picture1.Circle (OX1, OY1), Abs(R1), , 0, End1, 624 / 697Else '圆弧不经过X轴正方向Picture1.Circle (OX1, OY1), Abs(R1), , Start1, End1, 624 / 697End IfXx1 = -I2 '圆弧起点相对圆心坐标Yy1 = -J2 '圆弧终点相对圆心坐标Start2 = hudu(Xx1, Yy1) '第二段圆弧起点对应弧度Xx1 = X2 - OX2Yy1 = Y2 - OY2End2 = hudu(Xx1, Yy1) '第二段圆弧终点对应弧度If Option3.Value Then '画图时如果是顺圆，起点与终点弧度调换tt = Start2Start2 = End2End2 = ttEnd IfIf End2 < Start2 Then '圆弧经过X轴正方向Picture1.Circle (OX2, OY2), Abs(R2), , Start2, 2 * Pi, 624 / 697Picture1.Circle (OX2, OY2), Abs(R2), , 0, End2, 624 / 697Else '圆弧不经过X轴正方向Picture1.Circle (OX2, OY2), Abs(R2), , Start2, End2, 624 / 697End If'Picture1.Circle (3, 4), 5End Sub'=======================弧度计算函数===================== Function hudu(ByVal m As Single, ByVal n As Single) As SingleDim k As SingleIf m <> 0 Then '斜率存在时k = n / mIf m >= 0 And n >= 0 Then hudu = Atn(k)If m >= 0 And n < 0 Then hudu = Atn(k) + 2 * PiIf m < 0 And n >= 0 Then hudu = Atn(k) + PiIf m < 0 And n < 0 Then hudu = Atn(k) + PiElse '斜率不存在时If n >= 0 Thenhudu = Pi / 2Elsehudu = Pi / 2 + PiEnd IfEnd IfEnd Function'=============刀补运算=======================Private Sub Command3_Click()Picture1.DrawWidth = 1Dim X01 As Single '圆心相对圆弧交接点坐标Dim Y01 As SingleDim X02 As SingleDim Y02 As SingleDim Xl1 As Single '圆弧在交接点处的方向矢量Dim Yl1 As SingleDim Xl2 As SingleDim Yl2 As SingleX01 = X0 + I1 - X1Y01 = Y0 + J1 - Y1X02 = I2Y02 = J2Xl1 = -Y01 / R1Yl1 = X01 / R1Xl2 = -Y02 / R2Yl2 = X02 / R2Dim Cases As SingleDim Xs1 As Single '转接点坐标Dim Ys1 As SingleDim Xs2 As SingleDim Ys2 As SingleDim Xs3 As SingleDim Ys3 As SingleDim Xs4 As SingleDim Ys4 As SingleDim Xl As Single '书上公式中的变量Dim Yl As SingleDim D1 As SingleDim D2 As SingleDim Fs As SingleDim k As Single '中间变量Dim s As SingleDim Ss As SingleDim Mmx As SingleDim Mmy As SingleDim Mma As SingleDim Flag1 As BooleanDim Flag2 As BooleanDim tt As Single '中间变量Cases = Sgn(r) * (Yl2 * Xl1 - Xl2 * Yl1)If Cases > 0 Then'======================================缩短型====================================== 'MATLAB中得到的两圆交点公式k = (R1 ^ 2 + 4 * R1 * r + 2 * R1 * R2 - OY2 ^ 2 - OX1 ^ 