CN103994744B - Tooth profile measuring method - Google Patents
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Abstract
The invention relates a tooth profile measuring method. The tooth profile measuring method includes the following steps that (1) AutoCAD and Microsoft Excel library function parameters are loaded through Visual Basic 6.0, and a theoretical tooth profile data base is built; (2) tooth profile data of a gear to be measured are obtained; (3) tooth profile alignment is conducted through data comparison; (4) the step (3) is repeated many times, and a plurality of alignment points are found out; (5) multiple groups of actual tooth profile points to be detected are obtained through theoretical tooth profile points built in the step (1); (6) an arbitrary point A is set on the involute of the gear to be detected, and a tooth profile error is worked out through a Cartesian coordinate origin and a D point coordinate. The tooth profile measuring method is high in accuracy, low in hardware equipment requirement, wide in application range and high in efficiency.
Description
Technical field
The invention belongs to mechanical measurement field, it is related to a kind of measuring method, more particularly, to a kind of tooth profile measurement method.
Background technology
Using most actuated elements in gear chamber machine instrument, especially involute gear application is more extensive.Gear
Tooth pitch cumulative departure and profile error be reflection gear drive accuracy and stable working precision important indicator, profile of tooth
The measurement also most important thing.Existing tooth profile measurement major part is not very accurate, and step is very loaded down with trivial details,
It is inconvenient in real work.
Content of the invention
In order to solve the technical problem proposed in background technology, the present invention proposes a kind of tooth profile measurement method, effectively
The degree of accuracy that improve in measurement process and efficiency.
The technical scheme is that：A kind of tooth profile measurement method, it is characterized in that：As follows including step：
1】AutoCAD and Microsoft Excel built-in function parameter is loaded by VisualBasic6.0, theorize tooth
Graphic data storehouse；
2】Obtain gear under test flank profil data；
2.1] determine the flank profil cartesian coordinate system of gear under test, described coordinate origin needed the central axis of gear；
2.2] pass through scanner scanning gear under test, sweep limits is one week in the range of the facewidth；
2.3] coordinate data obtaining after scanning, first removes probe radius value, then obtains gear under test practical tooth and sits
Punctuate；
3】Profile of tooth centering is carried out by comparing；
3.1] first it is defined by theoretical profile of tooth reference circle, find in actual profile of tooth point group radius closest to reference radius
Point, is set to D point；
3.2] by D point place, radius of circle is defined again, calculate theoretical profile of tooth fall in point on the left flank of tooth on circle that D point is located and
Point on the right flank of tooth；Described D point is the centering point of any one tooth one side of gear under test；
3.3], after D point determines, find out step 3.2] the centering point of described any tooth another side, it is set to C point；
4】Repeat step 3】Several times, some centering points are found out；
5】By step 1】The coordinate of the actual profile of tooth of some groups of the theoretical profile of tooth database acquisition measuring point to be checked set up；
6】Arbitrfary point is set on gear under test involute as A, by cartesian coordinate initial point, D point coordinates, calculate profile of tooth
Error；
Above-mentioned steps 3.1 reference circle is between SAP～EAP, if reference circle is not between SAP～EAP, select SAP～
Any radius of circle between EAP.
The invention has the beneficial effects as follows：
1. high precision.The measuring method of the present invention can be applicable to the gear form error detection of any accuracy class.
2. hardware device requirement is low.The inventive method can be used by multiple testing equipments possessing scanning sampling site function.
3. applied range.It is applied to straight tooth column involute internal-gear, straight tooth column involute external tooth gear, helical teeth
Cylinder involute internal-gear, helical teeth cylinder involute external tooth gear.
4. efficiency high.The present invention only need to input the point coordinate data of external equipment offer, you can quick output profile of tooth report.
5. the actual profile of tooth of final drafting, theoretical profile of tooth can amplify analysis directly perceived in AutoCAD.
