CN105069271B - A kind of tooth surfaces of bevel gears mismachining tolerance modification method - Google Patents
A kind of tooth surfaces of bevel gears mismachining tolerance modification method Download PDFInfo
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Abstract
The present invention relates to a kind of tooth surfaces of bevel gears mismachining tolerance modification method, it comprises the following steps：Discretization tooth surfaces of bevel gears, obtains representing the flank of tooth point of the tooth surface shape feature, calculates flank of tooth point theory three-dimensional coordinate and flank of tooth normal vector；Calculate flank of tooth point information, the measurement actual three-dimensional coordinate of flank of tooth point and flank of tooth normal vector；Flank of tooth point actual measurement Gear shape process error is calculated, actual measurement Gear shape process error vector is set up；Small sample perturbations are applied to each machined parameters respectively, the Gear shape process error that each machined parameters small sample perturbations are produced at flank of tooth point is calculated, each machined parameters small sample perturbations Gear shape process error vector and each machined parameters sensitivity coefficient vector is set up；Carry out N wheel machined parameters selections, determine that n-th adjusts variable, calculate theoretical residual error, if meeting error correction requirement, or N reaches the upper limit, this N number of machined parameters is then taken as first to linear regression coeffficient when n-th adjustment variable, their combinations and carries out error correction as error transfer factor amount, otherwise proceeds the selection of next round machined parameters.
Description
Technical field
The present invention relates to a kind of machining error modification method, more particularly to a kind of tooth surfaces of bevel gears mismachining tolerance amendment
Method.
Background technology
Bevel gear (mainly including spiral bevel gear and hypoid gear) is the communications and transportation such as automobile, ship, aviation neck
Important drive disk assembly in domain, is also one of main source of vibration noise in transmission system.The performance of bevel gear and its flank of tooth
Precision is closely related, but the alignment error of the elastic deformation due to lathe kinematic error itself, lathe and cutter, cutter and workpiece
And the presence of the factor such as thermal deformation, inevitably there is certain mistake between the flank of tooth and the design flank of tooth that actual processing goes out
Difference.By ensure institute the processing flank of tooth and design the flank of tooth uniformity, generally require and processing suitably adjusted according to the size of tooth surface error
The Machine-settings of the flank of tooth, to realize the compensation to Gear shape process error.Existing Machine-settings adjustment amount calculating side
Method is all based on greatly the sensitivity coefficient matrix between machined parameters and tooth surface error, calculates the machined parameters obtained needed for error correction
Adjustment amount.The problem of this kind of method is present is often to be adjusted directly against all machined parameters, although in theoretical calculation and
It is preferable to the computational valid times of some examples fruit, but be not suitable for actual processing and use.This mainly due to Machine-settings it
Between mutually exist complexity coupling, for some machined parameters, when other machined parameters change, the ginseng
Number can also change for the sensitivity of tooth surface error.And existing method have ignored the influence that this coupled relation is produced, recognize
It is fixed for the sensitivity of tooth surface error for each machined parameters.Therefore when multiple machined parameters are adjusted simultaneously, especially
When it is that some parameter adjustment amounts are larger, actual Adjustment effect greatly differs from each other with predicting the outcome, and causes the amendment of mistake.Therefore
It is general in Practical Project that only 2-3 machined parameters are adjusted, and how to choose adjusting parameter then turns into the pass of error correction
Key, the research currently for this respect is still rare.
The content of the invention
In view of the above-mentioned problems, it is an object of the invention to provide a kind of tooth surfaces of bevel gears mismachining tolerance modification method, it is based on
Linear regression analysis can select the Machine-settings for needing most adjustment, and calculate adjustment amount.
To achieve the above object, the present invention takes following technical scheme：A kind of tooth surfaces of bevel gears mismachining tolerance modification method,
It comprises the following steps：
1) sliding-model control is carried out to a lateral tooth flank of the bevel gear gear teeth, obtains a series of expression tooth surface shape features
Flank of tooth point, calculates theory three-dimensional coordinate and flank of tooth normal vector of these flank of tooth points under gear coordinate system；
2) a kind of measuring apparatus is selected, flank of tooth point information of the flank of tooth point under the measuring apparatus is calculated, is believed according to flank of tooth point
Breath, the actual three-dimensional coordinate and flank of tooth normal vector of flank of tooth point are measured using measuring apparatus；
3) according to the theory three-dimensional coordinate and flank of tooth normal vector of flank of tooth point and actual three-dimensional coordinate and flank of tooth normal vector, calculate
The actual measurement Gear shape process error of flank of tooth point, sets up actual measurement Gear shape process error vector；
4) small sample perturbations are applied respectively to each machined parameters of bevel gear successively, calculates each machined parameters small sample perturbations in tooth
The Gear shape process error produced at millet cake, sets up the small sample perturbations Gear shape process error vector of each machined parameters, and further build
Found the sensitivity coefficient vector of each machined parameters；
5) first round machined parameters selection is carried out, first adjustment variable is determined：Successively using each machined parameters as variable,
Simple linear regression analysis is carried out to machined parameters sensitivity coefficient vector sum actual measurement Gear shape process error vector, the processing is solved
The linear regression coeffficient of parameter, and calculate the coefficient of determination of the machined parameters；The coefficient of determination of each machined parameters is contrasted, depends on fixed
The maximum machined parameters of coefficient are used as first adjustment variable；Theoretical residual error now is calculated, will if meeting error correction
Ask, then take the maximum machined parameters of the coefficient of determination as adjustment variable, the machined parameters linear regression coeffficient as error
