CN114800048B - Radial jump detection method based on tooth pitch measurement in gear on-machine measurement process - Google Patents
Radial jump detection method based on tooth pitch measurement in gear on-machine measurement process Download PDFInfo
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- CN114800048B CN114800048B CN202210493730.4A CN202210493730A CN114800048B CN 114800048 B CN114800048 B CN 114800048B CN 202210493730 A CN202210493730 A CN 202210493730A CN 114800048 B CN114800048 B CN 114800048B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
- B23Q17/00—Arrangements for observing, indicating or measuring on machine tools
- B23Q17/22—Arrangements for observing, indicating or measuring on machine tools for indicating or measuring existing or desired position of tool or work
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/16—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring distance of clearance between spaced objects
Abstract
The invention discloses a gear radial runout detection method based on tooth pitch measurement, which utilizes the on-machine measurement function of a numerical control machine tool to acquire an initial data value by measuring points at the pitch circle of each tooth slot of a gear through a trigger type measuring head. And constructing a calibration virtual sphere when calculating the radial runout, and ensuring that the contact points of the virtual sphere and tooth surfaces on two sides are positioned on a pitch circle. And respectively rotating the involute circles on the two sides of the tooth socket to the angles beta to be intersected in opposite directions, and solving the intersection point position of the two involute by homogeneous coordinate transformation according to the geometric relationship, so as to finish the determination of the internal diameter jump value of one tooth socket. The diameter of the virtual sphere is required to be calculated in advance according to the principle that the contact points of the calibration virtual sphere and the tooth socket of the gear are consistent with the detection points, a virtual sphere model is established, and the establishment of the virtual sphere model can obtain more comprehensive and visual information of the radial runout of the gear. The numerical value of the inner diameter jump of each tooth slot is directly obtained by solving an equation, so that the model and rounding errors caused by the traditional modeling and calculating method are avoided, and the obtained diameter jump value is more accurate and reliable.
Description
Technical Field
The invention belongs to the technical field of part machining quality detection, and particularly relates to a radial runout detection method based on tooth pitch measurement in a gear machining process.
Background
Radial runout is an essential item in the error detection of rotary moving parts. The radial runout error of the gear ring is caused by a plurality of reasons, and is mainly caused by geometric eccentricity, namely coaxiality error caused by a gap between a gear blank shaft hole and a clamp mandrel. In the actual production process, if the production batch is small, small clearance fit (gear hole and mandrel) can be adopted; if the batch is large, a tension sleeve type centering method is adopted to eliminate the gap. These approaches only reduce tooth jump to some extent and cannot be completely avoided. In addition, radial runout is also an important index for evaluating the machining quality of standard gears, gear shaping cutters, gear shaving cutters and small return difference gears, and is an important reference basis for gear shaping and design and adjustment machining strategies.
In the gear machining process, the geometric eccentricity of gear blank installation and the runout of a gear machine tool workbench or the installation eccentricity of a gear shaper cutter and the like can cause tooth runout, and the error can lead the gear ratio to be unstable in the process of rotating the gear for one circle and belongs to long-period errors.
In the current gear radial runout detection, special instruments and equipment are needed to measure, and the method is large in limitation, time-consuming, labor-consuming and only suitable for gears with certain size specifications; due to the influence of manual operation, the repeatability of the measurement position is poor, and a principle error is generated.
The on-machine measurement is an important means for realizing the gear precision detection in the gear closed-loop manufacturing, and compared with the off-position detection (adopting a gear measuring center in a constant-temperature quality inspection chamber), the on-machine measurement avoids the secondary clamping error and saves the production auxiliary time and labor expenditure; compared with borrowing detection (detection by a special detection device arranged on a processing machine tool), the method is convenient and fast to realize, has no special requirement on the structure of the processing machine tool, and can be seamlessly integrated with a numerical control system.
In the existing method for calculating the radial runout in the machine detection gear error project, the gear eccentric quantity e is generally calculated through the accumulated error of the tooth pitch, the radial runout value Fr is approximately replaced by 2e, or the radial runout value Fr is calculated by the range of a single tooth pitch error value, the radial runout value determined by the methods often has larger deviation from the actual value, the change rule of the radial runout and the phase relation between the maximum radial runout and the minimum radial runout cannot be accurately reflected, and the accuracy of gear precision evaluation and the reliability of guiding gear correction are affected; and secondly, the calculation is carried out by utilizing a triangle relation in a virtual sphere mode, a certain mathematical modeling and calculating error exists, and the measurement accuracy is reduced.
Disclosure of Invention
The invention aims to provide a radial jump detection method based on tooth pitch measurement in the gear on-machine measurement process, and the calculation result can also judge the geometric eccentric position of the gear and is used for guiding secondary machining. The detection principle is that an on-machine measurement function of the numerical control machine tool is utilized, and an initial data value is obtained by measuring points at the pitch circle of each tooth socket of the gear through the trigger type measuring head. And constructing a calibration virtual sphere when calculating the radial runout, and ensuring that the contact points of the virtual sphere and tooth surfaces on two sides are positioned on a pitch circle. And respectively rotating the involute circles on the two sides of the tooth socket to the angles beta to be intersected in opposite directions, and solving the intersection point position of the two involute by homogeneous coordinate transformation according to the geometric relationship, so as to finish the determination of the internal diameter jump value of one tooth socket.
