CN112666892A - Shafting measuring device based on mixed four-point method and shafting profile online reconstruction method - Google Patents
Shafting measuring device based on mixed four-point method and shafting profile online reconstruction method Download PDFInfo
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Abstract
The invention discloses a shafting measuring device based on a hybrid four-point method and an online reconstruction method of shafting profile, which are characterized in that through a directional equidistant moving fixing frame, an improved four-point error separation technology is carried out on a plurality of axial sections of a shaft to be measured, the relative variation of the center of each section to be measured is extracted, then a spatial central line is fitted according to the center position of each section, the extracted spatial central line is used as a reference axis, and the roundness error separated by each section is combined to the axis, so that the profile reconstruction of a rotary shafting is realized, and the shape error evaluation is further carried out. The invention can realize the accurate separation of the radial error motion and the tilt error motion of the rotary shaft system in the measuring process, thereby ensuring the accuracy of the profile of the reconstructed shaft system.
Description
Technical Field
The invention belongs to the technical field of precision shafting test technology and online measurement equipment detection, and particularly relates to a shafting measuring device based on a mixed four-point method and an online reconstruction method of shafting profile.
Background
The precise rotating shaft system is used as the core of a high-precision machine tool, the running state of the precise rotating shaft system directly influences the machining precision, the precise rotating shaft system is firstly studied to clearly know and describe the space motion state of the precise rotating shaft system, for the machine tool, the deviation of a machine tool rotating shaft can generate important influence on the machining precision, and the precise rotating shaft system can directly determine factors such as the shape, the roughness and the like of a machined part. Therefore, the rotation precision has direct influence on the operation of the precision rotating shaft system, and the accurate measurement and the accurate extraction of the rotation error of the precision rotating shaft system are very important research means. In a plurality of form and position error detection projects specified by the national standard, the detection of the cylindricity error of a cylindrical workpiece is a very important component, at present, instruments mainly used for measuring the cylindricity in China are a roundness measuring instrument, a three-coordinate measuring machine and the like, and the precision measuring instruments are expensive in cost, have high requirements on measuring environments and are difficult to meet the requirements of on-line measurement.
In order to realize the precise measurement of the shape error of the precise rotating shaft system, the precision of the measuring instrument is hardly improved, so that a plurality of scholars at home and abroad develop a new method for researching a measuring method with higher precision. The cylindrical part can be regarded as an overlap of countless cross-section circles along the axial direction, the online reconstruction of the cylinder can be realized by a cross-section method theoretically, and the error shape of the cylinder is combined by using a limited number of roundness errors on the cross section [ Lishengyi, Daisei and other works. The basic idea of Error Separation Techniques (ESTs) as a basic method for precision measurement is as follows: the characteristic that the contour surface of a measured workpiece is uniquely determined is utilized, a plurality of measuring heads are simultaneously applied to measure the surface of the measured part, a measured signal simultaneously contains the shape error of the measured part and the motion error of a measuring mechanism, the shape error of the measured part and the motion error of the measuring mechanism are separated by adopting a certain mathematical algorithm, and then the shape error of the measured workpiece and the motion error of the measuring mechanism are obtained, so that the precision measurement of the shape error of the measured part [ Bufu Hua, Li Shu, Zulon, etc.. the design of a cylindricity high-precision measuring system [ J ]. Loyang institute of technology (Nature science edition), 2002 (1): 46-48]. The traditional three-point method is also the key for measuring the shape error of a shafting part because the inherent first-order harmonic suppression problem [ Lishenyi, Daisei and the like, precision and ultra-precision machining in-place detection and error separation technology [ M ]. national defense science and technology university press, 2007] exists, the first-order harmonic component of the shafting gyration error and the shape error is difficult to accurately separate, the evaluation of the section roundness error cannot be influenced, the bending of the central axis of a cylinder is hidden, the difficulty is caused to the online reconstruction of the cylinder, and the evaluation of the cylindricity is also influenced.
Disclosure of Invention
In order to solve the technical problems, the invention provides a shafting measuring device based on a mixed four-point method and an online reconstruction method of shafting profile, which can realize the separation and removal of guide rail errors, shafting motion errors and inclination errors introduced by a measuring system from measured signals, thereby obtaining accurate signals to be measured and ensuring the accuracy of a reconstructed cylinder.
The invention relates to a shafting measuring device based on a mixed four-point method, which comprises: the device comprises a motor, a guide rail mechanism, a sliding frame, a fixed frame, a first displacement sensor, a second displacement sensor, a third displacement sensor and a fourth displacement sensor; the guide rail mechanism comprises two parallel guide rails, the sliding frame is arranged on the two guide rails in a spanning mode and can move along the guide rails, the fixed frame is arranged at the top of the sliding frame, and the fixed frame is provided with a circular arc-shaped through hole; the output shaft of the motor is connected with one end of the shaft to be measured, and the other end of the shaft to be measured penetrates through the through hole; the first displacement sensor, the second displacement sensor and the third displacement sensor are arranged on the fixed frame and positioned on a first plane, and the first plane is vertical to the axis of the shaft to be measured; the probes of the first displacement sensor, the second displacement sensor and the third displacement sensor are positioned in the through hole and positioned on the same concentric circumference of the shaft to be measured, the fourth displacement sensor is arranged on the fixed frame, and the probe of the fourth displacement sensor and the probe of the first displacement sensor are positioned on a straight line parallel to the axis of the shaft to be measured.
