CN114993230B - Normal meshing tooth profile measuring and evaluating method based on gear characteristic line unified model - Google Patents
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Abstract
The invention discloses a normal meshing tooth profile measuring and evaluating method based on a gear characteristic line unified model, which comprises the following steps of: establishing a gear characteristic line unified model; measuring a normal meshing tooth profile based on a gear characteristic line unified model; defining an evaluation index of a normal meshing tooth profile; calculating normal meshing tooth profile deviation and evaluating tooth surface quality. The method can realize the measurement of the normal meshing tooth profile without the derivation of a complex formula and complex coordinate change under the condition that the gear characteristic line type indication parameter in the gear characteristic line unified model is 3, and is simple, convenient and easy to operate. The method defines the evaluation indexes and signs of the normal meshing tooth profile: the normal meshing tooth profile total deviation, the normal meshing tooth profile shape deviation and the normal meshing tooth profile inclination deviation. The method can calculate various deviation values of the measured normal meshing tooth profile on the tooth surface; and calculating tolerance grade allowed by deviation of the left tooth surface and the right tooth surface according to the deviation value, and further evaluating the quality of the tooth surfaces.
Description
Technical Field
The invention relates to a gear measuring method, in particular to a normal meshing tooth profile measuring and evaluating method based on a gear characteristic line unified model.
Background
The tooth surface of the gear is an involute spiral surface, and four characteristic lines with special significance are arranged on the involute spiral surface: involute, spiral, normal mesh profile and contact line, as shown in figure 1. Involutes and spirals are well known as tooth flank characteristic lines due to their well-defined geometrical significance. In fact, the Profile of the Path of Contact (PPC) as another significant feature line on the tooth flank should be more worth paying attention.
The crossed shaft involute spiral cylindrical gear transmission belongs to point contact transmission, and the trace left on the tooth surface by a contact point is a normal meshing tooth profile. Therefore, the crossed shaft involute helical cylindrical gear is driven to move through a normal meshing tooth profile, and the normal meshing tooth profile is a working curve of a gear tooth surface and can reflect the actual movement condition of the gear. In generating method machining such as hobbing, shaving, worm grinding wheel grinding and the like, generating movement is theoretically based on the meshing principle of a crossed shaft involute spiral cylindrical gear, and a contact track of a cutter and a workpiece gear is a normal meshing tooth profile. Therefore, in the gear machining by the generating method, the normal meshing tooth profile of the gear is the machining curve formed by the tooth surface, and the control of the normal meshing tooth profile has unique advantages for controlling the machining quality of the gear.
The normal engaging tooth profile is unique as both the forming curve and the working curve on the tooth flank. In essence, the method is a result of the comprehensive action of the involute and the spiral line, can represent the quality of the gear, and can be used for not only analyzing and tracing the process error of the gear, but also forecasting the dynamic performance of the gear.
However, in the current international standard and national standard, the quality of the tooth surface of the gear is evaluated by measuring involute and spiral line. The measurement of the gear tooth surface adopts involute and spiral line measurement modes no matter a three-coordinate measuring machine or a gear measurement center, and sometimes the measurement mode cannot effectively reflect real information of gear transmission quality and machining quality. In the motion mode, a rotating shaft and a linear shaft are adopted, and the motion control of other shafts is not opened for users.
The patent (application number: 202110092932.3) proposes a unified characterization method for the characteristic lines of the three-dimensional errors of the gear, which is to perform two-dimensional characterization on the three-dimensional measurement errors on the tooth surface, analyze that four characteristic lines on the tooth surface are all straight lines in a meshing plane coordinate system, and realize unified mathematical characterization of all the characteristic lines in the meshing plane coordinate system. The gear characteristic line unified model is provided, four characteristic lines on the tooth surface are organically unified, and any one contour curve on the tooth surface can be expressed. However, the above patent is premised on acquiring the three-dimensional tooth surface of the gear, and then extracting corresponding characteristic lines on the three-dimensional tooth surface according to the characteristics of the unified model, and the characteristic lines are not directly measured. Meanwhile, the three-dimensional tooth surface of the gear is difficult to obtain, the quality of the tooth surface is often evaluated according to an evaluation standard, and only one characteristic line of the same type needs to be measured in most cases; and the evaluation standard is still based on the traditional involute and spiral evaluation standard, and the definition of the re-definite evaluation index needs to be solved urgently.
