WO2021128614A1 - 一种基于特征线的弧面凸轮廓面误差测量与评定方法 - Google Patents

一种基于特征线的弧面凸轮廓面误差测量与评定方法 Download PDF

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WO2021128614A1
WO2021128614A1 PCT/CN2020/080526 CN2020080526W WO2021128614A1 WO 2021128614 A1 WO2021128614 A1 WO 2021128614A1 CN 2020080526 W CN2020080526 W CN 2020080526W WO 2021128614 A1 WO2021128614 A1 WO 2021128614A1
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error
cam
line
characteristic line
characteristic
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PCT/CN2020/080526
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French (fr)
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孙树文
刘志峰
王建华
胡秋实
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北京工业大学
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
    • B23Q17/00—Arrangements for observing, indicating or measuring on machine tools
    • B23Q17/20—Arrangements for observing, indicating or measuring on machine tools for indicating or measuring workpiece characteristics, e.g. contour, dimension, hardness
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant

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  • the invention belongs to the technical field of arc cam error measurement and evaluation, and specifically relates to a characteristic line-based arc cam profile error measurement and evaluation method.
  • the arc cam is a key component of the automatic tool changer of CNC machine tools, and the automatic tool changer is an important functional component of medium and high-end CNC machine tools.
  • the kinematic relationship of the globular cam indexing mechanism is complicated, the machining and manufacturing of the globular cam profile is difficult, and the processing quality inspection is more difficult.
  • my country does not have completely independent production capacity for automatic tool changers of high-end CNC machine tools, and most of them rely on imports. For a long time, foreign companies have firmly occupied the Chinese market by virtue of their strong technical strength. Therefore, my country has a high degree of dependence on foreign businessmen in core technology.
  • the core technology of the arc cam automatic tool changer lies in the manufacturing and product quality inspection of the arc cam.
  • the working profile of the arc cam is a complex space that cannot be developed. It is difficult to measure and evaluate with conventional methods. At present, there is no mature arc cam profile error evaluation system in China.
  • the present invention is composed of a three-coordinate measuring machine and a turntable.
  • the four-axis measurement system realizes the measurement of the isometric profile characteristic line of the arc cam under the specified angle, avoids the probe radius compensation, and improves the measurement speed and accuracy; combined with the characteristics of the arc cam profile, the computer is used for data processing. Fast matching and error evaluation of characteristic lines.
  • the purpose of the present invention is to provide a characteristic line-based method for measuring and evaluating the error of the arc cam profile surface, which can quickly measure the machining accuracy of the arc cam profile and evaluate the processing quality.
  • the technical solution adopted by the present invention is: a method for measuring and evaluating the error of a curved camber profile based on a characteristic line.
  • the steps of the method are as follows:
  • Step 1 Construction of the error measurement system for the cambered cam profile
  • the measurement process of the characteristic line of the cambered cam profile 1) Rotation of the turntable makes the cambered cam stop at a certain cam angle, the cam angle is measured by a circular grating, and the digital display shows the accuracy (resolution 0.4 arc second); 2) Measurement The machine probe measures the characteristic line of the cambered cam in the shaft section (Y-axis is fixed); 3) The cambered cam profile error analysis and processing software conducts error evaluation, and unqualified products give suggestions for machine tool machining error adjustment.
  • Step 2 Plan the characteristic line to be measured on the camber profile surface
  • the measurement characteristic line is planned first, that is, according to the relationship between the cam rotation angle and the turntable rotation angle shown in Figure 2, the preliminary measurement plan of the globular cam characteristic line is carried out in Solidworks.
  • the arc cam includes three rest segments and three indexing segments during the movement.
  • the cam angle intervals of the rest segment are [358°, 2°], [52°, 122.5°], [237.5 °, 308°]; the cam angle intervals of the indexing section are [2°, 52°], [122.5°, 237.5°], [308°, 358°].
  • the cam rotation angle interval is [52°, 122.5°], [237.5°, 308°]
  • the cam rotation angle differs by 180° and the cam rotation angle is 70.5°.
  • the two intervals are equally divided For an equal number of characteristic lines, the cam rotation angles corresponding to the characteristic lines corresponding to the two intervals differ by 180°.
  • the measurement characteristic line Because the characteristic line of the resting section is always a straight line, the measurement is performed on a small number of characteristic points on the characteristic line, and each characteristic line measures 8 characteristic points; while the characteristic line of the arc cam in the indexing section is a spatial curve , In order to accurately analyze the feature line of the indexing section, measure the relatively large number of feature points on the feature line, and measure 12 feature points for each feature line.
  • the characteristic line of the indexing section It can be seen from Figure 3 that the arc cam has 3 indexing sections in a working cycle.
  • the measurement number and distribution interval of the characteristic line of the shaft section of each section are: a) Cam rotation angle interval [2° , 52°], plan 10 characteristic lines with a unit of 5° as shown in Figure 6; b) Cam rotation angle interval [122.5°, 237.5°], plan 23 measurement characteristic lines with a unit of 5° as shown in Figure 7 ; C) Cam rotation angle interval [308°, 358°], planning 10 characteristic lines with a unit of 5° as shown in Figure 8.
  • Step 3 Measure the characteristic points of the cambered profile surface
  • the arc cam measuring system composed of a three-coordinate measuring machine and a turntable is used to complete the error detection of the arc cam profile.
  • the detection steps and content are shown in Figure 9.
  • Step 4 Establish an error model of the camber profile measurement system
  • the measurement system includes a coordinate measuring machine base 1, a turntable 2, a camber 3, a coordinate measuring machine X axis 4, a coordinate measuring machine Y axis 5, a coordinate measuring machine Z axis 6 and Probe rotation axis 7.
  • the turntable 2 and the arc cam 3 are installed in the middle of the bottom of the coordinate measuring machine base 1, and the Y axis 5 of the coordinate measuring machine is installed on both sides of the coordinate measuring machine base 1 through the X axis 4 of the coordinate measuring machine;
  • the Z axis 6 of the measuring machine is installed on the Y axis 5 of the coordinate measuring machine, and the probe rotation axis 7 is installed at the end of the Z axis 6 of the coordinate measuring machine; the probe rotation axis 7 can pass through the X axis 4, Adjust the position of the coordinate measuring machine Y axis 5 and the coordinate measuring machine Z axis 6.