The invention discloses an online reconstruction method of shafting profile based on a mixed four-point method, which adopts a shafting measuring device based on the mixed four-point method as claimed in claim 1 to collect data, and comprises the following steps:
step 1: dividing the shaft to be measured into L measuring sections with the distance of d along the axial direction, moving the sliding frame to make the first plane align with the L sections respectively, and when the moving frame is positioned on the corresponding measuring section, rotating the shaft to be measured for a circle and acquiring the distance from the probe head to the shaft surface as measuring data through the first displacement sensor, the second displacement sensor, the third displacement sensor and the fourth displacement sensor:
step 2: performing discrete Fourier transform on the measurement data acquired in the step 1, and acquiring an s-order harmonic component of a roundness profile of a measurement section aligned with the first plane by a section three-point roundness error separation method, wherein s is 0,2,3, …, N-2, and N represents the total measurement point number of each sensor; obtaining a first-order harmonic component of a radial error separation result by an axial two-point method;
and step 3: calculating 1 order harmonic component of roundness profile of L measurement sections on the measured shaft:
and 4, step 4: and fitting a space central line according to 1-order harmonic components of the roundness profiles of the L positioning measurement sections, combining the profile shapes of all the sections to the space central line, and reconstructing the cylindrical profile of the shaft to be measured.
The shafting measuring device based on the mixed four-point method and the shafting profile online reconstruction method have the following beneficial effects:
1. the invention provides a mixed four-point method-based online reconstruction method of shafting profile, which is matched with a shafting measuring device to carry out data measurement: specifically, 4 displacement sensors are adopted to measure two axial sections and carry out error separation, and the relative change quantity of the centers of two section circles is extracted, and because the relative change is the inherent characteristic between the two sections and cannot be changed along with the rotation of a shaft system, the centers of all the section circles of a measured body are fitted, and the spatial central line of a reconstruction cylinder can be obtained.
2. The invention considers that the radial rotation error has no repeatability under the condition that the shafting rotates every week, and the three-point roundness error separation method and the axial two-point method are combined, so that the section roundness error, the radial error and the inclination error caused by the shafting rotation motion and the guide rail error motion in the error separation process can be accurately separated, which is one of innovations of a mixed four-point method different from the existing error separation method.
3. In the invention, because the error motion caused by shafting rotation and the error motion of the guide rail can be accurately separated in the error separation process, the guide rail in the measurement system has no overhigh precision requirement, and the online measurement cost of the shafting is greatly reduced, which is the application value of the invention.
4. The measuring method of the invention combines the error shapes of the cylinders by adopting the roundness error on each section and taking the fitted space central line as a reference. Therefore, the evaluation of the error of the cylindrical shape can be carried out more comprehensively, comprising the following steps: errors such as roundness, cylindricity and bus straightness, and the like, so the method has wider application.
In summary, the roundness error of each section is obtained by a section three-point roundness error separation method, the relative variation of the centers of two section circles is extracted by an axial two-point method, and the centers of the section circles are fitted to be used as the reference axis of a reconstruction cylinder, so that the problem that the variation of the centers of the section circles cannot be extracted due to first-order harmonic suppression is solved, the roundness profiles of the sections are combined by using the fitted central line as the reference axis, innovation from evaluation of single section roundness error variation to evaluation of whole cylinder profile error variation is realized, and a more comprehensive shape error evaluation method is provided.
Drawings
FIG. 1 is a schematic diagram of a shafting measuring device based on a hybrid four-point method according to an embodiment of the present invention;
FIG. 2 is a top view of a shafting measuring device based on a hybrid four-point method according to an embodiment of the present invention;
FIG. 3 is a flow chart of the online reconstruction method of the shafting profile based on the mixed four-point method;
FIG. 4 is a schematic diagram of the measurement of the shafting measuring device based on the mixed four-point method;
fig. 5 is a schematic diagram of the influence of the guide rail error motion and the shafting error motion on the measurement process.
