阅读说明：本技术 基于四轴数控铣床的涡旋盘体误差在机测量方法 (Vortex disc body error on-machine measurement method based on four-axis numerical control milling machine ) 是由 丁建军 宋明明 孙林 刘阳鹏 白杨 李冠群 蒋庄德 于 2020-12-28 设计创作，主要内容包括：本发明基于四轴数控铣床的涡旋盘体误差在机测量方法,目的是解决涡旋盘加工过程中的三维体误差在位快速测量的难题。该测量方法如下：基于涡旋盘数控加工机床,铣刀与测头具有同一安装接口,铣削完成后,以换刀形式将铣刀替换为测头。该测头为三并联电感集成测头,安装标定后一次测量可以获得涡旋盘竖直方向上的三组检测数据,完成涡旋盘涡旋体误差评价。基于以上本发明对涡旋盘误差的在机测量方法,避免了涡旋盘在传统量仪上测量时重复装夹误差的影响,提高了测量效率和测量精度。基于三维涡旋体误差的评价,在加工中适时评价工件、装夹误差或刀具局部磨损对涡旋面引起的制造误差,弥补传统测量中仅对单个涡旋线进行误差评价的局限性。(The invention discloses a vortex disc body error on-machine measuring method based on a four-axis numerical control milling machine, and aims to solve the problem of rapid in-place measurement of a three-dimensional body error in the processing process of a vortex disc. The measurement method comprises the following steps: based on the scroll numerical control machine tool, the milling cutter and the measuring head have the same mounting interface, and after milling is completed, the milling cutter is replaced by the measuring head in a tool changing mode. The measuring head is a three-parallel inductance integrated measuring head, three groups of detection data in the vertical direction of the scroll can be obtained by one-time measurement after installation and calibration, and error evaluation of the scroll is completed. Based on the on-machine measurement method for the error of the scroll plate, the influence of repeated clamping error of the scroll plate during measurement on the traditional measuring instrument is avoided, and the measurement efficiency and the measurement precision are improved. Based on the evaluation of the error of the three-dimensional vortex body, the manufacturing error caused by the workpiece, the clamping error or the local abrasion of the cutter on the vortex surface is evaluated in time in the machining process, and the limitation that only a single vortex line is subjected to error evaluation in the traditional measurement is made up.)

1. The method is characterized in that the four-axis numerical control milling machine based on the method comprises a base (1), a radial motion mechanism (2) arranged on the base, a vertical motion mechanism (3) arranged on the radial motion mechanism, a tangential motion mechanism (4) arranged on the vertical motion mechanism, a main shaft rotating part (5) arranged on the tangential motion mechanism, an inductance measuring head (6) arranged on the main shaft rotating part and a rotating mechanism (8) arranged on the base;

the method comprises the following steps: based on the scroll numerical control machine tool, the milling cutter and the three parallel inductance right angle integrated measuring heads have the same mounting interface, after the machining is completed, the cutter is replaced by the three parallel inductance right angle integrated measuring heads in a cutter changing mode, the measuring track is controlled through relative measurement, and the measured data is stored in a machine tool numerical control system in real time to complete the on-machine measurement of the scroll (7).

2. The on-machine measuring method for the error of the scroll plate body based on the four-axis numerically controlled milling machine is characterized in that the measuring head (6) is a three-parallel inductance right-angle integrated measuring head and is installed on a finish machining spindle through replacement, the measuring head (6) comprises three inductance displacement measuring heads which are arranged in parallel along the vertical direction and three measuring pins which are respectively fixedly connected to the measuring head and arranged in parallel, and the heads of the measuring pins are provided with ruby measuring balls.

3. The on-machine measuring method for the error of the scroll plate body based on the four-axis numerically controlled milling machine is characterized in that before measurement, the vector position of the three-parallel inductance right-angle integrated measuring head in the initial space direction is calibrated to determine the starting point of the three-parallel inductance right-angle integrated measuring head, the angle direction of a measuring rod of the three-parallel inductance right-angle integrated measuring head in the horizontal direction is mainly calibrated, and the space angle position of the three-parallel inductance right-angle integrated measuring head is determined to ensure that the direction of data collected by a measuring point in the measuring process is the compression amount direction of the measuring head; a calibration mode is as follows: and controlling a side plane of a workpiece clamping tool arranged on the slewing mechanism (8) to be a reference plane, placing the three parallel inductance right-angle integrated measuring head at the position close to the center of the reference plane, controlling the compression amount to be 1mm, rotating the slewing mechanism (8) at 5r/min, and taking the minimum position angle alpha of the measured data as the space angle position of the measuring head.