In order to achieve the above purpose, the present invention provides the following technical solutions: a radial jump detection method based on tooth pitch measurement in the gear on-machine measurement process comprises the following steps:
the first step: after the gear machining is finished, checking the clamping condition of the clamp of the rotary worktable and the gear to be measured, and ensuring the coaxiality of the central axis of the gear to be measured and the central axis of the rotary worktable; after the inspection is finished, installing a trigger type measuring head on the machine tool, acquiring an initial data value by measuring points at the pitch circle of each tooth socket of the gear through the trigger type measuring head, constructing a calibration virtual sphere when calculating the radial jump, and ensuring that the contact points of the virtual sphere and tooth surfaces at two sides are positioned on the pitch circle; calculating the diameter of an imaginary sphere in advance according to gear parameters;
the diameter of a sphere when contacting with two points of a pitch circle in a tooth socket of a theoretical tooth surface is taken as the diameter of an imaginary sphere, and the calculation formula is as follows:
wherein m is the normal modulus of the gear, Z is the number of teeth, and alpha is the pressure angle of the reference circle of the gear;
and a second step of: in order to accurately obtain the positional relationship between the machine coordinate system Sigma 4 (X-Y-Z) and the measurement coordinate system Sigma 3 (Xc-Yc-Zc), a magnetic gauge stand with a standard ball is fixed at any position on the upper end surface of a measured gear, and the center of the standard ball at the position is marked as O b1 The method comprises the steps of carrying out a first treatment on the surface of the The triggering type measuring head is utilized to uniformly collect the coordinates (x) of six measuring points on the half circumference of the measured truncated circle of the standard ball a ，y a ，z a )…(x f ，y f ，z f ) Calculating the standard sphere center O based on the least square method b1 Coordinate value (x) 1 ，y 1 ，z 1 ) The method comprises the following steps:
in formula (2): i=a to f
The rotation angle zeta of the machine tool C axis is recorded as O at the moment of the position of the sphere center of the standard sphere b2 The method comprises the steps of carrying out a first treatment on the surface of the Repeating the process of collecting the points by the measuring head, uniformly collecting six measuring points on the half circumference of the measured truncated circle of the standard ball again, and marking the sitting mark as (x) a2 ，y a2 ，z a2 )…(x f2 ，y f2 ，z f2 ) The least square method of reference (2) obtains the coordinate value (x) of Ob2 2 ，y 2 ，z 2 ) The method comprises the steps of carrying out a first treatment on the surface of the According to the standard sphere center position O b1 、O b2 The rotation angle zeta between the gear center O and the machine tool C axis can be obtained 2 Taking out a standard ball at the position in the X-O-Y plane under the machine tool coordinate system sigma 4, manually controlling the trigger type measuring head to touch any position of the upper end surface of the gear until triggering, acquiring the Z-axis coordinate of the upper end surface of the gear under the machine tool coordinate system, and uploading the three position coordinates to a machine tool numerical control system to finish the calibration process;
and a third step of: the triggering type measuring head approaches to the measured gear along the direction parallel to the X axis and is matched with the rotary motion of the measured gear to find a tooth slot; two points K, N are arranged on the pitch circle; the measuring head enters a position 2 in the tooth slot from a position 1, and a contact point of the measuring head and a tooth surface is positioned on a pitch circle at the radius of the position 2; the gear to be measured rotates along with the C axis of the machine tool, contacts the left tooth surface and the right tooth surface respectively, and acquires the position information of each axis of the machine tool after the trigger type measuring head triggers; after one tooth slot is detected, the measuring head exits from the tooth slot along the X axis, and the gear rotates with the workbench for indexing and rotates by one pitch angle; repeating the above process until all tooth grooves of the gear are detected; the triggering type measuring head exits and returns to the initial station, and the measuring work is ended to obtain a measured value;
fourth step: according to the gear on-machine measurement principle, the return values of the trigger type measuring head are all absolute coordinate values of all axes under a machine tool coordinate system where the spherical center of the measuring head is located; to obtain the actual angle of the tooth space on the pitch arc KO 2 N, radius compensation is needed to be carried out on the measured value; known M 1 -K is the gauge head radius, M 1 -O 2 The length of the pitch circle is calculated according to the radius of the point at the measured pitch circle, the normal vector and the radius of the measuring head and is marked as X m The method comprises the steps of carrying out a first treatment on the surface of the K and N are located on the pitch circle of the gear, so the angle K-O is calculated according to the cosine law 2 -M 1 P +.N-O 2 -M 2 The same calculation is performed; the actual angle corresponding to the tooth slot segment arc is:
∠KO 2 N＝|O 1c -O 2c |+2*∠K-O 2 -M 1 (3)
in the formula (3), O 1c For the ball center of the measuring head to reach M in actual measurement 1 Absolute coordinate of machine tool C axis in measurement coordinate system sigma 3, O obtained during processing 2c For the ball center of the measuring head to reach M in actual measurement 2 The absolute coordinate of the machine tool C axis in the measurement coordinate system sigma 3 is obtained during the processing; angle K-O 2 -M 1 The included angles among the sphere center of the measuring head, the contact points of the measuring head and the tooth surface and the connecting line of the circle center of the gear are respectively formed;
