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CN114199158A - Screw rod axis spatial bending measurement method based on laser correlation type edge detection - Google Patents

Screw rod axis spatial bending measurement method based on laser correlation type edge detection Download PDF

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CN114199158A
CN114199158A CN202111519746.XA CN202111519746A CN114199158A CN 114199158 A CN114199158 A CN 114199158A CN 202111519746 A CN202111519746 A CN 202111519746A CN 114199158 A CN114199158 A CN 114199158A
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screw rod
measurement
measured
section
eccentricity
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CN114199158B (en
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裴永臣
王斌
辛清源
王璐璐
罗梦演
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Jilin University
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    • 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
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • 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
    • G01B11/16—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge

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Abstract

The invention discloses a method for measuring the spatial bending of the axial lead of a screw rod, which is used for carrying out rotary continuous measurement and bending deformation calculation on the screw rod based on a laser correlation type edge detection sensor and comprises the following specific steps of: measuring the cross section profile of the workpiece to obtain a measurement indication value of a sensor; determining a data point of a superposition part of the indicating value and the upper envelope line and the lower envelope line; fitting the processed data points; and deducing the spatial bending deformation of the axis according to the fitted curve extreme value and the mathematical transformation. The measuring method is efficient and accurate, reduces workpiece abrasion, and provides an effective solution for the straightness measuring problem related to machining, manufacturing, straightening and using of various screw rod parts.

Description

Screw rod axis spatial bending measurement method based on laser correlation type edge detection
Technical Field
The invention relates to a method for measuring the spatial bending of an axial lead, in particular to a method for measuring the spatial bending of the axial lead of a screw rod.
Background
The screw rod is widely applied to the fields of production machinery, processing machinery and the like. The number of spiral grooves is used as a classification standard, common spiral rods are divided into a single-head spiral rod, a double-head spiral rod and a multi-head spiral rod, for example, a spiral feeding shaft of a spiral feeder is generally the single-head spiral rod, a guide part of an electric hammer drill bit is generally the double-head spiral rod, and a multi-head lead screw can also be called as the multi-head spiral rod. Because the work of hob is continuous in a period of time, and the working speed is faster, the transmission distance is bigger, therefore need to guarantee to have higher transmission precision. The straightness of the axial lead of the screw rod is one of important factors influencing the transmission precision, in the production practice, the measurement of the straightness of the axial lead of the screw rod is an important link for ensuring the mechanical quality and the working precision, and in the measurement of the straightness of the axial lead, how to realize the accurate measurement of the single-section eccentricity is of great importance.
The section shape of the screw rod is complex, and the distance from each point on the edge to the geometric center is not a fixed value and is between the radius of a circumscribed circle and the radius of an inscribed circle of the section. In engineering measurement, a common method for measuring the straightness of the axial lead of the screw rod is to support two ends of the screw rod on a V-shaped bracket, then beat the head of a dial indicator on the outer surface of the screw rod, rotate the screw rod for a circle in the circumferential direction, and record the jumping value of the dial indicator. When the measurement is carried out at a plurality of positions in the axial direction of the workpiece, the trend of the axial lead can be obtained by fitting according to the measurement result of each point, thereby approximately determining the straightness of the axial lead of the shaft. However, the traditional meter-making measurement is not suitable for a large-pitch screw rod, the measurement efficiency is low, the operation is complex, the requirement on an operator is high, and meanwhile, the contact measurement can abrade the measurement surface. Therefore, an efficient, automatic and non-contact measurement method is urgently needed to measure the spatial bending deformation of the axial lead of the screw rod so as to meet the requirements of practical production.
Disclosure of Invention
The invention aims to provide a method for measuring the spatial bending of the axial lead of a screw rod, which can accurately and conveniently carry out continuous rotation measurement on the spatial bending deformation of the axial lead of a screw rod part.