Detailed Description
The invention relates to a shafting measuring device based on a mixed four-point method, which comprises: the device comprises a motor, a guide rail mechanism, a sliding frame 9, a fixed frame 8, a first displacement sensor 1, a second displacement sensor 2, a third displacement sensor 3 and a fourth displacement sensor 4. The guide rail mechanism comprises two parallel guide rails 10, the sliding frame 9 is arranged on the two guide rails 10 in a crossing mode and can move along the guide rails 10, the fixed frame 8 is arranged at the top of the sliding frame 9, and the fixed frame 8 is provided with a circular arc-shaped through hole. The output shaft of the motor is connected with one end of the shaft to be measured 5, and the other end of the shaft to be measured 5 is arranged in the through hole in a penetrating mode. The first displacement sensor 1, the second displacement sensor 2 and the third displacement sensor 3 are arranged on the fixed frame 8 and are positioned on a first plane, and the first plane is vertical to the axis of the shaft to be measured; the probes of the first displacement sensor 1, the second displacement sensor 2 and the third displacement sensor 3 are positioned in the through hole and positioned on the same concentric circumference of the shaft to be measured, the fourth displacement sensor 4 is arranged on the fixed frame 8, and the probe of the fourth displacement sensor 4 and the probe of the first displacement sensor 1 are positioned on a straight line parallel to the axis of the shaft to be measured. The guide rail 10 is provided with scale marks. The fixed frame 8 is provided with 4 sensor positioning holes, and the first displacement sensor 1, the second displacement sensor 2, the third displacement sensor 3 and the fourth displacement sensor 4 are arranged in the corresponding sensor positioning holes and fixed through stop screws. The 4 sensors were located within 25 μm of the measured shaft surface. The included angle between the first displacement sensor 1 and the second displacement sensor 2 is 60 degrees, and the included angle between the first displacement sensor 1 and the third displacement sensor 3 is 120 degrees.
As shown in fig. 1 and 2, in the present embodiment, the rotating shaft system of the electric spindle 7 is taken as an example, and the rotating shaft system of the electric spindle is complicated in structure, so that the rotating shaft cannot be directly measured. In this embodiment, the connecting rod 6 is respectively connected to the electric spindle 7 and the shaft to be measured 5, and the roundness error of the rotating shaft of the electric spindle is detected by performing online reconstruction on the shaft to be measured 5.
The fixed frame 8 can move along the guide rail 10 in the Z direction under the support of the sliding frame 9. The electric spindle 7 is connected with the shaft to be measured 5 through the connecting rod 6 and drives the shaft to be measured 5 to rotate. The guide rail 10 is axially parallel to the shaft 5 to be measured. When the measurement is started, the fixed frame 8 moves to the axial end of the connecting rod 6 along the guide rail 10Z under the support of the sliding frame 9, so that the fixed frame 8 is located at a first position, and the sliding frame 9 moves a distance d each time along the Z direction. In the specific implementation, the online reconstruction method of the shafting profile based on the mixed four-point method obtains the roundness error of each section through a section three-point roundness error separation method, extracts the relative variation of the centers of two section circles through an axial two-point method, and fits the centers of the section circles to be used as the reference axis of a reconstruction cylinder, so that the problem that the variation of the centers of the section circles cannot be extracted due to first-order harmonic suppression is solved, the roundness error of each section is combined by using the fitted center line as the reference axis, the innovation from the roundness variation of a single section to the variation of the profile of the whole cylinder is realized, and a more comprehensive shape error evaluation method is provided.
As shown in fig. 3, a flow chart of an online reconstruction method of a shafting profile based on a mixed four-point method is shown, and the method adopts the shafting measurement device based on the mixed four-point method to acquire data, and specifically includes:
step 1: dividing a measured shaft into L measuring sections with the distance of d along the axial direction, moving the sliding frame to enable the first plane to be aligned with the L sections respectively, enabling the shaft to be measured to rotate for a circle when the moving frame is positioned on the corresponding section, and acquiring the distance between a probe and the shaft surface as measuring data through the first displacement sensor, the second displacement sensor, the third displacement sensor and the fourth displacement sensor, wherein the step 1 comprises the following steps:
step 1.1, arranging a first displacement sensor, a second displacement sensor and a third displacement sensor on a fixed frame according to a three-point roundness error separation method, enabling the three sensors to be positioned on a first plane, enabling the fourth displacement sensor to be positioned on a second plane, enabling the first plane and the second plane to be parallel and enabling the distance between the first plane and the second plane to be d,
step 1.2, defining the length direction of the guide rail as the Z-axis direction, the vertical direction as the Y-axis direction, the direction vertical to the Y-axis in the end face of the shaft to be measured as the X-axis direction, and transferring the first displacementThe angle between the sensor and the X axis is 0, and the included angle between the second displacement sensor and the first displacement sensor is beta1The included angle between the third displacement sensor and the first displacement sensor is beta2As shown in fig. 4;
step 1.3, dividing a measured shaft into L measuring sections with the distance d along the axial direction; defining the mapping sequence P-1, 2, …, L; the position measurement refers to a measurement cross section which is aligned with the first plane after the fixing frame moves a distance d along the Z-axis direction from the end part of the shaft to be measured;
step 1.4, initializing P to 1;
step 1.5, moving the fixing frame along the Z-axis direction to enable a first plane of the fixing frame to be aligned with a P-th measuring section of the shaft to be measured;
step 1.6, driving the shaft to be measured to rotate for a circle by a motor, and acquiring measurement data of the shaft to be measured rotating for a circle on the Pth measurement section through a first displacement sensor, a second displacement sensor and a third displacement sensor; the fourth displacement sensor collects the measurement data of one rotation on the P +1 th measurement section to complete the measurement of the P-th positioning;
and step 1.7, repeating the step 1.5 and the step 1.6, and measuring the P +1 positioning until the L-th positioning data measurement is finished, so as to obtain the L positioning measurement data.