fifth step: o (O) 1 C is the imaginary sphere center 1 -C 2 To calibrate a section of arc where the sphere center of the imaginary sphere is positioned, B 1 -B 2 Is the pitch circle arc of the gear, A 1 -A 2 Is a circular arc of a gear base circle; G. the H point is the intersection point of the pitch circle and the involute on the two sides of the tooth socket, and is also the tangential point of the imaginary sphere and the involute on the two sides, wherein the involute on the two sides is a left involute GD and a right involute HE; left involute GD is wound around the circle center O of the gear 2 Clockwise rotation of beta causes the left involute GD to pass through the imaginary sphere center O 1 The method comprises the steps of carrying out a first treatment on the surface of the Similarly, the right involute HE is wound around the circle center O 2 Counterclockwise rotation of beta also causes the right involute HE to pass through the imaginary sphere center O 1 Beta= D-O 2 -L; according to the property of the involute, the left involute GD section and the involute S obtained after rotation and translation can be known 1 The normal distance of the arc segments being equal everywhere, i.e. G-O 1 =df=imaginary sphere radius; as can be seen from the relationship of involute-generating curve FD to arc DL,therefore, it is
β＝d p /2/r b (4)；
In the formula (4), beta is the opposite rotation angle of involute on two sides, d p Is the diameter of an imaginary sphere, r b Is the radius of the base circle;
because the rotation transformation of both involute equations can complicate the calculation, only one side involute is rotated by 2β, i.e. the left side involute GD is moved to the involute S, in order to simplify the calculation without affecting the calculation result 3 At the position, the right involute HE is fixed, and the involute S is solved 3 An intersection point with the involute HE; while radial runout is based on the center O of the imaginary sphere 1 With the centre of a circle O of the gear 2 The distance between the two points is calculated, and the circle where the obtained intersection point is located is unchanged, so that the simplified calculation is feasible;
sixth step: the arc GH is a theoretical tooth pitch, the arc PH is an actual tooth pitch obtained by radius compensation according to actual measurement data, and when the width of a tooth slot is reduced, the center O of an imaginary sphere is caused 1 The position moves to the center O of the broken line sphere 1 At ' involute G ' D ' and involute S 1 The normal distance between' is unchanged and is the radius of an imaginary sphere; so that the involute G 'D' is rotated by 2 beta to the involute S 3 The' position and the right involute HE are crossed to obtain the center O of the broken line ball 1 ' coordinates;
seventh step: calculating the central angles of all actual tooth socket pitch arc sections by using all measured data after the measurement head radius compensation, and calculating the central angle corresponding to the arc line GP by making a difference with the central angle of the theoretical tooth socket pitch arc section, thereby obtaining the central angle corresponding to the arc line WD'
Solving the center O of the broken line sphere 1 ' coordinates (x o1′ ，y o1′ ) Then, the Pythagorean theorem is used to obtain the center O of the virtual sphere 1 The distance from the circle center of the gear is' the radial jump value of one tooth slot is obtained, and the same calculation process is carried out on each tooth slot, so that all radial jump values of the gear are obtained;
eighth step: because equation (11) is an transcendental equation, the analytical solution is difficult to calculate; using x' =x 1 Equal (or with y' =y 1 Equal), and the formula (11) is simplified to obtain:
G(t)＝cost*(m 1 +m 2 +(m 3 -m 4 )*t-r b )-sin t*(rb*t-(m 1 +m 2 )*t-(m 4 -m 3 ))＝0 (12)
in the formula (12), m 1 ＝r b *cosθ*cos(2β)
m 2 ＝r b *sinθ*sin(2β)
m 3 ＝r b *sinθ*cos(2β)
m 4 ＝r b *cosθ*sin(2β)
Deriving the two ends of (12)
G′(t)＝cost*(r b *t-(m 1 +m 2 )*t-(m 4 -m 3 ))+sin t*(r b -m 1 -m 2 )-cost*(m 3 -m 4 )+sint*(m 1 +m 2 +(m 3 -m 4 )*t-r b )＝0 (13)
Combining (12) and (13), adopting Newton iterative calculation
t k+1 ＝t k -G(t k )/G′(t k )(k＝0、1、2、3…)
Setting the iteration control precision as |t k+1 -t k |≤10 -10 And the result keeps four valid digits, and the involute intersection meeting the precision condition can be solved.
Preferably, in the seventh step, the center of the broken line ball is O 1 The' calculation process is:
1) In the coordinate system Σ1, the right involute equation is:
x 1 ＝r b *(cos t+tsin t)，y 1 ＝r b *(sin t-tcos t) (5)
in the coordinate system Σ2, the left involute equation is:
x 2 ＝r b *(cos t+t sin t)，y 2 ＝-r b *(sin t-tcos t) (6)
in the formulas (5) and (6), t is the spreading angle at any point on the tooth surface, r b Radius of base circle；
2) The involute G 'D' is rotated clockwise by 2β in the coordinate system Sigma 2 to S 3 ' position; the equation for involute G 'D' in coordinate system Σ2 at this time is:
3) Involute S to be expressed in coordinate system Σ2 3 Equation (7) of' is transformed into a coordinate system Σ1 for expression; subtracting the base circular groove angle deltaObtaining an angle theta to be rotated, wherein the base circle tooth groove angle delta is:
in the formula (8), Z is the number of teeth of the gear, and ψ is the pressure angle at the pitch circle;
therefore, it is
The rotational coordinates of the coordinate system Σ1 to the coordinate system Σ2 are converted into:
in the formula (10), (x ', y') is involute S 3 ' expression in coordinate system Σ1;
4) Calculating two involute equations in the same coordinate system, and solving the simultaneous equations (5), (6), (7) and (10) to obtain:
x 1 ＝r b *(cos t+tsin t)，y 1 ＝r b *(sin t-tcos t)
let x' =x 1 and y′＝y 1 (11)。
Compared with the prior art, the invention has the following beneficial effects:
the invention adopts an on-machine measurement triggering type measurement method, obtains data by measuring tooth pitch, and obtains the radial jump value of each tooth slot by using a mode of calibrating an imaginary sphere. Compared with the traditional radial jump gauge, the radial jump gauge omits a complex mechanical structure and manual operation, has less influence on the measurement repeatability precision due to human factors, and does not add additional detection steps.
According to the invention, parameters such as the ball crossing distance and the like can be directly calculated through accurate calculation of the radial runout, the phase change condition of the radial runout of one circle of the gear can be accurately reflected through subsequent data processing, the measuring steps can be reduced, and the realized measuring items are richer than the traditional measuring means.