Taking an electric hammer drill bit double-head screw rod as an example, the invention aims to realize the following technical scheme:
the tested piece is clamped on the three-jaw chuck, and the chuck is connected with the spindle encoder. During measurement, a measured piece is rotated, meanwhile, the laser correlation type edge detection sensor makes linear motion along the axial direction of the measured piece, the distance from the highest point of the measured section to the lowest edge of the parallel light is recorded in real time, and the rotation angle of a workpiece is recorded in real time by the spindle encoder. According to the geometric relationship, data fitting and mathematical derivation of each part, the functional relationship between the eccentricity and the known parameters of a certain section of the measured piece and the indicating values of the laser sensors can be obtained, and the spatial bending deformation of the axis line can be determined by continuously measuring the eccentricity of a plurality of sections of the measured piece.
The rotation center of the section of the screw rod is defined as the origin of coordinates O (0,0), the radius of the circumscribed circle of the screw rod is R, the radius of the inscribed circle is R, the eccentric amount (deflection) and the eccentric angle of the section are e and
Figure BDA0003407078980000021
the rotated angle is beta; the distance from the lower edge of the laser to the x axis is P, the measurement indication value of the laser sensor is I, and the geometric center of the section of the screw rod is O'; the highest point on the section outline is M (x)M,yM)。
Obtaining an equation of the sensor indication value according to the geometric principle:
I＝yM+P (1)
the measurement position of the peak point of the measurement indication value I is positioned on the circumscribed circle, and the measurement position of the valley point is positioned on the inscribed circle. The radiuses of two cylindrical parts to be measured are respectively R and R, the total length of the two cylindrical parts and the eccentricity of each measured section are equal to those of a screw rod to be measured, and the rotation axes of the two cylinders are consistent with those of the screw rod to be measured in an initial state. The two cylindrical measured pieces are measured in a measuring mode completely consistent with the screw rod, and the measured value equations of the sensors obtained according to the plane analytic geometry are respectively as follows:
Figure BDA0003407078980000022
Figure BDA0003407078980000023
according to the relationship between the surface profile of the screw rod and the two cylindrical surfaces, the fluctuation range of the measured value I of the screw rod section can be determined as follows:
I2≤I≤I1 (4)
curve I1And curve I2Are the upper and lower envelopes of the measured value I, and I1May actually consist of2The upward translation distance R-R is obtained, and for convenient data processing, only the actual data pair I is used1Or I2And carrying out approximate fitting analysis.
Since I is a function of β, the first derivative of I at the qth data point can be found as:
Figure BDA0003407078980000031
and m is the total data point number of the measured value I, and the value of the m is determined by the sampling frequency and the measuring time of the sensor.
Setting and judging a data point threshold gamma of the overlapped part as follows:
Figure BDA0003407078980000032
if the qth data point satisfies:
Figure BDA0003407078980000033
this data point can be considered as the data point where I coincides with the upper and lower envelope lines.
To fit I1For example, the data points of the overlapped part positioned in the lower envelope line are translated upwards by R-R units, and then the translated data points of the overlapped part are subjected to cubic spline interpolation fitting to obtain a theoretical indication curve L of the fitting measurement of the external cylindrical section1Ideally, there are:
Figure BDA0003407078980000034
due to the curve L1Is about a function of beta, and L1First derivative on β:
Figure BDA0003407078980000035
since e is not zero, when
Figure BDA0003407078980000041
Comprises the following steps:
Figure BDA0003407078980000042
get it solved
Figure BDA0003407078980000043
Or
Figure BDA0003407078980000044
At this time, L is obtained1The extreme value equation of (a):
Figure BDA0003407078980000045
substituting the known parameters and the sensor indication values into the function relation expression to obtain a plurality of solution values of the eccentricity and the initial eccentricity angle, and averaging the solution values to obtain the final measured eccentricity e at a certain specified section of the screw rodpAnd initial eccentric angle
Figure BDA0003407078980000046
In the same way, a plurality of sections of the screw rod are continuously measured, and the spatial bending deformation of the axial lead of the screw rod can be accurately determined according to the measurement results of all the measured sections.
The invention has the advantages that: the measuring method can realize the measurement of the spatial bending deformation of the axial lead of the screw rod, is simple and efficient, reduces the labor consumption, avoids the abrasion of workpieces, has high measuring precision and is suitable for various screw rods. The invention provides an effective solution for the engineering problems of straightness measurement, straightening and the like of the screw rod.