Step 2: performing discrete Fourier transform on the measurement data acquired in the step 1, and acquiring an s-order harmonic component of a roundness profile of a measurement section aligned with the first plane by a section three-point roundness error separation method, wherein s is 0,2,3, …, N-2, and N represents the total measurement point number of each sensor; obtaining a first-order harmonic component of a radial error separation result by an axial two-point method, wherein the step 2 comprises the following steps:
step 2.1, the measurement data collected by the first displacement sensor, the second displacement sensor and the third displacement sensor during the P-th position measurement is mi(lPK), wherein i ═ 1,2,3, k ═ 0,1, …, N-1; n represents the total number of points measured for each sensor, and the angular interval between samples is 2 pi/N, lPThe position is expressed as the axial positioning of the P-th positioning position of the axis to be measured; k represents the serial number of the measuring point of each sensor;
step 2.2, extracting by using a three-point roundness error separation methodTaking the s-harmonic component R (l) of the roundness profile on the P-th measured section of the axis to be measuredPS), s ═ 0,2,3, N-2 denotes the order of the harmonic component;
the measurement data acquired by the first displacement sensor, the second displacement sensor and the third displacement sensor are weighted and combined by using a three-point roundness error separation method, and the calculation is as follows:
due to the included angle beta between the first displacement sensor 1 and the X-axis1Since 0 is obtained, the weighting coefficients output by the first displacement sensor 1, the second displacement sensor 2, and the third displacement sensor 3 are: a is1＝1,a2＝-sinβ2/sin(β2-β1)，a3＝sinβ1/sin(β2-β1) Thus, the radial motion error of the shafting in the weighted signal and the linear motion error of the guide rail are removed, and the separation of the roundness error is realized;
when the harmonic order s is not equal to 1, N-1, all s satisfy the condition that G (l, s) is not equal to 0, the roundness error of the measured section can be obtained by performing inverse discrete Fourier transform on the harmonic component R (l, s) of the roundness of the measured section, and the time delay phase shift property of the Fourier transform is applied, so that the method can be obtained:
wherein the transfer function is:
in the formula, s (s ═ 0, 1.., N-1) is the order of harmonic waves, and G (l, s) is the transfer function of a three-point roundness error separation method; r (l, s) ═ DFT [ R (l, k) ] represents the s harmonic component of the measured section roundness. Substituting the weighting function coefficients into the error separation transfer function equation (3), which is in discrete form:
by selecting the appropriate p1,p2So that p is1,p2When the greatest common factor with N is 1, the transfer function g(s) ≠ 0(s ═ 0,2, …, N-2) except for s ═ 1 and N-1, and the harmonic component R (l, k) ═ IFFT [ R (l, s) of the measured cross-sectional roundness profile can be obtained]。
It has been proved that, when the harmonic order s is 1 and s is N-1, the transfer function G(s) is 0 and G (s-1) is 0, the three-point error separation technique cannot effectively obtain the harmonic component R (l, s) of the roundness profile of the measured section, and thus cannot accurately obtain the roundness error R (l, k) of the measured section, which makes it difficult to separate the axle roundness error and the gyration error, so-called "first harmonic suppression". Therefore, the three-point roundness error separation method has an inherent first-order harmonic suppression problem, and has no influence on the error separation process, but has a very important influence on the evaluation of the bending change of the central axis of the cylinder, and causes difficulty on the online reconstruction of the cylinder. The first harmonic component of the roundness profile of the measured section is the eccentric error of the least square circle center of the measured section, so the eccentric coordinate of the measured section is calculated, and the eccentric vector of the roundness profile of the measured section, namely the first harmonic component, is further solved.
Step 2.3, performing discrete Fourier transform on data collected by the first displacement sensor and the fourth displacement sensor in the P-th positioning measurement data, and acquiring a first-order harmonic component of a radial error separation result by an axial two-point method, specifically:
and (3) rotating the shaft to be measured for one circle at the P-th position measurement, and respectively acquiring data of the measured section P and the P +1 for one circle by using the first displacement sensor and the fourth displacement sensor:
in the formula: r (l)p,k)，r(lp+1K) k is 0,2,3 …, and N-2 are respectively roundness profiles of the P th and P +1 th measured positions of the axis to be measured; epsilonx(lpK) is the run-out of the first displacement sensor at the P-th position measured by the X-direction error motion without tilt error at the shaft end; d × β (l)pK) is the runout of the X-direction error motion caused by the inclination error at the shaft end of the first displacement sensor on the P +1 th positioning position;
respectively causing the X-direction deviation of the fixed frame on the P-th and P + 1-th position measuring positions of the shaft to be measured in the linear motion process of the sliding frame; m is1(lp,k)，m4(lpAnd k) respectively represents the measured data of one rotation of the shaft to be measured, which are collected by the first displacement sensor and the fourth displacement sensor at the P-th positioning position. Fig. 5 is a schematic diagram showing the influence of the guide rail error motion and the shafting error motion on the measurement process.