The gear detection point is a point on the gear tooth groove pitch circle, the diameter of the virtual sphere is obtained in advance according to the principle that the calibration virtual sphere and the gear tooth groove contact point are consistent with the detection point, a virtual sphere model is built, and the building of the virtual sphere model can obtain information that the gear diameter jump is more comprehensive and visual.
The calculation of the inner diameter jump value of each tooth slot is directly obtained by solving an equation, so that calculation errors caused by modeling precision and a method are avoided, and the diameter jump value is more accurate and reliable.
The radial jump measuring method can be synchronously overlapped with the tooth pitch detection, and the tooth pitch detection is commonly used for on-machine measurement of gears, so that the measuring method is very mature and can be popularized and used for expanding the function of on-machine measurement of gears.
Drawings
FIG. 1 is a schematic diagram of the positional relationship between the detection coordinate system Sigma 3 (Xc-YC-Zc) and the machine tool coordinate system Sigma 4 (X-Y-Z) on the machine tool, wherein a) is a top view, and b) is a front view;
FIG. 2 is a schematic diagram of a sequence of probe detection actions according to the present invention;
FIG. 3 is a schematic view of the calculation of the actual tooth groove angle by radius compensation according to the present invention;
FIG. 4 is a schematic diagram of a search method for theoretical centers of virtual spheres according to the present invention;
FIG. 5 is a schematic diagram of a search method for a virtual sphere center with pitch error according to the present invention;
FIG. 6 is a schematic diagram of the present invention for solving the coordinates of the center of an imaginary sphere in coordinate systems Σ2 and Σ1;
FIG. 7 is a flow chart of a method of detection and assessment calculation of the present invention;
FIG. 8 shows measured calculation values of each tooth slot runout according to the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1-8, the present invention provides a technical solution: a radial jump detection method based on tooth pitch measurement in the gear on-machine measurement process comprises the following steps:
the first step: after the gear machining is finished, checking the clamping condition of the clamp of the rotary worktable and the gear to be measured, and ensuring the coaxiality of the central axis of the gear to be measured and the central axis of the rotary worktable; after the inspection is finished, a trigger type measuring head is arranged on the machine tool.
The diameter of a sphere when contacting with two points of a pitch circle in a tooth socket of a theoretical tooth surface is taken as the diameter of an imaginary sphere, and the calculation formula is as follows:
wherein m is the normal modulus of the gear, Z is the number of teeth, and alpha is the pressure angle of the reference circle of the gear.
And a second step of: FIG. 1 shows the relationship between the machine coordinate system Sigma 4 (X-Y-Z) and the measurement coordinate system Sigma 3 (Xc-Yc-Zc)It is intended that in order to accurately determine the positional relationship between the machine coordinate system sigma 4 (X-Y-Z) and the measurement coordinate system sigma 3 (Xc-Yc-Zc), it is necessary to fix the magnetic gauge stand with the standard ball at an arbitrary position on the upper end face of the gear to be measured, and the center of the standard ball at this position is denoted as O b1 The method comprises the steps of carrying out a first treatment on the surface of the The trigger probe is used to uniformly collect the coordinates (x) of six measuring points on the half circumference of the measured pitch circle of the standard ball a ，y a ，z a )…(x f ，y f ，z f ) Calculating the standard sphere center O based on the least square method b1 Coordinate value (x) 1 ，y 1 ，z 1 ) Is that
I=a to f in formula (2)
The rotation angle zeta of the machine tool C axis is recorded as O at the moment of the position of the sphere center of the standard sphere b2 The method comprises the steps of carrying out a first treatment on the surface of the Repeating the process of collecting the points by the measuring head, uniformly collecting six measuring points on the half circumference of the measured truncated circle of the standard ball again, and marking the sitting mark as (x) a2 ，y a2 ，z a2 )…(x f2 ，y f2 ，z f2 ). The least square method of reference (2) obtains the coordinate value (x) of Ob2 2 ，y 2 ，z 2 ). According to the standard sphere centre position O b1 、O b2 The rotation angle zeta between the gear center O and the machine tool C axis can be obtained 2 The position in the X-O-Y plane under the machine coordinate system Σ4 is shown in fig. 1 a). And (3) taking the standard ball away, and manually controlling the trigger type measuring head to touch any position of the upper end surface of the gear until triggering, so as to obtain the Z-axis coordinate of the upper end surface of the gear under the coordinate system of the machine tool, namely the distance value of MP shown in b) in fig. 1. And uploading the three position coordinates to a machine tool numerical control system to complete the calibration process.
And a third step of: the trigger type measuring head approaches to the measured gear along the direction parallel to the X axis (shown in figure 2) and is matched with the rotary motion of the measured gear to find tooth grooves. As shown in figure 2, the pitch circle has two points K, N, the measuring head enters the tooth groove from the 1 position to the 2 position, and the contact point of the measuring head and the tooth surface is positioned on the pitch circle at the radius of the 2 position. The gear to be measured rotates along with the C axis of the machine tool (the rotation direction is shown by 3 and 4 arrows in fig. 2), the gear to be measured contacts the left tooth surface and the right tooth surface respectively, and the trigger type measuring head triggers and then acquires the position information of each axis of the machine tool. After one tooth slot is detected, the measuring head exits from the tooth slot along the X axis, and the gear rotates with the workbench for indexing and rotates by one pitch angle; repeating the above process until all tooth grooves of the gear are detected. The trigger type measuring head exits and returns to the initial station to finish the measuring work.