2 - OY1 ^ 2 - OX2 ^ 2 + 4 * R2 * r + 2 * OY1 * OY2 + R2 ^ 2 + 4 * r ^ 2 + 2 * OX2 * OX1)s = (-OY2 ^ 2 - OY1 ^ 2 + 2 * OY1 * OY2 + 2 * OX2 * OX1 - 2 * R1 * R2 + R1 ^ 2 + R2 ^ 2 - OX1 ^ 2 - OX2 ^ 2)Ss = -2 * OY2 * OY1 * OX2 ^ 2 + OX2 ^ 2 * OY2 ^ 2 + OY1 * (-(OX1 - OX2) ^ 2 * (-OY2 ^ 2 - OY1 ^ 2 + 2 * OY1 * OY2 + 2 * OX2 * OX1 - 2 * R1 * R2 + R1 ^ 2 + R2 ^ 2 - OX1 ^ 2 - OX2 ^ 2) * (R1 ^ 2 + 4 * R1 * r + 2 * R1 * R2 - OY2 ^ 2 - OX1 ^ 2 - OY1 ^ 2 - OX2 ^ 2 + 4 * R2 * r + 2 * OY1 * OY2 + R2 ^ 2 + 4 * r ^ 2 + 2 * OX2 * OX1)) ^ (1 / 2) + 2 * OY2 * OX1 ^ 2 * OY1 + 2 * OX2 * OX1 * R2 ^ 2 - 2 * OX2 * OX1 * R1 ^ 2 - 2 * OX2 ^ 2 * R2 * r + 2 * R1 * r * OX2 ^ 2 - 2 * OX1 ^ 2 * R2 * r + 2 * OX1 ^ 2 * R1 * r - 4 * OX2 * OX1 * R1 * r + 4 * OX2 * OX1 * R2 * r + R1 ^ 2 * OX1 ^ 2 + R1 ^ 2 * OX2 ^ 2 - OX1 ^ 2 * OY1 ^ 2 - OX1 ^ 2 * R2 ^ 2 - OX1 ^ 2 * OY2 ^ 2 + OY1 ^ 2 * OX2 ^ 2 - R2 ^ 2 * OX2 ^ 2 - OX1 ^ 4 + OX2 ^ 4 + 2 * OX2 * OX1 ^ 3 - 2 * OX2 ^ 3 * OX1 - OY2 * (-(OX1 - OX2) ^ 2 * s * k) ^ (1 / 2)Mmx = -1 / 2 * Ss / (-2 * OX2 * OX1 - 2 * OY1 * OY2 + OX1 ^ 2 + OY1 ^ 2 + OX2 ^ 2 + OY2 ^ 2) / (OX1 - OX2)Mmy = -1 / 2 * (-R1 ^ 2 * OY2 - OY1 ^ 3 - OX1 ^ 2 * OY2 + 2 * OY2 * R2 * r + 2 * OX2 * OX1 * OY1 + 2 * OX2 * OX1 * OY2 - 2 * OY2 * R1 * r - 2 * OY1 * R2 * r + 2 * OY1 * R1 * r + R1 ^ 2 * OY1 - OY1 * OX2 ^ 2 - OX1 ^ 2 * OY1 + OY1 ^ 2 * OY2 - OY1 * R2 ^ 2 - OY2 * OX2 ^ 2 + OY1 * OY2 ^ 2 + OY2 * R2 ^ 2 - OY2 ^ 3 - (-(OX1 - OX2) ^ 2 * (-OY2 ^ 2 - OY1 ^ 2 + 2 * OY1 * OY2 + 2 * OX2 * OX1 - 2 * R1 * R2 + R1 ^ 2 + R2 ^ 2 - OX1 ^ 2 - OX2 ^ 2) * (R1 ^ 2 + 4 * R1 * r + 2 * R1 * R2 - OY2 ^ 2 - OX1 ^ 2 - OY1 ^ 2 - OX2 ^ 2 + 4 * R2 * r + 2 * OY1 * OY2 + R2 ^ 2 + 4 * r ^ 2 + 2 * OX2 * OX1)) ^ (1 / 2)) / (-2 * OX2 * OX1 - 2 * OY1 * OY2 + OX1 ^ 2 + OY1 ^ 2 + OX2 ^ 2 + OY2 ^ 2)Xx1 = Mmx - OX1Yy1 = Mmy - OY1Mma = hudu(Xx1, Yy1)If End1 < Start1 Then '判断该点是否满足第一段圆弧If Mma < Start1 And Mma > End1 ThenFlag1 = FalseElseFlag1 = TrueEnd IfElseIf Mma > Start1 And Mma < End1 ThenFlag1 = TrueElseFlag1 = FalseEnd IfEnd IfXx1 = Mmx - OX2Yy1 = Mmy - OY2Mma = hudu(Xx1, Yy1)If End2 < Start2 Then '判断该点是否满足第二段圆弧If Mma < Start2 And Mma > End2 ThenFlag2 = FalseElseFlag2 = TrueEnd IfElseIf Mma > Start2 And Mma < End2 ThenFlag2 = TrueElseFlag2 = FalseEnd IfEnd IfIf Flag1 And Flag2 Then '判断得到的点是否满足条件Xs1 = MmxYs1 = MmyEnd Ifk = R1 ^ 2 + 4 * R1 * r + 2 * R1 * R2 - OY2 ^ 2 - OX1 ^ 2 - OY1 ^ 2 - OX2 ^ 2 + 4 * R2 * r + 2 * OY1 * OY2 + R2 ^ 2 + 4 * r ^ 2 + 2 * OX2 * OX1s = -(OX1 - OX2) ^ 2 * (-OY2 ^ 2 - OY1 ^ 2 + 2 * OY1 * OY2 + 2 * OX2 * OX1 - 2 * R1 * R2 + R1 ^ 2 + R2 ^ 2 - OX1 ^ 2 - OX2 ^ 2)Ss = (-2 * OY2 * OY1 * OX2 ^ 2 + OX2 ^ 2 * OY2 ^ 2 - OY1 * (-(OX1 - OX2) ^ 2 * (-OY2 ^ 2 - OY1 ^ 2 + 2 * OY1 * OY2 + 2 * OX2 * OX1 - 2 * R1 * R2 + R1 ^ 2 + R2 ^ 2 - OX1 ^ 2 - OX2 ^ 2) * (R1 ^ 2 + 4 * R1 * r + 2 * R1 * R2 - OY2 ^ 2 - OX1 ^ 2 - OY1 ^ 2 - OX2 ^ 2 + 4 * R2 * r + 2 * OY1 * OY2 + R2 ^ 2 + 4 * r ^ 2 + 2 * OX2 * OX1)) ^ (1 / 2) + 2 * OY2 * OX1 ^ 2 * OY1 + 2 * OX2 * OX1 * R2 ^ 2 - 2 * OX2 * OX1 * R1 ^ 2 - 2 * OX2 ^ 2 * R2 * r + 2 * R1 * r * OX2 ^ 2 - 2 * OX1 ^ 2 * R2 * r + 2 * OX1 ^ 2 * R1 * r - 4 * OX2 * OX1 * R1 * r + 4 * OX2 * OX1 * R2 * r + R1 ^ 2 * OX1 ^ 2 + R1 ^ 2 * OX2 ^ 2 - OX1 ^ 2 * OY1 ^ 2 - OX1 ^ 2 * R2 ^ 2 - OX1 ^ 2 * OY2 ^ 2 + OY1 ^ 2 * OX2 ^ 2 - R2 ^ 2 * OX2 ^ 2 - OX1 ^ 4 + OX2 ^ 4 + 2 * OX2 * OX1 ^ 3 - 2 * OX2 ^ 3 * OX1 + OY2 * (s * k) ^ (1 / 2))Mmx = -1 / 2 * Ss / (-2 * OX2 * OX1 - 2 * OY1 * OY2 + OX1 ^ 2 + OY1 ^ 2 + OX2 ^ 2 + OY2 ^ 2) / (OX1 - OX2)Mmy = -1 / 2 * (-R1 ^ 2 * OY2 - OY1 ^ 3 - OX1 ^ 2 * OY2 + 2 * OY2 * R2 * r + 2 * OX2 * OX1 * OY1 + 2 * OX2 * OX1 * OY2 - 2 * OY2 * R1 * r - 2 * OY1 * R2 * r + 2 * OY1 * R1 * r + R1 ^ 2 * OY1 - OY1 * OX2 ^ 2 - OX1 ^ 2 * OY1 + OY1 ^ 2 * OY2 - OY1 * R2 ^ 2 - OY2 * OX2 ^ 2 + OY1 * OY2 ^ 2 + OY2 * R2 ^ 2 - OY2 ^ 3 + (-(OX1 - OX2) ^ 2 * (-OY2 ^ 2 - OY1 ^ 2 + 2 * OY1 * OY2 + 2 * OX2 * OX1 - 2 * R1 * R2 + R1 ^ 2 + R2 ^ 2 - OX1 ^ 2 - OX2 ^ 2) * (R1 ^ 2 + 4 * R1 * r + 2 * R1 * R2 - OY2 ^ 2 - OX1 ^ 2 - OY1 ^ 2 - OX2 ^ 2 + 4 * R2 * r + 2 * OY1 * OY2 + R2 ^ 2 + 4 * r ^ 2 + 2 * OX2 * OX1)) ^ (1 / 2)) / (-2 * OX2 * OX1 - 2 * OY1 * OY2 + OX1 ^ 2 + OY1 ^ 2 + OX2 ^ 2 + OY2 ^ 2)Xx1 = Mmx - OX1Yy1 = Mmy - OY1Mma = hudu(Xx1, Yy1)If End1 < Start1 Then '判断该点是否满足第一段圆弧If Mma < Start1 And Mma > End1 ThenFlag1 = FalseElseFlag1 = TrueEnd IfElseIf Mma > Start1 And Mma < End1 ThenFlag1 = TrueElseFlag1 = FalseEnd IfEnd IfXx1 = Mmx - OX2Yy1 = Mmy - OY2Mma = hudu(Xx1, Yy1)If End2 < Start2 Then '判断该点是否满足第二段圆弧If Mma < Start2 And Mma > End2 ThenFlag2 = FalseElseFlag2 = TrueEnd IfElseIf Mma > Start2 And Mma < End2 ThenFlag2 = TrueElseFlag2 = FalseEnd IfEnd IfIf Flag1 And Flag2 Then '判断得到的点是否满足条件Xs1 = MmxYs1 = MmyEnd IfPicture1.DrawWidth = 3 '线宽Picture1.PSet (Xs1, Ys1) '画点Picture1.Print "(" & Xs1 & "," & Ys1 & ")" '打印坐标Picture1.DrawWidth = 1 '线宽' '---------------------------------画刀补轨迹--------------------------------- Xx1 = -I1Yy1 = -J1Start1 = hudu(Xx1, Yy1)Xx1 = Xs1 - OX1Yy1 = Ys1 - OY1End1 = hudu(Xx1, Yy1)If Option1.Value Thentt = Start1Start1 = End1End1 = ttEnd IfIf End1 < Start1 Then '画第一段圆弧Picture1.Circle (OX1, OY1), Abs(R1 + r), vbGreen, Start1, 2 * Pi, 624 / 697Picture1.Circle (OX1, OY1), Abs(R1 + r), vbGreen, 0, End1, 624 / 697 ElsePicture1.Circle (OX1, OY1), Abs(R1 + r), vbGreen, Start1, End1, 624 / 697 End IfXx1 = Xs1 - X1 - I2Yy1 = Ys1 - Y1 - J2Start2 = hudu(Xx1, Yy1)Xx1 = X2 - OX2Yy1 = Y2 - OY2End2 = hudu(Xx1, Yy1)If Option3.Value Thentt = Start2Start2 = End2End2 = ttEnd IfIf End2 < Start2 Then '画第二段圆弧Picture1.Circle (OX2, OY2), Abs(R2 + r), vbGreen, Start2, 2 * Pi, 624 / 697Picture1.Circle (OX2, OY2), Abs(R2 + r), vbGreen, 0, End2, 624 / 697ElsePicture1.Circle (OX2, OY2), Abs(R2 + r), vbGreen, Start2, End2, 624 / 697End IfElseIf Yl2 * Yl1 + Xl2 * Xl1 >= 0 Then'======================================伸长型====================================== Xs1 = X1 - r * Yl1Ys1 = Y1 + r * Xl1Xs2 = X1 + (Xl2 - Xl1) * r / (Xl1 * Yl2 - Xl2 * Yl1)Ys2 = Y1 + (Yl2 - Yl1) * r / (Xl1 * Yl2 - Xl2 * Yl1)Xs3 = X1 - r * Yl2Ys3 = Y1 + r * Xl2If End1 < Start1 Then '画第一段圆弧Picture1.Circle (OX1, OY1), Abs(R1 + r), vbGreen, Start1, 2 * Pi, 624 / 697Picture1.Circle (OX1, OY1), Abs(R1 + r), vbGreen, 0, End1, 624 / 697ElsePicture1.Circle (OX1, OY1), Abs(R1 + r), vbGreen, Start1, End1, 624 / 697End IfIf End2 < Start2 Then '画第二段圆弧Picture1.Circle (OX2, OY2), Abs(R2 + r), vbGreen, Start2, 2 * Pi, 624 / 697Picture1.Circle (OX2, OY2), Abs(R2 + r), vbGreen, 0, End2, 624 / 697ElsePicture1.Circle (OX2, OY2), Abs(R2 + r), vbGreen, Start2, End2, 624 / 697End IfPicture1.Line (Xs1, Ys1)-(Xs2, Ys2), vbGreen '画两段直线Picture1.Line (Xs2, Ys2)-(Xs3, Ys3), vbGreenPicture1.DrawWidth = 3 '线宽Picture1.PSet (Xs1, Ys1) '画点Picture1.Print "(" & Xs1 & "," & Ys1 & ")" '打印坐标值Picture1.PSet (Xs2, Ys2)Picture1.Print "(" & Xs2 & "," & Ys2 & ")"Picture1.PSet (Xs3, Ys3)Picture1.Print "(" & Xs3 & "," & Ys3 & ")"Else'======================================插入型====================================== Xs1 = X1 - r * Yl1Ys1 = Y1 + r * Xl1Xs2 = Xs1 + Abs(r) * Xl1Ys2 = Ys1 + Abs(r) * Yl1Xs3 = X1 - r * Yl2 - Abs(r) * Xl2Ys3 = Y1 + r * Xl2 - Abs(r) * Yl2Xs4 = X1 - r * Yl2Ys4 = Y1 + r * Xl2If End1 < Start1 Then '画第一段圆弧Picture1.Circle (OX1, OY1), Abs(R1 + r), vbGreen, Start1, 2 * Pi, 624 / 697Picture1.Circle (OX1, OY1), Abs(R1 + r), vbGreen, 0, End1, 624 / 697ElsePicture1.Circle (OX1, OY1), Abs(R1 + r), vbGreen, Start1, End1, 624 / 697End IfIf End2 < Start2 Then '画第二段圆弧Picture1.Circle (OX2, OY2), Abs(R2 + r), vbGreen, Start2, 2 * Pi, 624 / 697Picture1.Circle (OX2, OY2), Abs(R2 + r), vbGreen, 0, End2, 624 / 697ElsePicture1.Circle (OX2, OY2), Abs(R2 + r), vbGreen, Start2, End2, 624 / 697End IfPicture1.Line (Xs1, Ys1)-(Xs2, Ys2), vbGreen '画三段直线Picture1.Line (Xs2, Ys2)-(Xs3, Ys3), vbGreenPicture1.Line (Xs3, Ys3)-(Xs4, Ys4), vbGreenPicture1.DrawWidth = 3Picture1.PSet (Xs1, Ys1)Picture1.Print "(" & Xs1 & "," & Ys1 & ")"Picture1.PSet (Xs2, Ys2)Picture1.Print "(" & Xs2 & "," & Ys2 & ")"Picture1.PSet (Xs3, Ys3)Picture1.Print "(" & Xs3 & "," & Ys3 & ")"Picture1.PSet (Xs4, Ys4)Picture1.Print "(" & Xs4 & "," & Ys4 & ")"End IfEnd IfEnd SubPrivate Sub Form_Load()Command1.Enabled = TrueCommand2.Enabled = TrueCommand3.Enabled = TrueEnd Sub。