4. The on-machine measurement method for the error of the scroll plate body based on the four-axis numerically controlled milling machine is characterized in that a precise standard ball is used as a calibration standard in the calibration method, the calibration standard ball is placed at any non-interference position in a rotation positioning mechanism (8), the position of the standard ball is firstly determined and determined once, then the vertical direction angle information of three measuring heads in three-parallel inductance right angle integration is calibrated respectively, the three-parallel inductance right angle integration measuring heads are controlled to be close to the calibration ball, the points are collected on the spherical surface through the three-parallel inductance right angle integration measuring heads, at least 4 points are collected, and the rotation mechanism rotates for one angle and then is measured again; the central position of the standard ball can be fitted by the four-point data of each group, and the position of the standard ball on the rotary mechanism (8) can be determined by combining the two groups of data; based on the spatial angle position of the measuring rod, the measuring rod is in contact with a standard ball in the angle direction, 1mm is taken as a compression amount, the feedback value of the measuring head is smaller than 1mm due to the angle, cosine and sine are adopted to solve the angle, the subsequent measurement data need to be based on the above, the three measuring heads are calibrated according to the above angles in sequence, and all data are collected after being calibrated and processed through the above angles.

5. The on-machine measurement method for the error of the scroll plate body based on the four-axis numerically controlled milling machine according to claim 1, characterized by realizing measurement data error compensation and gauge head radius compensation based on calibration of a three-parallel inductance right-angle integrated gauge head, comprising the following specific steps of:

the first step is as follows: establishing an X, Y, Z axis error model of a four-axis vortex disc machine tool, and establishing a geometric error model of the four-axis numerical control machine tool by using a homogeneous coordinate transformation method to obtain an error model of the machine tool:

the second step is that: obtaining a turntable error of a four-axis scroll processing machine tool, and extracting a position error generated when a scroll rotates on a turntable;

the third step: establishing a three-parallel inductance right-angle integrated measuring head error compensation model, and moving the measured data by one measuring head radius in the normal vector direction of a measured point as a real coordinate when processing the measured data based on the measuring head arranged on the main shaft:

in the formula: p_rAs true coordinates of the measuring points, P_fIs the sphere center coordinate of the measuring sphere, r is the measuring head radius,the normal vector direction of each point can be calculated according to the measuring curve as the normal vector direction of the measuring point.

6. The on-machine measurement method for the error of the scroll plate body based on the four-axis numerical control milling machine is characterized in that specific measurement of the scroll profile of the scroll plate is realized, the scroll profile of the scroll plate is a variable base circle involute-arc-variable base circle involute combined profile, when the on-machine measurement method is specifically realized, an Archimedes spiral line segment with the same direction as the scroll profile is adopted to fit the partial profile, the scroll curve is divided into a plurality of segments, an Archimedes spiral equation of the segment is fitted according to the polar angle and the polar radius of two end points of each segment, and finally, the Archimedes spiral fitting equations of the scroll inner wall curve, the transition arc and the scroll outer wall curve are obtained, and the polar coordinate equation of the Archimedes spiral is as follows: p ═ p₀+ v θ, during measurement, by controlThe three parallel inductors are used for realizing the radial movement of the right-angle integrated measuring head on a machine tool and the rotary motion of a scroll on a turntable, so that the Archimedes spiral error of the scroll profile can be measured.

7. The on-machine measurement method for the error of the scroll plate body of the four-axis numerical control milling machine is characterized in that the body error of the scroll plate is evaluated, three pieces of vortex line data with different heights are obtained based on the measurement data of the three parallel inductance right-angle integrated measuring heads, and a difference curved surface formed by the error of an actual measurement point in the normal direction of a theoretical point is used as the body error evaluation of the vortex line based on the theoretical vortex curved surface.