Adjustment amount carries out error correction；If theoretical residual error is unsatisfactory for error correction requirement, proceed next step；
6) carry out second and take turns machined parameters selection, determine second adjustment variable：Successively will except first adjustment variable it
Outer remaining machined parameters and as first adjustment variable machined parameters together as variable, to their sensitivity coefficient to
The progress binary linear regression analysis of Gear shape process error vector is measured and surveyed, the first adjustment variable is solved and is respectively processed with residue respectively
The linear regression coeffficient of parameter combination, and calculate the coefficient of determination of each machined parameters combination；Contrast determining for each machined parameters combination
Determine coefficient, the remaining machined parameters in machined parameters combination when taking the coefficient of determination maximum are used as second adjustment variable；Calculate
Theoretical residual error now, if meeting error correction requirement, takes machined parameters combination to become as first, second adjustment
Linear regression coeffficient when amount, their combinations is used as error transfer factor amount progress error correction；If theoretical residual error is unsatisfactory for missing
Difference amendment is required, then proceeds next step；
7) N wheel machined parameters selections are carried out, determine that n-th adjusts variable：Successively will be in addition to first N-1 adjusts variable
Remaining machined parameters and as first N-1 adjustment variable N-1 machined parameters together as variable, to their sensitive system
Number vector and actual measurement tooth surface error vector progress N member linear regression analyses, N-1 adjustment variable respectively adds with remaining respectively before solving
The linear regression coeffficient of work parameter combination, and calculate the coefficient of determination of each machined parameters combination；Contrast each machined parameters combination
The coefficient of determination, that remaining machined parameters when taking the coefficient of determination maximum are used as n-th adjustment variable；Calculate now theoretical residual
Remaining error, if meeting error correction requirement, it is determined that take this N number of machined parameters as first to n-th and adjust variable, their groups
Linear regression coeffficient during conjunction is used as error transfer factor amount progress error correction；Will if theoretical residual error is unsatisfactory for error correction
Ask, but be selected as N number of machined parameters of adjustment variable and reached the adjustment variables number upper limit, then equally take this N number of processing ginseng
Linear regression coeffficient when number adjusts variable, their combinations as first to n-th is as error transfer factor amount progress error correction；
Otherwise the selection of next round machined parameters is proceeded.
The step 1) in flank of tooth discretization and calculate the flank of tooth point theory three-dimensional coordinate and flank of tooth method under gear coordinate system
Vector comprises the following steps：1. a number of grid is evenly dividing on the flank of tooth, grid vertex is flank of tooth point；2. by the flank of tooth
Spot projection is on the shaft section of bevel gear, as the subpoint on shaft section；3. the shaft staggered point using bevel gear is the origin of coordinates,
X-axis is Gear axis direction, and Y-axis is gear radial direction, and planar two dimensional coordinate system is set up in shaft section, calculates subpoint and exists
Coordinate under the two-dimensional coordinate system；4. according to the two-dimensional coordinate of subpoint, the flank of tooth of flank of tooth point corresponding with the subpoint is calculated
Parameter；5. the tooth surface parameters of flank of tooth point are substituted into the tooth surface equation of the bevel gear, reason of the flank of tooth point under gear coordinate system is calculated
By three-dimensional coordinate and flank of tooth normal vector.
The step 5. in the tooth surface equation of bevel gear be：
In formula, θ andFor tooth surface parameters, r represents three-dimensional coordinate of the flank of tooth point under gear coordinate system, and n represents flank of tooth point
Flank of tooth normal vector under gear coordinate system.
The step 3) calculating flank of tooth point surveys Gear shape process error and actual measurement Gear shape process error vector calculation formula is：
In formula, riWithThe theoretical and actual three-dimensional coordinate of respectively i-th flank of tooth point；niFor the reason of i-th of flank of tooth point
By flank of tooth normal vector, eiFor the actual measurement Gear shape process error of i-th of flank of tooth point, e for institute's geared surface point on the flank of tooth the actual measurement flank of tooth
Mismachining tolerance vector.
The step 4) in machined parameters small sample perturbations the Gear shape process error and machined parameters that are produced at flank of tooth point it is micro-
The calculation formula of the Gear shape process error vector of microvariations is：
In formula, ζjRepresent the initial value of j-th of machined parameters, Δ ζjRepresent the small sample perturbations of j-th of machined parameters, ri
(ζj) represent i-th of flank of tooth point theory three-dimensional coordinate, ri(ζj+Δζj) represent the three-dimensional coordinate after i-th of flank of tooth point disturbance, ni
The theoretical flank of tooth normal vector of i-th of flank of tooth point is represented,Represent that i-th of flank of tooth point during small sample perturbations occurs for j-th of machined parameters
The Gear shape process error of upper generation, εjRepresent that the Gear shape process that small sample perturbations when institute geared surface point occurs for j-th of machined parameters is missed
Difference vector；
Each machined parameters sensitivity coefficient vector calculation formula be：
In formula, s (ζj) represent machined parameters ζjSensitivity coefficient vector between Gear shape process error.
The step 5) in the mathematical modeling of simple linear regression analysis be：
find αj
min(||e+αjs(ζj)||2)
In formula, αjRepresent the linear regression coeffficient of j-th of machined parameters, that is, machined parameters ζjAdjustment amount.
The step 6) in binary linear regression analyze mathematical modeling be：
find αf, αj
min(||e+αfs(ζf)+αjs(ζj)||2)
s.t.j≠f
In formula, ζfTo be used as the machined parameters of first adjustment variable, αfAnd αjFor linear regression coeffficient.
The tooth top of the Edge Distance tooth surfaces of bevel gears of grid, tooth root and size end edge circle 3-5mm on the flank of tooth.
The N is not more than 3；The type and quantity of the machined parameters and the type and processing mode of gear match.