The patent (application number: 202011542413.4) proposes a normal meshing tooth profile measuring method of an involute spiral cylindrical gear, and measurement can be realized through a gear measuring center. However, the above patent requires complicated mathematical derivation and coordinate transformation, and the establishment of coordinate system and the requirement of gear initial angle position are higher when measuring normal engagement tooth profile by using four-axis method and three-axis method. Meanwhile, the above patent only realizes complex measurement on gear measurement equipment, and does not relate to tooth surface quality assessment and determination of evaluation indexes.
Based on the current situation and the problems, a normal meshing tooth profile measuring and evaluating method based on a gear characteristic line unified model is provided, the normal meshing tooth profile can be rapidly measured, the evaluation index of the normal meshing tooth profile is defined, and a tooth surface quality evaluation system is perfected.
Disclosure of Invention
The invention aims to provide a method for measuring and evaluating a normal meshing tooth profile on a tooth surface of a gear, which can be used for measuring working curves actually participating in meshing and machining on the tooth surface, reflecting real information of gear transmission quality and machining quality and determining the quality condition of the gear by defining evaluation indexes of the normal meshing tooth profile.
The invention provides a normal meshing tooth profile measuring and evaluating method based on a gear characteristic line unified model, which has the technical scheme that:
step 1: and establishing a gear characteristic line unified model.
According to the patent (application number: 202110092932.3), the expression of the gear characteristic line unified model is formula (1)
Wherein, Y n ，Z n Two coordinate axes under the gear meshing coordinate system. Y is n Along the expansion direction of the gear tooth profile, L is the expansion length and is also Y n The extent of the axis. Z is a linear or branched member n B is the tooth width along the axial direction of the gearIs also Z n The extent of the axis is large. Delta norm For tooth flank errors of a gear, F () is a functional expression of the tooth flank error. A. B and C are gain parameters of the unified model and are constants. k is a gear characteristic line type indicator, beta b Is the gear base circle helix angle.
And 2, step: and measuring the normal meshing tooth profile based on the gear characteristic line unified model.
Based on the unified gear characteristic line model established in step 1, it can be known that when k =3, the tooth surface characteristic line represented by the unified gear characteristic line model is the normal meshing tooth profile, that is, the equation shown in equation (2).
Wherein r is b Is the radius of the gear base circle, and the gear base circle,
is the spread angle difference of the gears. />
Is a function of the spread angle, and Z is given by equation (2) n As well as a function of the spread angle.
To achieve the measurement of the normal engagement tooth profile, it is necessary to use a gear measuring device such as a gear measuring center or a three-coordinate measuring machine, as shown in fig. 2. During movement of the gear measuring device, Y n The shaft moves along the extending direction of the gear tooth profile, namely the X-axis direction of the gear measuring equipment; z n The shaft is moved in the tooth width direction of the gear, i.e. in the Z-axis direction of the gear measuring device.
The gear to be measured is arranged on a rotary main shaft of the gear measuring equipment and can rotate at a certain speed along with the main shaft. And then moving a contact measuring head of the gear measuring device, and when the measuring head contacts the tooth surface, controlling a rotary main shaft of the gear measuring device and the measuring head to move according to a model of a formula (2), namely an X axis and a Z axis of the gear measuring device are linked with the rotary main shaft simultaneously, wherein the track measured by the measuring head on the spatial tooth surface is the normal meshing tooth profile, as shown in fig. 3. In essence, the normal tooth flank profile deviation is the result of the combined effect of the involute and the helix, as can be seen in the gear profile unified model, as shown in FIG. 4. The measurement process of the normal meshing tooth profile does not need derivation of a complex formula and complex coordinate change, the measurement of the normal meshing tooth profile can be realized according to the gear characteristic line unified model, and the method is simple, convenient and easy to operate.
