A gear arbitrary tooth thickness measurement method integrating multiple line structured light probes

Abstract

The application relates to a gear arbitrary tooth thickness measurement method integrating multiple line structure light heads, and belongs to the technical field of precise testing and instruments and mechanical transmission. A three-dimensional mathematical model of a gear and a coordinate system of a measured gear are established according to input gear parameters, so as to determine and calculate the pose parameters of four line structure light heads. A corresponding reference coordinate system is established through the pose parameters of the four heads, then left and right tooth surface data of all gear teeth are acquired, and threshold extraction is performed on the complete tooth profile. Through the pose relationship between the reference coordinate system of each head and the coordinate system of the measured gear, the left and right tooth surface data acquired by the head is converted into the coordinate system of the measured gear. An actual gear tooth thickness calculation model is determined, the tooth thickness deviation ΔE of an arbitrary radius r x of a circle is calculated, the radial tooth thickness average deviation ΔE s , the tooth width direction tooth thickness average deviation ΔE sr and the evaluation of the tooth width direction tooth thickness average deviation ΔE sb are realized, and then the evaluation of the entire tooth surface tooth thickness deviation ΔE s面 is realized.

Description

TECHNICAL FIELD

[0001] The application relates to a gear arbitrary tooth thickness measurement method integrating multiple line structure optical heads, and belongs to the technical field of precision testing and instruments and mechanical transmission. BACKGROUND

[0002] Gear transmission is an important transmission form in various machines, vehicles, instruments, meters and machine tools, and is mainly used for transmitting motion and power. With the rapid development of modern industrial technology, higher and higher requirements are put forward for the performance of gear transmission, and thus higher and higher requirements are put forward for the quality of gears. In particular, in the fields of aviation and military, the demand for precision gears is increasing, which poses a challenge to the design, manufacturing and measurement of gears. However, errors may be introduced in each link of gear design and manufacturing, which not only affects the transmission accuracy of gears, but also increases the vibration, noise and dynamic load of the system, and even greatly reduces the service life of gears.

[0003] Tooth thickness deviation is one of the key errors in gear manufacturing, which refers to the error between the actual tooth thickness and the theoretical tooth thickness, and essentially represents the manufacturing error of the tooth circumferential direction. The deviation has an important influence on gear transmission: first, it directly affects the meshing tooth profile of the gear, thereby affecting the time-varying meshing stiffness of the gear; second, the tooth thickness deviation is an index for evaluating the gear backlash, and the change of the tooth thickness deviation will inevitably affect the size of the gear backlash. Too small gear backlash will destroy the lubricating oil film formed during gear transmission, thereby aggravating the wear of the gear tooth surface and causing the gear to fail prematurely. Too large gear backlash will affect the smoothness of gear transmission, thereby aggravating the vibration and noise of the gear transmission system. It can be seen that gear measurement urgently needs to develop tooth thickness measurement methods and devices.

[0004] The existing gear tooth thickness measurement method mainly adopts a contact type measurement method, but in the measurement, the direct contact between the measuring head and the workpiece may scratch the surface of the workpiece, and in the measurement of small gears, the small radius of the measuring head used and the insufficient rigidity of the material may easily lead to wear and cracking of the measuring head, thereby affecting the measurement accuracy; in the measurement of large quantities or high-precision gears, the measurement efficiency is low; in addition, the data obtained by the method is small sample data, and the arbitrary tooth thickness cannot be measured. The so-called arbitrary tooth thickness refers to the tooth thickness deviation of the gear on the circle with an arbitrary radius. In order to solve the limitations of the traditional contact type measurement, non-contact measurement technology is introduced into the field of gear precision measurement.

[0005] The non-contact measurement technology represented by the structured light measurement is based on technologies such as light, electricity, machines and computers, and the parameter information of the measured gear is obtained through measurement and computer analysis without contacting the measured gear. At present, the measurement method based on a single line structured light probe can only obtain single-sided tooth surface point cloud data through one-time scanning measurement, and cannot quickly and effectively realize the tooth thickness measurement. The measurement method based on two line structured light probes has ZL201711236551.8, and the measurement efficiency still needs to be improved, secondly, the tooth thickness representation parameters are not comprehensive, and the tooth thickness of the whole tooth surface cannot be represented, and in addition, adjusting the pose of the line structured light probe in the method is easy to introduce the machine tool geometric error and reduce the measurement efficiency. SUMMARY

[0006] The present application aims at the limitations of the existing contact measurement method and the deficiencies of the gear measurement method based on a single line structured light probe, and proposes a gear arbitrary tooth thickness measurement method integrating multiple line structured light probes, which can obtain all tooth surface point cloud data through one-time measurement. In the measurement process, the measurement method of the application not only improves the measurement efficiency by several times, but also improves the accuracy of the measurement result by the complete gear tooth surface point cloud data.

[0007] The application adopts the following technical scheme:

[0008] The gear arbitrary tooth thickness measurement method integrating multiple line structured light probes comprises the following steps:

[0009] W1: Establish a three-dimensional model of the measured gear

[0010] (1) The inner hole of the measured gear is clamped by the three-jaw chuck on the precision turntable to constrain the six degrees of freedom of the gear, so as to realize the coaxial rotation of the measured gear and the precision turntable.