The step 4) in machined parameters apply small sample perturbations refer on the basis of the machined parameters initial value increase
One fractional increments, wherein, for representing that the machined parameters increment of length or distance takes 0.01mm, the processing for representing angle
Parameter increase takes 0.01rad, and 0.001 is taken for nondimensional machined parameters increment.
The present invention is due to taking above technical scheme, and it has advantages below：1st, the present invention proposes a kind of bevel gear teeth
Face mismachining tolerance modification method, can choose most related according to the distribution situation of actual Gear shape process error based on regression analysis
Machined parameters as adjustment variable, the selection of machined parameters provides foundation during for tooth surface error amendment；2nd, the present invention is adopted
Method can reduce the adjustment amount of each machined parameters, and can reach while the less machined parameters of selection are adjusted
To preferable correction effect, solve existing computational methods and be adjusted using whole machined parameters, each machined parameters adjustment amount
It is big and the problem of be likely to occur error correction；3rd, the method applied in the present invention is based on reliable theoretical direction, principle it is simple and
Realization is easily programmed, error correction problem in all kinds of bevel gear making manufacturing processes is the composite can be widely applied to.
Brief description of the drawings
Fig. 1 is the implementation process flow chart of the present invention；
Fig. 2 is flank of tooth discretization schematic diagram.
Embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
As shown in figure 1, the present invention proposes a kind of tooth surfaces of bevel gears mismachining tolerance modification method, it comprises the following steps：
1) lateral tooth flank of a gear teeth for selection actual processing bevel gear, carries out sliding-model control to the flank of tooth, that is, chooses
A number of flank of tooth point represents tooth surface shape feature on the flank of tooth, and calculates selected flank of tooth point under gear coordinate system
Theory three-dimensional coordinate and flank of tooth normal vector.
Wherein, the origin of coordinates of gear coordinate system is in the shaft staggered point of bevel gear, and X-axis is Gear axis direction, Y-axis and Z
Axle is gear radial direction.
Flank of tooth discretization and selected theory three-dimensional coordinate and flank of tooth normal vector of the flank of tooth point under gear coordinate system of calculating
Specific method comprise the following steps：
1. a number of quadrilateral mesh is evenly dividing on the flank of tooth of selection, the summit of grid is being used for for selection
Represent the flank of tooth point of tooth surface shape feature.
2. by the flank of tooth spot projection of selection to the shaft section of bevel gear, as the subpoint on shaft section；
3. the shaft staggered point using bevel gear is the origin of coordinates, and X-axis is Gear axis direction, and Y-axis is gear radial direction,
Planar two dimensional coordinate system is set up in shaft section, coordinate of the subpoint under the two-dimensional coordinate system is calculated；
4. according to the two-dimensional coordinate of subpoint, the tooth surface parameters of flank of tooth point corresponding with the subpoint are calculated；
The theory three-dimensional coordinate of calculating flank of tooth point and the equation group of flank of tooth normal vector are：
In formula, xiAnd yiThe two-dimensional coordinate of subpoint corresponding with i-th of flank of tooth point is represented, r represents that flank of tooth point is sat in gear
Three-dimensional coordinate under mark system, p is Gear axis direction vector, i.e. X-direction vector；The equation can be solved by binary iteration
Group, obtains the tooth surface parameters of flank of tooth point.
5. the tooth surface parameters of obtained flank of tooth point are substituted into the tooth surface equation of the bevel gear, you can obtain flank of tooth point in gear
Theory three-dimensional coordinate and flank of tooth normal vector under coordinate system.
The tooth surface equation of the bevel gear is：
In formula, θ andFor tooth surface parameters, n represents flank of tooth normal vector of the flank of tooth point under gear coordinate system.
2) a kind of measuring apparatus is selected, by step 1) theory three-dimensional coordinate under gear coordinate system of obtained flank of tooth point and
Flank of tooth normal vector is transformed under the measurement coordinate system of the measuring apparatus, is obtained theory three-dimensional of the flank of tooth point under measurement coordinate system and is sat
Mark and flank of tooth normal vector, referred to as flank of tooth point information；According to flank of tooth point information, flank of tooth point is measured in measurement coordinate using measuring apparatus
Actual three-dimensional coordinate and flank of tooth normal vector under system.
Wherein, measuring apparatus can be gear measuring center or three-coordinates measuring machine, and measurement coordinate system is set according to measurement
Standby type and model are determined.
3) according to step 2) the theory three-dimensional coordinate and flank of tooth normal vector and reality of obtained flank of tooth point under measurement coordinate system
Border three-dimensional coordinate and flank of tooth normal vector, calculate the actual measurement Gear shape process error for obtaining flank of tooth point, so as to set up actual measurement Gear shape process
Error vector.
Gear shape process error is defined as along in the theoretical normal orientation of flank of tooth point, between true tooth and the theoretical flank of tooth away from
From therefore, the calculation formula of Gear shape process error is：
In formula, riWithThe theoretical and actual three-dimensional coordinate of respectively i-th flank of tooth point；niFor the reason of i-th of flank of tooth point
By flank of tooth normal vector, eiFor the actual measurement Gear shape process error of i-th of flank of tooth point, e for institute's geared surface point on the flank of tooth the actual measurement flank of tooth
Mismachining tolerance vector.
4) increase a fractional increments on the basis of a bevel gear making initial parameter value, be referred to as to the machined parameters
Apply small sample perturbations；Only a machined parameters are applied with small sample perturbations, and other machined parameters keep constant, with now all cones
Gear Processing parameter can calculate the D coordinates value after the disturbance of flank of tooth point, and D coordinates value is not with disturbing after the disturbance of flank of tooth point
The error between theory three-dimensional coordinate value when dynamic, is the Gear shape process mistake that machined parameters disturbance is produced at flank of tooth point
Difference；The Gear shape process error disturbed according to the machined parameters, you can set up sensitive system of the machined parameters to Gear shape process error
Number vector.