Drawings
FIG. 1 is a schematic view of screw rod measurement
FIG. 2 is a schematic view of a cross section of a screw rod
FIG. 3 is a schematic view of the circumscribed circle and the inscribed circle of the cross section of the screw rod
FIG. 4 is a schematic view of a measurement curve
FIG. 5 is a schematic view of a fitted curve
FIG. 6 is a flow chart of the logical structure of the measurement procedure of the method of the present invention
Detailed description of the invention
The invention is further described below with reference to the accompanying drawings:
as shown in fig. 1, the sensor for measuring the screw rod is a correlation laser edge detection sensor. Before measurement, a measured piece is clamped on a three-jaw chuck, and the chuck is connected with a spindle encoder. During measurement, the screw rod is arranged in parallel light rays emitted by the sensor, the rotation axis of the screw rod is ensured to be vertical to the smooth surface formed by the parallel light rays, and the positions of the screw rod and the sensor are adjusted to ensure that the screw rod is in the measurement range of the sensor. The screw rod is rotated to shield light to form a shadow, the size of the shadow can directly reflect the outline size of a measured section, the sensor makes linear motion along the axial direction of a measured piece and records the distance from the highest point of the shadow to the lowest edge of the opposite light in real time, and the main shaft encoder records the rotation angle of the workpiece in real time.
As shown in FIG. 2, the center of rotation of a section of the screw is defined as the origin of coordinates O (0,0), the radius of the circumscribed circle of the screw is R, the radius of the inscribed circle is R, and the eccentricity (deflection) and the eccentricity angle of the section are e and
Figure BDA0003407078980000051
the rotated angle is beta; the distance from the lower edge of the laser to the x axis is P, the measurement indication value of the laser sensor is I, and the geometric center of the section of the screw rod is O'; the highest point on the cross-sectional profile isM(xM,yM)。
Obtaining an equation of the sensor indication value according to the geometric principle:
I＝yM+P (1)
as shown in fig. 3 and 4, the measurement indication value I shows reciprocating fluctuation along with the rotation of the measured piece in the measurement process, and since the section profile of the screw rod is positioned between the circumscribed circle (with the radius R) and the inscribed circle (with the radius R), and the circumscribed circle and the inscribed circle are concentric, the measurement position of the peak point can be determined to be positioned on the circumscribed circle, and the measurement position of the valley point is positioned on the inscribed circle. Assuming two cylindrical parts to be measured, the radiuses of the two cylindrical parts are R and R respectively, and the total length of the two cylindrical parts and the eccentricity of each section to be measured are equal to those of the screw rod to be measured. The measured parts of the two cylinders are measured in a measuring mode completely consistent with the screw rod, and the rotation axes of the two cylinders are consistent with the initial state of the measured screw rod. For the radii R and R, the eccentricity is e and the initial phase angle is
Figure BDA0003407078980000052
The two cylindrical workpieces have the following measurement value equations of the sensors obtained according to the plane analytic geometry:
Figure BDA0003407078980000061
Figure BDA0003407078980000062
according to the relationship between the surface profile of the screw rod and the two cylindrical surfaces, the fluctuation range of the measured value I of the screw rod section can be determined as follows:
I2≤I≤I1 (4)
curve I therefore1And curve I2Are the upper and lower envelopes of the measured value I, and I1May actually consist of2Upward translation by a distance R-R is obtained due to I1And I2For the imaginary curve, the fitting is required to obtain through actual data. For convenience of data processing, only for I1Or I2And carrying out approximate fitting analysis.
As shown in fig. 4, the absolute value of the slope of the portion where the measured value I coincides with the upper and lower envelopes is significantly smaller than the absolute value of the slope of the other portion, and thus the data point of the portion where I coincides with the upper and lower envelopes is determined by differentiating I. Since I is a function of β, the first derivative of I at the qth data point can be found as:
Figure BDA0003407078980000063
and m is the total data point number of the measured value I, and the value of the m is determined by the sampling frequency and the measuring time of the sensor.