[0011] (2) First, input the measured gear parameters, and then establish the measured gear coordinate system σ o according to the right-hand rule o , o , o ], which is a Cartesian rectangular coordinate system, O is the origin of the measured gear coordinate system, Z o axis is the rotation axis, K(x k , k , k ) is the three-dimensional coordinates of any point on the measured gear tooth surface, and the involute tooth surface equation of the K point is:

[0012]

[0013]

[0014] In the formula, r bR is the base circle radius of the measured gear, φ is the initial phase angle of the involute, α k and θ k are the development angle, pressure angle and polar angle of the involute at point K, respectively. The physical meaning of θ k is expressed as:

[0015]

[0016] W2: calibrate and determine the pose parameters of the line structured light probe

[0017] In order to ensure that the pose between the line structured light probe and the measured gear reaches the best pose during measurement, the measurement angle and position of the line structured light probe need to be calibrated. When adjusting the position of the line structured light probe, in order to determine the positional relationship between the four probes and the measured gear, the center of the probe is selected as the reference point, and the coordinates of the reference point in the coordinate system of the measured gear are taken as the relative position parameters of the two. Among them, the positions of the left two probes are realized by driving the left X-axis guide rail and the left Y-axis guide rail respectively, and the positions of the right two probes are realized by driving the right X-axis guide rail and the right Y-axis guide rail respectively. And the linear grating installed on the guide rail can detect the guide rail position data in real time, so as to fine-tune the position of each guide rail, so as to realize the best measurement position of the probe during measurement. The probe attitude angle [γ,η] is determined by the installation angle γ of the auxiliary part wedge block and the wedge angle η. The positional relationship between the line structured light probe and the coordinate system of the measured gear is:

[0018] Left rear probe P1: a1 is the distance from the center of the probe to the X Ο axis of the coordinate system of the measured gear, g1 is the distance from the center of the probe to the Y Ο axis of the coordinate system of the measured gear, c1 is the distance from the center of the probe to the Z Ο axis of the coordinate system of the measured gear.

[0019] Right front probe P2: a2 is the distance from the center of the probe to the X Ο axis of the coordinate system of the measured gear, g2 is the distance from the center of the probe to the Y Ο axis of the coordinate system of the measured gear, c2 is the distance from the center of the probe to the Z Ο axis of the coordinate system of the measured gear, h2 is the thickness of the right front adjustment block, and the value of c2 is:

[0020] c2=c1+h2 (3)

[0021] Left front probe P3: a3 is the distance from the center of the probe to the X Ο axis of the coordinate system of the measured gear, g3 is the distance from the center of the probe to the Y Ο axis of the coordinate system of the measured gear, c3 is the distance from the center of the probe to the ZΟ The distance of the axis.

[0022] Right rear measuring head P4: a4 is the distance of the measuring head center to the measured gear coordinate system X Ο The distance of the axis, g4 is the distance of the measuring head center to the measured gear coordinate system Y Ο The distance of the axis, c4 is the distance of the measuring head center to the measured gear coordinate system axis Z Ο The distance, h4 is the right rear adjusting amount block thickness, and the value of c4 is:

[0023] c4 = c3 + h4 (4)

[0024] In order to effectively obtain the tooth surface data, the installation angle γ and the wedge angle η of the auxiliary wedge-shaped block need to be determined. The installation angle of the wedge-shaped block is determined by the following method: a bolt hole is opened at one end of the wedge-shaped block, and the other end is also fixed by a bolt hole. When adjusting the installation angle, loosen the bolts at both ends, and rotate the wedge-shaped block around the bolt hole. The installation angle γ of the wedge-shaped block is calculated by the following formula:

[0025]

[0026] In the formula, T1 is the distance between the centers of the bolt holes on the two wedge-shaped blocks, and T2 is the distance from the center of the bolt hole to the intersection point of the two wedge-shaped blocks.

[0027] The wedge angle η is calculated by the size of the wedge-shaped block:

[0028]

[0029] In the formula, h o and h1 are the height of the wedge-shaped block, and t is the length of the wedge-shaped block.

[0030] W3: Establish four line structured light measuring head reference coordinate systems

[0031] In order to facilitate coordinate transformation, an auxiliary four reference coordinate system is established for calculation, and the transformation process is as follows:

[0032] Taking the gear as the center, the left rear measuring head P1 coordinate system is σ1' = [O1; X1', Y1', Z1'], (U1, V1, W1) are the measured values in the left rear measuring head P1 coordinate system, and the auxiliary reference coordinate system is σ1 = [O1; X σ1 , Y σ1 , Z σ1 ]. Among them, the directions of the reference coordinate system X σ1 axis, Y σ1 axis and Z σ1 axis are respectively the same as the directions of the measured gear coordinate system X o axis, Y o axis and Z oIf the directions of the X-axis and the Y-axis are the same, the coordinate conversion of the left rear probe P1 is:

[0033]

[0034] With the gear as the center, the coordinate system of the right front probe P2 is σ2' = [O2; X2', Y2', Z2'], (U2, V2, W2) are the measured values in the coordinate system of the right front probe P2, and the auxiliary reference coordinate system is σ2 = [O2; X σ2 ,Y σ2 ,Z σ2 ]. Among them, the directions of the X σ2 axis and the Y σ2 axis of the reference coordinate system are opposite to the directions of the X o axis and the Y o axis of the measured gear coordinate system, and the direction of the Z σ2 axis is the same as the direction of the Z o axis of the measured gear coordinate system. The coordinate conversion of the right front probe P2 is:

[0035]

[0036] With the gear as the center, the coordinate system of the left front probe P3 is σ3' = [O3; X3', Y3', Z3'], (U3, V3, W3) are the measured values in the coordinate system of the left front probe P3, and the auxiliary reference coordinate system is σ3 = [O3; X σ3 ,Y σ3 ,Z σ3 ]. Among them, the directions of the X σ3 axis, the Y σ3 axis and the Z σ3 axis of the reference coordinate system are the same as the directions of the X o axis, the Y o axis and the Z o axis of the measured gear coordinate system. The coordinate conversion of the left front probe P3 is:

[0037]

[0038] With the gear as the center, the coordinate system of the right rear probe P4 is σ4' = [O4; X4', Y4', Z4'], (U4, V4, W4) are the measured values in the coordinate system of the right rear probe P4, and the auxiliary reference coordinate system is σ4 = [O4; X σ4 ,Y σ4 ,Z σ4 ]. Among them, the directions of the X σ4 axis and the Y σ4 axis of the reference coordinate system are opposite to the directions of the X o axis and the Y o axis of the measured gear coordinate system, and the direction of the Z σ4 axis is the same as the direction of the Zo The direction of the shaft is the same, and the coordinate of the right rear probe P4 is converted as:

[0039]

[0040] In the formula, γ is the installation angle of the probe, and η is the wedge angle.