Brief description
Fig. 1 is method of the present invention flow chart of steps；
Fig. 2 is profile error profile error computational methods schematic diagram of the present invention；
Fig. 3 defines figure for profile error
Wherein 1- cartesian coordinate system initial point, 2- centering point D coordinate, certain point A coordinate, 4- generating circle radius in the actual profile of tooth of 3-
Rb.
Specific embodiment
Referring to Fig. 1-3, the present invention is a kind of tooth profile measurement method；As follows including step：
1】The profile of tooth that theorizes database；
2】Obtain gear under test flank profil data；
2.1] determine the flank profil cartesian coordinate system of gear under test, described coordinate origin needed the central axis of gear；
2.2] pass through scanner scanning gear under test, sweep limits is one week in the range of the facewidth；
2.3] coordinate data obtaining after scanning, first removes probe radius value, then obtains gear under test practical tooth and sits
Punctuate；
3】Profile of tooth centering is carried out by comparing；
3.1] first it is defined by theoretical profile of tooth reference circle, find in actual profile of tooth point group radius closest to reference radius
Point, is set to D point；
3.2] by D point place, radius of circle is defined again, calculates theoretical profile of tooth and falls in the left point on justifying that D point is located and right point；Institute
State the centering point that D point is any one tooth one side of gear under test；
3.3], after D point determines, find out the centering point of any tooth another side described in step 3.2, be set to C point；
4】Repeat step 3】Several times, some centering points are found out；
5】By step 1】The actual profile of tooth of some groups of the theoretical profile of tooth point acquisition measuring point to be checked set up；
6】Arbitrfary point is set on gear under test involute as A, by cartesian coordinate initial point, D point coordinates, calculate profile of tooth
Error.
Above-mentioned steps 3.1 reference circle is between SAP～EAP, if reference circle is not between SAP～EAP, select SAP～
Any radius of circle between EAP.
Above-mentioned steps 1】Middle theory profile of tooth database loads AutoCAD and Microsoft by VisualBasic6.0
Excel built-in function parameter is set up.
Step 3.1] reference circle is between SAP～EAP, if reference circle is not between SAP～EAP, select SAP～EAP it
Between any radius of circle.
Taking one gear of three coordinate Scanning Detction as a example：
1. the acquisition of flank profil data
(1) scanning flank profil before determine cartesian coordinate system it is desirable to：Coordinate origin crosses Cylinder Gear
The central axis of wheel.
(2) scan when probe be in run-down in the range of the facewidth it is desirable to：Cleaning of Parts is clean, axial coordinate during scanning
Value constant (Z axis are constant, only run-down in X-Y plane), the scanning step of three coordinates and sweep speed are according to the outside diameter of gear
Size is chosen (selection principle is shown in that Part III (1) bar illustrates).
(3) coordinate data that obtains removes probe radius value, obtains practical tooth coordinate points, export as a file format with
Excel opens point row, and institute's X-coordinate value a little is placed on A to arrange, and Y-coordinate value is placed on B row, saves as Excel file form.
2. running software and algorithm detailed annotation
(1) runs software, the parameter of Input Software interface requirements, VisualBasic6.0 loads Microsoft Excel
Function library can extract the Excel file data of gear under test flank profil coordinate value, and coordinate value is removed Z value, and X and Y value are stored in
In array Dzb1 (), now background program simulates two groups of theoretical teeth according to the gear theoretical parameter of software interface input
Shape." theoretical profile of tooth " mentioned above refers to one of the whole gear that calculates with coordinate origin tooth for the basic circle center of circle
The left and right flank of tooth, and this tooth is symmetrical with regard to Y-axis.
First group of theoretical profile of tooth takes the left and right flank of tooth each from involute starting point (SAP) to involute terminating point (EAP)
100 points (Part III 2. article explanation is shown in the selection of points) and the left and right flank of tooth is symmetrical with regard to Y-axis, coordinate origin is in gear
On central axis.Algorithm is as follows：
Theoretical involute takes on involute 100 points between SAP-EAP along the high direction of tooth
(2) centering of actual profile of tooth and theoretical profile of tooth
Theoretical profile of tooth, actual profile of tooth have the cartesian coordinate system of oneself respectively, but two coordinate origin reality and reasons excessively
By Gear axis and two axial lines overlap, by around Gear axis (coordinate system Z axis) rotate actual profile of tooth centering.