  • the measurement system is divided into two branches, as shown in b) of Figure 10, which are the probe branch and the workpiece branch:
  • Probe branch CMM frame 1— CMM X axis 4— CMM Y axis 5— CMM Z axis 6—Rotating axis 7 of the probe.
  • the measurement system error includes the error of the coordinate measuring machine and the error of the turntable. Since the error detection of the coordinate measuring machine is regularly detected and compensated in its measurement software system, this method only considers the error of the turntable in the measurement system.
  • the turntable includes 6
  • the term error as shown in Figure 11, includes 3 linear displacement errors and 3 angular displacement errors. According to the multi-body theory, the transformation matrix between the turntable coordinate system and the cam coordinate system is determined as.
  • the linear displacement transformation matrix is:
  • t SZ Linear displacement matrix along the Z axis of the turntable coordinate system
  • the angular displacement transformation matrix is:
  • r SY The angular displacement matrix rotating around the Y axis of the turntable coordinate system
  • r SZ Angular displacement matrix rotating around the Z axis of the turntable coordinate system
  • x s , y s , z s represent the coordinates of point P on the arc cam in the turntable coordinate system
  • p represents the position vector of point P on the arc cam in the machining coordinate system
  • t SZ Linear displacement matrix along the Z axis of the turntable coordinate system
  • r SX The angular displacement matrix rotating around the X axis of the turntable coordinate system
  • r SY The angular displacement matrix rotating around the Y axis of the turntable coordinate system
  • r SZ The angular displacement matrix rotating around the Z axis of the turntable coordinate system.
  • the purpose of establishing the error model of the measurement system is to eliminate its influence on the measurement results and to provide a theoretical basis for improving the accuracy of data processing through error compensation in the process of error evaluation.
  • Step 5 Evaluation of the error of the characteristic line of the camber profile
  • the line profile error evaluation method is based on the definition in GB/T 1182-2008.
  • the tolerance zone of line profile is the two envelopes of a series of circles with a diameter equal to the tolerance value w and a circle center located on a theoretically correct geometric shape. The area defined by the line. As shown in Figure 12, w is the curve profile error.
  • the contour error evaluation of complex curves often adopts the method of calculating the distance between the corresponding points after corresponding theoretical points and measured points as the contour error.
  • the two-end point method refers to the ideal contour line passing through the two ends of the actual measured contour line as the evaluation reference, and the difference between the maximum deviation value and the minimum deviation value of the deviation value of each point relative to it is taken as the line contour
  • the minimum area evaluation method is the basic principle of shape error evaluation. The minimum area means that when the actual contour line is contained by two curves, the ideal contour line passes through the actual measured contour line, and the two curves reach the ideal contour line respectively. The normal distances are equal and the width between them is the smallest containment area.
  • the line profile error evaluation is divided into two cases: one is based on the theoretical contour line, and the error of each measurement point is obtained by calculating the distance between the actual measurement point and the theoretical contour line, such as As shown in Figure 4; the other is based on the measured contour line, and calculate the distance from the theoretical contour point to the measured contour line, as shown in Figure 5. It can be seen from the definition of profile that when the positions of the measured points are consistent with the theoretical points, the evaluation results of the two cases are the same.
  • the characteristic line of the resting section is a straight line, and the two-end point method is proposed for error evaluation; the characteristic line of the indexing section is a curve, and the minimum area method is proposed for error evaluation; both the rest section and the indexing section use the measured contour line as the benchmark for error evaluation .
  • the data processing methods and basic steps are different. The following will discuss in detail the evaluation process of the characteristic lines of the resting section and the indexing section.
  • x, y, z— represent the coordinate of the characteristic point of the arc cam
  • b zi —— represents the intercept of the straight line formed by adjacent measuring points
  • i represents the feature point number of the arc cam.
  • k represents the average value of the slope of the straight line formed by the measuring points
  • b z Indicates the average value of the intercept of the straight line formed by the measuring points.
  • the characteristic line equation is in formula (9)
  • ⁇ is the known cam rotation angle
  • ⁇ can be obtained through the curve relationship of the indexing mechanism motion law
  • the parameters b min and b max correspond to
  • ⁇ , ⁇ , b min and ⁇ , ⁇ , b max correspond to
  • (X 1 ,z 1 ), (X 2 ,z 2 ) indicate the coordinate values of the two ends of the resting section under the axis section.
  • the theoretical profile feature line of the indexing section is not a straight line, and the same evaluation method as the rest section cannot be used. Through the comparison of the minimum area method and the least square method, the minimum area evaluation method with better evaluation accuracy is finally selected as the method of line profile error evaluation.
  • the specific process of the error evaluation of the feature line of the indexing section is: 1) Select the curve fitting method, and fit the actual measurement points into the curve as the error evaluation benchmark; 2) Determine the number of theoretical feature points, and discretely solve the theoretical feature points. Coordinate value; 3) Solve the distance from the theoretical characteristic point to the measured characteristic line respectively; 4) Determine whether the error value of the characteristic line of the indexing section is within the given tolerance range.
  • the error of the characteristic line of the indexing section is not a straight line.
  • the method of calculating the distance from the theoretical characteristic point to the measured characteristic line is different from the rest section.
  • the segmentation search method is used to find the minimum distance between the theoretical feature point and the measured feature line, and the maximum value of the minimum distance is taken as the line profile error. This method conforms to the principle of minimum area evaluation for profile error. 15 shown.
  • the points on the theoretical characteristic line are a 1 , a 2 , a 3 , a 4 , a, 5 a 6
  • the points on the measured characteristic line are b 1 , b 2 , b 3 , b 4 , b 5 , for the theoretical feature point a 4 , there is and only one point b 3 located on the measured feature line, so that the distance between a 4 and the measured feature line is minimized, namely:
  • each theoretical feature point exists and there is only one point on the measured feature line to minimize the distance d between the two. These two points are also used as matching points between the measured data and the theoretical data.