Fourth step: according to the gear on-machine measurement principle, the return values of the trigger type measuring head are all absolute coordinate values of all axes under a machine tool coordinate system where the spherical center of the measuring head is located. As shown in FIG. 3, to obtain the actual angle of the tooth space on the pitch arc, KO 2 And N, radius compensation is needed for the measured value. Known M 1 -K is the gauge head radius, M 1 -O 2 The length of the measuring head is calculated according to the radius of the point at the measured pitch circle, the normal vector and the measuring head radius, and is marked as X m . K and N are located on the pitch circle of the gear, so the angle K-O can be calculated according to the cosine law 2 -M 1 (p.o.) 2 -M 2 May be calculated as such). The actual angle corresponding to the tooth socket joint arc is
∠KO 2 N＝|O 1c -O 2c |+2*∠K-O 2 -M 1 (3)
In the formula (3), O 1c And O 2c Respectively the ball center of the measuring head in actual measurement reaches M 1 And M is as follows 2 The absolute coordinate of the machine tool C axis in the measurement coordinate system sigma 3 is obtained during the processing; angle K-O 2 -M 1 Is the included angle between the sphere center of the measuring head, the contact point of the measuring head and the tooth surface and the connecting line of the circle center of the gear respectively.
Fifth step: as shown in FIG. 4, O 1 C is the imaginary sphere center 1 -C 2 To calibrate a section of arc where the sphere center of the imaginary sphere is positioned, B 1 -B 2 Is the pitch circle arc of the gear, A 1 -A 2 Is a circular arc of a gear base circle. G. The point H is the intersection point of the involute on the two sides of the pitch circle and the tooth slot, and is the tangential point of the imaginary sphere and the involute on the two sides, and the involute on the two sides is the left involute GD and the right involute HE. Left involute GD is wound around the circle center O of the gear 2 Time-to-timeThe needle rotates beta to make the left involute GD pass through the virtual sphere center O 1 The method comprises the steps of carrying out a first treatment on the surface of the Similarly, the right involute HE is wound around the circle center O 2 Counterclockwise rotation of beta also causes the right involute HE to pass through the imaginary sphere center O 1 Beta= D-O 2 -L. According to the property of the involute, the left involute GD section and the involute S obtained after rotation and translation can be known 1 The normal distance of the arc segments being equal everywhere, i.e. G-O 1 =df=imaginary sphere radius d p /2. As can be seen from the relationship of involute-generating curve FD to arc DL,therefore, it is
β＝d p /2/r b (4)
In the formula (4), beta is the opposite rotation angle of involute on two sides, d p Is the diameter of an imaginary sphere, r b Radius of base circle, r in the figure b ＝D-O 2 。
Because the rotation transformation of both involute equations can complicate the calculation, only one side involute is rotated by 2β, i.e. the left side involute GD is moved to the involute S, in order to simplify the calculation without affecting the calculation result 3 At the position, the right involute HE is fixed, and the involute S is solved 3 An intersection with the involute HE. While radial runout is based on the center O of the imaginary sphere 1 With the centre of a circle O of the gear 2 The distance between the two points is calculated, and the circle where the obtained intersection point is located is unchanged, so that the simplified calculation is feasible.
Sixth step: as shown in fig. 5, the arc GH is a theoretical pitch, and the arc PH is a measured pitch obtained after radius compensation according to measured data. As can be seen, the width of the tooth slot is reduced to make the center of the imaginary sphere O 1 Position is moved to O 1 At' (center of dotted sphere), involute G ' D ' and involute S 1 The normal distance between' is unchanged and is the radius of the probe. So that the involute G 'D' is rotated by 2 beta to the involute S 3 The' position and the right involute HE are crossed to obtain the center O of the broken line ball 1 ' coordinates.
Seventh step: calculating all actual tooth socket pitch arcs by using all measured data after measuring head radius compensationThe central angle of the segment is differed from the central angle of the theoretical tooth space pitch arc segment, so that the central angle corresponding to the arc line GP can be calculated, and the central angle corresponding to the arc line WD' can be obtained. The dashed sphere center O can be obtained according to the measurement method description in combination with FIG. 6 1 The' calculation process is:
1) In the coordinate system Σ1, the right involute equation is:
x 1 ＝r b *(cos t+tsin t)，y 1 ＝r b *(sin t-tcos t) (5)
in the coordinate system Σ2, the left involute equation is:
x 2 ＝r b *(cos t+t sin t)，y 2 ＝-r b *(sin t-tcos t) (6)
in the formulas (5) and (6), t is the spreading angle at any point on the tooth surface, r b Is the base radius.
2) Rotating involute G 'D' clockwise by 2β in coordinate system Σ2 to S 3 ' position; the equation of involute G 'D' in coordinate system Sigma 2 at this time is
3) Involute S to be expressed in coordinate system Σ2 3 Equation (7) of' is transformed into the coordinate system Σ1 for expression. Subtracting the base circular groove angle deltaObtaining an angle theta to be rotated, wherein the base circle tooth groove angle delta is:
in the formula (8), Z is the number of teeth of the gear, and ψ is the pressure angle at the pitch circle.
Therefore, it is
The rotational coordinate transformation of the coordinate system Σ1 to the coordinate system Σ2 is
In the formula (10), (x ', y') is involute S 3 ' expression in coordinate system Σ1.