Aligning method：Being defined by theoretical profile of tooth reference circle, (precondition is that reference circle is between SAP～EAP, if indexing
Circle does not then select any radius of circle between SAP～EAP between SAP～EAP, sees that Part III (3) bar illustrates), look for
To in actual profile of tooth point group, closest to the point (centering point D) of reference radius, (point D determines method to radius：Travel through actual profile of tooth point
Distance to initial point (0,0) is made comparisons with theoretical profile of tooth reference radius value, takes that point immediate), do yellow cross
Note, the left flank of tooth or the right flank of tooth according to residing for display selected marker point.
D point might not fall on reference circle, simply close to reference circle, so, then be defined by D point place radius of circle, meter
Calculate the point that theoretical profile of tooth falls on the circle of D point place.Algorithm is as follows：
Centering point D coordinate (Dzb1 (Xuhao, 1), Dzb1 (Xuhao, 2)), two in theoretical profile of tooth point：Zuo Dian
(PointL (1), PointL (2)), right point (PointR (1), PointR (2)).
In example, actual profile of tooth centering point is in the right flank of tooth, thus must integral-rotation actual profile of tooth a angle so that D point and reason
Overlap by the right point of profile of tooth.And all point coordinates values of actual profile of tooth have stored in RectDzb1 () array.
So far, first tooth right flank of tooth centering of gear under test, centering point is D point.Actual profile of tooth each point at this moment
Coordinate value has been shifted in RectDzb1 () array, next does two step computings on this basis：First step computing：Will
RectDzb1 () array rotate respectively Z 3/Z*360 ° and Z 3/Z*2*360 ° (" " symbol represents division in VisualBasic
Round fractional part) new data is respectively stored into Dzb2 () array and Dzb3 () array.General form of gear tooth detection selects uniform
Three teeth, the left and right flank of tooth of each tooth will do profile error detection, so rotating twice here, but Dzb2 () array and
Dzb3 () array is not and that is theoretical profile of tooth centering does not have centering point, simply near theory profile of tooth, subsequent calculations
Also centering is needed, the second step computing in the same manner of concrete aligning method before profile error.
Second step computing：Because the right flank of tooth centering of current first tooth for this example, but the left flank of tooth is
, there is not centering point, remove now the left flank of tooth of centering first tooth in overall close theory profile of tooth：
Aligning method：Left point (PointL (1), PointL (2)) is the point in above-mentioned theory profile of tooth left flank of tooth profile of tooth, and should
Point close to reference circle and between SAP to EAP, (choose and see the 3rd to do the circle as 1mm for the radius centered on this point by radius size
Divide (4th) article of explanation) because now actual profile of tooth is very close to theoretical profile of tooth, and this circular diameter is more than the step-length of collection point, institute
Fallen in this circle with having partial dot in RectDzb1 (), these coordinate values put extracted successively and leaves in con () array,
Then the element number S in con () array it is known that select again S 2 (" " symbol represents division round numbers in VisualBasic
Part) individual point, it is B (con (S 2,1) that this point is denoted as B point coordinates value, con (S 2,2)).B point is actual profile of tooth RectDzb1 ()
In point, with B point to origin of coordinates O apart from BO as radius, calculate the left flank of tooth of theoretical profile of tooth be located at this circle on left point
(PointL1 (1,1) PointL1 (1,2)), is calculated B point and is rotated to this left point (PointL1 (1,1) centered on initial point
PointL1 (1,2)) angle b, now by RectDzb1 () point group integral-rotation b angle (B point also together rotation and with left point
(PointL1 (1,1) PointL1 (1,2)) overlaps) obtain new point group and be stored in RectDzb12 () array, after the rotation of B point
It is denoted as C point, the centering point of the left flank of tooth of as first tooth of C point.