[0041] After establishing the reference coordinate system of the four line structured light probes, the probes start scanning and measuring. After the measured gear rotates one revolution, the two-side tooth surface data of all the teeth of the measured gear are obtained.

[0042] W4: Threshold extraction of complete tooth profile

[0043] Generally, the gear data obtained by the line structured light probe often contains a small amount of speckle and noise, and the data amount of each tooth surface is as high as hundreds of millions, and the data in the unnecessary area affects the operation efficiency, so it is necessary to perform threshold processing on the measured gear data to extract the complete tooth profile data. The following four steps are performed:

[0044] Step one: select the involute tooth profile on any one side tooth surface, and set the starting threshold x l1 and the ending threshold x l2 of the effective tooth profile, wherein x l1 is the intersection of the gear transition curve and the tooth profile, and x l2 is the intersection of the gear addendum circle and the tooth profile;

[0045] Step two, after setting the starting threshold x l1 and the ending threshold x l2 of the effective tooth profile, extract the tooth profile in the interval (x l1 , x l2 );

[0046] Step three, the tooth profile of the same side tooth surface is rotated by an angle θ' around the measured gear coordinate system Z Ο , and the tooth profile of the tooth surface in the interval (x l1 , x l2 ) is extracted;

[0047]

[0048] In the formula, z is the number of teeth of the measured gear.

[0049] Step four: until the measured gear rotates 360°, the extraction of the single-side complete tooth profile of all the teeth is realized.

[0050] The single-side complete tooth profile of the other side of all the teeth is also extracted by the above four steps.

[0051] W5: Conversion of the reference coordinate system of the four probes to the coordinate system of the measured gear

[0052] Since the gear under test has left and right tooth surfaces, the data acquired by probes P1 and P2 are the data for the right tooth surface. However, the tooth thickness deviation evaluation is performed in the coordinate system of the gear under test. Therefore, it is necessary to transform the right tooth surface data acquired by probes P1 and P2 into the coordinate system of the gear under test. That is, the reference coordinate system of probes P1 and P2 is transformed to the coordinate system of the gear under test through translation and rotation.

[0053]

[0054]

[0055] The data acquired by probes P3 and P4 are the left tooth surface data of the gear. However, the tooth thickness deviation evaluation is performed in the coordinate system of the gear being measured. Therefore, it is necessary to transform the left tooth surface data acquired by probes P3 and P4 to the coordinate system of the gear being measured. That is, the reference coordinate systems of probes P3 and P4 are transformed to the coordinate system of the gear being measured through translation and rotation.

[0056]

[0057]

[0058] Equations (12), (13), (14) and (15) can be used to convert the tooth surface data obtained by probes P1, P2, P3 and P4 into the coordinate system of the gear being measured.

[0059] W6: Evaluation of tooth thickness deviation in the coordinate system of the gear under test

[0060] Tooth thickness deviation ΔE s This is the difference between the actual and true tooth thickness. Tooth thickness measurement is generally performed on the pitch cylinder surface, but using only the tooth thickness on the pitch cylinder surface as an evaluation criterion is insufficient to assess the tooth thickness deviation of the gear tooth surface. To evaluate the tooth thickness deviation across the entire tooth surface, it is necessary to take the tooth thickness deviation of any circle with any radius on any cross-section, calculate the radial average tooth thickness deviation and the average tooth thickness deviation in the tooth width direction, and then obtain the average of the two.

[0061] Based on any radius r on a standard gear x The tooth thickness s of the circle x and the actual tooth thickness s obtained x ', to obtain any radius r x Tooth thickness deviation ΔE of the circle s Calculation formula:

[0062] ΔE s =s x '-s x (16)

[0063] This method evaluates ΔE using the tooth thickness. sFirst, the tooth thickness s of the circle where any radius r on the standard gear is located is calculated x x s = r sin α

[0064]

[0065]

[0066]

[0067]

[0068] where s, r, α and θ are the pitch circle tooth thickness, radius, pressure angle and polar angle respectively, x corresponding to the central angle.

[0069] Second, the actual tooth thickness s of the circle where any radius r on the gear is located is calculated according to the measured data x x The coordinates of L1' and L2' are

[0070]

[0071]

[0072]

[0073]

[0074] where s, r, α and θ are the pitch circle tooth thickness, radius, pressure angle and polar angle respectively, x corresponding to the central angle.

[0075] Radial tooth thickness average deviation ΔE sr

[0076] When calculating the radial tooth thickness deviation, in order to reduce the error caused by random factors and improve the accuracy of measurement, the average value ΔE of the tooth thickness deviation of the circle where any radius on a certain cross section is located is taken sr As the final result, its value is:

[0077]

[0078] where n is the n radial tooth thicknesses measured in turn from the root to the top of the same tooth.

[0079] Tooth width direction tooth thickness average deviation ΔE sb

[0080] ​​​​​In order to reduce the error caused by random factors and improve the accuracy of measurement, the average value ΔE of the tooth thickness deviation of the circle at a certain radius in the tooth width direction is taken sb As the final result, the value is:

[0081]

[0082] In the formula, m is the m axial tooth thicknesses measured in turn at different tooth width positions on a certain evaluation cylinder.