  • the maximum distance between each theoretical feature point and the measured feature point is regarded as the line profile error, namely:
  • d i is the distance from the theoretical to the measured feature point feature point.
  • Step 6 Evaluation of the error of the camber profile
  • the surface profile error evaluation method is defined in GB/T1182-2008.
  • the tolerance zone of the surface profile is a series of spheres whose diameter is equal to the tolerance value t and the center of the sphere is located on the measured element with theoretically correct geometric shapes.
  • Section method which refers to the measurement of the line profile error of several sections of the actual measured profile surface, and the maximum value of the error value of each section is taken as the profile surface.
  • the error value of the surface profile is taken as the profile surface.
  • Three-distance point method refers to the ideal contour surface that passes through the three furthest points on the actual measured contour surface as the evaluation standard, and takes the measured distance of each point relative to its normal distance. The difference between the maximum deviation value and the minimum deviation value is used as the surface profile error value. The deviation value of the measuring point above it is taken as a positive value, and the deviation value of the measuring point below it is taken as a negative value.
  • the minimum area method is used to determine the surface profile error value.
  • the minimum area method is the basic principle of the evaluation of the surface profile error.
  • the minimum area means that when the actual contour surface is contained by two curved surfaces, the ideal contour surface passes through the actual measured contour surface.
  • the normal distances between the two curved surfaces to the ideal contour surface are equal and the width between them is the minimum containment area.
  • the measurement method using the isometric profile axis section characteristic line is consistent with the section method in the surface profile error evaluation method, so the section method is used as the evaluation method of the arc cam surface profile error.
  • the method for evaluating the error of the arc cam profile based on the characteristic line proposed by the present invention effectively avoids the error of the detection equipment itself through the error modeling of the three-coordinate measuring machine, and uses the error measurement and evaluation of the characteristic line to measure and evaluate the error of the arc cam. Line error and area error are defined.
  • the method of the present invention makes the detection result more accurate, and provides a method for evaluating the machining error of the cambered cam, and provides theoretical support for improving the machining accuracy of the cambered cam in my country and specifying quality testing technical standards.
  • Fig. 1 The structure diagram of the camber profile error measurement system.
  • Figure 3 The planning of the measurement characteristic line in the cam rotation angle interval [358°, 2°].
  • Figure 4 The measurement characteristic line planning of the cam rotation angle interval [52°, 122.5°].
  • Fig. 5 The measurement characteristic line planning of the cam rotation angle interval [237.5°, 308°].
  • Fig. 6 The planning of the measurement characteristic line in the cam rotation angle interval [2°, 52°].
  • Figure 7 The measurement characteristic line planning of the cam rotation angle interval [122.5°, 237.5°].
  • Figure 8 The measurement characteristic line planning of the cam rotation angle interval [308°, 358°].
  • Figure 14 Measured contour line as a reference.
  • Figure 15 The principle of solving the contour error of the dividing period line.
  • Figure 17 Virtual coordinate measurement system with turntable.
  • Figure 18 The theoretical characteristic line and the measured characteristic line of the upper profile surface with a cam angle of 30°.
  • Figure 19 The theoretical characteristic line and the measured characteristic line of the lower profile with a cam angle of 30°.
  • Figure 20 The theoretical characteristic line and the measured characteristic line of the upper profile surface with a cam angle of 40°.
  • Figure 21 The theoretical and measured characteristic lines of the lower profile with a cam angle of 40°.
  • the theoretical model of the camber and the model of the camber with machining errors were established in the virtual measurement environment, as shown in Figure 17.
  • the contour error of the upper profile surface line with a cam rotation angle of 60° is evaluated as follows:
  • the calculated line profile error is 0.1132mm, and the sensitivity coefficient when the cam rotation angle is 60° is 0.4051mm/deg, so the machine tool error is:
  • the calculated line profile error is 0.485mm, and the sensitivity coefficient of the lower profile surface at a cam angle of 60° is 1.735, so the machine tool error is:
  • the characteristic lines of the upper profile surface and the lower profile surface of the arc cam at 60° are under different cutting paths, and the sensitivity coefficients at the rest section are the same. After measuring according to the given arc cam characteristic line measurement plan The calculation result of the data is the same as the calculation result when the cam rotation angle is 60°.
  • Table 4 The coordinate of the characteristic point containing the angular displacement error of the A axis around the Y direction when the cam rotation angle is 30° (mm)
  • the minimum distance from the point on the theoretical characteristic line to the measured characteristic line is solved by the segmentation search method as the line profile error.
  • the evaluation method for the contour error of the upper profile surface line with a cam angle of 30° is as follows: First, use the NURBS curve to fit the measured characteristic points with errors, and the curve equation after fitting is:
  • the combined error of the final solution is 0.035mm.
  • the error ⁇ Y (A) 0.005rad approximation.
  • the evaluation process of the contour error of the upper profile surface and the lower profile surface with a cam rotation angle of 40° is the same as the evaluation process for the cam rotation angle of 30°.
  • the comprehensive error of the upper profile surface after evaluation is 0.1842mm, and the cam rotation angle is 30°.