So far, first tooth left flank of tooth centering of gear under test, centering point is C point.Followed by Dzb2 () array
Respectively obtain flank of tooth centering array and centering point about second, third tooth with Dzb3 () array.
(3) in actual profile of tooth tested measuring point selection
The flank profil (left and right flank of tooth of respectively uniform three teeth) having the actual scanning of six centerings till now waits
Detection profile error, the selection of the tested measuring point of each flank of tooth in the same manner, so as a example this sentences the left flank of tooth of first tooth, that is,
RectDzb12 () storage of array the actual profile of tooth of the left flank of tooth of the first tooth centering, and centering point is C point.Next select
Take the point group that in actual profile of tooth, the left flank of tooth of the first tooth is detected.(points selecting here are effectively gradually to be opened according to SAP and EAP
Line length and sampling site step-length are determining) this example chooses at 100 points.
Choosing method：100 on the theoretical left flank of tooth are had in " left flank of tooth mathematical point () " array before having obtained
Individual mathematical point.It is directed to each point from the 1st mathematical point to the 100th mathematical point and do computing same as follows：
Algorithm：Be denoted as E point, (radius size is chosen and seen Part III to do the circle as 1mm for the radius centered on E point at 1st point
Article (4), illustrate) because now actual profile of tooth is very close to theoretical profile of tooth, and this circular diameter 1mm is more than the step-length of collection point,
So have partial dot in RectDzb12 () falling in this circle, these coordinate values put being extracted successively and leaves con12 () number in
In group, then the element number T in con12 () array it is known that select again T 2 (" " symbol represents in VisualBasic and removes
Method rounds fractional part) individual point, it is F (con12 (T 2,1), con12 (T 2,2)) that this point is denoted as F point coordinates value.Define a number
100 two bit elements can be stored in group Dcd (1to100,1to2), F point is put in Dcd (1,1) and Dcd (1,2).With such
Push away, have 100 points in first after last centering left flank of tooth profile of tooth RectDzb12 () and be determined and stored in tested measuring point group
In Dcd ().
So far, we have obtained the left and right centering profile of tooth of three teeth in actual profile of tooth (i.e.：6 groups of centering profile of tooth point groups and 6
Individual centering point)
(4) calculating (referring to Fig. 2, the definition of profile error is referring to Fig. 3 for the calculating of profile error) of profile error
Obtained by involute property：A releases Q, known to Q point coordinates；
Known to AQ length
Obtained by involute property：Centering point D releases P, then known to P point coordinates；
There is involute property：BQ=PD+PQ (arc length)；
AB=AQ-BQ
(5) process of result of calculation, output
6 groups of profile errors CXl (), CXl2 (), CXl3 (), CXr (), CXr2 (), CXr3 () regard as in two-dimensional array respectively
Wherein one-dimensional Y value, X value represents increment on radius (because the increment on the basis for selecting radius of theoretical 100 points of profile of tooth comes
Calculate.The length of run of involute profile can also be converted to, the selection so requiring theoretical 100 points of profile of tooth will be according to theory
Length of run is choosing), finally use least square method to solve the average flank profil line of profile error.
Make interface output profile of tooth error curve,
Whether qualified evaluate this tooth-formation of gear finally according to detected accuracy of gear class requirement and this profile error value.
(6) automatically draw in theoretical, actual centering profile of tooth AutoCAD, partial enlargement is analyzed
VisualBasic6.0 loads AutoCAD function library, automatic running AutoCAD program, transfers the profile of tooth after centering
(theoretical profile of tooth is only with respect to Y-axis here for point group (the profile of tooth point group after 6 centerings transfers analysis respectively) and theoretical profile of tooth point group
A symmetrical tooth, need to be by it with regard to Z tooth of initial point (0,0) array) it is plotted in the ModelSpace of "current" model space.Draw
When, point-to-point transmission straight line AcadLine connects.
Correlative code：
Finally give theory, the CAD X-Y scheme of actual centering profile of tooth and can partial enlargement analyze.