Successively each machined parameters are applied with small sample perturbations respectively, each machined parameters small sample perturbations is calculated and is produced at flank of tooth point
Gear shape process error, set up the small sample perturbations Gear shape process error vector of each machined parameters, and further set up it is each processing ginseng
Several sensitivity coefficient vectors.
According to Gear shape process error calculation formula, the Gear shape process error meter of machined parameters small sample perturbations generation can be obtained
Calculating formula is：
In formula, ζjRepresent the initial value of j-th of machined parameters, Δ ζjRepresent the small sample perturbations of j-th of machined parameters, ri
(ζj) represent i-th of flank of tooth point theory three-dimensional coordinate, ri(ζj+Δζj) represent the three-dimensional coordinate after i-th of flank of tooth point disturbance, ni
The theoretical flank of tooth normal vector of i-th of flank of tooth point is represented,Represent that i-th of flank of tooth point during small sample perturbations occurs for j-th of machined parameters
The Gear shape process error of upper generation, εjRepresent that the Gear shape process that small sample perturbations when institute geared surface point occurs for j-th of machined parameters is missed
Difference vector.
Between each machined parameters and Gear shape process error sensitivity coefficient vector calculation formula be：
In formula, s (ζj) represent machined parameters ζjSensitivity coefficient vector between Gear shape process error.
For representing that the machined parameters increment of length or distance can take 0.01mm, for representing that the machined parameters of angle increase
Amount can take 0.01rad, and 0.001 can be taken for nondimensional machined parameters increment.
The type and quantity of bevel gear making parameter according to the type of gear and the difference of processing mode used not
Together, the relevant parameter of the cutter or emery wheel used in cutting gear is also included in machined parameters, to process the knife of hypoid gear
Incline exemplified by half spreading out principle, machined parameters when steamboat is processed include：Horizontal wheels position, workhead offset, Installing machine tool root angle, bed
Position, radial, angular cutter spacing angle, tilt child's hair twisted in a knot-childhood, swivel angle, rolling ratio, cutter radius and totally 11, tool-tooth profile angle.
5) first round machined parameters selection is carried out, first adjustment variable is determined：Successively using each machined parameters as variable,
To step 4) the obtained machined parameters sensitivity coefficient vector sum step 3) obtained actual measurement Gear shape process error vector carries out one
First linear regression analysis, solved using least square approximation mode (only as example, however it is not limited to this) lines of the machined parameters
Property regression coefficient, and calculate the coefficient of determination of the machined parameters；The coefficient of determination of each machined parameters is contrasted, takes the coefficient of determination maximum
Machined parameters be used as first adjustment variable.Theoretical residual error now is calculated, if meeting error correction requirement, it is determined that
Take the maximum machined parameters of the coefficient of determination as adjustment variable, the machined parameters linear regression coeffficient as error transfer factor amount
Carry out error correction；If theoretical residual error is unsatisfactory for error correction requirement, proceed next step.
The mathematical modeling of simple linear regression analysis is expressed as：
find αj
min(||e+αjs(ζj)||2) (6)
In formula, αjRepresent the linear regression coeffficient of j-th of machined parameters, that is, machined parameters ζjAdjustment amount.
Error correction requirement can be set according to actual needs, such as require that the maximum residual error of flank of tooth point is given less than certain
Amount, or require that the residual error root-mean-square value of institute's geared surface point is less than certain specified rate.
6) carry out second and take turns machined parameters selection, determine second adjustment variable：Successively will except first adjustment variable it
Outer remaining machined parameters and step 5) determine as first adjustment variable machined parameters together as variable, to them
Sensitivity coefficient vector sum actual measurement Gear shape process error vector carry out binary linear regression analysis, solve first and adjust variable difference
The linear regression coeffficient combined with remaining each machined parameters, and calculate the coefficient of determination of each machined parameters combination；Each processing of contrast
The coefficient of determination of parameter combination, the remaining machined parameters in machined parameters combination when taking the coefficient of determination maximum are used as second tune
Integer variable.Theoretical residual error now is calculated, if meeting error correction requirement, it is determined that take step 5) machined parameters that determine
Linear regression coeffficient when the second adjustment variable, their combinations is used as the machined parameters of the first adjustment variable, this determination
Error correction is carried out as error transfer factor amount；If theoretical residual error is unsatisfactory for error correction requirement, proceed next step.
The mathematical modeling of binary linear regression analysis is expressed as：
findαf, αj
min(||e+αfs(ζf)+αjs(ζj)||2) (7)
s.t.j≠f
In formula, ζfTo be used as the machined parameters of first adjustment variable, αfAnd αjFor linear regression coeffficient.
7) N wheel machined parameters selections are carried out, determine that n-th adjusts variable：Successively will be in addition to first N-1 adjusts variable
Remaining machined parameters and as first N-1 adjustment variable N-1 machined parameters together as variable, to their sensitive system
Number vector and actual measurement tooth surface error vector progress N member linear regression analyses, N-1 adjustment variable respectively adds with remaining respectively before solving
The linear regression coeffficient of work parameter combination, and calculate the coefficient of determination of each machined parameters combination；Contrast each machined parameters combination
The coefficient of determination, that remaining machined parameters when taking the coefficient of determination maximum are used as n-th adjustment variable.Calculate now theoretical residual
Remaining error, if meeting error correction requirement, it is determined that take this N number of machined parameters as first to n-th and adjust variable, their groups
Linear regression coeffficient during conjunction is used as error transfer factor amount progress error correction；Will if theoretical residual error is unsatisfactory for error correction
Ask, but be selected as N number of machined parameters of adjustment variable and reached the adjustment variables number upper limit, then equally take this N number of processing ginseng
Linear regression coeffficient when number adjusts variable, their combinations as first to n-th is as error transfer factor amount progress error correction；
Otherwise the selection of next round machined parameters is proceeded.