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Abstract

一种基于特征线的弧面凸轮廓面误差测量与评定方法，该方法的实现步骤如下，构建三坐标测量机搭配转台的四轴测量系统；规划弧面凸轮廓面待测特征线；测量弧面凸轮廓面特征点；建立弧面凸轮廓面测量系统误差模型；弧面凸轮廓面特征线误差评定；弧面凸轮廓面误差评定；通过建立测量系统的误差建模，有效规避掉检测设备本身的误差对测量结果的影响，并且采用指定角度下弧面凸轮等距廓面特征线误差进行分段测量和评定，避免了测头半径补偿，提高了测量速度和计算精度，检测的结果更加的精确，利于提升弧面凸轮的加工精度、制定质量检测标准。

Description

一种基于特征线的弧面凸轮廓面误差测量与评定方法 技术领域
本发明属于弧面凸轮误差测量与评价技术领域，具体涉及一种基于特征线的弧面凸轮廓面误差测量与评定方法。
背景技术
弧面凸轮是数控机床自动换刀装置的关键零部件，自动换刀装置是中高档数控机床的重要功能部件。弧面凸轮分度机构运动关系复杂，弧面凸轮廓面加工制造难度大，加工质量检测更加困难。目前，我国不具备用于高档数控机床自动换刀装置的完全自主生产能力，大部分依赖进口。一直以来，国外企业凭借强大的技术实力，牢牢占领着中国的市场，因此，我国在核心技术上对外商的依赖程度相当高。弧面凸轮自动换刀装置的核心技术在于弧面凸轮的加工制造和产品质量检测。弧面凸轮的工作廓面为复杂空间不可展曲面，很难用常规的方法进行测量与评价，目前国内尚无成熟的弧面凸轮廓面误差评价体系，本发明通过三坐标测量机搭配转台构成四轴测量系统，实现指定角度下弧面凸轮等距廓面特征线的测量，避免了测头半径补偿，提高了测量速度和精度；结合弧面凸轮廓面的特点，利用计算机进行数据处理实现特征线的快速匹配与误差评定。
发明内容
本发明目的在于提供了一种基于特征线的弧面凸轮廓面误差测量与评定方法，对弧面凸轮廓面加工精度进行快速测量，并对加工质量进行评定。
为了实现上述目的，本发明采用的技术方案是：一种基于特征线的弧面凸轮廓面误差测量与评定方法，该方法的实现步骤如下，
S1、构建三坐标测量机搭配转台的四轴测量系统；
S2、规划弧面凸轮廓面待测特征线；
S3、测量弧面凸轮廓面特征点；
S4、建立弧面凸轮廓面测量系统误差模型；
S5、弧面凸轮廓面特征线误差评定；
S6、弧面凸轮廓面误差评定；
步骤一：弧面凸轮廓面误差测量系统构建；
为提高测量速度与测量准确性，采用三坐标测量机搭配转台构成新的测量系统，弧面凸轮廓面误差测量系统整体结构如图1所示。
弧面凸轮廓面特征线的测量过程：1)转台旋转使弧面凸轮在一定凸轮转角下停止，凸轮转角由圆光栅测量，数显表显示精确度数(分辨率0.4角秒)；2)测量机测头在轴截面内测量弧面凸轮特征线(Y轴固定 不动)；3)弧面凸轮廓面误差分析处理软件进行误差评定，不合格产品给出机床加工误差调整建议。
步骤二：规划弧面凸轮廓面待测特征线；
为了方便三坐标测量机进行弧面凸轮特征线测量，首先对测量特征线进行规划，即根据图2所示凸轮转角与转盘转角的关系，在Solidworks中进行弧面凸轮特征线的初步测量规划。
由图4看出，弧面凸轮在运动过程中包括三个停歇段和三个分度段，停歇段凸轮转角区间分别为[358°，2°]、[52°，122.5°]、[237.5°，308°]；分度段凸轮转角区间分别为[2°，52°]、[122.5°，237.5°]、[308°，358°]。凸轮转角区间为[52°，122.5°]、[237.5°，308°]时，凸轮转角相差180°且凸轮所转角度均为70.5°，在进行测量特征线规划时，将两个区间等分相等数量的特征线，两个区间对应的特征线所对应的凸轮转角相差180°。
在规划测量特征线时，由于停歇段特征线始终为直线，针对特征线上少量特征点进行测量，每条特征线测量8个特征点；而弧面凸轮在分度段的特征线为空间曲线，为精确分析分度段的特征线，针对特征线上相对较多的特征点进行测量，每条特征线测量12个特征点。
综上所述，弧面凸轮测量特征线的规划如下：
(1)停歇段测量特征线通过图2可知，弧面凸轮在一个工作周期内有三段停歇，每段的轴截面特征线的测量数量及分布间隔如下：
a)凸轮转角区间[358°，2°]，以1°为单位规划4条特征线如图3所示。
b)凸轮转角区间[52°，122.5°]、[237.5°，308°]，以5°为单位规划10条特征线，分别如图4和图5所示。
(2)分度段特征线通过图3可知，弧面凸轮在一个工作周期内有3分度段，每段的轴截面特征线的测量数量及分布间隔为：a)凸轮转角区间[2°，52°]，以5°为单位规划10条特征线如图6所示；b)凸轮转角区间[122.5°，237.5°]，以5°为单位规划23条测量特征线如图7所示；c)凸轮转角区间[308°，358°]，以5°为单位规划10条特征线如图8所示。
步骤三：测量弧面凸轮廓面特征点；
由三坐标测量机和转台构成的弧面凸轮测量系统，用来完成弧面凸轮廓面的误差检测，检测步骤和内容如图9所示。
步骤四：建立弧面凸轮廓面测量系统误差模型；
针对本发明提出的基于弧面凸轮廓面特征线测量方法建立的测量系统进行误差分析，测量系统的结构示意图和抽象描述拓扑结构如图10所示。图10的a)中，测量系统包括三坐标测量机机座1、转台2、弧面凸轮3、三坐标测量机X轴4、三坐标测量机Y轴5、三坐标测量机Z轴6和测头旋转轴7。转台2和弧面凸轮3安装在三坐标测量机机座1的底部中间，三坐标测量机Y轴5通过三坐标测量机X轴4安装在三坐标测量机机座1的两侧；三坐标测量机Z轴6安装在三坐标测量机Y轴5上，且测头旋转轴7安装在三坐 标测量机Z轴6的端部；测头旋转轴7能够通过三坐标测量机X轴4、三坐标测量机Y轴5和三坐标测量机Z轴6调整位置。
根据多体理论，将测量系统分为两个分支，如图10的b)所示，分别为测头分支和工件分支：