[0083] The whole tooth surface tooth thickness deviation ΔE s面

[0084] The average value of the radial tooth thickness average deviation and the tooth width direction tooth thickness average deviation is taken as the whole tooth surface tooth thickness deviation ΔE s面 The result is:

[0085]

[0086] The present application has the following advantages:

[0087] I. The tooth thickness deviation measurement efficiency of the method can be improved by several times, and compared with the contact tooth thickness measurement method or the single line structure light measuring head, the tooth thickness data of the measured gear can be obtained simultaneously by four line structure light measuring heads.

[0088] II. The method has fast measurement speed and more comprehensive data, and can meet the tooth thickness measurement of large quantities and high precision gears.

[0089] III. The method can obtain tooth surface data on the complete tooth width, and combined with the measuring heads on the left and right sides of different tooth width positions, the tooth thickness measurement of all gear teeth on different cross sections can be realized.

[0090] IV. The method can comprehensively evaluate the machining errors on different evaluation circles of the same cross section, and can quickly evaluate the tooth thickness deviation of any radius.

[0091] V. The method proposes radial tooth thickness average deviation, tooth width direction tooth thickness average deviation and whole tooth surface tooth thickness deviation three indexes, reduces the influence of random factors in the measurement process, and can more comprehensively evaluate the key index of tooth thickness. DETAILED DESCRIPTION

[0092] Figure 1 Three-dimensional mathematical model of the measured gear tooth surface.

[0093] Figure 2 The parameter diagram of the reference coordinate system of the measuring heads P1 and P2 relative to the measured gear coordinate system.

[0094] Figure 3A schematic diagram of the parameters of the reference coordinate system of probes P3 and P4 relative to the coordinate system of the gear being measured.

[0095] Figure 4 Schematic diagram for determining the probe installation angle.

[0096] Figure 5 Schematic diagram for determining the wedge angle of the probe.

[0097] Figure 6 The complete tooth profile is extracted using the probe coordinate system.

[0098] Figure 7 Actual gear tooth thickness calculation model.

[0099] Figure 8 Structural diagram of a gear measuring device integrating multiple line structure optical probes.

[0100] Figure 9 Flowchart for measuring arbitrary tooth thickness of the gear under test. Detailed Implementation

[0101] The following description, in conjunction with the accompanying drawings, further illustrates a method for measuring arbitrary tooth thickness of gears using multiple integrated linear optical probes. Figure 8 As shown, this method is applied to a gear measuring device that integrates multiple line structure optical probes.

[0102] The gear measuring device integrating multiple line structured optical probes comprises three parts: a gear measuring table, a left-side component, and a right-side component. The gear measuring table includes a precision rotary table, a three-jaw chuck, a Z-axis ball screw guide, a Z-axis sliding slide, and a center. The precision rotary table is equipped with a circular grating to detect the gear rotation angle. The center is mounted on the Z-axis sliding slide, and its position can be adjusted by driving the Z-axis ball screw guide. The left-side component includes a left X-axis guide, a left Y-axis guide, a left mounting plate, a left wedge block, and two left-side line structured optical probes. Horizontal movement along the X and Y axes is achieved by driving the left X-axis and left Y-axis guides. The corresponding linear gratings on the two guides detect position data in real time, which is then fed back to the control system to further adjust the positions of the two left-side line structured optical probes. The right-side component includes a right X-axis guide, a right Y-axis guide, a right mounting plate, a right wedge block, two right-side adjustment blocks, and two right-side line structured optical probes. Horizontal movement along the X and Y axes can be achieved by driving the right-side X-axis and Y-axis guide rails. The corresponding linear gratings on the two guide rails can detect position data in real time, which is then fed back to the control system to further adjust the positions of the two linear structured optical probes on the right side. The gear under test is mounted on a three-jaw chuck. The parameters of the gear under test are: m = 3mm, z = 41, α = 20°, b = 72mm, h... * =1, c * =0.25, r=61.5mm, rb = 57.7911 mm.

[0103] W1: Establishing the 3D model of the measured gear

[0104] (1) The six degrees of freedom of the measured gear are constrained by clamping the inner hole of the measured gear with a three-jaw chuck on a precision turntable, so as to realize the coaxial rotation of the measured gear and the precision turntable.

[0105] (2) As shown in Figure 1 , first input the parameters of the measured gear, and then establish the measured gear coordinate system σ o = [O; X o , Y o , Z o ] according to the right-hand rule, which is a Cartesian rectangular coordinate system, O is the origin of the measured gear coordinate system, Z o axis is the rotation axis, K(x k , y k , z k ) is the three-dimensional coordinates of any point on the tooth surface of the measured gear, and the involute tooth surface equation of the point K is:

[0106]

[0107]

[0108] In the formula, r b is the base circle radius of the measured gear, is the initial phase angle of the involute, α k and θ k are the development angle, pressure angle and polar angle of the involute at point K respectively. The physical meaning of θ k is expressed as:

[0109]

[0110] W2: Calibration and determination of the pose parameters of the linear structured light probe head

[0111] In order to ensure that the pose between the line structured light probe and the measured gear reaches the best pose at the time of measurement, the measurement angle and position of the line structured light probe need to be adjusted. When adjusting the position of the line structured light probe, in order to determine the positional relationship between the four probes and the measured gear, the center of the probe is selected as the reference point, and the coordinates of the reference point in the coordinate system of the measured gear are taken as the relative position parameters of the two. Among them, the positions of the left two probes are realized by driving the left X-axis guide rail and the left Y-axis guide rail respectively, and the positions of the right two probes are realized by driving the right X-axis guide rail and the right Y-axis guide rail respectively. And the linear grating installed on the guide rail can detect the guide rail position data in real time, so as to fine-tune the position of each guide rail, so as to realize the best measurement position of the probe at the time of measurement. The probe attitude angle [γ,η] is determined by the installation angle γ of the auxiliary part wedge block and the wedge angle η. As shown in Figures 2-3 , the positional relationship between the line structured light probe and the coordinate system of the measured gear is:

[0112] The left rear probe P1: a1 is the distance from the center of the probe to the X Ο axis of the coordinate system of the measured gear, g1 is the distance from the center of the probe to the Y Ο axis of the coordinate system of the measured gear, c1 is the distance from the center of the probe to the Z Ο axis of the coordinate system of the measured gear.