In above-described embodiment, the tooth top of the Edge Distance tooth surfaces of bevel gears of quadrilateral mesh, tooth root and big small end on the flank of tooth
Border 3-5mm.
In above-described embodiment, to eliminate some random errors, for 3-5 flank of tooth of a gear general measure, by gained
Tooth surface error is used as final measurement after carrying out averagely.
In above-described embodiment, be elected to be adjustment variable the machined parameters number upper limit according to actual error amendment it needs to be determined that,
For ordinary circumstance, it is proposed that the selected machined parameters number upper limit is less than or equal to 3 no more than 3, i.e. N.
The present invention can be widely applied to the Gear shape process error correction of various bevel gears.Below with applied to a accurate double
The Gear shape process error correction of curved surface gear steamboat concave surface, illustrates the application method of the present invention：
The hypoid gear is processed using slope knife half spread out method, and its basic parameter includes：
| Title | Numerical value | Title | Numerical value |
| Big tooth number | 37 | Small tooth number | 9 |
| Modulus | 11.49mm | The bull wheel face width of tooth | 61mm |
| Offset | 26mm | Crossed axis angle | 90° |
| Steamboat designs helical angle | 43.65° | Average pressure angle | 22.5° |
| Bull wheel pitch cone angle | 73.87° | Steamboat pitch cone angle | 15.99° |
The initial manufacture parameter of the hypoid gear steamboat concave surface includes：
| Machined parameters title | Machined parameters initial value |
| Angular cutter spacing/° | 60.3220 |
| Workhead offset/mm | 18.0000 |
| Horizontal wheels position/mm | 0.7360 |
| Installation root angle/° | -4.5273 |
| Radial/mm | 151.2363 |
| Rolling ratio | 5.4328 |
| Bed/mm | 14.1914 |
| Swivel angle/° | 151.1859 |
| Cutter tilt/° | -17.6359 |
| Nose radius/mm | 149.0029 |
| Tool-tooth profile angle/° | 20.0000 |
As shown in Fig. 2 selecting a lateral tooth flank of the hypoid gear steamboat concave surface, an edge is evenly dividing on the flank of tooth
Tooth length direction has 9 row, has the quadrilateral mesh of 5 rows along the high direction of tooth, amounts to and forms 45 mesh points, and this 45 grids are clicked through
Line number；Tooth top, tooth root and the size end edge circle 3-5mm of the grid Edge Distance flank of tooth.
45 mesh points are projected on the shaft section of the hypoid gear, as the subpoint on shaft section.
Shaft staggered point using the hypoid gear is the origin of coordinates, and X-axis is Gear axis direction, and Y-axis is gear radial direction
Direction, planar two dimensional coordinate system is set up in the shaft section of the hypoid gear, and each mesh point is determined by interpolation method
The two-dimensional coordinate of two-dimensional coordinate in shaft section two-dimensional coordinate system, i.e. subpoint.
According to the two-dimensional coordinate of each subpoint, equation group (1) is solved, the tooth surface parameters of each mesh point are calculated；By net
The tooth surface parameters of lattice point substitute into the tooth surface equation of the hypoid gear steamboat concave surface, solve these flank of tooth mesh points and are sat in gear
Theory three-dimensional coordinate and flank of tooth normal vector under mark system.
Gear measuring center is selected, three-dimensional coordinate of the flank of tooth mesh point under gear coordinate system and flank of tooth normal vector are changed
To under the measurement coordinate system of the gear measuring center, obtain theory three-dimensional coordinate of the flank of tooth mesh point under the measurement coordinate system and
Flank of tooth normal vector；Actual three-dimensional coordinate and flank of tooth normal direction of the mesh point under measurement coordinate system are measured using gear measuring center
Amount.
According to theory three-dimensional coordinate and flank of tooth normal vector and actual three-dimensional coordinate and tooth of the mesh point under measurement coordinate system
Face normal vector, calculates the actual measurement Gear shape process error for obtaining each mesh point；According to the numbering of 45 mesh points, the actual measurement tooth of gained
Face mismachining tolerance value is (wherein unit for μm)：
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
| 1 | 49.4 | 39.1 | 23.5 | 12.5 | 5.5 | -3.0 | -9.7 | -15.6 | -19.6 |
| 2 | 49.6 | 36.6 | 21.0 | 10.9 | 3.6 | -4.8 | -11.9 | -16.8 | -21.6 |
| 3 | 47.5 | 30.7 | 18.4 | 7.8 | 0.0 | -7.9 | -13.5 | -18.7 | -23.6 |
| 4 | 44.4 | 27.9 | 16.5 | 7.0 | -1.5 | -9.0 | -14.1 | -20.7 | -25.9 |
| 5 | 40.2 | 27.4 | 16.7 | 7.1 | -3.4 | -11.4 | -16.9 | -22.7 | -30.0 |
The actual measurement Gear shape process error of 45 mesh points is write as to the vector of one 45 × 1, as surveys Gear shape process and misses
Difference vector.
On the basis of the machined parameters initial value of the hypoid gear steamboat concave surface, micro- are applied to each machined parameters respectively
Microvariations, wherein, for representing that the machined parameters increment of length or distance can take 0.01mm, for representing that the processing of angle is joined
Number increment can take 0.01rad, and 0.001 can be taken for nondimensional machined parameters increment, every time only to a machined parameters
Apply disturbance, other machined parameters keep constant.