It should be explained here that, firstly, the first displacement sensor 1 is repeatedly used, and is respectively applied to the three-point roundness error separation method and the axial two-point method of the measured section, so that the number of sensors is reduced, and the uncertain influence caused by a large number of sensors in the error separation process is reduced; secondly, the first displacement sensor 1 is located at the shaft end where the tilt error is zero, see fig. 2.
And (3) performing discrete Fourier transform on two sides of the formula (5.1) and the formula (5.2) to obtain a first-order harmonic component of a section radial error separation result:
M1(lp,1)＝R(lp,1)+Ex(lp,1) (6.1)
M4(lp,1)＝R(lp+1,1)+Ex(lp,1)+d×Φ(1) (6.2)
in the formula, R (l)p,1)＝DFT[r(lp,1)]A 1 st harmonic component of the profile of the measured cross section for the P-th position finding; ex(lp,1)＝DFT[εx(lp,1)]1 order harmonic component of radial motion error of the measured P-th position measuring section; dxΦ (1) ═ DFT [ d × β (l)p,1)]Is the 1 st harmonic component of X-direction motion error caused by shafting inclination error.
The displacement signal of the fixing frame 8 in the X-axis direction is a constant in a period caused by the P-th and P + 1-th position measurement of the shaft 5 to be measured in the linear motion process of the guide rail 10, and the first harmonic component of the constant is zero after discrete Fourier transform, namely the constant is zero
Therefore, the linear motion error of the guide rail 10 is removed in the equations (6.1) and (6.2).
And step 3: calculating 1 order harmonic component of roundness profiles of L measuring sections on the measured shaft, wherein the step 3 comprises the following steps:
step 3.1, initializing P to 1;
step 3.2, the fourier series form of the roundness profile of the measurement section of the shaft to be measured at the P-th position can be written as formula (7):
in the formula, r0(α) is the dc harmonic component of the roundness profile of the measured section, which is also the radius of the profile of the measured section; r is1＝a1cosα+b1sin alpha is the first harmonic component R (l) of the measured cross-sectional profileP,1)，(a1,b1) The eccentric coordinates are expressed as the center of a circle of the measured section profile and the center of a least square circle;
the harmonic component of the roundness profile of the measured section is the roundness profile error of each section;
order to
Representing the known harmonic components, equation (7) can be written as:
r(α)＝r1(α)+r2(α) (8)
step 3.3, the measurement data of the first displacement sensor and the second displacement sensor are as follows:
m1(l,k)＝r(l,k)+εx(l,k) (9.1)
m2(l,k)＝r(l,k+p1)+εx(l,k)×cosβ1+εy(l,k)×sinβ1 (9.2)
the discrete form is as follows:
wherein k is 0,1, and N-1 represents the measurement point of each sensor, and N represents the total measurement point; alpha 2 pi/N is a sampling interval and is the number of spacing points between the first displacement sensor and the X axis, namely p1α is the angle between the first displacement sensor and the X-axis; p is a radical of2＝β2/α(p2N-1) is the number of spaced points between the second displacement sensor and the X-axis;
step 3.4, transforming according to the formulas (10.1) and (10.2), and knowing that:
a1 cos(kα)+b1 sin(kα)+εx(k)＝m1(k)-r2(k)＝h1 (11.1)
in the formula, m1(k),m2(k) The output signals from which the 1 st harmonic component and the N-1 st harmonic component are removed for the first and second displacement sensors are known discrete sequences; r is2(k),r2(k+p1) Removing 1 st order harmonic component and N-1 st order harmonic component for first and second displacement sensorsA roundness error sequence measuring three-point roundness error separation; the right side of the equation is a known quantity, and the right side of the equation (11.1) is h1Equation (11.2) is given as h on the right2；
The shafting radial rotation error is expressed by epsilon (k), and the component epsilon of the shafting radial rotation error on X, Y axesx(k),εy(k)]Can be expressed as:
εx(k)＝ε(k)×cos(kα) (12.1)
εy(k)＝ε(k)×sin(kα) (12.2)
the coupling type (11.1), (11.2), (12.1) and (12.2) can eliminate the component of the shafting radial rotation error in the formulas (12.1) and (12.2) on the XY axis, and can obtain:
h2(k)cos(kα)-h1sin(kα)＝b1cos(2kα)-a1sin(2kα) (13)
step 3.5, obtaining the eccentric coordinates (a) of the circle center and the least square circle center of the measured section profile1,b1) Multiplying the two sides of the equation (13) by trigonometric functions sin (2k alpha) and cos (2k alpha) respectively, and summing in a measurement period, according to the orthogonality of the trigonometric functions, obtaining:
step 3.6, obtaining a first-order harmonic component R (l) of the roundness profile of the measured cross section at the P-th position measuring position on the shaft 5 to be measured according to the following formulaP,1)：
R(lP,1)＝r1(α)＝a1cosα+b1cosα (15)
