CN105069271A - Bevel gear tooth surface machining error correction method - Google Patents
Bevel gear tooth surface machining error correction method Download PDFInfo
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- CN105069271A CN105069271A CN201510252788.XA CN201510252788A CN105069271A CN 105069271 A CN105069271 A CN 105069271A CN 201510252788 A CN201510252788 A CN 201510252788A CN 105069271 A CN105069271 A CN 105069271A
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Abstract
The present invention relates to a bevel gear tooth surface machining error correction method. The method comprises the steps of discretizing a bevel gear tooth surface to obtain tooth surface points representing shape features of the tooth surface, and calculating theoretical three-dimensional coordinates of the tooth surface points and a tooth surface normal vector; calculating tooth surface information and measuring actual three-dimensional coordinates of the tooth surface points and the tooth surface normal vector; calculating measured tooth surface machining errors of the tooth surface points, and establishing a measured tooth surface machining error vector; applying tiny disturbances to machining parameters individually, calculating tooth surface machining errors generated by the tiny disturbances of the machining parameters onto the tooth surface points, and establishing tiny disturbance tooth surface machining error vectors of the machining parameters and sensitivity ratio vectors of the machining parameters; carrying out the N-th machining parameter selection, determining the N-th adjustment variable, calculating theoretical residual errors; if error correction requirements are met or N reaches the upper limit, the N machining parameters are selected as the fist to N-th adjustment variables, and a linear regression coefficient when the N machining parameters are combined serves as an error adjustment amount for error correction; or a next round of machining parameter selection is continuously carried out otherwise.
Description
Technical field
The present invention relates to a kind of machining error modification method, particularly relate to a kind of tooth surfaces of bevel gears mismachining tolerance modification method.
Background technology
Bevel gear (mainly comprising spiral bevel gear and hypoid gear) is the important drive disk assembly in the traffic and transport fields such as automobile, boats and ships, aviation, is also one of main source of vibration noise in kinematic train.The performance of bevel gear and its tooth accuracy closely related, but due to the existence of the factors such as the alignment error of the elastic deformation of the kinematic error of lathe own, lathe and cutter, cutter and workpiece and thermal deformation, between the actual flank of tooth that processes and the design flank of tooth, inevitably there is certain error.By ensureing the consistance of institute's processing flank of tooth and the design flank of tooth, general needs suitably adjust the Machine-settings processing the flank of tooth, to realize Gear shape process compensation of error according to the size of tooth surface error.Existing Machine-settings adjustment amount computing method, mostly based on the sensitivity coefficient matrix between machined parameters and tooth surface error, calculate the machined parameters adjustment amount needed for error correction.This class methods Problems existing is often direct adjustment for all machined parameters, although in theory calculate and the computational valid time fruit ideal to some examples, be not suitable for actual processing and use.This is mainly owing to also existing mutually complicated coupling between Machine-settings, for some machined parameters, when other machined parameters change, this parameter also can change for the sensitivity of tooth surface error.And existing method have ignored the impact that this coupled relation produces, think that each machined parameters is fixing for the sensitivity of tooth surface error.Therefore, when multiple machined parameters adjusts simultaneously, when especially some parameter adjustment amounts are larger, actual Adjustment effect greatly differs from each other with predicting the outcome, the correction made the mistake.Therefore generally only adjust 2-3 machined parameters in Practical Project, how to choose the key that adjustment parameter then becomes error correction, the research at present for this respect is still rare.
Summary of the invention
For the problems referred to above, the object of this invention is to provide a kind of tooth surfaces of bevel gears mismachining tolerance modification method, it can select the Machine-settings needing most adjustment based on linear regression analysis, and calculates adjustment amount.