Technical Field

The invention belongs to the technical field of precision measurement, and particularly relates to an on-machine measurement method for an error of a scroll plate body based on a four-axis numerical control milling machine.

Background

Compared with the traditional compressor, the electric scroll compressor has the characteristics of low noise, high volume rate, cleanness, high conversion efficiency and the like, and is widely applied to an automobile air conditioning system. The machining and manufacturing precision of the scroll plate, which is a key component of the electric scroll compressor, determines the reliability and the efficiency of the operation of the scroll compressor, and the machining method and the precision evaluation mode of the scroll plate with high precision and high efficiency are the key parts for manufacturing the scroll plate.

At present, the detection of the scroll is usually realized by adopting a three-coordinate measuring machine, the detection efficiency is low, and the detection is required to be carried out in a special metering chamber, so that the production efficiency of the scroll is reduced.

Disclosure of Invention

The invention aims to provide a four-axis numerical control milling machine-based online measurement method for the error of a scroll plate body.

The invention is realized by adopting the following technical scheme:

the method is based on a four-axis numerical control milling machine, and the four-axis numerical control milling machine comprises a base, a radial motion mechanism arranged on the base, a vertical motion mechanism arranged on the radial motion mechanism, a tangential motion mechanism arranged on the vertical motion mechanism, a main shaft rotating part arranged on the tangential motion mechanism, a motor sensing head arranged on the main shaft rotating part, and a rotating mechanism arranged on the base;

the method comprises the following steps: based on the scroll numerical control machine tool, the milling cutter and the three parallel inductance right angle integrated measuring heads have the same mounting interface, after the machining is completed, the cutter is replaced by the three parallel inductance right angle integrated measuring heads in a cutter changing mode, the measuring track is controlled through relative measurement, and the measured data is stored in a machine tool numerical control system in real time to complete on-machine measurement of the scroll.

The measuring head is a three-parallel inductance right-angle integrated measuring head and is arranged on a finish machining main shaft in a replacement mode, the measuring head comprises three inductance displacement measuring heads which are arranged in parallel along the vertical direction and three measuring pins which are fixedly connected to the measuring heads and arranged in parallel, and ruby measuring balls are arranged at the heads of the measuring pins.

The invention is further improved in that before measurement, the vector position of the three parallel inductance right-angle integrated measuring heads in the initial space direction is calibrated to determine the starting point of the three parallel inductance right-angle integrated measuring heads, the angle direction of a measuring rod of the three parallel inductance right-angle integrated measuring heads in the horizontal direction is mainly calibrated, and the space angle position of the three parallel inductance right-angle integrated measuring heads is determined to ensure that the direction of data acquisition of a measuring point in the measurement process is the compression direction of the measuring heads; a calibration mode is as follows: controlling a side plane of a workpiece clamping tool arranged on a slewing mechanism to be a reference plane, placing a three-parallel inductance right-angle integrated measuring head at the position close to the center of the reference plane, controlling the compression amount to be 1mm, rotating the slewing mechanism at 5r/min, and taking the minimum position angle alpha of the measured data as the space angle position of the measuring head.

The invention has the further improvement that the calibration method adopts a precise standard ball as a calibration reference, places the precise standard ball at any non-interference position in a rotation positioning mechanism (8), firstly determines the position of the standard ball and determines the position once, then calibrates the vertical direction angle information of three measuring heads in the three parallel inductance right angle integration respectively, controls the three parallel inductance right angle integration measuring heads to be close to the calibration ball, adopts points on the spherical surface through the three parallel inductance right angle integration measuring heads, collects at least 4 points, and re-measures after the rotation mechanism rotates for an angle; the central position of the standard ball can be fitted by the four-point data of each group, and the position of the standard ball on the rotary mechanism (8) can be determined by combining the two groups of data; based on the spatial angle position of the measuring rod, the measuring rod is in contact with a standard ball in the angle direction, 1mm is taken as a compression amount, the feedback value of the measuring head is smaller than 1mm due to the angle, cosine and sine are adopted to solve the angle, the subsequent measurement data need to be based on the above, the three measuring heads are calibrated according to the above angles in sequence, and all data are collected after being calibrated and processed through the above angles.