Step 3.7, moving the sliding frame 9 to enable the fixing frame 8 to be positioned at the P +1 th position of the shaft 5 to be measured, and repeatedly executing the step 3.2 to obtain the first-order harmonic component R (l) of the roundness profile of the section to be measured at the P +1 th position on the shaft to be measuredP+1,1)；
Step 3.8, obtaining a first-order harmonic component of the cylinder inclination error at the P-th position-measuring right section on the axis to be measured according to the following formula:
d×Φ(1)＝M4(lP,1)-M1(lP,1)-R(lP+1,1)+R(lP,1) (16)
step 3.9, when the measured body position 5 is positioned at the P +1 th measuring position, obtaining the first harmonic component R (l) of the roundness profile of the measured section at the P +2 th measuring position according to the formula (17)P+2,1)：
R(lP+2,1)＝M4(lP+1,1)-M1(lP+1,1)-d×Φ(1)+R(lP+1,1) (17)
Step 3.10, based on the N-1 th harmonic component R (l)P+1N-1) is the first harmonic component R (l)P+1And 1) obtaining the N-1 order harmonic component of the roundness profile of the measured section of the shaft 5 to be measured at the P-th position by using the complex conjugate;
and 3.11, assigning the P +1 to the P, and repeatedly executing the step 3.9 until the first-order harmonic component and the (N-1) th-order harmonic component of the roundness profile of the L measured sections are obtained.
It should be noted here that the first harmonic component of the roundness profile of the measured cross section can be iteratively calculated from the P +2 th positioning by calculating the first harmonic component of the roundness profile of the measured cross section at the P th positioning and the P +1 th positioning, and then the first harmonic component of the roundness profile of the measured cross section can be measured by the equation (17).
And 4, step 4: fitting a space central line according to 1-order harmonic components of the L measured section roundness profiles, combining the shapes of the section profiles onto the space central line, and reconstructing a cylindrical profile, wherein the step 4 comprises the following steps of:
step 4.1, the s-order harmonic component R (l) is subjected to the equation (18)PS) (s ═ 0,1,2, …, N-1) by inverse discrete fourier transform to obtain the profile shape r (l) of the P-th measured cross section of the axis to be measuredP,k)：
r(lP,k)＝IDFT[R(lP,s)]，k＝0,1,2,…,N-1 (18)
Step 4.2, after obtaining each harmonic component of the L positioning measurement cross section shapes, repeating the step 4.1 to obtain L positioning cross section profile shapes;
step 4.3, center vector 2R (l) of each section profileP1)/N, P is 1,2, …, L is fitted to a spatial central line as a reference axis of L measured cross sections, and the profile of the shaft 5 to be measured is reconstructed, thereby realizing the evaluation of the shape error of the shaft 5 to be measured.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the scope of the present invention, which is defined by the appended claims.
Claims (9)
1. Shafting measuring device based on mix four point method, its characterized in that includes: the device comprises a motor, a guide rail mechanism, a sliding frame, a fixed frame, a first displacement sensor, a second displacement sensor, a third displacement sensor and a fourth displacement sensor; the guide rail mechanism comprises two parallel guide rails, the sliding frame is arranged on the two guide rails in a spanning mode and can move along the guide rails, the fixed frame is arranged at the top of the sliding frame, and the fixed frame is provided with a circular arc-shaped through hole; the output shaft of the motor is connected with one end of the shaft to be measured, and the other end of the shaft to be measured penetrates through the through hole; the first displacement sensor, the second displacement sensor and the third displacement sensor are arranged on the fixed frame and positioned on a first plane, and the first plane is vertical to the axis of the shaft to be measured; the probes of the first displacement sensor, the second displacement sensor and the third displacement sensor are positioned in the through hole and positioned on the same concentric circumference of the shaft to be measured, the fourth displacement sensor is arranged on the fixed frame, and the probe of the fourth displacement sensor and the probe of the first displacement sensor are positioned on a straight line parallel to the axis of the shaft to be measured.
2. The shafting measuring device based on the hybrid four-point method according to claim 1, wherein the fixing frame is provided with 4 sensor positioning holes, and the first displacement sensor, the second displacement sensor, the third displacement sensor and the fourth displacement sensor are arranged in the corresponding sensor positioning holes and fixed by stop screws.
3. The shafting measuring device based on the hybrid four-point method according to claim 1, wherein the guide rail is provided with scale marks.