For achieving the above object, the present invention takes following technical scheme: a kind of tooth surfaces of bevel gears mismachining tolerance modification method, and it comprises the following steps:
1) sliding-model control is carried out to a lateral tooth flank of the bevel gear gear teeth, obtain the flank of tooth point of this tooth surface shape feature of a series of expression, calculate the theory three-dimensional coordinate of these flank of tooth points under gear coordinate system and flank of tooth normal vector;
2) select a kind of measuring equipment, calculate the flank of tooth dot information of flank of tooth point under this measuring equipment, according to flank of tooth dot information, adopt measuring equipment to measure actual three-dimensional coordinate and the flank of tooth normal vector of flank of tooth point;
3) according to the theory three-dimensional coordinate of flank of tooth point and flank of tooth normal vector and actual three-dimensional coordinate and flank of tooth normal vector, calculate the actual measurement Gear shape process error of flank of tooth point, set up actual measurement Gear shape process error vector;
4) successively respectively small sample perturbations is applied to each machined parameters of bevel gear, calculate the Gear shape process error that each machined parameters small sample perturbations produces at flank of tooth point place, set up the small sample perturbations Gear shape process error vector of each machined parameters, and set up the sensitivity coefficient vector of each machined parameters further;
5) first round machined parameters selection is carried out, determine first adjustment variable: successively using each machined parameters as variable, simple linear regression analysis is carried out to this machined parameters sensitivity coefficient vector sum actual measurement Gear shape process error vector, solve the linear regression coeffficient of this machined parameters, and calculate the coefficient of determination of this machined parameters; Contrast the coefficient of determination of each machined parameters, get the maximum machined parameters of the coefficient of determination as first adjustment variable; Calculate theoretical residual error now, if meet error correction requirement, then get the maximum machined parameters of this coefficient of determination and carry out error correction as the linear regression coeffficient of adjustment variable, this machined parameters as error transfer factor amount; If theoretical residual error does not meet error correction requirement, then proceed next step;
6) carry out second and take turns machined parameters selection, determine second adjustment variable: successively using except first adjustment variable except residue machined parameters with as first adjust variable machined parameters together with as variable, binary linear regression analysis is carried out to their sensitivity coefficient vector sum actual measurement Gear shape process error vector, solve the linear regression coeffficient that the first adjustment variable combines with each machined parameters of residue respectively, and calculate the coefficient of determination of each machined parameters combination; Contrast each machined parameters combination the coefficient of determination, get the coefficient of determination maximum time machined parameters combination in residue machined parameters as second adjustment variable; Calculate theoretical residual error now, if meet error correction requirement, then get the combination of this machined parameters and carry out error correction as linear regression coeffficient when first, second adjustment variable, their combinations as error transfer factor amount; If theoretical residual error does not meet error correction requirement, then proceed next step;
7) carry out N and take turns machined parameters selection, determine N number of adjustment variable: successively using except front N-1 adjustment variable except residue machined parameters with as front N-1 adjust variable N-1 machined parameters together with as variable, the linear regression analysis of N unit is carried out to their sensitivity coefficient vector sum actual measurement tooth surface error vector, solve the linear regression coeffficient that front N-1 adjustment variable combines with each machined parameters of residue respectively, and calculate the coefficient of determination of each machined parameters combination; Contrast each machined parameters combination the coefficient of determination, get the coefficient of determination maximum time that residue machined parameters as N number of adjustment variable; Calculate theoretical residual error now, if meet error correction requirement, then determine that getting this N number of machined parameters carries out error correction to linear regression coeffficient when N number of adjustment variable, their combinations as error transfer factor amount as first; If theoretical residual error does not meet error correction requirement, but select the N number of machined parameters as adjustment variable to reach the adjustment variables number upper limit, then get this N number of machined parameters equally and carry out error correction to linear regression coeffficient when N number of adjustment variable, their combinations as error transfer factor amount as first; Otherwise proceed next round machined parameters to select.
Described step 1) in flank of tooth discretize and calculate flank of tooth point theory three-dimensional coordinate and flank of tooth normal vector under gear coordinate system and comprise the following steps: the grid 1. evenly dividing some on the flank of tooth, grid vertex is flank of tooth point; 2. by flank of tooth spot projection on the shaft section of bevel gear, become the subpoint on shaft section; 3. with the shaft staggered point of bevel gear for true origin, X-axis is Gear axis direction, and Y-axis is gear radial direction, sets up planar two dimensional coordinate system in shaft section, calculates the coordinate of subpoint under this two-dimensional coordinate system; 4. according to the two-dimensional coordinate of subpoint, the tooth surface parameters of the flank of tooth point corresponding with this subpoint is calculated; 5. the tooth surface parameters of flank of tooth point is substituted into the tooth surface equation of this bevel gear, calculate theory three-dimensional coordinate under gear coordinate system of flank of tooth point and flank of tooth normal vector.
Described step 5. in the tooth surface equation of bevel gear be:
In formula, θ and
for tooth surface parameters, r represents the three-dimensional coordinate of flank of tooth point under gear coordinate system, and n represents the flank of tooth normal vector of flank of tooth point under gear coordinate system.