In this case, the real-time displayed index value of the measuring head of the gear measuring device during the spatial movement is the error of the normal tooth profile on the tooth surface.
And 3, step 3: and defining an evaluation index of the normal engagement tooth profile.
Further defining normal conjugate profile variations, including total normal conjugate profile variation (symbol F) based on the normal conjugate profile error measured in step 2 PPC ) Normal meshing tooth profile shape deviation (symbol defined as f) fPPC ) Normal mating tooth profile skew deviation (symbol defined as f) HPPC )。
Total normal flank profile deviation (F) PPC ): within the normal meshing tooth profile evaluation range, the two designed normal meshing tooth profile lines are wrapped around the actually measured normal meshing tooth profile, and the distance between the two designed normal meshing tooth profile lines is the total deviation of the normal meshing tooth profile, as shown in fig. 5.
Normal mating tooth profile shape deviation (f) fPPC ): within the normal engaging tooth profile evaluation range, the normal engaging tooth profile is measured by two average normal engaging tooth profile envelopes, and the distance between the two average normal engaging tooth profiles is the normal engaging tooth profile shape deviation, as shown in fig. 6.
Normal mating tooth profile skew deviation (f) HPPC ): within the span length range of the normal mating tooth profile, the extension lines of the average normal mating tooth profile line intersect at the span length starting point and the span length ending point, and the distance between the two designed normal mating tooth profiles passing through the two intersection points is the normal mating tooth profile inclination deviation, as shown in fig. 7.
And 4, step 4: calculating the normal meshing tooth profile deviation and evaluating the tooth surface quality.
Based on the normal meshing tooth profile error measured in the step 2 and the normal meshing tooth profile evaluation index defined in the step 3, deviation values of the measured normal meshing tooth profile on the tooth surface can be calculated according to the definition: f PPC 、f fPPC 、f HPPC . Next, the tooth surface quality is evaluated based on the above-described deviation values.
Determining the allowable tolerance level for tooth flank error is the accepted primary method of assessing tooth flank quality.
For normal conjugate flank profile shape deviations, the tolerance grade can be calculated from equation (3).
Wherein the content of the first and second substances,
code number, P, for tolerance class of shape deviation of normal meshing profile f Radial gain factor, Q, for normal conjugate flank profile shape deviation f Axial gain factor, m, for normal conjugate flank profile shape deviation n Is the module of the gear, r m Is the measured circle radius of the gear.
According to the calculation formula of the tolerance grade, the tolerance grade of the shape deviation of the left tooth surface normal meshing tooth profile of one tooth of the gear can be expressed as
The tolerance level for the deviation in shape of the right flank normal engaging profile can be expressed as ^ or ^>
For normal conjugate flank profile pitch deviation, the tolerance grade can be calculated from equation (4).
Wherein the content of the first and second substances,
code number, P, for normal meshing profile slope deviation tolerance grade H Radial gain factor, Q, for normal conjugate flank profile slope deviation H An axial gain factor that is the deviation of normal conjugate flank profile pitch.
According to the calculation formula of the tolerance grade, the tolerance grade of the deviation of the normal meshing tooth profile inclination of the left tooth surface of one tooth of the gear can be expressed as
The tolerance level for the deviation in the normal engaging flank profile inclination of the right flank can be expressed as ^ 4>
For total normal conjugate flank profile deviation, the tolerance level can be calculated from equation (5).
According to the calculation formula of the tolerance grade, the tolerance grade of the total deviation of the left tooth surface normal meshing tooth profile of one tooth of the gear can be expressed as
The tolerance level for the total deviation of the right flank normal engaging profile may be expressed as ≧ or @>
Therefore, the tooth surface quality grade of the whole gear is determined by the item with the highest tolerance grade of the left and right tooth surfaces, and can be expressed as:
and i is the number of gear teeth. Since the evaluation of the tooth surface quality of a gear is generally carried out by selecting 4 uniformly distributed gear teeth, i =1,2,3,4 is taken as the number of gear teeth.