4. The method for reconstructing the shafting profile on line based on the mixed four-point method is characterized in that the shafting measuring device based on the mixed four-point method in claim 1 is adopted for data acquisition, and the method comprises the following steps:
step 1: dividing the shaft to be measured into L measurement sections with the distance d along the axial direction, moving the sliding frame to enable the first plane to be aligned with the L sections respectively, positioning the moving frame on the corresponding measurement sections to enable the shaft to be measured to rotate for a circle, and acquiring the distance from the probe to the shaft surface through the first displacement sensor, the second displacement sensor, the third displacement sensor and the fourth displacement sensor to serve as measurement data:
step 2: performing discrete Fourier transform on the measurement data acquired in the step 1, and acquiring an s-order harmonic component of a roundness profile of a measurement section aligned with the first plane by a section three-point roundness error separation method, wherein s is 0,2,3, …, N-2, and N represents the total measurement point number of each sensor; obtaining a first-order harmonic component of a radial error separation result by an axial two-point method;
and step 3: calculating 1 order harmonic component of roundness profile of L measurement sections on the measured shaft:
and 4, step 4: and fitting a space central line according to 1-order harmonic components of the roundness profiles of the L positioning measurement sections, combining the profile shapes of all the sections to the space central line, and reconstructing the cylindrical profile of the shaft to be measured.
5. The method for reconstructing the shafting profile on line based on the hybrid four-point method according to claim 4, wherein the step 1 comprises the following steps:
step 1.1, arranging a first displacement sensor, a second displacement sensor and a third displacement sensor on a fixed frame according to a three-point roundness error separation method, enabling the three sensors to be positioned on a first plane, enabling the fourth displacement sensor to be positioned on a second plane, enabling the first plane and the second plane to be parallel and enabling the distance between the first plane and the second plane to be d,
step 1.2, defining the length of the guide railThe degree direction is Z-axis direction, the vertical direction is Y-axis direction, the direction perpendicular to the Y-axis direction in the end face of the shaft to be measured is X-axis direction, the angle between the first displacement sensor and the X-axis is 0, and the included angle between the second displacement sensor and the first displacement sensor is beta1The included angle between the third displacement sensor and the first displacement sensor is beta2
Step 1.3, dividing a measured shaft into L measuring sections with the distance d along the axial direction; defining the mapping sequence P-1, 2, …, L; the position measurement refers to a measurement cross section which is aligned with the first plane after the fixing frame moves a distance d along the Z-axis direction from the end part of the shaft to be measured;
step 1.4, initializing P to 1;
step 1.5, moving the fixing frame along the Z-axis direction to enable a first plane of the fixing frame to be aligned with a P-th measuring section of the shaft to be measured;
step 1.6, driving the shaft to be measured to rotate for a circle by a motor, and acquiring measurement data of the shaft to be measured rotating for a circle on the Pth measurement section through a first displacement sensor, a second displacement sensor and a third displacement sensor; the fourth displacement sensor collects the measurement data of one rotation on the P +1 th measurement section to complete the measurement of the P-th positioning;
and step 1.7, repeating the step 1.5 and the step 1.6, and measuring the P +1 positioning until the L-th positioning data measurement is finished, so as to obtain the L positioning measurement data.
6. The method for reconstructing the shafting profile on line based on the hybrid four-point method according to claim 4, wherein the step 2 comprises the following steps:
step 2.1, the measurement data collected by the first displacement sensor, the second displacement sensor and the third displacement sensor during the P-th position measurement is mi(lPK), wherein i ═ 1,2,3, k ═ 0,1, …, N-1; n represents the total number of points measured for each sensor, and the angular interval between samples is 2 pi/N, lPThe position is expressed as the axial positioning of the P-th positioning position of the axis to be measured; k represents the serial number of the measuring point of each sensor;
step 2.2, extracting the s-order harmonic component of the roundness profile on the measuring section of the P-th positioning of the shaft to be measured by using a three-point roundness error separation methodAmount R (l)PS), s ═ 0,2,3, N-2 denotes the order of the harmonic component;
step 2.3, performing discrete Fourier transform on data collected by the first displacement sensor and the fourth displacement sensor in the P-th positioning measurement data, and obtaining a first-order harmonic component M of a radial error separation result by an axial two-point method1(lp1) and M4(lP,1)。
7. The method for reconstructing the shafting profile on line based on the hybrid four-point method according to claim 6, wherein the step 2.3 is specifically as follows:
and (3) rotating the shaft to be measured for one circle at the P-th position measurement, and respectively acquiring data of the measured section P and the P +1 for one circle by using the first displacement sensor and the fourth displacement sensor:
and (3) performing discrete Fourier transform on two sides of the formula (5.1) and the formula (5.2) to obtain a first-order harmonic component of a section radial error separation result:
M1(lp,1)＝R(lp,1)+Εx(lp,1) (6.1)
M4(lp,1)＝R(lp+1,1)+Εx(lp,1)+d×Φ(1) (6.2)
in the formula, R (l)p,1)＝DFT[r(lp,1)]A 1 st harmonic component of the profile of the measured cross section for the P-th position finding; ex(lp,1)＝DFT[εx(lp,1)]1 order harmonic component of radial motion error of the measured P-th position measuring section; dxΦ (1) ═ DFT [ d × β (l)p,1)]Is the 1 st harmonic component of X-direction motion error caused by shafting inclination error.