[0113] The right front probe P2: a2 is the distance from the center of the probe to the X Ο axis of the coordinate system of the measured gear, g2 is the distance from the center of the probe to the Y Ο axis of the coordinate system of the measured gear, c2 is the distance from the center of the probe to the Z Ο axis of the coordinate system of the measured gear, h2 is the thickness of the right front adjustment block, and the value of c2 is:

[0114] c2=c1+h2 (30)

[0115] The left front probe P3: a3 is the distance from the center of the probe to the X Ο axis of the coordinate system of the measured gear, g3 is the distance from the center of the probe to the Y Ο axis of the coordinate system of the measured gear, c3 is the distance from the center of the probe to the Z Ο axis of the coordinate system of the measured gear.

[0116] The right rear probe P4: a4 is the distance from the center of the probe to the X Ο axis of the coordinate system of the measured gear, g4 is the distance from the center of the probe to the Y Ο axis of the coordinate system of the measured gear, c4 is the distance from the center of the probe to the Z Ο axis of the coordinate system of the measured gear, h4 is the thickness of the right rear adjustment block, and the value of c4 is:

[0117] c4=c3+h4 (31)

[0118] To effectively obtain tooth surface data, it is necessary to determine the installation angle γ and wedge angle η of the calculation auxiliary component, the wedge block. The installation angle of the wedge block is determined as follows: one end of the wedge block has a bolt hole for bolt connection and fixation, and the other end has an arc groove, also fixed with bolts. To adjust the installation angle, loosen the bolts at both ends, allowing the wedge block to rotate around the bolt hole. For example... Figure 4 As shown, the formula for calculating the installation angle γ of the wedge block is:

[0119]

[0120] In the formula, T1 is the distance between the centers of the bolt holes on the two wedges, and T2 is the distance from the center of the bolt holes to the intersection of the lines connecting the two wedges.

[0121] like Figure 5 As shown, the wedge angle η is calculated using the dimensions of the wedge block:

[0122]

[0123] In the formula, h o h1 is the height of the wedge block, and t is the length of the wedge block.

[0124] W3: Establish four line structured light probe reference coordinate systems

[0125] like Figures 2-3 As shown, to facilitate coordinate transformation, four auxiliary reference coordinate systems are established for calculation. The transformation process is as follows:

[0126] Centered on the gear, the coordinate system of the probe P1 on the left rear is σ1'=[O1;X1',Y1',Z1'], where (U1,V1,W1) are the measured values ​​in the coordinate system of the probe P1 on the left rear. The auxiliary reference coordinate system is σ1=[O1;X1',Y1',Z1']. σ1 ,Y σ1 Z σ1 ]. Wherein, the reference coordinate system X σ1 Axis, Y σ1 Axis and Z σ1 The directions of the axes are respectively relative to the X coordinate system of the gear being measured. o Axis, Y o Axis and Z o If the axes are in the same direction, the coordinates of the probe P1 on the left rear side are converted to:

[0127]

[0128] The gear is taken as the center, the coordinate system of the right front probe P2 is σ2' = [O2; X2', Y2', Z2'], (U2, V2, W2) are measured values in the coordinate system of the right front probe P2, and the auxiliary reference coordinate system is σ2 = [O2; X σ2 ,Y σ2 ,Z σ2 ]. Wherein, the directions of the reference coordinate system X σ2 axis and Y σ2 axis are opposite to the directions of the measured gear coordinate system X o axis, Y o axis and Z σ2 axis, and the direction of the Z o axis is the same as the direction of the Z σ3 axis. The coordinate conversion of the right front probe P2 is as follows:

[0129]

[0130] The gear is taken as the center, the coordinate system of the left front probe P3 is σ3' = [O3; X3', Y3', Z3'], (U3, V3, W3) are measured values in the coordinate system of the left front probe P3, and the auxiliary reference coordinate system is σ3 = [O3; X σ3 ,Y σ3 ,Z σ3 ]. Wherein, the directions of the reference coordinate system X σ3 axis, Y σ3 axis and Z σ3 axis are the same as the directions of the measured gear coordinate system X o axis, Y o axis and Z o axis. The coordinate conversion of the left front probe P3 is as follows:

[0131]

[0132] The gear is taken as the center, the coordinate system of the right rear probe P4 is σ4' = [O4; X4', Y4', Z4'], (U4, V4, W4) are measured values in the coordinate system of the right rear probe P4, and the auxiliary reference coordinate system is σ4 = [O4; X σ4 ,Y σ4 ,Z σ4 ]. Wherein, the directions of the reference coordinate system X σ4 axis and Y σ4 axis are opposite to the directions of the measured gear coordinate system X o axis, Y o axis, and the direction of the Z σ4 axis is the same as the direction of the Z o axis. The coordinate conversion of the right rear probe P4 is as follows:

[0133]

[0134] where γ is the installation angle of the probe, and η is the wedge angle.

[0135] After the reference coordinate system of the four line structured light probes is established, the probes start to scan and measure. After the measured gear rotates one round, the two-side tooth surface data of all the teeth of the measured gear are obtained.