xxxx 学院课程设计说明书设计题目：逐点比较法逆圆弧插补的程序设计系 (部)：机电工程系专业：自动化（数控技术）班级： 08数控本（1）班姓名：学号：指导老师（签名）：起止时间：20 11年 12月 5 日至20 11年 12月 9 日共 1 周20 11 年 12 月 11 日目录一．课程设计的目的 (1)二．课程设计的任务 (1)三．逐点比较法基本原理 (1)四．算法描述 (6)五．具体算法程序 (10)六．各象限选例展示 (17)七．心得体会 (19)八．参考文献 (19)正文：数控原理与系统课程设计说明书一、课程设计的目的1）了解连续轨迹控制数控系统的组成原理。

2) 掌握逐点比较法插补的基本原理。

3）握逐点比较法插补的软件实现方法。

二．课程设计的任务逐点比较法插补是最简单的脉冲增量式插补算法之一，其过程清晰，速度平稳，但一般只用于一个平面内两个坐标轴的插补运算。

其基本原理是在刀具按要求轨迹运动加工零件轮廓的过程中，不断比较刀具与被加工零件轮廓之间的相对位置，并根据比较结果决定下一步的进给方向，使刀具向减小偏差的方向进给，且只有一个方向的进给。

也就是说，逐点比较法每一步均要比较加工点瞬时坐标与规定零件轮廓之间的距离，依此决定下一步的走向。

如果加工点走到轮廓外面去了，则下一步要朝着轮廓内部走；如果加工点处在轮廓的内部，则下一步要向轮廓外面走，以缩小偏差，这样周而复始，直至全部结束，从而获得一个非常接近于数控加工程序规定轮廓的轨迹。

逐点比较法插补过程中的每进给一步都要经过偏差判别、坐标进给、偏差计算和终点判别四个节拍的处理，其工作流程图如图所示。

三.逐点比较法基本原理逐点比较法I象限逆圆插补在加工圆弧过程中，人们很容易联想到使用动点到圆心的距离与该圆弧的名义半径进行比较来反映加工偏差。

假设被加工零件的轮廓为第Ⅰ象限逆走向圆弧SE ，，圆心在O （0，0），半径为R ，起点为S （XS ，YS ），终点为E （Xe ，Ye ），圆弧上任意加工动点为N （Xi ，Yi ）。

数控技术课程讲课方案 / 讲稿逐点比较法圆弧插补教师姓名：杨丽梅学院（部、中心）：机电工程学院教研室∕实验室：机电教研室联系电话：2009年7月长春工业大学课程教案∕讲稿用纸讲授内容讲课方案∕备注逐点比较法圆弧插补重点内容：掌握什么是逐点比较法及逐点比较法在圆弧插补中的应用。

难点内容：逐点比较法插补在顺圆弧和逆圆弧插补中的差异。

讲课内容共分为四部分：一、逐点比较法1、逐点比较法的基根源理：每次仅向一个坐标轴输出一个进给脉冲，而每走一步都要经过误差函数计算，判断误差点的瞬时坐标同规定加工轨迹之间的误差，今后决定下一步的进给方向。

逐点比较法又称为代数运算法或醉步法，是我国早期数控机床中广泛采用的一种方法。

2、逐点比较法的应用：可用于直线插补、圆弧插补和其他曲线的插补。

3、逐点比较法的特点：运算直观、插补误差不大于一个脉冲当量，脉冲输出均匀，调治方便。

二、逐点比较法圆弧插补1、加工点与圆弧之间的关系（1）点在圆弧上；（2）点位于圆弧外；（3）点位于圆弧内。

图 1 加工点与圆弧的关系加工点与圆弧的关系如图 1 所示。

2、误差函数构造如图 1 所示，若加工半径为R 的圆弧 AB ，将坐标原点定在圆心上，如右图所示。

对于任意加工点P i ( X i ,Y i ) ，其误差函数 F i可表示为：F i X i2Y i2R2（1）（1）若F i0 ，表示加工点位于圆上；（2）若（3）若F i0 ，表示加工点位于圆内；F i0 ，表示加工点位于圆外；3、误差函数的递推计算为了对（ 1）式进行简化计算，需采用递推式（或迭代式）。

以第一象限圆弧为例，对误差函数进行推导。

第一象限的圆弧分为顺圆弧和逆圆弧，即有顺圆弧和逆圆弧插补两种方式。

（1）逆圆弧插补若 F i0 ，规定向X 方向走一步，有X i1X i1（2）F i 1 ( X i 1) 2Y i2R2F i 2 X i 1若 F i 0，规定向Y方向走一步，有Y i 1 Y i1（3）Fi 1X2(Y 1)2R2Fi2Y 1i i i（2）顺圆弧插补若 F i0 ，规定向Y 方向走一步，有Y i1Y i 1（4）F i 1 X i2(Y i1)2R2F i 2Y i 1若 F i 0，规定向X方向走一步，有X i1X i1（5）Fi 1( Xi1) 2Y2R2Fi2 Xi1i4、终点鉴识终点鉴识可采用以下两种方法：（1）判断插补或进给的总步数：N X a X b Y a Y b（6）（2）分别判断各坐标轴的进給步数：N x X a X b（7）N Y Y a Y b三、逐点比较法圆弧插补举例已知第一象限内的圆弧AB ，起点 A(4,0) ，终点 B(0,4) ，如图2所示。