The method for measuring and evaluating the normal meshing tooth profile based on the gear characteristic line unified model has the following remarkable characteristics:
1. the method can realize the measurement of the normal meshing tooth profile without the derivation of a complex formula and complex coordinate change under the condition that the gear characteristic line type indication parameter in the gear characteristic line unified model is 3, and is simple, convenient and easy to operate.
2. The method defines evaluation indexes and signs of normal meshing tooth profiles: total normal flank profile deviation (F) PPC ) Normal meshing tooth profile shape deviation (f) fPPC ) Normal mating tooth profile skew deviation (f) HPPC )。
3. According to the method, various deviation values of the measured normal meshing tooth profile on the tooth surface can be calculated and obtained on the basis of the measured normal meshing tooth profile error and the defined normal meshing tooth profile evaluation index; and calculating the tolerance grade allowed by the deviation of the left tooth surface and the right tooth surface according to the deviation value, and further evaluating the tooth surface quality.
Drawings
Fig. 1 shows four characteristic lines on the involute helicoid.
FIG. 2 is a schematic view of a gear measurement apparatus.
FIG. 3 is a process of normal conjugate tooth profile measurement.
FIG. 4 is a graph of involute, helical and normal conjugate tooth profile.
FIG. 5 shows the total normal conjugate flank profile deviation.
FIG. 6 is a normal conjugate mating profile shape deviation.
FIG. 7 is a normal mating profile pitch deviation.
FIG. 8 is a normal conjugate tooth profile deviation evaluation.
1. Measured normal engaging tooth profile, 2, normal engaging tooth profile evaluation range, 3, normal engaging tooth profile extension range, 401, design normal engaging tooth profile 1, 402, design normal engaging tooth profile 2, 403, design normal engaging tooth profile 3, 404, design normal engaging tooth profile 4, 501, average normal engaging tooth profile 1, 502, average normal engaging tooth profile 2, 503, average normal engaging tooth profile 3, 601, extension starting point, 602, evaluation range starting point, 603, evaluation range ending point, 604, extension ending point.
Detailed Description
The invention is described in further detail below with reference to the figures and the detailed description. However, it should not be understood that the scope of the above-described subject matter of the present invention is limited to the following embodiments, and any technique realized based on the present invention is within the scope of the present invention.
The basic parameters of the selected characteristic gear are shown in table 1.
TABLE 1 measured Gear parameters
| Parameter(s) | Number of teeth | Modulus of elasticity | Angle of pressure | Helix angle | Direction of rotation | Shape modification | Width of tooth | Tolerance class |
| Numerical value | 48 | 4mm | 20° | 30° | Right hand rotation | Middle drum | 40mm | Grade 10 |
The selected measured characteristic gear is installed on a rotary main shaft of the gear measurement center by means of the gear measurement center and can rotate along with the main shaft at a certain speed. And then moving a contact measuring head of the gear measuring center, and controlling the rotation main shaft of the gear measuring center and the measuring head to move according to the model of the formula (2) when the measuring head contacts the right tooth face of the gear, as shown in figure 3. The curve swept by a contact measuring head of a gear measuring center on the tooth surface of the measured gear is the normal meshing tooth profile on the tooth surface, and the real-time displayed numerical value of the measuring head is the error of the normal meshing tooth profile on the tooth surface.
And evaluating the obtained normal meshing tooth profile error, and defining various deviations of the normal meshing tooth profile. As shown in FIG. 3, total normal mating tooth profile deviation (F) PPC ): within the normal mating tooth profile evaluation range 2, the two designed normal mating tooth profiles 401 and 402 envelope the measured normal mating tooth profile 1, and the distance between the two designed normal mating tooth profiles 401 and 402 is the total normal mating tooth profile deviation. As shown in FIG. 4, the normal conjugate tooth profile shape deviation (f) fPPC ): within normal conjugate profile evaluation range 2, normal conjugate profile 1 is enveloped by two average normal conjugate tooth profiles 502 and 503, and the distance between the two average normal conjugate tooth profiles 502 and 503 is the normal conjugate profile shape deviation. As shown in FIG. 5, normal conjugate profile slope deviation (f) HPPC ): in the span length range 3 of the normal engaging tooth profile, the extended line of the average normal engaging tooth profile 501 intersects with the span length start point 602 and the span length end point 604, and the distance between the two designed normal engaging tooth profiles 403 and 404 passing through the two intersection points is the normal engaging tooth profile lean deviation.