The invention has the further improvement that the method realizes the measurement data error compensation and the measuring head radius compensation under the calibration of the three parallel inductors and the right angle integrated measuring head, and comprises the following specific steps:

the first step is as follows: establishing an X, Y, Z axis error model of a four-axis vortex disc machine tool, and establishing a geometric error model of the four-axis numerical control machine tool by using a homogeneous coordinate transformation method to obtain an error model of the machine tool:

the second step is that: obtaining a turntable error of a four-axis scroll processing machine tool, and extracting a position error generated when a scroll rotates on a turntable;

the third step: establishing a three-parallel inductance right-angle integrated measuring head error compensation model, and moving the measured data by one measuring head radius in the normal vector direction of a measured point as a real coordinate when processing the measured data based on the measuring head arranged on the main shaft:

in the formula: p_rAs true coordinates of the measuring points, P_fIs the sphere center coordinate of the measuring sphere, r is the measuring head radius,the normal vector direction of each point can be calculated according to the measuring curve as the normal vector direction of the measuring point.

The invention has the further improvement that the specific measurement of the vortex molded line of the vortex disc is realized, the vortex molded line of the vortex disc is a variable base circle involute-arc-variable base circle involute combined molded line, when the specific measurement is realized, a section of Archimedes spiral line segment with the same direction as the vortex line profile is adopted to fit the partial profile, the vortex curve is divided into a plurality of sections, and the two ends of each section are usedFitting the polar angle and the polar radius of the point to obtain an Archimedes spiral equation of the section, and finally obtaining an Archimedes spiral fitting equation of a vortex inner wall curve, a transition circular arc and a vortex outer wall curve, wherein the polar coordinate equation of the Archimedes spiral is as follows: p ═ p₀And + v theta, during measurement, the Archimedes spiral error of the vortex molded line is measured by controlling the radial movement of the three parallel inductance right-angle integrated measuring head on the machine tool and the rotary motion of a vortex plate on the rotary table.

The invention has the further improvement that the body error evaluation of the vortex plate is realized, three pieces of vortex line data with different heights are obtained based on the measurement data of the three parallel inductance right-angle integrated measuring heads, and a difference curved surface formed by the error of an actual measurement point in the normal direction of a theoretical point is used as the body error evaluation of the vortex line on the basis of the theoretical vortex curved surface.

The invention has at least the following beneficial technical effects:

1. compared with the traditional three-coordinate machine detection, the online measurement method for the error of the scroll plate body based on the four-axis numerical control milling machine can carry out measurement without secondary clamping, and improves the detection efficiency and the measurement precision. And the measuring unit is arranged on the vortex disc processing machine tool, so that the measuring cost is reduced.

2. When the three-parallel inductance right-angle integrated measuring head provided by the invention is used for measuring a scroll plate, only one measuring path needs to be operated, so that the scroll line data of three different positions in the vertical direction can be obtained, and the detection efficiency is improved.

3. Compared with the error evaluation of the conventional vortex line, the error evaluation algorithm of the vortex disc body provided by the invention has higher practical value.

In conclusion, the method can directly measure the scroll plate after the scroll plate is machined, improves the detection efficiency, avoids the measurement error caused by secondary clamping, adopts the three-parallel inductance right-angle integrated measuring head to finish the three-dimensional surface type error evaluation of the scroll surface through one-time measurement, can intuitively reflect whether the problem of the local error of the scroll surface caused by the inclination of the position of the cutter and a workpiece or the local abrasion of the cutter in the current machining or not compared with the traditional scroll line measurement, and has important significance for improving the manufacturing efficiency and the quality of the scroll plate process.

Drawings

FIG. 1 is a complete machine view of a scroll on-machine measurement.

Fig. 2 is a schematic diagram of three parallel inductance integrated probe measurement.

Fig. 3 is a schematic diagram of an angle error of a three-parallel inductor right-angle integrated probe.

Fig. 4 to 6 are schematic diagrams of error evaluation of the scroll plate body.

Detailed Description

The following describes the implementation process of the present invention with reference to the accompanying drawings.