4) Calculating two involute equations in the same coordinate system, and solving the simultaneous equations (5), (6), (7) and (10) to obtain:
x 1 ＝r b *(cos t+tsin t)，y 1 ＝r b *(sin t-tcos t)
let x' =x 1 and y′＝y 1 (11)
Solving the center O of the broken line sphere 1 ' coordinates (x o1′ ，y o1′ ) Then, the Pythagorean theorem is used to obtain the center O of the virtual sphere 1 The distance from the circle center of the gear is' the radial jump value of one tooth slot is obtained, and the same calculation process is carried out on each tooth slot, so that all radial jump values of the gear are obtained;
eighth step: because equation (11) is an overrun equation, the analytical solution is difficult to solve; x' =x can be used 1 Equal (with y' =y 1 Equality can be solved, the two modes only have the difference in iterative formulas, the calculation results are completely consistent through verification), and the formula (11) is simplified to be:
G(t)＝cos t*(m 1 +m 2 +(m 3 -m 4 )*t-r b )-sin t*(rb*t-(m 1 +m 2 )*t-(m 4 -m 3 ))＝0 (12)
in the formula (12), m 1 ＝r b *cosθ*cos(2β)
m 2 ＝r b *sinθ*sin(2β)
m 3 ＝r b *sinθ*cos(2β)
m 4 ＝r b *cosθ*sin(2β)
Deriving the two ends of (12)
G′(t)＝cos t*(r b *t-(m 1 +m 2 )*t-(m 4 -m 3 ))+sin t*(r b -m 1 -m 2 )-cost*(m 3 -m 4 )+sin t*(m 1 +m 2 +(m 3 -m 4 )*t-r b )＝0 (13)
Combining (12) and (13), adopting Newton iterative calculation
t k+1 ＝t k -G(t k )/G′(t k )(k＝0、1、2、3…)
Setting the iteration control precision as |t k+1 -t k |≤10 -10 And the result keeps four valid digits, and the involute intersection meeting the precision condition can be solved.
During actual measurement, the measuring head, the measured piece and the measuring equipment are free from interference in the measuring process, and the measuring data of the sensor are effective.
Example verification is as follows:
the on-machine measurement experiment is completed on a YK73125A numerical control grinding wheel forming gear grinding machine. The measured gear parameters are shown in table 1.
| Modulus of | Tooth number | Tooth width/mm | Circle dividing pressure angle/° |
| 12 | 97 | 220 | 20° |
| Coefficient of tooth tip/mm | Roof clearance coefficient/mm | Helix angle/° | Coefficient of deflection/mm |
| 1 | 0.25 | 0 | -0.4 |
Note that: modulus, tooth top coefficient, top gap coefficient and deflection coefficient refer to the normal direction of the gear.
The triggering type probe is a Ranshao triggering type LP2 probe with the radius of 2.5mm. And detecting the diameter jump precision of the gear after machining by using a method for detecting the tooth pitch precision of a machine tool.
1. Installing a trigger type measuring head, checking a gear to be measured, and setting measuring parameters.
2. Placing a magnetic seat with a standard ball on the outer end surface of the gear, and running a machine tool calibration program; and after the calibration is finished, returning a result.
3. And running a measuring program, detecting the detected gear, obtaining and storing data of the C axis and the X axis measured at the pitch circle in each tooth slot.
4. Because the first half part of the data obtained after detection is all right tooth surface data and the second half part is all left tooth surface data, the measured data are separated first, and two corresponding groups of detection values are found for two sides of each tooth slot. After the separation, data processing is carried out, and the diameter jump value in each tooth slot is solved by the tooth surface diameter jump calculation method provided by the invention.
The experimental results were compared as follows:
the method of the invention is adopted to carry out on-machine measurement of gears, as shown in figure 1; all tooth space diameter jump value calculation results after the evaluation calculation method is improved are shown in figure 8; the comparison of the theoretical runout of the gear under test, the gauge measurement, the on-machine measurement before modification, and the on-machine measurement after modification is shown in table 2.
Table 2 comparison of theoretical values with measurement results of different measurement data processing methods
Note that: 1) According to the national standard of GB/T10095.2-2008, the gear radial runout evaluation index is Fr (the difference between the maximum and minimum radial distances from its center of sphere to the gear axis when the probe is positioned in each tooth slot in succession). 2) The radial distance refers to the distance between the gear axis and the center of the imaginary sphere.
As can be seen from FIG. 1, the measured tooth slot diameter jump value varies more severely, and the difference between the tooth slot corresponding to the maximum diameter jump value and the minimum diameter jump value is about 120 degrees. This is different from the fact that only the radial jump phase change rule caused by geometric eccentricity exists, mainly because in actual production, besides geometric installation deviation, many other error factors are included, such as machine tool calibration errors, rotating shaft errors, transmission chain errors and the like. In actual on-machine measurement, the geometric eccentricity of gear blank installation can be reduced by respectively correcting the installation position of the detected gear in the direction of the connecting line between the tooth slot and the center of the gear at the position of the tooth slot when the maximum radial jump and the minimum radial jump occur.
As is clear from Table 2, the diameter jump value of the gear obtained by the method of the invention is 0.0222mm, and the gear is known to be four-level precision according to national standard of GB/T10095.2-2008. The measurement results generally have good agreement with the actual results. The difference between the theoretical radial distance from the sphere center of the imaginary sphere to the axis of the gear and the actual radial distance measured after improvement is 0.3806mm, and the main reason is that the gear transmission state corresponding to the theoretical value is in backlash-free engagement, but in practical application, a transmission clearance is reserved in gear processing in order to facilitate the entering of lubricating oil, compensate manufacturing errors and the like. In the table 1, the center distance range is 800-1250 mm during gear transmission, the standard backlash is 0.4200mm and the maximum backlash is allowed to be 0.8500mm by inquiring the common cylindrical gear transmission backlash table, so that the calculation result is consistent with the actual situation.
The detection and calculation method can realize calculation of the diameter jump in the machining precision of the cylindrical gear. The detection method is based on a two-point contact method in a measuring head and a tooth socket defined by national standards. And calculating the radial jump value by using a virtual sphere method on the premise of ensuring to follow national standard definition by combining specific use conditions of on-machine detection. The method can also very easily deduce and calculate important parameters such as the ball crossing distance and the like, does not need additional detection actions, and does not reduce the overall detection efficiency.