Described step 3) calculating flank of tooth point surveys Gear shape process error and actual measurement Gear shape process error vector computing formula is:
In formula, r
iwith
be respectively the theory of i-th flank of tooth point and actual three-dimensional coordinate; n
ibe the theoretical flank of tooth normal vector of i-th flank of tooth point, e
ibe the actual measurement Gear shape process error of i-th flank of tooth point, e is the actual measurement Gear shape process error vector of institute's geared surface point on the flank of tooth.
Described step 4) in the computing formula of Gear shape process error vector of the Gear shape process error that produces at flank of tooth point place of machined parameters small sample perturbations and machined parameters small sample perturbations be:
In formula, ζ
jrepresent the initial value of a jth machined parameters, Δ ζ
jrepresent the small sample perturbations of a jth machined parameters, r
i(ζ
j) represent the theory three-dimensional coordinate of i-th flank of tooth point, r
i(ζ
j+ Δ ζ
j) represent the three-dimensional coordinate after i-th flank of tooth point disturbance, n
irepresent the theoretical flank of tooth normal vector of i-th flank of tooth point,
gear shape process error when representing jth machined parameters generation small sample perturbations, i-th flank of tooth point produced, ε
jrepresent the Gear shape process error vector of a jth machined parameters generation small sample perturbations time institute geared surface point;
The computing formula of the sensitivity coefficient vector of each machined parameters is:
In formula, s (ζ
j) represent machined parameters ζ
jand the sensitivity coefficient vector between Gear shape process error.
Described step 5) in the mathematical model of simple linear regression analysis be:
findα
j
min(||e+α
js(ζ
j)||
2)
In formula, α
jrepresent the linear regression coeffficient of a jth machined parameters, namely machined parameters ζ
jadjustment amount.
Described step 6) in the mathematical model of binary linear regression analysis be:
findα
f，α
j
min(||e+α
fs(ζ
f)+α
js(ζ
j)||
2)
s.t.j≠f
In formula, ζ
ffor the machined parameters as first adjustment variable, α
fand α
jfor linear regression coeffficient.
The tooth top of the Edge Distance tooth surfaces of bevel gears of grid, tooth root and large small end border 3-5mm on the described flank of tooth.
Described N is not more than 3; Type and the processing mode of the type of described machined parameters and quantity and gear match.
Described step 4) in machined parameters apply small sample perturbations refer on the basis of this machined parameters initial value increase a fractional increments, wherein, for representing that the machined parameters increment of length or distance gets 0.01mm, for representing that the machined parameters increment of angle gets 0.01rad, 0.001 is got for nondimensional machined parameters increment.
The present invention is owing to taking above technical scheme, it has the following advantages: 1, the present invention proposes a kind of tooth surfaces of bevel gears mismachining tolerance modification method, can according to the distribution situation of actual Gear shape process error, maximally related machined parameters is chosen as adjustment variable, for during tooth surface error correction, the selection of machined parameters provides foundation based on regretional analysis; 2, while the method applied in the present invention can carry out adjusting choosing less machined parameters, reduce the adjustment amount of each machined parameters, and desirable correction effect can be reached, solving existing computing method adopts whole machined parameters to adjust, and each machined parameters adjustment amount is large and may occur the problem of error correction; 3, the method applied in the present invention is based on reliable theoretical direction, and principle is simple and be easy to programming realization, and the present invention can be widely used in all kinds of bevel gear making manufacture process medial error correction problem.
Accompanying drawing explanation
Fig. 1 is implementation process process flow diagram of the present invention;
Fig. 2 is flank of tooth discretize schematic diagram.
Embodiment
Below in conjunction with drawings and Examples, the present invention is described in detail.
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 gear teeth of actual machining of bevel gears is selected, sliding-model control is carried out to this flank of tooth, namely choose the flank of tooth point of some on the flank of tooth to represent tooth surface shape feature, and calculate the theory three-dimensional coordinate of selected flank of tooth point under gear coordinate system and flank of tooth normal vector.
Wherein, the true origin of gear coordinate system is at the shaft staggered point of bevel gear, and X-axis is Gear axis direction, and Y-axis and Z axis are gear radial direction.
Flank of tooth discretize and the concrete grammar calculating the theory three-dimensional coordinate of selected flank of tooth point under gear coordinate system and flank of tooth normal vector comprise the following steps:
1. on the flank of tooth selected, evenly divide the quadrilateral mesh of some, the summit of grid is the flank of tooth point for representing tooth surface shape feature chosen.