The invention provides a four-axis numerical control milling machine-based online measurement method for errors of a scroll body, which is based on a four-axis scroll numerical control machine tool, wherein the four-axis numerical control scroll online measurement machine tool comprises a base 1, a radial movement mechanism 2 arranged on the base, a vertical movement mechanism 3 arranged on the radial movement mechanism, a tangential movement mechanism 4 arranged on the vertical movement mechanism, a main shaft revolving part 5 arranged on the tangential movement mechanism, an inductance measuring head 6 arranged on the main shaft part, a revolving mechanism 8 arranged on the base and a Siemens machine tool numerical control system. The tangential motion mechanism and the radial motion mechanism are both linear motor linear guide rail structures, the motion precision is high, the vertical motion mechanism is of a ball screw and linear guide rail structure, and the driving is realized through a servo motor. The main shaft rotating part adopts a high-precision ball bearing structure, the movement precision is high, the three parallel inductance right-angle integrated measuring head can be installed by replacing a tool magazine through the main shaft, the scroll plate is fixed on the plane of a rotary table of a machine tool, and the measurement on the scroll plate is realized through the linear shaft movement of the machine tool and the rotation of the rotary table.

The three parallel inductance right-angle integrated measuring heads comprise three inductance measuring heads of the same type which are arranged in parallel along the vertical direction and three measuring pins which are respectively fixedly connected to the measuring heads and are arranged in parallel, and ruby measuring balls are arranged at the heads of the measuring pins. When in measurement, the measuring surface of the vortex disc is touched, the measuring needle is stressed, and the measuring head fixedly connected with the measuring needle generates compression quantity, so that the measurement of the contact is completed.

The vector position of the three-parallel inductance right-angle integrated measuring head in the initial space direction is realized to determine the starting point of the measuring head, the angle direction of a measuring rod of the three-parallel inductance right-angle integrated measuring head in the horizontal direction is mainly calibrated, and the space angle position of the three-parallel inductance right-angle integrated measuring head is determined, so that the direction of data acquisition of a measuring point in the measuring process is ensured to be the direction of the compression amount of the three-parallel inductance right-angle integrated measuring head. And controlling a side plane of a workpiece clamping tool arranged on the slewing mechanism 8 to be a reference plane, placing the three parallel inductance right-angle integrated measuring heads at the position close to the center of the reference plane, controlling the compression amount to be 1mm, slowly rotating the slewing mechanism 8 for about 5r/min, and obtaining the minimum position angle of the measured data, namely the space angle position of the three parallel inductance right-angle integrated measuring heads.

The calibration of the three parallel inductance right-angle integrated measuring head is realized, so that more accurate error data of the scroll body can be obtained. The calibration method is characterized in that a precise standard ball is used as a calibration reference and is placed at any non-interference position in the rotary positioning mechanism 8. The method comprises the steps of firstly determining the position of a standard ball once, and then calibrating the angle information of the three measuring heads in the three parallel inductance right-angle integrated measuring heads in the vertical direction. And controlling the three-parallel inductance right-angle integrated measuring head to be close to the calibration ball, collecting points on the spherical surface through the measuring head, collecting at least 4 points, and re-measuring after the slewing mechanism rotates for an angle. The four-point data of each group can be fitted to the central position of the standard ball, and the position of the standard ball on the slewing mechanism 8 can be determined by combining the two groups of data. Based on the spatial angle position of the measuring rod in claim 3, the angular direction is in contact with a standard ball, 1mm is used as a compression amount, the feedback value of the three parallel inductance right-angle integrated measuring head is less than 1mm due to the angle, and the actual sampling point coordinates are obtained as follows:

(x+lcosθ₁sinθ₂,y+lcosθ₁cosθ₂,z+lcosθ₁)

the error transformation matrix is:

wherein: x, y, z are machine tool seatsThe mark information, i is the length from the center of the measuring head to the center of the ruby measuring ball, theta₁For measuring the angular error of the probe about the horizontal direction, theta₂The angle error of the measuring head around the vertical direction is adopted;

substituting the coordinates into the spherical coordinate formula of the precise calibration ball

(x-a)²+(y-b)²+(z-c)²＝r²；

Wherein: a, b and c are coordinates of the sphere center of the precise calibration sphere, and r is the radius of the precise calibration sphere;

determining error values for the coordinates of the sampling points

p_i(a,b,c,r)＝(x_i-a)²+(y_i-b)²+(z_i-c)²-r²；

By the sum of the squares of the coordinate error values of the pointsThe determination of the standard sphere center coordinates is realized by the basis least square principle as an objective function. The position of the measuring head in the machine tool can be obtained according to the position information of the center of the standard ball and the rotation angle of the rotary table.