A certain machined parameters are applied after disturbance, the disturbance three-dimensional for calculating flank of tooth mesh point according to machined parameters now is sat
Mark, error when flank of tooth point disturbs three-dimensional coordinate and is undisturbed between theory three-dimensional coordinate is the tooth of machined parameters disturbance
Face mismachining tolerance；Further set up sensitivity coefficient vector of the machined parameters to Gear shape process error.
All machined parameters are applied successively and disturbed, the Gear shape process error of each machined parameters disturbance is calculated, and set up each
The sensitivity coefficient vector of machined parameters.
Setting error correction is required：For residual error, it is desirable to which the residual error maximum of mesh point is no more than 2 μm；
The upper limit of selection machined parameters is set as 3.
Carry out first round machined parameters selection：Successively using each machined parameters as variable, to each machined parameters sensitivity coefficient
Vector sum actual measurement Gear shape process error vector carries out simple linear regression analysis, solves the linear regression coeffficient of each machined parameters,
And calculate the coefficient of determination of each machined parameters；The coefficient of determination of each machined parameters is contrasted, the coefficient of determination of linear regression is drawn most
Big machined parameters are " beds ", and the coefficient of determination is 0.9572, therefore selection " bed " is used as first adjustment variable.Work as selection
" bed ", as adjustment variable, when its linear regression coeffficient is as adjustment amount, the theoretical residual error maximum of linear regression is
10.1 μm, it is unsatisfactory for requiring, it is therefore desirable to carry out the second wheel selection.
Carry out second and take turns machined parameters selection：Successively by the machined parameters in addition to " bed " and " bed " together as change
Amount, surveys Gear shape process error vector to their sensitivity coefficient vector sum and carries out binary linear regression analysis, solve " bed "
The linear regression coeffficient combined respectively with remaining each machined parameters, and calculate the coefficient of determination of each combination；Contrast each machined parameters
The coefficient of determination of combination, show that coefficient of determination when " radial " is combined with " bed " is maximum, the coefficient of determination now is
0.9951, therefore selection " radial " is used as second adjustment variable.First adjustment variable, " radial direction are used as using " bed "
Cutter spacing " is as second adjustment variable, and linear regression coeffficient when they are combined is used as adjustment amount, theoretical residual error now
Maximum be 3.4 μm, be still unsatisfactory for require, it is therefore desirable to carry out third round selection.
Carry out third round machined parameters selection：Successively by the machined parameters in addition to " bed " and " radial " and " bed
Position " and " radial " survey Gear shape process error vector to their sensitivity coefficient vector sum and carry out three together as variable
First linear regression analysis, solves the linear regression coeffficient that " bed " and " radial " is combined with remaining each machined parameters respectively,
And calculate the coefficient of determination of each combination；Contrast the coefficient of determination of each machined parameters combination, draw " cutter tilt " and " bed " and
Coefficient of determination when " radial " is combined is maximum, and the coefficient of determination now is 0.9955, therefore selection " cutter tilt " is used as the
Three adjustment variables.Second adjustment variable, " cutter tilt " are used as using " bed " as first adjustment variable, " radial "
As the 3rd adjustment variable, linear regression coeffficient when they are combined is as adjustment amount, and theoretical residual error now is most
Big value is 3.6 μm, is still unsatisfactory for requiring；But selected machined parameters quantity has reached the upper limit, therefore no longer carry out next
Wheel selection.
Final choice " bed ", " radial " and " cutter tilt " is as adjustment variable, linear regression when they combine
Coefficient is 0.2951, -1.9655 and -0.0150 respectively, thus three machined parameters adjustment amount be respectively 0.2951mm, -
1.9655mm and -0.0150rad.Gear is re-worked using the machined parameters after adjustment and detects that the revised actual flank of tooth adds
Work error is as a result following (unit μm)：
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
| 1 | -4.6 | -0.7 | -4.2 | -3.2 | -1.9 | -0.2 | -0.9 | -2.5 | -2.5 |
| 2 | -3.9 | -4.9 | -4.3 | -2.2 | 0.4 | 1.4 | 1.2 | 0.2 | -0.7 |
| 3 | -3.5 | -5.9 | -4.4 | -2.7 | 0 | 0.3 | 1.5 | 2.4 | 0.7 |
| 4 | -7.6 | -5.9 | -3.2 | -0.8 | 0.7 | 1.7 | 4.5 | 4.5 | 2.6 |
| 5 | -7 | -2.6 | -0.8 | 1.7 | 2.2 | 3.9 | 5.4 | 5.4 | 1.8 |
It can be seen that, revised actual Gear shape process error has reached preferable correction effect within 10 μm.
The various embodiments described above are merely to illustrate the present invention, wherein the structure of each part, set location and its connected mode etc.
It can all be varied from, every equivalents carried out on the basis of technical solution of the present invention and improvement should not be arranged
In addition in protection scope of the present invention.