[0136] W4: Threshold extraction of complete tooth profile

[0137] As shown in Figure 6 , in general, the gear data obtained by the line structured light probe often contains a small amount of speckle and noise, and the data amount of each tooth surface is as high as hundreds of millions, and the data in the unnecessary area affects the operation efficiency, so it is necessary to perform threshold processing on the measured gear data to extract the complete tooth profile data. The following four steps are performed:

[0138] Step one: select the involute tooth profile on any one side tooth surface, and set the starting threshold x l1 and the ending threshold x l2 of the effective tooth profile, where x l1 is the intersection of the gear transition curve and the tooth profile, and x l2 is the intersection of the gear addendum circle and the tooth profile;

[0139] Step two, after setting the starting threshold x l1 and the ending threshold x l2 of the effective tooth profile, extract the tooth profile in the interval (x l1 , x l2 );

[0140] Step three, rotate the tooth profile of the same side tooth surface by an angle θ' around the measured gear coordinate system Z Ο , and extract the tooth profile of the tooth profile in the interval (x l1 , x l2 );

[0141]

[0142] where z is the number of teeth of the measured gear.

[0143] Step four: until the measured gear rotates 360°, the extraction of the single-side complete tooth profile of all the teeth is realized.

[0144] The single-side complete tooth profile of the other side of all the teeth is also extracted by the above four steps.

[0145] W5: Conversion of the reference coordinate system of the four probes to the coordinate system of the measured gear

[0146] Since the gear under test has left and right tooth surfaces, the data acquired by probes P1 and P2 are the data for the right tooth surface. However, the tooth thickness deviation evaluation is performed in the coordinate system of the gear under test. Therefore, it is necessary to transform the right tooth surface data acquired by probes P1 and P2 into the coordinate system of the gear under test. That is, the reference coordinate system of probes P1 and P2 is transformed to the coordinate system of the gear under test through translation and rotation.

[0147]

[0148]

[0149] The data acquired by probes P3 and P4 are the left tooth surface data of the gear. However, the tooth thickness deviation evaluation is performed in the coordinate system of the gear being measured. Therefore, it is necessary to transform the left tooth surface data acquired by probes P3 and P4 to the coordinate system of the gear being measured. That is, the reference coordinate systems of probes P3 and P4 are transformed to the coordinate system of the gear being measured through translation and rotation.

[0150]

[0151]

[0152] Equations (39), (40), (41) and (42) can be used to convert the tooth surface data obtained by probes P1, P2, P3 and P4 into the coordinate system of the gear being measured.

[0153] W6: Evaluation of tooth thickness deviation in the coordinate system of the gear under test

[0154] like Figure 7 As shown, tooth thickness deviation ΔE s This is the difference between the actual and true tooth thickness. Tooth thickness measurement is generally performed on the pitch cylinder surface, but using only the tooth thickness on the pitch cylinder surface as an evaluation criterion is insufficient to assess the tooth thickness deviation of the gear tooth surface. To evaluate the tooth thickness deviation across the entire tooth surface, it is necessary to take the tooth thickness deviation of any circle with any radius on any cross-section, calculate the radial average tooth thickness deviation and the average tooth thickness deviation in the tooth width direction, and then obtain the average of the two.

[0155] Based on any radius r on a standard gear x The tooth thickness s of the circle x and the actual tooth thickness s obtained x ', to obtain any radius r x Tooth thickness deviation ΔE of the circle s Calculation formula:

[0156] ΔE s =s x '-s x (43)

[0157] This method evaluates ΔE using the tooth thickness. sFirst, the tooth thickness s of the circle where the arbitrary radius r of the standard gear x is located is found x :

[0158]

[0159]

[0160]

[0161]

[0162] where s, r, a and θ are the pitch circle tooth thickness, radius, pressure angle and polar angle, respectively, is the central angle corresponding to s x .

[0163] Second, the actual tooth thickness s of the circle where the arbitrary radius r of the gear x is located is found according to the measured data x The coordinates of L1' and L2' are L2' coordinates are

[0164]

[0165]

[0166]

[0167]

[0168] where is s x corresponding to the central angle.

[0169] Radial tooth thickness average deviation ΔE sr

[0170] When finding the radial tooth thickness deviation, in order to reduce the error caused by random factors and improve the accuracy of the measurement, the average value ΔE of the tooth thickness deviation of the circle where the arbitrary radius of a certain cross section is located sr is taken as the final result, and its value is:

[0171]

[0172] where n is the n radial tooth thicknesses measured in order from the root to the top of the same tooth.

[0173] Tooth width direction tooth thickness average deviation ΔE sb

[0174] In order to reduce the error caused by random factors and improve the accuracy of measurement, the average value ΔE of the tooth thickness deviation of the circle with a certain radius in the tooth width direction is taken sb As the final result, the value is:

[0175]

[0176] In the formula, m is the m axial tooth thicknesses measured in turn at different tooth width positions on a certain evaluation cylinder.

[0177] The whole tooth surface tooth thickness deviation ΔE s面

[0178] The average value of the radial tooth thickness average deviation and the tooth width direction tooth thickness average deviation is taken as the whole tooth surface tooth thickness deviation ΔE s面 The result is:

[0179]

[0180] The detailed measurement flow chart of the measured gear arbitrary tooth thickness is shown in Figure 9 .