Wherein: a and b are two position points of the center of the standard ball on the rotary table, and theta is the rotation angle of the rotary table.

The three parallel inductance right-angle integrated measuring heads complete data acquisition of the error curve of the scroll body by a relative measurement method, and each inductance displacement measuring head takes the obtained displacement variation as sampling data, namely reflects the measured error value. The relative measurement is characterized in that the front and back position errors of the ruby measuring ball generated by three measuring heads in the key direction in the three parallel inductance right-angle integrated measuring heads do not influence the measured value, the measured value is the relative compression quantity of the measuring heads instead of the absolute value, and the problems of the absolute errors generated by manufacturing and the like of the traditional measuring heads in the absolute position and the data loss possibly generated by the absolute measurement of a plurality of measuring heads are solved.

The method realizes error model compensation of the measured data of the scroll plate, and the compensation method comprises the following specific steps.

The first step is as follows: an X, Y, Z axis error model of the four-axis vortex disc machine tool is established, and a geometric error model is established by using a homogeneous coordinate transformation method. Measuring a scroll numerical control machining tool by adopting a laser interferometer, carrying out space grid division on the machine tool, and respectively measuring X, Y, Z axes of the machine tool in a segmented manner to obtain 21 errors such as 3 straightness errors, three corner errors and corresponding perpendicularity errors of each axis.

When the machine tool moves, a straightness error and a positioning error are generated, and a generated motion transformation matrix is as follows:

wherein: delta delta_x、Δδ_y、Δδ_zRespectively, indicating errors in the direction X, Y, Z.

When the machine tool runs, a rotation angle error is generated in the direction X, Y, Z, and a rotation error matrix can be obtained simply due to the fact that the rotation angle is small

Wherein: α, β, γ represent rotation error angles in the direction X, Y, Z.

And then a geometric error transformation matrix when three translational shafts of the scroll numerical control machine move can be obtained:

the second step is that: the position error generated when the scroll rotates on the turntable is extracted aiming at the turntable error of the four-axis scroll processing machine tool.

Wherein: alpha is alpha_px、β_pyRepresenting the X component and the Y component of the parallelism of the rotating shaft and the Z axis;

δ and ∈ indicate errors occurring when the rotation shaft rotates.

The third step: and establishing a three-parallel inductance right-angle integrated measuring head compensation model. Based on the three parallel inductance right-angle integrated measuring heads arranged on the main shaft, in the measuring process, a ruby measuring ball surface is in contact with the scroll, and the coordinate calibrated by the three parallel inductance right-angle integrated measuring heads is the center of the ruby measuring ball, so that when measured data is processed, the measured data needs to be moved by an envelope radius in the normal vector direction of a measured point to serve as a real coordinate.

In the formula: p_rAs true coordinates of the measuring points, P_fIs the coordinate of the center of the main shaft, r is the distance between a measuring point and the center of the main shaft,is the normal vector direction of the measurement point.

Establishing an error compensation model of measured data during on-machine measurement, wherein the homogeneous coordinate of a theoretical measurement point is P_m＝[P_mx,P_my,P_mz，1]At the coordinates of the measuring headThe theoretical transformation matrix in the series is T_mThe actual error transformation matrix is T_m′＝P_mT_pdT_dcThe space position deviation matrix of the theoretical measurement point under the measuring head coordinate system can be obtained as follows:

E_m＝[μ_x,μ_y,μ_z,1]＝(T_m′P_m-T_mP_m)T_b

the combined molded line of the vortex disc is a variable base circle involute-arc-variable base circle involute, and the equation is as follows:

the above equation is a parameter equation of the outer wall of the vortex line, wherein: s is 76.3. ltoreq. s.ltoreq. 710.3 (unit: degree).

(x-1.44)²+(y+3.44)²＝1.25²

(x+1.78)²+(y-2.69)²＝5.55²

The above equation is the two transition arc equations of the vortex line.