测头分支：三坐标测量机机座1—三坐标测量机X轴4—三坐标测量机Y轴5—三坐标测量机Z轴6—测头旋转轴7。
工件分支：三坐标测量机1—转台2—弧面凸轮3。
测量系统误差包括三坐标测量机的误差及转台的误差，由于三坐标测量机的误差检测定期检测并在其测量软件系统中进行补偿，因此本方法只考虑测量系统中转台的误差，转台包括6项误差，如图11所示，包括3项线位移误差和3项角位移误差。根据多体理论，确定转台坐标系与凸轮坐标系之间的变换矩阵为。
线位移变换矩阵为：
Figure PCTCN2020080526-appb-000001
Figure PCTCN2020080526-appb-000002
Figure PCTCN2020080526-appb-000003
式中t SX——沿转台坐标系X轴方向的线位移矩阵；
t SY——沿转台坐标系Y轴方向的线位移矩阵；
t SZ——沿转台坐标系Z轴方向的线位移矩阵；
δ X(S)——沿转台坐标系X轴方向的线位移误差；
δ Y(S)——沿转台坐标系Y轴方向的线位移误差；
δ Z(S)——沿转台坐标系Z轴方向的线位移误差。
角位移变换矩阵为：
Figure PCTCN2020080526-appb-000004
Figure PCTCN2020080526-appb-000005
Figure PCTCN2020080526-appb-000006
式中r SX——绕转台坐标系X轴旋转的角位移矩阵；
r SY——绕转台坐标系Y轴旋转的角位移矩阵；
r SZ——绕转台坐标系Z轴旋转的角位移矩阵；
ε X(S)——绕转台坐标系X轴旋转的角位移误差；
ε Y(S)——绕转台坐标系Y轴旋转的角位移误差；
ε Z(S)——绕转台坐标系Z轴旋转的角位移误差。
根据式(1)至式(6)以及多体理论，求得在转台坐标系下，弧面凸轮上P点的位置矢量p s：
Figure PCTCN2020080526-appb-000007
式中x s，y s，z s——表示弧面凸轮上P点在转台坐标系下的坐标；
p——表示弧面凸轮上P点在加工坐标系下的位置矢量；
t SX——沿转台坐标系X轴方向的线位移矩阵；
t SY——沿转台坐标系Y轴方向的线位移矩阵；
t SZ——沿转台坐标系Z轴方向的线位移矩阵；
r SX——绕转台坐标系X轴旋转的角位移矩阵；
r SY——绕转台坐标系Y轴旋转的角位移矩阵；
r SZ——绕转台坐标系Z轴旋转的角位移矩阵。
至此，测量系统误差模型建立完成。
建立测量系统误差模型的目的是为了消除其对测量结果的影响，为在误差评定过程中通过误差补偿的方法提高数据处理的准确性提供理论依据。
步骤五：弧面凸轮廓面特征线误差评定
(1)线轮廓度误差评定方法根据GB/T 1182-2008中的定义，线轮廓度的公差带为直径等于公差值w、圆心位于具有理论正确几何形状上的一系列圆的两包络线所限定的区域。如图12所示，w即为曲线轮廓度误差。
复杂曲线的轮廓度误差评定，常采用使理论点和实测点相对应后，求对应点间的距离作为轮廓度误差的方法。线轮廓度误差的评定方法通常有三种方法：1)最小二乘评定法，是用理想曲线的等距线逼近实际曲线，并使残差平方和最小，这时的残差是指等距曲线与实际曲线的法向距离。与最小区域评定法相比，虽存在一定的误差，但它完全能满足实际生产要求，因而在形状误差评定中被广泛采用。2)两端点法，是指以通过实际被测轮廓线两端点的理想轮廓线作为评定基准，取测得各点相对于它的偏差值中的最大偏差值与最小偏差值之差作为线轮廓度误差值，在其上面的测点的偏离值取正值，在它下面的测点的偏离值取负值。3)最小区域评定法，是形状误差评定的基本原则，最小区域是指由两条曲线包容实际轮廓线时，理想轮廓线穿过实际被测轮廓线，这两条曲线分别至理想轮廓线的法向距离相等且它们之间的宽度为最小包容区域。
根据零件生产中实际需要，线轮廓度误差评定分为两种情况：一种是以理论轮廓线为基准，通过计算实际测量点到理论轮廓线的距离，来求得各测量点的误差，如图4所示；另一种是以实测轮廓线为基准，求理论轮廓点到实测轮廓线的距离，如图5所示。从轮廓度定义可知，当实测点与理论点的位置一致时，这两种情况的评定结果相同。
根据弧面凸轮廓面特点和轴截面特征线的分析，拟采用不同的方法对弧面凸轮不同工作廓面的特征线进行误差评定。停歇段的特征线为直线，拟采用两端点法进行误差评定；分度段的特征线为曲线拟采用最小区域法进行误差评定；停歇段和分度段都采用实测轮廓线作为基准进行误差评定。选择不同的方法对弧面凸轮的线轮廓度误差进行评定时，数据处理的方式和基本步骤有所不同。下面将对停歇段和分度段特征线的评定过程进行详细论述。
(2)停歇段特征线的误差评定停歇段的理论廓面特征线为直线，直线段的误差最大值通常在端点处，因此采用两端点法求出弧面凸轮停歇段特征线的误差。具体过程为：1)将实际测量点拟合成直线，作为误 差评定基准；2)求解理论特征线两端点的坐标值；3)分别求解理论特征线两端点到拟合实测特征线的距离；4)确定停歇段特征线的误差值是否在给定的公差范围内。
a)停歇段实测特征点拟合在实际测量过程中无法准确测量到端点的坐标，因此先根据实测数据拟合为特征线，为后续评定做准备。这个过程能够消除测量时的随机误差。根据轴截面及其特征线的定义，特征线方程表示为：
Figure PCTCN2020080526-appb-000008
式中x，y，z——表示弧面凸轮测量特征点坐标；
k i——表示相邻测量点构成直线的斜率；
b zi——表示相邻测量点构成直线的截距；
i——表示弧面凸轮测量特征点编号。
分别利用直线拟合方式进行弧面凸轮相邻测量点之间的直线方程，最后对求得特征线的斜率及截距求平均值得到弧面凸轮轴截面的特征线，若将
Figure PCTCN2020080526-appb-000009
设为X，则式(8)修改为：
L＝k*X+b z       (9)
式中k——表示测量点构成直线的斜率的平均值；