Setting a threshold gamma for judging the data points of the overlapped part as follows:
Figure BDA0003407078980000064
if the qth data point satisfies:
Figure BDA0003407078980000065
this data point can be considered as the data point where I coincides with the upper and lower envelope lines.
As shown in FIG. 5, coincident portion data points are determined according to equation (7) for fit analysis I1For example, the data points of the overlapped part positioned in the lower envelope line are translated upwards by R-R units, and then the translated data points of the overlapped part are subjected to cubic spline interpolation fitting to obtain a theoretical indication curve L of the fitting measurement of the external cylindrical section1Ideally, there are:
Figure BDA0003407078980000071
due to the curve L1Is about a function of beta, and L1To beta first orderAnd (5) obtaining a derivative:
Figure BDA0003407078980000072
since e is not zero, when
Figure BDA0003407078980000073
Comprises the following steps:
Figure BDA0003407078980000074
get it solved
Figure BDA0003407078980000075
Or
Figure BDA0003407078980000076
At this time, L is obtained1The extreme value equation of (a):
Figure BDA0003407078980000077
due to L1For fitting the curve, the extreme points and extreme values are known, the extreme point is betakExtreme value of EkAnd k is 1,2,3, …, the drive formula (11) can obtain a plurality of solutions of the eccentricity and the initial phase angle:
Figure BDA0003407078980000078
Figure BDA0003407078980000079
the eccentricity e obtained by the solution of the formulas (12) and (13)kAnd initial phase angle
Figure BDA00034070789800000710
Averaging to obtain the most specific cross section of screw rodFinal measurement of eccentricity epAnd initial eccentric angle
Figure BDA00034070789800000711
Figure BDA00034070789800000712
The measurement of the screw rod is continuous in rotation, so that the eccentricity and the initial eccentricity of a plurality of sections can be obtained in the whole measurement process, and the axial lead trend can be accurately fitted according to the measurement results of all the measured sections, so that the spatial bending deformation of the axial lead of the screw rod is determined.
Fig. 6 is a flow chart of the logic structure of the present invention. The measurement program of the spatial bending deformation of the shaft axis of the screw rod can be written according to the logical structure diagram shown in FIG. 6.

Claims (4)

1.一种螺旋杆轴心线空间弯曲测量方法，其特征在于：1. a method for measuring the space bending of a screw rod axis, characterized in that: 定义螺旋杆截面回转中心为坐标原点O(0,0)，螺旋杆外接圆半径为R，内切圆半径为r，截面偏心量(挠度)和偏心角为e和
Figure FDA0003407078970000011
转动过的角度为β；激光下边缘到x轴的距离为P，激光传感器测量示值为I，螺旋杆截面几何中心为O′；截面轮廓上最高点为M(xM,yM)。Define the rotation center of the screw rod section as the coordinate origin O(0,0), the radius of the circumscribed circle of the screw rod is R, the radius of the inscribed circle is r, and the eccentricity (deflection) and eccentric angle of the section are e and
Figure FDA0003407078970000011
The rotated angle is β; the distance from the lower edge of the laser to the x-axis is P, the measured value of the laser sensor is I, and the geometric center of the screw rod section is O'; the highest point on the section profile is M (x M , y M ). 根据几何原理得到传感器示值的方程：According to the geometric principle, the equation of the sensor indication value is obtained: I＝yM+P (1)I = y M + P (1) 2.根据权利要求1所述的一种螺旋杆轴心线空间弯曲测量方法，其特征在于：2. a kind of screw rod axis space bending measurement method according to claim 1 is characterized in that: 测量示值I在测量过程中随被测件的旋转而呈现出往复波动变化，可以确定波峰点的测量位置位于外接圆上，而波谷点的测量位置位于内切圆上。假设两个圆柱被测零件，半径分别为R和r，两圆柱零件总长以及各被测截面偏心都与被测螺旋杆相等。