The deviations of the normal meshing tooth profiles are calculated according to the above definition of the evaluation index, as shown in table 2. Because the selected gear has the mid-drum modification, the obtained numerical value of the shape deviation of the normal meshing tooth profile and the total deviation of the normal meshing tooth profile is large, and the actual measurement condition is met.
TABLE 2 Normal intermeshing tooth profile deviation
And (3) further determining the allowable tolerance level of the tooth surface error according to the selected measured characteristic gear parameters and the deviation of the normal meshing tooth profile obtained by the calculation as follows:
/>
according to the steps, 4 gear teeth are uniformly distributed and selected in the circumferential direction of the selected measured characteristic gear to measure and calculate each deviation of the normal meshing tooth profile of the left tooth surface and the right tooth surface respectively, and the quality tolerance grade of the tooth surface of the whole gear of A can be obtained PPC And =10, the same as the selected measured characteristic gear parameter.
The invention can express the advantage of any profile curve on the tooth surface by utilizing a gear characteristic line unified model, provides a method for measuring and evaluating the normal meshing tooth profile on the tooth surface of the gear, avoids complex formula derivation and coordinate transformation, can measure the working curves actually participating in meshing and actually participating in processing on the tooth surface, reflects the real information of the transmission quality and the processing quality of the gear, and has important application value for analyzing and tracing the process error of the gear and forecasting the dynamic performance of the gear. The measuring method is simple, convenient and easy to operate. The patent defines the description and symbol definition of the normal meshing tooth profile evaluation index, and calculates the tolerance grade allowed by the tooth surface deviation based on each deviation of the normal meshing tooth profile and the evaluation index, so as to evaluate the tooth surface quality and further perfect the tooth surface quality evaluation system.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (2)
1. A normal meshing tooth profile measuring and evaluating method based on a gear characteristic line unified model is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
step 1: establishing a gear characteristic line unified model;
the expression of the gear characteristic line unified model is formula (1)
Wherein, Y n ，Z n Two coordinate axes under a gear meshing coordinate system; y is n Along the expansion direction of the gear tooth profile, L is the expansion length and is also Y n The extent of the axis; z n In the axial direction of the gear, b is the tooth width, also Z n The extent of the axis; delta norm For tooth flank errors of a gear, F () is a functional expression of the tooth flank error; A. b and C are gain parameters of the unified model; k is a gear characteristic line type indicator, beta b Is a gear base circle helical angle;
step 2: measuring a normal meshing tooth profile based on a gear characteristic line unified model;
based on the unified gear characteristic line model established in the step 1, when k =3, a tooth surface characteristic line represented by the unified gear characteristic line model is a normal meshing tooth profile, namely an equation shown in a formula (2);
wherein r is b Is the radius of the gear base circle, and the gear base circle,
is the spread angle difference of the gear; />
Is a function of the spread angle, according to equation (2), Z n As well as a function of the spread angle;
the numerical value displayed in real time when the measuring head of the gear measuring equipment moves in space is the error of the normal meshing tooth profile on the tooth surface;
and 3, step 3: defining an evaluation index of a normal meshing tooth profile;
defining various deviations of the normal engaging tooth profile based on the normal engaging tooth profile error measured in the step 2, wherein the various deviations comprise a total deviation F of the normal engaging tooth profile PPC Normal meshing tooth profile shape deviation f fPPC Normal meshing profile slope deviation f HPPC ；
And 4, step 4: calculating normal meshing tooth profile deviation and evaluating tooth surface quality;
and (3) calculating various deviation values of the measured normal meshing tooth profile on the tooth surface according to the definition based on the normal meshing tooth profile error measured in the step (2) and the normal meshing tooth profile evaluation index defined in the step (3): f PPC 、f fPPC 、f HPPC (ii) a Then evaluating the quality of the tooth surface based on the deviation value;
for the shape deviation of the normal engagement tooth profile, the tolerance grade is calculated by the formula (3);