b z——表示测量点构成直线的截距的平均值。
b)停歇段特征线误差求解具体过程为：特征线方程即式(9)中，α为已知的凸轮转角，通过分度机构运动规律曲线关系可求出β，参数b min和b max对应α角度下特征线的两个端点，将α，β，b min和α，β，b max分别代入式(9)，求出特征线两个端点的坐标值，求两个端点到实测特征线的距离，则其中的较大的值为α角度下特征线的轮廓度误差：
Figure PCTCN2020080526-appb-000010
式中
Figure PCTCN2020080526-appb-000011
—表示测量点到停歇段理想曲线的距离，(X 1,z 1)、(X 2,z 2)表示停歇段两端点在轴截面下的坐标值。
(3)分度段特征线的误差评定分度段的理论廓面特征线不是直线，无法采用与停歇段相同的评定方法。通过最小区域法和最小二乘法的比较，最终选择评价精度更好的最小区域评定法作为线轮廓度误差评定的 方法。分度段特征线误差评定的具体过程为：1)选定曲线拟合方法，将实际测量点拟合成曲线，作为误差评定基准；2)确定理论特征点的数量，离散求解理论特征点的坐标值；3)分别求解理论特征点到拟合实测特征线的距离；4)确定分度段特征线的误差值是否在给定的公差范围内。
a)分度段实测特征点拟合分度段实际测量特征点通过NURBS曲线拟合分度段实测特征线。
b)分度段理论特征点求解分度段理论特征点求解方法在采用牛顿迭代法依据最小距离原则进行求解。
c)分度段特征线误差求解分度段的特征线不是直线，求理论特征点到实测特征线的距离的方法与停歇段不同。在分度段采用分割搜索法寻找理论特征点到实测特征线的最小距离，取最小距离中的最大值作为线轮廓度误差，这种方法符合轮廓度误差评定得最小区域原则，其原理如图15所示。
图15中，设理论特征线上的点分别为a 1、a 2、a 3、a 4、a、 5a 6，实测特征线上的点为b 1、b 2、b 3、b 4、b 5，对于理论特征点a 4而言，存在且仅有一个位于实测特征线的点b 3使得a 4与实测特征线的距离达到最小，即：
Figure PCTCN2020080526-appb-000012
根据上述方法，每个理论特征点均存在且仅有一个位于实测特征线上的点使其两者之间的距离d最小，这两点也作为实测数据与理论数据的匹配点。根据线轮廓度误差的定义，将各个理论特征点到实测特征点的距离最大值作为线轮廓度误差，即：
max(mind i)i＝1,2,...,n         (12)
其中d i为理论特征点到实测特征点的距离。
步骤六：弧面凸轮廓面误差评定
(1)面轮廓度误差评定方法根据GB/T1182-2008中定义，面轮廓度的公差带为直径等于公差值t、球心位于被测要素具有理论正确几何形状上的一系列圆球的两包络面所限定的区域。如图16所示，t即为面轮廓度误差。
面轮廓度误差常用的评定方法有三种方法：1)截面法，截面法是指测量实际被测轮廓面的若干截面的线轮廓度误差，取各个截面的误差值中的最大值作为该轮廓面的面轮廓度误差值。2)三远点法，三远点法是指以通过实际被测轮廓面上相距最远的三个点的理想轮廓面作为评定基准，取测得各点相对于它的法向距离中的最大偏差值与最小偏差值之差作为面轮廓度误差值。在它上面的测点的偏离值取正值，在它下面的测点的偏离值取负值。3)最小区域法，最小区域法是面轮廓度误差评定的基本原则。最小区域是指由两个曲面包容实际轮廓面时，理想轮廓面穿过实际被测轮廓面，这两个曲面分别至理想轮廓面的法向距离相等且它们之间的宽度为最小包容区域。
采用等距廓面轴截面特征线的测量方法和面轮廓度误差评定方法中的截面法一致，所以采用截面法作 为弧面凸轮面轮廓度误差的评定方法。
(2)弧面凸轮廓面误差的求解采用截面法评定弧面凸轮廓面误差时，利用上一小节特征线误差评定的结果进行面轮廓度误差的评定。根据弧面凸轮廓面的特点和传动精度仿真分析的结果，分度段和停歇段需要分别进行面轮廓度的评定。具体评定方法为：
分别求解多条弧面凸轮特征线的误差，取这些误差的最大值作为面轮廓度误差，即：
max[ΔL i]         (13)
相对于现有技术，本发明的有益效果为：
本发明提出的基于特征线的弧面凸轮廓面误差评定方法，通过三坐标测量机的误差建模，有效规避掉检测设备本身的误差，并且采用特征线误差测量和评定分别对弧面凸轮的线误差和面误差进行了定义。本发明的方法使得检测的结果更加的精确，并提供一种弧面凸轮加工误差的评价方法，为提升我国弧面凸轮的加工精度、指定质量检测技术标准提供理论支撑。
附图说明
图1弧面凸轮廓面误差测量系统结构图。
图2弧面凸轮运动规律曲线图。
图3凸轮转角区间[358°，2°]下的测量特征线规划。
图4凸轮转角区间[52°，122.5°]下的测量特征线规划。
图5凸轮转角区间[237.5°，308°]下的测量特征线规划。
图6凸轮转角区间[2°，52°]下的测量特征线规划。
图7凸轮转角区间[122.5°，237.5°]下的测量特征线规划。
图8凸轮转角区间[308°，358°]下的测量特征线规划。
图9廓面误差检测流程图。
图10测量系统结构拓扑图a)测量系统结构图b)测量系统结构拓扑图。
图11转台误差定义。
图12曲线轮廓度误差定义。
图13理论轮廓线作基准。
图14实测轮廓线作基准。
图15分度期线轮廓度误差求解原理。
图16曲面轮廓度误差定义。
图17搭配转台的虚拟坐标测量系统。
图18凸轮转角为30°的上廓面理论特征线和实测的特征线。
图19凸轮转角为30°的下廓面理论特征线和实测特征线。
图20凸轮转角为40°的上廓面理论特征线和实测特征线。
图21凸轮转角为40°的下廓面理论特征线和实测特征线。
具体实施方式
弧面凸轮廓面加工误差评定方法验证