Claims (10)
1. a kind of tooth surfaces of bevel gears mismachining tolerance modification method, it comprises the following steps：
1) sliding-model control is carried out to a lateral tooth flank of the bevel gear gear teeth, obtains a series of flank of tooth of expression tooth surface shape features
Point, calculates theory three-dimensional coordinate and flank of tooth normal vector of these flank of tooth points under gear coordinate system；
2) a kind of measuring apparatus is selected, flank of tooth point information of the flank of tooth point under the measuring apparatus is calculated, according to flank of tooth point information, adopts
The actual three-dimensional coordinate and flank of tooth normal vector of flank of tooth point are measured with measuring apparatus；
3) according to the theory three-dimensional coordinate and flank of tooth normal vector of flank of tooth point and actual three-dimensional coordinate and flank of tooth normal vector, the flank of tooth is calculated
The actual measurement Gear shape process error of point, sets up actual measurement Gear shape process error vector；
4) small sample perturbations are applied respectively to each machined parameters of bevel gear successively, calculates each machined parameters small sample perturbations in flank of tooth point
Locate the Gear shape process error produced, set up the small sample perturbations Gear shape process error vector of each machined parameters, and further set up each
The sensitivity coefficient vector of machined parameters；
5) first round machined parameters selection is carried out, first adjustment variable is determined：Successively using each machined parameters as variable, to this
Machined parameters sensitivity coefficient vector sum actual measurement Gear shape process error vector carries out simple linear regression analysis, solves the machined parameters
Linear regression coeffficient, and calculate the coefficient of determination of the machined parameters；The coefficient of determination of each machined parameters is contrasted, the coefficient of determination is taken
Maximum machined parameters are used as first adjustment variable；Theoretical residual error now is calculated, if meeting error correction requirement,
Take the maximum machined parameters of the coefficient of determination as adjustment variable, the machined parameters linear regression coeffficient as error transfer factor amount
Carry out error correction；If theoretical residual error is unsatisfactory for error correction requirement, proceed next step；
6) carry out second and take turns machined parameters selection, determine second adjustment variable：Successively by addition to first adjusts variable
Remaining machined parameters and as first adjustment variable machined parameters together as variable, to their sensitivity coefficient vector sum
Survey Gear shape process error vector and carry out binary linear regression analysis, solve first adjust variable respectively with remaining each machined parameters
The linear regression coeffficient of combination, and calculate the coefficient of determination of each machined parameters combination；Contrast the decision system of each machined parameters combination
Number, the remaining machined parameters in machined parameters combination when taking the coefficient of determination maximum are used as second adjustment variable；Calculate now
Theoretical residual error, if meet error correction requirement, take the machined parameters combination as first, second adjustment variable, it
Linear regression coeffficient when combining as error transfer factor amount carry out error correction；If theoretical residual error is unsatisfactory for error correction
It is required that, then proceed next step；
7) N wheel machined parameters selections are carried out, determine that n-th adjusts variable：Successively will be surplus in addition to first N-1 adjusts variable
Remaining machined parameters and as first N-1 adjustment variable N-1 machined parameters together as variable, to their sensitivity coefficient to
Amount and actual measurement tooth surface error vector carry out N member linear regression analyses, and N-1 adjustment variable is joined with remaining each processing respectively before solving
The linear regression coeffficient that array is closed, and calculate the coefficient of determination of each machined parameters combination；Contrast the decision of each machined parameters combination
Coefficient, that remaining machined parameters when taking the coefficient of determination maximum are used as n-th adjustment variable；The theory calculated now is remaining by mistake
Difference, if meeting error correction requirement, it is determined that take this N number of machined parameters as first to when n-th adjustment variable, their combinations
Linear regression coeffficient be used as error transfer factor amount carry out error correction；If theoretical residual error is unsatisfactory for error correction requirement, but
The N number of machined parameters for being selected as adjustment variable have reached the adjustment variables number upper limit, then equally take this N number of machined parameters conduct
First carries out error correction to linear regression coeffficient when n-th adjustment variable, their combinations as error transfer factor amount；Otherwise after
It is continuous to carry out next round machined parameters selection.
2. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 1, it is characterised in that the step 1) in
Flank of tooth discretization and the calculating flank of tooth point theory three-dimensional coordinate and flank of tooth normal vector under gear coordinate system comprise the following steps：
1. grid is evenly dividing on the flank of tooth, grid vertex is flank of tooth point；
2. by the shaft section of flank of tooth spot projection to bevel gear, as the subpoint on shaft section；
3. the shaft staggered point using bevel gear is the origin of coordinates, and X-axis is Gear axis direction, and Y-axis is gear radial direction, is cut in axle
Planar two dimensional coordinate system is set up in face, coordinate of the subpoint under the two-dimensional coordinate system is calculated；
4. according to the two-dimensional coordinate of subpoint, the tooth surface parameters of flank of tooth point corresponding with the subpoint are calculated；
5. the tooth surface parameters of flank of tooth point are substituted into the tooth surface equation of the bevel gear, theory of the flank of tooth point under gear coordinate system is calculated
Three-dimensional coordinate and flank of tooth normal vector.
3. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 2, it is characterised in that the step 5. in
The tooth surface equation of bevel gear be：
In formula, θ andFor tooth surface parameters, r represents three-dimensional coordinate of the flank of tooth point under gear coordinate system, and n represents flank of tooth point in gear
Flank of tooth normal vector under coordinate system.
4. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as described in claim 1 or 2 or 3, it is characterised in that the step
Rapid 3) calculating flank of tooth point actual measurement Gear shape process error and actual measurement Gear shape process error vector calculation formula are：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>e</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>r</mi>
<mi>c</mi>
<mi>i</mi>
</msubsup>
<mo>-</mo>
<msup>
<mi>r</mi>
<mi>i</mi>
</msup>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<msup>
<mi>n</mi>
<mi>i</mi>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>e</mi>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>e</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>e</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>e</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula, riWithThe theoretical and actual three-dimensional coordinate of respectively i-th flank of tooth point；niFor the theoretical flank of tooth of i-th of flank of tooth point
Normal vector, eiFor the actual measurement Gear shape process error of i-th of flank of tooth point, e misses for the actual measurement Gear shape process of institute's geared surface point on the flank of tooth
Difference vector.
5. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 4, it is characterised in that the step 4) in
Gear shape process error and the Gear shape process error of machined parameters small sample perturbations that machined parameters small sample perturbations are produced at flank of tooth point
Vector calculation formula be：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>&epsiv;</mi>
<mi>j</mi>
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</msubsup>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msup>
<mi>r</mi>
<mi>i</mi>
</msup>
<mo>(</mo>
<mrow>
<msub>
<mi>&zeta;</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;&zeta;</mi>
<mi>j</mi>
</msub>
</mrow>
<mo>)</mo>
<mo>-</mo>
<msup>
<mi>r</mi>
<mi>i</mi>
</msup>
<mo>(</mo>
<msub>
<mi>&zeta;</mi>
<mi>j</mi>
</msub>
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</mrow>
<mo>&CenterDot;</mo>
<msup>
<mi>n</mi>
<mi>i</mi>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&zeta;</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
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<mi>&epsiv;</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&epsiv;</mi>
<mi>j</mi>
<mn>1</mn>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>&epsiv;</mi>
<mi>j</mi>
<mn>2</mn>
</msubsup>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
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<mi>&epsiv;</mi>
<mi>j</mi>
<mi>i</mi>
</msubsup>
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<mo>)</mo>
</mrow>
<mi>T</mi>
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</mtd>
</mtr>
</mtable>
</mfenced>
In formula, ζjRepresent the initial value of j-th of machined parameters, Δ ζjRepresent the small sample perturbations of j-th of machined parameters, ri(ζj) represent
The theory three-dimensional coordinate of i-th of flank of tooth point, ri(ζj+Δζj) represent the three-dimensional coordinate after i-th of flank of tooth point disturbance, ni(ζj) represent
The theoretical flank of tooth normal vector of i-th of flank of tooth point,Represent that j-th of machined parameters occurs to produce on i-th of the flank of tooth point during small sample perturbations
Raw Gear shape process error, εjRepresent j-th machined parameters occur the Gear shape process error of small sample perturbations when institute geared surface point to
Amount；
Each machined parameters sensitivity coefficient vector calculation formula be：
<mrow>
<mi>s</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&zeta;</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msub>
<mi>&epsiv;</mi>
<mi>j</mi>
</msub>
<mrow>
<msub>
<mi>&Delta;&zeta;</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
</mrow>
In formula, s (ζj) represent machined parameters ζjSensitivity coefficient vector between Gear shape process error.
6. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 5, it is characterised in that the step 5) in
The mathematical modeling of simple linear regression analysis is：
find αj
min(||e+αjs(ζj)||2)
In formula, αjRepresent the linear regression coeffficient of j-th of machined parameters, that is, machined parameters ζjAdjustment amount.
7. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 6, it is characterised in that the step 6) in
Binary linear regression analysis mathematical modeling be：
find αf, αj
min(||e+αfs(ζf)+αjs(ζj)||2)
s.t.j≠f
In formula, ζfTo be used as the machined parameters of first adjustment variable, αfAnd αjFor linear regression coeffficient.
8. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 2, it is characterised in that the flank of tooth online
Tooth top, tooth root and the size end edge circle 3-5mm of the Edge Distance tooth surfaces of bevel gears of lattice.
9. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as described in claim 1 or 2 or 3 or 5 or 7 or 8, its feature exists
In the N is not more than 3；The type and quantity of the machined parameters and the type and processing mode of gear match.
10. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 9, it is characterised in that the step 4)
In to machined parameters apply small sample perturbations refer on the basis of the machined parameters initial value increase a fractional increments, wherein,
For representing that the machined parameters increment of length or distance takes 0.01mm, for representing that the machined parameters increment of angle takes 0.01rad,
0.001 is taken for nondimensional machined parameters increment.
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| CN105538035B (en) * | 2015-12-24 | 2018-05-29 | 广东省自动化研究所 | A kind of metal parts precise machining equipment and method |
| CN108274081B (en) * | 2017-02-14 | 2020-11-10 | 中国航发哈尔滨东安发动机有限公司 | Deformation compensation machining method for spiral bevel gear |
| DE102017103115A1 (en) * | 2017-02-16 | 2018-08-16 | Klingelnberg Ag | Method for laying out and machining a gear and corresponding machine and software |
| CN107133405B (en) * | 2017-05-09 | 2019-09-27 | 清华大学 | Consider the spiral bevel gear flank of tooth loading performance optimization method of teeth bending strength |
| CN108470102B (en) * | 2018-03-21 | 2021-10-22 | 西安科技大学 | Small wheel tooth surface design method and machining method for meshing performance pre-control |
| CN108873809B (en) * | 2018-07-02 | 2020-12-04 | 中南大学 | High-order tooth surface error correction method for spiral bevel gear |
| CN110645933A (en) * | 2018-08-22 | 2020-01-03 | 黑龙江工程学院 | Method for measuring tooth surface parameters of straight-tooth conical gear |
| CN109343466B (en) * | 2018-09-04 | 2021-01-01 | 中南大学 | Helical bevel gear shape cooperative machining parameter mixing back-adjustment correction method |
| CN109164756A (en) * | 2018-09-07 | 2019-01-08 | 中南大学 | Consider the numerically-controlled machine tool machined parameters modification method of cutterhead shaped position error |
| CN110252937A (en) * | 2019-06-19 | 2019-09-20 | 江苏太平洋齿轮传动有限公司 | A kind of point-to-point correction method of tooth surfaces of bevel gears suitable for forging technology |
| CN110568816B (en) * | 2019-08-26 | 2020-10-09 | 重庆大学 | Hobbing tooth surface error compensation method and system based on equivalent transmission chain error calculation |
| CN110802278B (en) * | 2019-11-26 | 2020-08-25 | 二重（德阳）重型装备有限公司 | Carburizing and quenching gear pre-quenching machining method |
| CN113175903B (en) * | 2021-04-07 | 2022-11-01 | 湖北文理学院 | Face gear error detection and machining control method, device and system |
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