Claims

1. A method for measuring the arbitrary tooth thickness of a gear by integrating a plurality of line structured light probes, characterized in that: The method comprises six steps of establishing a three-dimensional model of the measured gear, determining a pose parameter of the line structured light probe, establishing four line structured light probe reference coordinate systems, threshold value extraction of the complete tooth profile, conversion of the four probe reference coordinate systems to the measured gear coordinate system, and tooth thickness deviation evaluation in the measured gear coordinate system, and the specific steps are as follows, W1: Establishing a three-dimensional model of the measured gear (1) The inner hole of the measured gear is clamped by the three-jaw chuck on the precision turntable to constrain the six degrees of freedom of the gear, so as to realize the coaxial rotation of the measured gear and the precision turntable; (2) First, input the measured gear parameters, and then establish the measured gear coordinate system σ according to the right-hand rule ο = [0; X ο , Y ο , Z ο ], the coordinate system is a Cartesian rectangular coordinate system, O is the origin of the measured gear coordinate system, Z ο axis is the rotation axis, K (x k , y k , z k ) is the three-dimensional coordinates of any point on the measured gear tooth surface, and the involute tooth surface equation of the K point is: wherein r b is the base circle radius of the measured gear, is the initial phase angle of the involute, α k and θ k are the developed angle, pressure angle and polar angle of the involute at point K, respectively, the physical meaning of θ k is expressed as: W2: Calibration and determination of the pose parameter of the line structured light probe In order to ensure that the pose between the line structured light probe and the measured gear reaches the best pose during measurement, the measurement angle and position of the line structured light probe need to be calibrated. In order to determine the positional relationship between the four probes and the measured gear during adjustment of the position of the line structured light probe, the center of each probe is selected as a reference point, and the coordinates of the reference points in the measured gear coordinate system are taken as the relative position parameters of the two. Among them, the positions of the left two probes are realized by driving the left X-axis guide rail and the left Y-axis guide rail respectively, and the positions of the right two probes are realized by driving the right X-axis guide rail and the right Y-axis guide rail respectively. The linear grating installed on the guide rail can detect the guide rail position data in real time, so as to fine-tune the position of each guide rail, so that the probe has the best measurement position during measurement. The probe attitude angle [γ,η] is determined by the installation angle γ and the wedge angle η of the auxiliary part wedge block. The positional relationship between the line structured light probe and the measured gear coordinate system is: Left rear face probe P1: a1 is the distance from the probe center to the coordinate system X of the measured gear Ο the distance of the axis, g1 is the distance from the probe center to the coordinate system Y of the measured gear Ο the distance of the axis, c1 is the distance from the probe center to the coordinate system Z of the measured gear Ο the distance of the axis; Right front face probe P2: a2 is the distance from the probe center to the coordinate system X of the measured gear Ο Right front face probe P2: a2 is the distance from the probe center to the coordinate system X of the measured gear Ο Right front face probe P2: a2 is the distance from the probe center to the coordinate system X of the measured gear Ο Right front face probe P2: a2 is the distance from the probe center to the coordinate system X of the measured gear c2=c1+h2 (3) Left front probe P3: a3 is the distance from the probe center to the coordinate system X of the measured gear Ο the distance of the axis, g3 is the distance from the probe center to the coordinate system Y of the measured gear Ο the distance of the axis, c3 is the distance from the probe center to the coordinate system Z of the measured gear Ο the distance of the axis; Right rear probe P4: a4 is the distance from the probe center to the coordinate system X of the measured gear Ο the distance of the axis, g4 is the distance from the probe center to the coordinate system Y of the measured gear Ο the distance of the axis, c4 is the distance from the probe center to the coordinate system axis Z of the measured gear Ο the distance of the axis, h4 is the thickness of the right rear adjustment block, and the value of c4 is: c4=c3+h4 (4) In order to effectively obtain the tooth surface data, it is necessary to determine the installation angle γ and the wedge angle η of the auxiliary part wedge block. The installation angle of the wedge block is determined as follows: one end of the wedge block is provided with a bolt hole and is fixed by a bolt, the other end is provided with a circular arc groove and is also fixed by a bolt. When adjusting the installation angle, loosen the bolts at both ends, rotate the wedge block around the bolt hole, and the installation angle γ of the wedge block is calculated as follows: In the formula, T1 is the distance between the centers of the bolt holes on the two wedge blocks, and T2 is the distance from the center of the bolt hole to the intersection point of the two wedge blocks. The wedge angle η is calculated by the size of the wedge block as follows: where h ο and hi is the height of the wedge, t is the length of the wedge. W3: Establishing four line structured light probe reference coordinate systems In order to facilitate coordinate conversion, four auxiliary reference coordinate systems are established for calculation, and the conversion process is as follows: With the gear as the center, the coordinate system of the left rear probe P1 is σ1' = [O1; X1', Y1', Z1'], (U1, V1, W1) are measured values in the coordinate system of the left rear probe P1, and the auxiliary reference coordinate system is σ1 = [O1; X σ1 ,Y σ1 ,Z σ1 ], wherein the directions of the X σ1 -axis, the Y σ1 -axis and the Z σ1 -axis of the reference coordinate system are the same as the directions of the X ο -axis, the Y ο -axis and the Z ο -axis of the measured gear coordinate system, and the coordinate conversion of the left rear probe P1 is as follows: With the gear as the center, the right front probe P2 coordinate system is σ2' = [O2; X2', Y2', Z2'], (U2, V2, W2) are measured values in the right front probe P2 coordinate system, and the auxiliary reference coordinate system is σ2 = [O2; X2, Y2, Z2], wherein the directions of the reference coordinate system X2 axis and Y2 axis are opposite to the directions of the measured gear coordinate system X1 axis and Y1 axis, and the direction of the Z2 axis is the same as the direction of the Z1 axis. σ2 ,Y σ2 ,Z σ2 ], wherein the directions of the reference coordinate system X σ2 axis and Y σ2 axis are opposite to the directions of the measured gear coordinate system X ο axis and Y ο axis, and the direction of the Z σ2 axis is the same as the direction of the Z ο axis, and the coordinate conversion of the right front probe P2 is as follows: With the gear as the center, the coordinate