为了方便验证弧面凸轮廓面加工误差评定方法的可行性，通过建立的弧面凸轮理论模型和含加工误差的弧面凸轮模型分别在构建的虚拟测量环境中进行测量，如图17所示，利用提出的评定方法分段进行误差评定。所用弧面凸轮型号：TC40，其参数：弧面凸轮外径D＝265mm，中心距a＝160mm，刀具垂直滚子轴线截面到转盘中心的距离b的范围是39.5mm≤b≤54.5mm，刀具直径d＝30mm。
(1)停歇段误差评定以60°下凸轮的上廓面和下廓面特征线为例进行停歇段误差的评定，将数据汇总如表3所示。
表3凸轮转角为60°的含有A轴绕Y方向角位移误差的特征点坐标(mm)
Figure PCTCN2020080526-appb-000013
Figure PCTCN2020080526-appb-000014
根据停歇段线轮廓度误差评定方法，对于凸轮转角为60°下的上廓面线轮廓度误差的评定如下：
将测量点进行按照式(8)拟合得到的实测特征线的方程为：
L u1＝-1.713x+245.1       (20)
经过计算得到的线轮廓度误差为0.1132mm，凸轮转角为60°下的敏感度系数为0.4051mm/deg，因此机床误差为：
0.1132/0.4051＝0.2794°＝0.0049rad
与给定机床误差ε Y(A)＝0.005rad近似。
同理，对于凸轮转角为60°下的下廓面线轮廓度误差的评定如下：
将测量点进行按照式(8)拟合得到的实测特征线的方程为：
L d1＝0.5836x-75.224      (21)
根据停歇段评定原理，经过计算得到的线轮廓度误差为0.485mm，凸轮转角为60°下的下廓面敏感度系数为1.735，因此机床误差为：
0.485/1.735＝0.2796°＝0.0049rad
与给定机床误差ε Y(A)＝0.005rad近似。
弧面凸轮在60°下的上廓面和下廓面特征线，分别处于不同走刀轨迹下，并且在停歇段的敏感度系数相同，按照给出的弧面凸轮特征线测量方案进行测量后的数据计算结果与凸轮转角为60°下的计算结果相同。
综上所述，根据本文提出的弧面凸轮停歇段线轮廓度评定方法以及求解结果，可知本文提出的停歇段线轮廓度误差评定方法可行，能够用于弧面凸轮在线检测中进行廓面轮廓度误差的评定。
(2)分度段误差评定为了验证提出的凸轮分度段的评定方法，由于弧面凸轮在分度期的敏感度系数互不相同，因此，以弧面凸轮转角分别为30°和40°进行评定，根据提出的分度段特征线不为直线，为了保证NURBS曲线拟合精度，在凸轮转角为30°和40°下分别测量15个特征点并汇总分别如表4和表5所示。
根据本方法提出的分度段线轮廓度误差的评定方法以及表4，将上廓面和下廓面的理论特征线和实测特征线在Matlab中进行拟合如图18和19所示。
表4凸轮转角为30°下含有A轴绕Y方向的角位移误差的特征点坐标(mm)
Figure PCTCN2020080526-appb-000015
Figure PCTCN2020080526-appb-000016
Figure PCTCN2020080526-appb-000017
表5凸轮转角为40°下含有A轴绕Y方向的角位移误差的特征点坐标(mm)
Figure PCTCN2020080526-appb-000018
Figure PCTCN2020080526-appb-000019
将凸轮转角为40°的上廓面和下廓面理论特征线及实测误差特征线拟合分别如图20和图21所示。
结合图18和图19可知，在分度段，凸轮理论廓面特征线和误差特征线在同一凸轮转角下不相同。
根据分度段误差的评定方法，利用分割搜索法求解理论特征线上的点到实测特征线的最小距离作为线轮廓度误差。
针对凸轮转角为30°下的上廓面线轮廓度误差的评定方法如下：首先对实测含误差的特征点运用NURBS曲线进行拟合，拟合后的曲线方程为：
L ue6＝4E-5x 3-0.0202x 2+3.0729x-151.21   (22)
然后在Matlab中利用理论点到实测特征线的最小距离进行求解，最终求解的线轮廓度误差为0.2510mm；根据对A轴绕Y方向的角位移误差ε Y(A)的求解得出凸轮转角为30°的上廓面影响系数为0.8718mm/deg，因此机床误差为0.2510/0.8718＝0.2879°＝0.005rad，与给定机床误差ε Y(A)＝0.005rad相等。
同理可求得下廓面实测特征线方程为：
L de6＝9E-5x 3-0.0194x 2+2.0103x-143.04  (23)
最终求解的综合误差为0.035mm，根据对ε Y(A)的求解得出凸轮转角为30°的下廓面影响系数为0.1178mm/deg，因此机床误差为0.2971°＝0.0051rad与给定机床误差ε Y(A)＝0.005rad近似。
对于凸轮转角为40°的上廓面和下廓面线轮廓度误差评定与凸轮转角为30°的评定过程相同，评定后的上廓面综合误差为0.1842mm，而凸轮转角为30°的上廓面影响系数为0.6392mm/deg，因此机床误差为0.2882°＝0.005030rad，与给定机床误差ε Y(A)＝0.005rad近似；评定后的下廓面综合误差为0.2580mm，而凸轮转角为30°的下廓面敏感度系数为0.8948mm/deg，因此机床误差为0.2883°＝0.005031rad，与给定机床误差ε Y(A)＝0.005rad近似。
综上所述，根据提出的弧面凸轮分度段线轮廓度评定方法以及求解结果，可知本文提出的分度段线轮廓度误差评定方法可行，能够用于弧面凸轮在线检测中进行廓面轮廓度误差的评定。

Claims (7)

  1. 一种基于特征线的弧面凸轮廓面误差测量与评定方法，其特征在于：该方法的实现步骤如下，
    S1、构建三坐标测量机搭配转台的四轴测量系统；
    S2、规划弧面凸轮廓面待测特征线；
    S3、测量弧面凸轮廓面特征点；
    S4、建立弧面凸轮廓面测量系统误差模型；
    S5、弧面凸轮廓面特征线误差评定；
    S6、弧面凸轮廓面误差评定。