By adopting the method for measuring the pitch error, after the measured data are separated, the experimental result shows that the method can reduce the evaluation error, has high measurement precision and can meet the precision requirement of on-machine measurement. The measuring and evaluating method can be programmed and written into the gear on-machine measuring software, thereby realizing automatic and rapid radial jump detection and providing important basis for analyzing the gear tooth thickness change
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (1)
1. The radial jump detection method based on tooth pitch measurement in the gear on-machine measurement process is characterized by comprising the following steps of:
the first step: after the gear machining is finished, checking the clamping condition of the clamp of the rotary worktable and the gear to be measured, and ensuring the coaxiality of the central axis of the gear to be measured and the central axis of the rotary worktable; after the inspection is finished, installing a trigger type measuring head on the machine tool, acquiring an initial data value by measuring points at the pitch circle of each tooth socket of the gear through the trigger type measuring head, constructing a calibration virtual sphere when calculating the radial jump, and ensuring that the contact points of the virtual sphere and tooth surfaces at two sides are positioned on the pitch circle; calculating the diameter of an imaginary sphere in advance according to gear parameters;
the diameter of a sphere when contacting with two points of a pitch circle in a tooth socket of a theoretical tooth surface is taken as the diameter of an imaginary sphere, and the calculation formula is as follows:
wherein m is the normal modulus of the gear, Z is the number of teeth, and alpha is the pressure angle of the reference circle of the gear;
and a second step of: in order to accurately obtain the positional relationship between the machine coordinate system Sigma 4 (X-Y-Z) and the measurement coordinate system Sigma 3 (Xc-Yc-Zc), a magnetic gauge stand with a standard ball is fixed at any position on the upper end surface of a measured gear, and the center of the standard ball at the position is marked as O b1 The method comprises the steps of carrying out a first treatment on the surface of the The triggering type measuring head is utilized to uniformly collect the coordinates (x) of six measuring points on the half circumference of the measured truncated circle of the standard ball a ，y a ，z a )…(x f ，y f ，z f ) Calculating the standard sphere center O based on the least square method b1 Coordinate value (x) 1 ，y 1 ，z 1 ) The method comprises the following steps:
in formula (2): i=a to f
The rotation angle zeta of the machine tool C axis is recorded as O at the moment of the position of the sphere center of the standard sphere b2 The method comprises the steps of carrying out a first treatment on the surface of the Repeating the process of collecting the points by the measuring head, uniformly collecting six measuring points on the half circumference of the measured truncated circle of the standard ball again, and marking the sitting mark as (x) a2 ，y a2 ，z a2 )…(x f2 ，y f2 ，z f2 ) Obtaining O by the least square method of the reference formula (2) b2 Coordinate value (x) 2 ，y 2 ，z 2 ) The method comprises the steps of carrying out a first treatment on the surface of the According to the standard sphere center position O b1 、O b2 The rotation angle zeta between the gear and the C axis of the machine tool can be used for obtaining the circle center O of the gear 2 The standard ball is taken away from the position in the X-O-Y plane under the machine tool coordinate system sigma 4, and the trigger is controlled manuallyThe measuring head touches any position of the upper end face of the gear until triggering, a Z-axis coordinate of the upper end face of the gear under a machine tool coordinate system is obtained, and the three position coordinates are uploaded to a machine tool numerical control system to complete a calibration process;
and a third step of: the triggering type measuring head approaches to the measured gear along the direction parallel to the X axis and is matched with the rotary motion of the measured gear to find a tooth slot; two points K, N are arranged on the pitch circle; the measuring head enters a position 2 in the tooth slot from a position 1, and a contact point of the measuring head and a tooth surface is positioned on a pitch circle at the radius of the position 2; the gear to be measured rotates along with the C axis of the machine tool, contacts the left tooth surface and the right tooth surface respectively, and acquires the position information of each axis of the machine tool after the trigger type measuring head triggers; after one tooth slot is detected, the measuring head exits from the tooth slot along the X axis, and the gear rotates with the workbench for indexing and rotates by one pitch angle; repeating the above process until all tooth grooves of the gear are detected; the triggering type measuring head exits and returns to the initial station, and the measuring work is ended to obtain a measured value;
fourth step: according to the gear on-machine measurement principle, the return values of the trigger type measuring head are all absolute coordinate values of all axes under a machine tool coordinate system where the spherical center of the measuring head is located; to obtain the actual angle of the tooth space on the pitch arc KO 2 N, radius compensation is needed to be carried out on the measured value; known M 1 -K is the gauge head radius, M 1 -O 2 The length of the pitch circle is calculated according to the radius of the point at the measured pitch circle, the normal vector and the radius of the measuring head and is marked as X m The method comprises the steps of carrying out a first treatment on the surface of the K and N are located on the pitch circle of the gear, so the angle K-O is calculated according to the cosine law 2 -M 1 P +.N-O 2 -M 2 The same calculation is performed; the actual angle corresponding to the tooth slot segment arc is:
∠KO 2 N＝|O 1c -O 2c |+2*∠K-O 2 -M 1 (3)