8. The method for reconstructing the shafting profile on line based on the hybrid four-point method according to claim 4, wherein the step 3 comprises the following steps:
step 3.1, initializing P to 1;
step 3.2, the fourier series form of the roundness profile of the measurement section of the shaft to be measured at the P-th position can be written as formula (7):
in the formula, r0(α) is the dc harmonic component of the roundness profile of the measured section, which is also the radius of the profile of the measured section; r is1＝a1cosα+b1sin alpha is the first harmonic component R (l) of the measured cross-sectional profileP,1)，(a1,b1) The eccentric coordinates are expressed as the center of a circle of the measured section profile and the center of a least square circle;
the harmonic component of the roundness profile of the measured section is the roundness profile error of each section;
order to
Representing the known harmonic components, equation (7) can be written as:
r(α)＝r1(α)+r2(α) (8)
step 3.3, the measurement data of the first displacement sensor and the second displacement sensor are as follows:
m1(l,k)＝r(l,k)+εx(l,k) (9.1)
m2(l,k)＝r(l,k+p1)+εx(l,k)×cosβ1+εy(l,k)×sinβ1 (9.2)
the discrete form is as follows:
wherein k is 0,1, and N-1 represents the measurement point of each sensor, and N represents the total measurement point; α -2 π/N as the sampling interval, p1＝β1/α(p1N-1) is the number of spaced points between the first displacement sensor and the X-axis, i.e. p1α is the angle between the first displacement sensor and the X-axis; p is a radical of2＝β2/α(p2N-1) is the number of spaced points between the second displacement sensor and the X-axis;
step 3.4, the transformation is carried out according to the formulas (10.1) and (10.2), and the right edges of the formulas (11.1) and (11.2) are named as h1,h2Thus, it can be seen that:
a1cos(kα)+b1sin(kα)+εx(k)＝m1(k)-r2(k)＝h1 (11.1)
step 3.5, obtaining the eccentric coordinates (a) of the circle center of the measured section profile and the circle center of the least square by calculation1,b1)：
Step 3.6, the 1 st harmonic component R (l) of the roundness profile of the measurement cross section of the P-th position measurement on the axis to be measured can be obtained according to the following formulaP,1)：
R(lP,1)＝r1(α)＝a1cosα+b1cosα (15)
Step 3.7, moving the sliding frame to enable the first plane to be positioned at the P +1 th position of the shaft to be measured, repeatedly executing the step 3.2, and obtaining the 1 st harmonic component R (l) of the roundness profile of the measuring section at the P +1 th position on the shaft to be measuredP+1,1)；
Step 3.8, simultaneous equations 6.1 and 6.2 obtain the first harmonic component of the cylinder tilt error at the second plane of the P-th positioning on the axis to be measured:
d×Φ(1)＝M4(lP,1)-M1(lP,1)-R(lP+1,1)+R(lP,1) (16)
step 3.9, when the axis to be measured is positioned at the P +1 th position, obtaining the first-order harmonic component R (l) of the roundness profile of the measured section at the P +2 th position according to the formula (17)P+2,1)：
R(lP+2,1)＝M4(lP+1,1)-M1(lP+1,1)-d×Φ(1)+R(lP+1,1) (17)
Step 3.10, based on the N-1 th harmonic component R (l)P+1N-1) is the first harmonic component R (l)P+11) obtaining the N-1 order harmonic component of the roundness profile of the P-th measured section of the shaft to be measured;
and 3.11, assigning the P +1 to the P, and repeatedly executing the step 3.9 until 1 order harmonic component and the N-1 order harmonic component of the roundness profile of the L measured sections are obtained.
9. The method for reconstructing the shafting profile on line based on the hybrid four-point method according to claim 4, wherein the step 4 comprises the following steps:
step 4.1, the s-order harmonic component R (l) is subjected to the equation (18)PS) (s ═ 0,1,2, …, N-1) by inverse discrete fourier transform to obtain the profile shape r (l) of the P-th measured cross section of the axis to be measuredP,k)：
r(lP,k)＝IDFT[R(lP,s)]，k＝0,1,2,…,N-1 (18)
Step 4.2, after obtaining each harmonic component of the L positioning measurement cross section shapes, repeating the step 4.1 to obtain L positioning cross section profile shapes;
step 4.3, center vector 2R (l) of each section profilePAnd 1)/N, wherein P is 1,2, …, L is fitted into a space central line and used as a reference axis of the L measurement sections to reconstruct the profile of the axis to be measured, thereby realizing the evaluation of the shape error of the axis to be measured.
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