The above equation is a parameter equation of the inner wall of the vortex line, wherein: s satisfies 62.554141 ≦ s ≦ 697.137677 (unit: degree).

The polar equation for an archimedean spiral is: p ═ p₀+vθ。

Wherein: p is a radical of₀Is the initial polar radius of the curve; v is a constant; θ is the polar angle at any point on the curve.

The section of Archimedes spiral line with the same direction as the vortex line profile is adopted to fit the partial profile, in order to ensure the fitting precision of the Archimedes spiral, the vortex curve is divided into a plurality of sections, and the Archimedes spiral equation of the section is obtained by the polar angle and the polar radius of two end points of each section:

wherein: theta_i,θ_i+1Polar angles of two end points; p is a radical of_i,p_i+1The polar radii of the two endpoints.

The fitting error of the Archimedes spiral is the difference of the polar radii of the measuring points:

wherein: p is the polar radius of the theoretical measurement point, and p' is the polar radius of the actual measurement value.

On the premise that the fitting error of the Archimedes spiral is calculated to meet the measurement accuracy, the fitting equation of the Archimedes spiral of the vortex inner wall curve, the transition circular arc and the vortex outer wall curve can be obtained.

According to the equation of the Archimedes spiral, when in measurement, the measurement of the vortex molded line can be realized only by controlling the radial movement of the three parallel inductance right-angle integrated measuring head on a machine tool and the rotary motion of a vortex plate on a rotary table.

The body error evaluation of the scroll is realized, three pieces of vortex line data with different heights are obtained based on the measurement data of the three parallel inductance right-angle integrated measuring heads, and a difference curved surface formed by the error of an actual measurement point in the normal direction of a theoretical point is used as the body error evaluation of the scroll on the basis of the theoretical vortex curved surface.

The error for each measurement point is:

wherein: (x)_i,y_i,z_i) In order to actually measure the coordinates of the object,the normal vector direction of the theoretical measurement point is shown, and (x, y, z) is a theoretical coordinate.

Because the theoretical equation of the difference surface is difficult to write, discrete points on the difference surface are generally obtained, and an approximate equation is fitted to the discrete points. The difference surface equation is represented by a set of bases in surface space:

z＝a₀+a₁x+a₂y+a₃x²+a₄y²+a₅xy+...

the evaluation of the poor curved surface of the scroll profile can reflect the machining condition of the machine tool, and the reprocessing of the scroll can be guided by the evaluation result. The zero order error in the difference surface reflects the relative error between the spiral profile and the tool path, i.e. the machining allowance, as shown in fig. 4; the first order error is used for reflecting the verticality error of the vortex line and the tool abrasion condition during processing, and is shown in figure 5; the second order error may reflect whether a drum error exists during the machining of the scroll profile, as shown in fig. 6. The concrete implementation is as follows:

(1) the zero order error is equivalent to the fact that the vortex surface translates a distance in the normal direction, the zero order error is an actual machining allowance and indicates that a positioning error exists during measurement, in order to accurately extract the manufacturing error of the vortex surface, the vortex surface is unfolded, the error of measured data is also located in the normal direction of each measuring point on the unfolded surface, the measured data is parallel to the unfolded surface, and the least square method is adopted for carrying out plane fitting, namely the square sum sigma delta of the measured error_i ²And (5) calculating the distance between the two planes as the machining allowance.

(2) The vortex surface is unfolded, the perpendicularity error of a vortex molded line in the vertical direction and the machining error of the molded line in the direction can be obtained through the first-order error, and the base of the first-order error is z ═ a₀+a₁x+a₂y, in sigma delta_i ²＝∑(z_i-a₀-a₁x_i-a₂y_i)²The method is an objective function, machining errors of the vortex surface in two directions can be obtained by solving the measurement points after expansion based on a least square method, and the abrasion condition of the cutter in the machining process can be obtained through the errors in the molded line direction.

(3) The vortex surface is expanded, and the second-order error can reflect the vortexWhether the spiral line has drum error in the processing process or not is judged, and the base is z ═ a₀+a₁x+a₂y+a₃x²+a₄y²+a₅And xy, solving by least square of the measurement points after expansion to obtain whether a drum error occurs in the vortex surface machining process.