in the formula (3), o 1c For the absolute coordinate of the C axis of the machine tool in the measurement coordinate system sigma 3, o, which is obtained when the spherical center of the measuring head reaches the position M1 in the actual measurement 2c For the ball center of the measuring head to reach M in actual measurement 2 The absolute coordinate of the machine tool C axis in the measurement coordinate system sigma 3 is obtained during the processing; angle K-O 2 -M 1 Is connected with the spherical center of the measuring head, the measuring head and the tooth surfaceIncluded angles between the contact points and the connecting lines of the circle centers of the gears respectively;
fifth step: o (O) 1 C is the imaginary sphere center 1 -C 2 To calibrate a section of arc where the sphere center of the imaginary sphere is positioned, B 1 -B 2 Is the pitch circle arc of the gear, A 1 -A 2 Is a circular arc of a gear base circle; G. the H point is the intersection point of the pitch circle and the involute on the two sides of the tooth socket, and is also the tangential point of the imaginary sphere and the involute on the two sides, wherein the involute on the two sides is a left involute GD and a right involute HE; left involute GD is wound around the circle center O of the gear 2 Clockwise rotation of beta causes the left involute GD to pass through the imaginary sphere center O 1 The method comprises the steps of carrying out a first treatment on the surface of the Similarly, the right involute HE is wound around the circle center O 2 Counterclockwise rotation of beta also causes the right involute HE to pass through the imaginary sphere center O 1 Beta= D-O 2 -L; according to the property of the involute, the left involute GD section and the involute S obtained after rotation and translation can be known 1 The normal distance of the arc segments being equal everywhere, i.e. G-O 1 =df=imaginary sphere radius; as can be seen from the relationship between involute generating curve FD and arc DL,therefore, it is
β＝d p /2/r b (4)；
In the formula (4), beta is the opposite rotation angle of involute on two sides, d p Is the diameter of an imaginary sphere, r b Is the radius of the base circle;
because the rotation transformation of both involute equations can complicate the calculation, only one side involute is rotated by 2β, i.e. the left side involute GD is moved to the involute S, in order to simplify the calculation without affecting the calculation result 3 At the position, the right involute HE is fixed, and the involute S is solved 3 An intersection point with the involute HE; while radial runout is based on the center O of the imaginary sphere 1 With the centre of a circle O of the gear 2 The distance between the two points is calculated, and the circle where the obtained intersection point is located is unchanged, so that the simplified calculation is feasible;
sixth step: the arc GH is a theoretical tooth pitch, the arc PH is an actual tooth pitch obtained by radius compensation according to actual measurement data, and when the width of a tooth slot is reduced, an imaginary sphere is formedHeart O 1 The position moves to the center O of the broken line sphere 1 At ' involute G ' D ' and involute S 1 The normal distance between' is unchanged and is the radius of an imaginary sphere; so that the involute G 'D' is rotated by 2 beta to the involute S 3 The' position and the right involute HE are crossed to obtain the center O of the broken line ball 1 ' coordinates;
seventh step: calculating the central angles of all actual tooth socket pitch arc sections by using all measured data after the measurement head radius compensation, and calculating the central angle corresponding to the arc line GP by making a difference with the central angle of the theoretical tooth socket pitch arc section, thereby obtaining the central angle corresponding to the arc line WD'
Solving the center O of the broken line sphere 1 ' coordinates (x o1′ ，y o1′ ) Then, the Pythagorean theorem is used to obtain the center O of the virtual sphere 1 The distance from the circle center of the gear is' the radial jump value of one tooth slot is obtained, and the same calculation process is carried out on each tooth slot, so that all radial jump values of the gear are obtained;
the center O of the broken line ball in the seventh step 1 The' calculation process is:
1) In the coordinate system Σ1, the right involute equation is:
x 1 ＝r b *(cost+tsint)，y 1 ＝r b *(sint-tcost) (5)
in the coordinate system Σ2, the left involute equation is:
x 2 ＝r b *(cost+tsint)，y 2 ＝-r b *(sint-tcost) (6)
in the formulas (5) and (6), t is the spreading angle at any point on the tooth surface, r b Is the radius of the base circle;
2) The involute G 'D' is rotated clockwise by 2β in the coordinate system Sigma 2 to S 3 ' position; the equation for involute G 'D' in coordinate system Σ2 at this time is:
3) Involute S to be expressed in coordinate system Σ2 3 Equation (7) of' is transformed into a coordinate system Σ1 for expression; subtracting the base circular groove angle deltaObtaining an angle theta to be rotated, wherein the base circle tooth groove angle delta is:
in the formula (8), Z is the number of teeth of the gear, and ψ is the pressure angle at the pitch circle;
therefore, it is
The rotational coordinates of the coordinate system Σ1 to the coordinate system Σ2 are converted into:
in the formula (10), (x ', y') is involute S 3 ' expression in coordinate system Σ1;
4) Calculating two involute equations in the same coordinate system, and solving the simultaneous equations (5), (6), (7) and (10) to obtain:
x 1 ＝r b *(cost+tsint),y 1 ＝rb*(sint-tcost)
let x' =x 1 and y′＝y 1 (11)；
Eighth step: because equation (11) is an overrun equation, the solution is resolvedDifficult to find; using x' =x 1 Equal (or with y' =y 1 Equal), and the formula (11) is simplified to obtain:
G(t)＝cost*(m 1 +m 2 +(n 3 -m 4 )*t-r b )-sint*(rb*t-(m 1 +m 2 )*t-(m 4 -m 3 ))＝0 (12)
in the formula (12), m 1 ＝r b *cosθ*cos(2β)
n 2 ＝r b *sinθ*sin(2β)
m 3 ＝r b *sinθ*cos(2β)
m 4 ＝r b *cosθ*sin(2β)
Deriving the two ends of (12)
G′(t)＝cost*(r b *t-(m 1 +m 2 )*t-(m 4 -m 3 ))+sint*(r b -m 1 -m 2 )-cost*(m 3 -m 4 )+sint*(m 1 +m 2 +(m 3 -m 4 )*t-r b )＝0 (13)
Combining (12) and (13), adopting Newton iterative calculation
t k+1 ＝t k -G(t k )/G′(t k )(k＝0、1、2、3…)
Setting the iteration control precision as |t k+1 -t k |≤10 -10 And the result keeps four valid digits, and the involute intersection meeting the precision condition can be solved.
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