对两圆柱被测件采用与螺旋杆完全一致的测量方式进行测量，两圆柱的回转轴线与初始状态与被测螺旋杆一致，依据平面解析几何可得传感器的测量值方程分别为：The measurement indication I shows a reciprocating fluctuation change with the rotation of the DUT during the measurement process. It can be determined that the measurement position of the peak point is located on the circumscribed circle, and the measurement position of the trough point is located on the inscribed circle. Assuming two cylindrical parts to be measured, the radii are R and r respectively, the total length of the two cylindrical parts and the eccentricity of each measured section are equal to the measured screw rod. The measurement method of the two cylinders to be measured is completely consistent with the screw rod. The rotation axis of the two cylinders and the initial state are consistent with the measured screw rod. According to the plane analytic geometry, the measured value equations of the sensor can be obtained as follows:
Figure FDA0003407078970000012
Figure FDA0003407078970000012
Figure FDA0003407078970000013
Figure FDA0003407078970000013
 依据螺旋杆表面轮廓与两圆柱表面的关系，可以确定螺旋杆截面的测量值I波动范围为：According to the relationship between the surface profile of the screw rod and the surfaces of the two cylinders, the fluctuation range of the measured value I of the screw rod section can be determined as: I2≤I≤I1 (4)I 2 ≤I≤I 1 (4) 3.根据权利要求1所述的一种螺旋杆偏心测量方法，其特征在于：3. a kind of screw rod eccentricity measuring method according to claim 1 is characterized in that: I是关于β的函数，可以得I在第q个数据点的一阶导数为：I is a function of β, and the first derivative of I at the qth data point can be obtained as:
Figure FDA0003407078970000014
Figure FDA0003407078970000014
 式中m为测量值I的总数据点个数，其取值由传感器的采样频率和测量时间决定。In the formula, m is the total number of data points of the measurement value I, and its value is determined by the sampling frequency and measurement time of the sensor. 设定判断重合部分数据点的阈值γ为：The threshold γ for judging the overlapping data points is set as:
Figure FDA0003407078970000021
Figure FDA0003407078970000021
 若第q个数据点满足：If the qth data point satisfies:
Figure FDA0003407078970000022
Figure FDA0003407078970000022
 可认为该数据点为I与上下包络线重合部分的数据点。This data point can be considered as the data point of the overlapping portion of I and the upper and lower envelopes. 4.根据权利要求2所述的一种螺旋杆轴心线空间弯曲测量方法，其特征在于：4. a kind of screw rod axis space bending measurement method according to claim 2 is characterized in that: 对经过平移处理后的重合部分数据点进行三次样条插值拟合，得外接圆柱(或内切圆柱)截面拟合测量理论示值曲线L1，理想情况下，有：The cubic spline interpolation fitting is performed on the coincident data points after translation processing, and the fitting measurement theoretical indication curve L 1 of the circumscribed cylinder (or inscribed cylinder) section is obtained. Ideally, there are:
Figure FDA0003407078970000023
Figure FDA0003407078970000023
 通过数学计算可得L1的极值方程：The extreme value equation of L 1 can be obtained by mathematical calculation:
Figure FDA0003407078970000024
Figure FDA0003407078970000024
 由于L1为拟合曲线，其各极值点和极值都为已知，极值点为βk，极值为Ek，k＝1,2,3,…，带入式(11)可得偏心量与初始相角：Since L 1 is a fitted curve, its extreme points and extreme values are all known, the extreme point is β k , the extreme value is E k , k=1, 2, 3, . . . Available eccentricity and initial phase angle:
Figure FDA0003407078970000025
Figure FDA0003407078970000025
Figure FDA0003407078970000026
Figure FDA0003407078970000026
 将由式(12)(13)解得的偏心量ek和初始相角
Figure FDA0003407078970000031
平均化，即可解得螺旋杆某指定截面处的预测的偏心量ep和初始偏心角
Figure FDA0003407078970000032
The eccentricity ek and the initial phase angle obtained from equations (12) and (13)
Figure FDA0003407078970000031
Averaged, the predicted eccentricity ep and initial eccentricity angle at a specified section of the screw rod can be solved
Figure FDA0003407078970000032
Figure FDA0003407078970000033
Figure FDA0003407078970000033
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