system of the left front probe P3 is σ3' = [O3; X3', Y3', Z3'], (U3, V3, W3) are the measured values in the coordinate system of the left front probe P3, and the auxiliary reference coordinate system is σ3 = [O3; X σ3 ,Y σ3 ,Z σ3 ], wherein the directions of the reference coordinate system X σ3 axis, Y σ3 axis and Z σ3 axis are the same as the directions of the measured gear coordinate system X ο axis, Y ο axis and Z ο axis, and the coordinate conversion of the left front probe P3 is: With the gear as the center, the coordinate system of the right rear probe P4 is σ4' = [O4; X4', Y4', Z4'], (U4, V4, W4) are the measured values in the coordinate system of the right rear probe P4, and the auxiliary reference coordinate system is σ4 = [O4; X4, Y4, Z4], wherein the directions of the X4 axis and the Y4 axis of the reference coordinate system are opposite to the directions of the X4' axis and the Y4' axis of the measured gear coordinate system, and the direction of the Z4 axis is the same as the direction of the Z4' axis. σ4 σ4 σ4 σ4 σ4 ο ο σ4 ο The coordinate transformation of the right rear probe P4 is:​​​​​​​​ In the formula, γ is the installation angle of the probe, and η is the wedge angle. After establishing the reference coordinate systems of the four line structured light probes, the probes start scanning and measuring. After the measured gear rotates one revolution, the two-side tooth surface data of all teeth of the measured gear is obtained. W4: Threshold value extraction of the complete tooth profile Under normal circumstances, the gear data obtained by the line structured light probe often contains a small amount of speckle and noise, and the data amount of each tooth surface is as high as hundreds of millions, and the data in the unnecessary area affects the operation efficiency. Therefore, the measured gear data needs to be threshold processed to extract the complete tooth profile data, which is carried out according to the following four steps: Step 1: Select the involute tooth profile on any side of the tooth surface and set the initial threshold x for the effective tooth profile. l1 and termination threshold x l2 , where x l1 x is the intersection of the gear transition curve and the tooth profile. l2 This is the intersection of the gear's addendum circle and tooth profile; Step 2: Complete the initial threshold x for the effective tooth profile. l1 and termination threshold x l2 Extract after setting (x) l1 ,x l2 Tooth profile within the interval; Step three, the same side tooth surface profile in turn around the measured gear coordinate system Z Ο Rotating θ' angle, extracting the tooth profile of the tooth surface profile in (x l1 ,x l2 ) interval; In the formula, z is the number of teeth of the measured gear. Step four: until the measured gear rotates 360°, the extraction of the complete profile of all teeth on one side is realized; The complete profile of all teeth on the other side is also extracted by the above four steps; W5: four probe reference coordinate system conversion to the measured gear coordinate system Since the measured gear has left and right tooth surfaces, the data obtained by probes P1 and P2 is the right tooth surface data of the gear, but the tooth thickness deviation evaluation is carried out in the measured gear coordinate system, so it is necessary to convert the right tooth surface data obtained by probes P1 and P2 to the measured gear coordinate system, that is, to transform the reference coordinate system of probes P1 and P2 to the measured gear coordinate system by translation and rotation: The data obtained by probes P3 and P4 is the left tooth surface data of the gear, but the tooth thickness deviation evaluation is carried out in the measured gear coordinate system, so it is necessary to convert the left tooth surface data obtained by probes P3 and P4 to the measured gear coordinate system, that is, to transform the reference coordinate system of probes P3 and P4 to the measured gear coordinate system by translation and rotation: Through equations (12), (13), (14) and (15), the tooth surface data obtained by probes P1, P2, P3 and P4 can be converted to the measured gear coordinate system; W6: tooth thickness deviation evaluation in the measured gear coordinate system Tooth thickness deviation ΔE s is the difference between the actual value and the true value of tooth thickness, generally tooth thickness measurement is carried out on the division cylindrical surface, but only the tooth thickness on the division cylindrical surface is taken as the evaluation basis, which cannot evaluate the tooth thickness deviation of the gear tooth surface. In order to evaluate the tooth thickness deviation of the whole tooth surface, it is required to take the tooth thickness deviation of the circle with arbitrary radius on arbitrary section, calculate the radial tooth thickness average deviation, the tooth width direction tooth thickness average deviation and the average value of the two. According to the standard gear tooth thickness s x at the circle where the radius r x is located x and the actual tooth thickness s x obtained s Calculation formula: ΔE s = s x -s x (16) The arc thickness is used to evaluate the ΔE s First, the thickness s of the circle where the arbitrary radius r on the standard gear x is found x as: In the formula, NN represents a physical meaning of a circular segment corresponding to the actual tooth thickness on an arbitrary evaluation circle, ∠MOM represents an evaluation circle center angle corresponding to the NN circular segment, 2∠MON represents a circle center angle corresponding to the theoretical tooth thickness, s, r, α, and θ represent the pitch circle tooth thickness, the radius, the pressure angle, and the polar angle, respectively, s x corresponding central angle; Second, the actual tooth thickness s of the circle where the gear is located is calculated from the measured data x at the radius r x The coordinates of L1' and L2' are calculated from the measured data The coordinates of L1' and L2' are calculated from the measured data In the formula, s x corresponding central angle; Radial tooth thickness average deviation ΔE sr In order to reduce the error caused by random factors and improve the accuracy of measurement, the average value ΔE of the tooth thickness deviation of the circle with any radius on a certain cross section is taken when the radial tooth thickness deviation is obtained sr As a final result, the value is: In the formula, n is the n radial tooth thicknesses measured in turn from the root to the top of the same tooth; tooth width direction tooth thickness average deviation ΔE sb In order to reduce the error caused by random factors and improve the accuracy of measurement, the average value ΔE of the tooth thickness deviation of the circle at a certain radius in the tooth width direction is taken when the tooth thickness deviation in the tooth width direction is obtained sb As a final result, the value is: In the formula, m is the m axial tooth thicknesses measured in turn at different tooth width positions on a certain evaluation cylinder; entire tooth face tooth thickness deviation ΔE s面 The average value of both the average deviation of the radial tooth thickness and the average deviation of the tooth width direction tooth thickness is taken as the tooth thickness deviation ΔE of the entire tooth surface s面 The results are:

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