wherein the content of the first and second substances,
code number, P, for tolerance class of shape deviation of normal meshing profile f For normal meshing tooth profileRadial gain coefficient of form deviation, Q f Axial gain factor, m, for normal conjugate flank profile shape deviation n Is the module of the gear, r m Is the measured circle radius of the gear; />
According to the calculation formula of tolerance grade, the tolerance grade of the shape deviation of the left tooth surface normal meshing tooth profile of one tooth of the gear is expressed as
The tolerance level for the deviation in the shape of the right-hand normal engaging profile is expressed as @>
For normal meshing tooth profile pitch deviation, the tolerance grade is calculated by formula (4);
wherein, the first and the second end of the pipe are connected with each other,
code number, P, of normal meshing tooth profile slope deviation tolerance class H Radial gain factor, Q, for normal conjugate flank profile slope deviation H An axial gain factor that is the normal meshing profile pitch deviation;
according to the calculation formula of tolerance grade, the tolerance grade of the inclination deviation of the left tooth surface normal meshing tooth profile of one tooth of the gear is expressed as
The tolerance level for the deviation in the normal engaging flank profile inclination of the right flank can be expressed as ^ 4>
For the total deviation of the normal meshing tooth profile, the tolerance grade is calculated by the formula (5);
according to the calculation formula of tolerance grade, the tolerance grade of the total deviation of the left tooth surface normal meshing tooth profile of one tooth of the gear is expressed as
The tolerance level of the total deviation of the normal engaging flank profile of the right flank is expressed as ^>
The tooth surface quality grade of the whole gear is determined by the highest item of the tolerance grade of the left tooth surface and the right tooth surface, and is represented as:
i is the number of gear teeth; 4 uniformly distributed gear teeth are selected for evaluating the gear surface quality of one gear, and the number of the gear teeth is i =1,2,3,4;
the evaluation index defining the normal conjugate tooth profile in step 3 is described below,
total deviation of normal meshing profile F PPC : in the normal meshing tooth profile evaluation range, two designed normal meshing tooth profile lines wrap around the actually measured normal meshing tooth profile, and the distance between the two designed normal meshing tooth profile lines is the total deviation of the normal meshing tooth profile;
deviation of shape f of normal engagement profile fPPC : in the normal meshing tooth profile evaluation range, the two average normal meshing tooth profile lines are wound to measure the normal meshing tooth profile, and the distance between the two average normal meshing tooth profile lines is the shape deviation of the normal meshing tooth profile;
normal mating profile skew deviation f HPPC : within the span length range of the normal meshing tooth profile, the extension lines of the average normal meshing tooth profile line intersect at the span length starting point and the span length ending point, and two design normal meshing tooth profile lines passing through the two intersection pointsThe distance therebetween is the normal conjugate profile pitch deviation.
2. The method for measuring and evaluating a normal meshing tooth profile based on the gear characteristic line unified model according to claim 1, wherein: comprises the following steps of (a) preparing a solution,
for measuring normal tooth profile, Y is measured by means of a gear measuring center or a three-coordinate measuring machine during the movement of the gear measuring device n The motion mode of the shaft is along the extending direction of the gear tooth profile, namely the X-axis direction of the gear measuring equipment; z n The motion mode of the shaft is along the tooth width direction of the gear, namely the Z-axis direction of the gear measuring equipment;
mounting a gear to be measured on a rotary main shaft of gear measuring equipment, and rotating at a certain speed along with the main shaft; then moving a contact measuring head of the gear measuring equipment, and when the measuring head contacts the tooth surface, controlling a rotary main shaft and the measuring head of the gear measuring equipment to move according to a model of a formula (2), namely an X axis and a Z axis of the gear measuring equipment are linked with the rotary main shaft simultaneously, wherein the track measured by the measuring head on the spatial tooth surface is a normal meshing tooth profile, and the deviation of the normal meshing tooth profile is the result of the comprehensive action of an involute and a spiral line; and measuring the normal meshing tooth profile according to a gear characteristic line unified model.
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