  2. 根据权利要求1所述的一种基于特征线的弧面凸轮廓面误差测量与评定方法，其特征在于：采用三坐标测量机搭配转台构成新的测量系统，弧面凸轮廓面特征线的测量过程：1)转台旋转使弧面凸轮在一定凸轮转角下停止，凸轮转角由圆光栅测量，数显表显示精确度数；2)测量机测头在轴截面内测量弧面凸轮特征点；3)弧面凸轮廓面误差分析处理软件进行误差评定。
  3. 根据权利要求1所述的一种基于特征线的弧面凸轮廓面误差测量与评定方法，其特征在于：对测量特征线进行规划，即根据凸轮转角与转盘转角的关系，在Solidworks中进行弧面凸轮特征线的初步测量规划；
    弧面凸轮在运动过程中包括三个停歇段和三个分度段，停歇段凸轮转角区间分别为[358°，2°]、[52°，122.5°]、[237.5°，308°]；分度段凸轮转角区间分别为[2°，52°]、[122.5°，237.5°]、[308°，358°]；凸轮转角区间为[52°，122.5°]、[237.5°，308°]时，凸轮转角相差180°且凸轮所转角度均为70.5°，在进行测量特征线规划时，将两个区间等分相等数量的特征线，两个区间对应的特征线所对应的凸轮转角相差180°；
    在规划测量特征线时，由于停歇段特征线始终为直线，针对特征线上少量特征点进行测量，每条特征线测量8个特征点；而弧面凸轮在分度段的特征线为空间曲线，为精确分析分度段的特征线，针对特征线上的特征点进行测量，每条特征线测量12个特征点。
  4. 根据权利要求1所述的一种基于特征线的弧面凸轮廓面误差测量与评定方法，其特征在于：
    由三坐标测量机和转台构成的弧面凸轮测量系统，用来完成弧面凸轮廓面的误差检测。
  5. 根据权利要求3所述的一种基于特征线的弧面凸轮廓面误差测量与评定方法，其特征在于：将测量系统分为两个分支，分别为测头分支和工件分支：
    测头分支：三坐标测量机机座—三坐标测量机X轴—三坐标测量机Y轴—三坐标测量 机Z轴—测头旋转轴；
    工件分支：三坐标测量机—转台—弧面凸轮；
    测量系统误差包括三坐标测量机的误差及转台的误差，由于三坐标测量机的误差检测定期检测并在其测量软件系统中进行补偿；根据多体理论，确定转台坐标系与凸轮坐标系之间的变换矩阵；
    在求得在转台坐标系下，弧面凸轮上P点的位置矢量p s：
    Figure PCTCN2020080526-appb-100001
    式中x s，y s，z s——表示弧面凸轮上P点在转台坐标系下的坐标；
    p——表示弧面凸轮上P点在加工坐标系下的位置矢量；
    t SX——沿转台坐标系X轴方向的线位移矩阵；
    t SY——沿转台坐标系Y轴方向的线位移矩阵；
    t SZ——沿转台坐标系Z轴方向的线位移矩阵；
    r SX——绕转台坐标系X轴旋转的角位移矩阵；
    r SY——绕转台坐标系Y轴旋转的角位移矩阵；
    r SZ——绕转台坐标系Z轴旋转的角位移矩阵；
    至此，测量系统误差模型建立完成。
  6. 根据权利要求1所述的一种基于特征线的弧面凸轮廓面误差测量与评定方法，其特征在于：线轮廓度的公差带为直径等于公差值w、圆心位于具有理论正确几何形状上的一系列圆的两包络线所限定的区域；w即为曲线轮廓度误差；
    根据轴截面及其特征线的定义，弧面凸轮停歇段特征线方程表示为：
    Figure PCTCN2020080526-appb-100002
    Figure PCTCN2020080526-appb-100003
    式中x，y，z——表示弧面凸轮测量特征点坐标；
    k i——表示相邻测量点构成直线的斜率；
    b zi——表示相邻测量点构成直线的截距；
    i——表示弧面凸轮测量特征点编号；
    利用直线拟合方式进行弧面凸轮相邻测量点之间的直线方程，最后对求得特征线的斜率及截距求平均值得到弧面凸轮轴截面的特征线，若将
    Figure PCTCN2020080526-appb-100004
    设为X，则式(8)修改为：
    L＝k*X+b z
    式中k——表示测量点构成直线的斜率的平均值；
    b z——表示测量点构成直线的截距的平均值；
    特征线方程中，α为已知的凸轮转角，通过分度机构运动规律曲线关系可求出β，参数b min和b max对应α角度下特征线的两个端点，将α，β，b min和α，β，b max分别代入特征线方程，求出特征线两个端点的坐标值，求两个端点到实测特征线的距离，则其中的较大的值为α角度下特征线的轮廓度误差：
    Figure PCTCN2020080526-appb-100005
    式中
    Figure PCTCN2020080526-appb-100006
    —表示测量点到停歇段理想曲线的距离，(X 1,z 1)、(X 2,z 2)表示停歇段两端点在轴截面下的坐标值。
  7. 根据权利要求1所述的一种基于特征线的弧面凸轮廓面误差测量与评定方法，其特征在于：
    设弧面凸轮分度段理论特征线上的点分别为a 1、a 2、a 3、a 4、a 5、a 6，实测特征线上的点为b 1、b 2、b 3、b 4、b 5，对于理论特征点a 4而言，存在且仅有一个位于实测特征线的点b 3使得a 4与实测特征线的距离达到最小，即：
    Figure PCTCN2020080526-appb-100007
    每个理论特征点均存在且仅有一个位于实测特征线上的点使两者之间的距离d最小，这两点也作为实测数据与理论数据的匹配点；根据线轮廓度误差的定义，将各个理论特征点到实测特征点的距离最大值作为线轮廓度误差，即：
    max(mind i) i＝1,2,...,n
    其中d i为理论特征点到实测特征点的距离。
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