3. declaratives
The scanning step of (1) three coordinate and the selection of sweep speed：
It is little that step-length is little, speed then gathers slowly points are many and probe steady is beated, and so more can accurately reflect reality
Border profile of tooth.Advise that three coordinate step-lengths choose 0.2mm～0.1mm.Sweep speed is come according to gear size (parameter such as modulus, external diameter)
Fixed.If the use of other sampling site equipment being also same thought.
(2) first groups of theoretical profiles of tooth take the flank of tooth each 100 points in left and right from involute starting point to involute terminating point
The determination that " first group of theoretical profile of tooth " counts is that involute rises in order to obtain " tested measuring point group " in actual profile of tooth
That length between initial point SAP to involute terminating point EAP is to determine it is known that sampling site step-length, be also known that EAP～SAP it
Between collection points Q, so " first group theoretical profile of tooth " as long as points less than or close to Q, tooth then occurs if greater than Q
There is the equal situation of some consecutive values, if being computed repeatedly because doing in actual profile of tooth tested measuring point group in shape error amount
Output.
(3), when determining centering point, need first to determine a theoretical circle, this theoretical circle necessarily be between SAP～EAP,
Each of algorithm whole process centering point all must be on the basis of the point on the flank of tooth about the theoretical profile of tooth on this circle that falls.This
In example, reference circle is in the range of SAP～EAP, if reference circle, not in the range of SAP～EAP, selects in the range of SAP～EAP
Arbitrarily theoretical circle is all achievable.
(4) all in this algorithm be related to the circle of 1mm " radius be ", algorithm idea is all the same, and theoretical and actual profile of tooth is non-
Very close to it is therefore an objective to the point in the range of 1mm around on the basis of capture centre point, and the determination of " 1mm " radius value and sampling site step-length
Relevant, general radius value chooses 5～8 times of step-lengths.Avoid the point capturing in adjacent teeth because radius value is excessive.
Claims (3)
1. a kind of tooth profile measurement method it is characterised in that：As follows including step：
1】The profile of tooth that theorizes database；
2】Obtain gear under test flank profil data；
2.1] determine the flank profil cartesian coordinate system of gear under test, the initial point of described coordinate system needed the central axis of gear；
2.2] pass through scanner scanning gear under test, sweep limits is one week in the range of the facewidth；
2.3] coordinate data obtaining after scanning, first removes probe radius value, then obtains gear under test practical tooth coordinate points；
3】Profile of tooth centering is carried out by comparing；
3.1] first it is defined by theoretical profile of tooth reference circle, find in actual profile of tooth point group radius closest to the point of reference radius, if
For D point；
3.2] by D point place, radius of circle is defined again, calculates the point on the left flank of tooth that theoretical profile of tooth falls on D point place is round and right tooth
Point on face；Described D point is the centering point of any one tooth one side of gear under test；
3.3], after D point determines, find out step 3.2] the centering point of described any tooth another side, it is set to C point；
4】Repeat step 3】Several times, some centering points are found out；
5】By step 1】The coordinate of the actual profile of tooth of some groups of the theoretical profile of tooth database acquisition measuring point to be checked set up；
6】Arbitrfary point is set on gear under test involute as A, by cartesian coordinate initial point and D point coordinates, calculate profile of tooth by mistake
Difference.
2. tooth profile measurement method according to claim 1 it is characterised in that：Described step 3.1] reference circle is in SAP～EAP
Between, if reference circle is not between SAP～EAP, select any radius of circle between SAP～EAP.
3. tooth profile measurement method according to claim 1 it is characterised in that：Described step 1】Middle theory profile of tooth database leads to
Cross VisualBasic6.0 and load the foundation of AutoCAD and Microsoft Excel built-in function parameter.
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Application publication date: 20140820 Assignee: Shaanxi French Walker Gear Co., Ltd. Assignor: Shaanxi Fashite Gear Co., Ltd. Contract record no.: 2018610000018 Denomination of invention: Tooth profile measuring method Granted publication date: 20170215 License type: Common License Record date: 20180604 |