2. by the flank of tooth spot projection chosen on the shaft section of bevel gear, become the subpoint on shaft section;
3. with the shaft staggered point of bevel gear for true origin, X-axis is Gear axis direction, and Y-axis is gear radial direction, sets up planar two dimensional coordinate system in shaft section, calculates the coordinate of subpoint under this two-dimensional coordinate system;
4. according to the two-dimensional coordinate of subpoint, the tooth surface parameters of the flank of tooth point corresponding with this subpoint is calculated;
The system of equations of the theory three-dimensional coordinate and flank of tooth normal vector that calculate flank of tooth point is:
In formula, x
iand y
irepresent the two-dimensional coordinate of the subpoint corresponding with i-th flank of tooth point, r represents the three-dimensional coordinate of flank of tooth point under gear coordinate system, and p is Gear axis direction vector, and namely X-direction is vectorial; This system of equations can be solved by binary iteration, obtain the tooth surface parameters of flank of tooth point.
5. the tooth surface parameters of the flank of tooth obtained point is substituted into the tooth surface equation of this bevel gear, the theory three-dimensional coordinate of flank of tooth point under gear coordinate system and flank of tooth normal vector can be obtained.
The tooth surface equation of this bevel gear is:
In formula, θ and
for tooth surface parameters, n represents the flank of tooth normal vector of flank of tooth point under gear coordinate system.
2) a kind of measuring equipment is selected, by step 1) under theory three-dimensional coordinate under gear coordinate system of the flank of tooth point that obtains and flank of tooth normal vector be transformed into the surving coordinate system of this measuring equipment, obtain the theory three-dimensional coordinate of flank of tooth point under surving coordinate system and flank of tooth normal vector, be called flank of tooth dot information; According to flank of tooth dot information, measuring equipment is adopted to record the actual three-dimensional coordinate of flank of tooth point under surving coordinate system and flank of tooth normal vector.
Wherein, measuring equipment can be gear measuring center or three-coordinates measuring machine, and surving coordinate system determines according to the type of measuring equipment and model.
3) according to step 2) theory three-dimensional coordinate under surving coordinate system of the flank of tooth point that obtains and flank of tooth normal vector and actual three-dimensional coordinate and flank of tooth normal vector, calculate the actual measurement Gear shape process error of flank of tooth point, thus 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, the distance between true tooth and the theoretical flank of tooth, and therefore, the computing formula of Gear shape process error is:
In formula, r
iwith
be respectively the theory of i-th flank of tooth point and actual three-dimensional coordinate; n
ibe the theoretical flank of tooth normal vector of i-th flank of tooth point, e
ibe the actual measurement Gear shape process error of i-th flank of tooth point, e is the actual measurement Gear shape process error vector of institute's geared surface point on the flank of tooth.
4) on the basis of a bevel gear making initial parameter value, increase a fractional increments, be called and small sample perturbations is applied to this machined parameters; Only small sample perturbations is applied to a machined parameters, and other machined parameters remain unchanged, the D coordinates value after the disturbance of flank of tooth point can be calculated by now all bevel gear making parameters, error after the disturbance of flank of tooth point between D coordinates value and theory three-dimensional coordinate figure when being undisturbed, is the Gear shape process error that this machined parameters disturbance produces at flank of tooth point place; According to the Gear shape process error of this machined parameters disturbance, the sensitivity coefficient vector of this machined parameters to Gear shape process error can be set up.
Successively respectively small sample perturbations is applied to each machined parameters, calculate the Gear shape process error that each machined parameters small sample perturbations produces at flank of tooth point place, set up the small sample perturbations Gear shape process error vector of each machined parameters, and set up the sensitivity coefficient vector of each machined parameters further.
According to Gear shape process error calculation formula, the Gear shape process error calculation formula that can obtain the generation of machined parameters small sample perturbations is:
In formula, ζ
jrepresent the initial value of a jth machined parameters, Δ ζ
jrepresent the small sample perturbations of a jth machined parameters, r
i(ζ
j) represent the theory three-dimensional coordinate of i-th flank of tooth point, r
i(ζ
j+ Δ ζ
j) represent the three-dimensional coordinate after i-th flank of tooth point disturbance, n
irepresent the theoretical flank of tooth normal vector of i-th flank of tooth point,
gear shape process error when representing jth machined parameters generation small sample perturbations, i-th flank of tooth point produced, ε
jrepresent the Gear shape process error vector of a jth machined parameters generation small sample perturbations time institute geared surface point.
The computing formula of the sensitivity coefficient vector between each machined parameters and Gear shape process error is:
In formula, s (ζ
j) represent machined parameters ζ
jand the sensitivity coefficient vector between Gear shape process error.
For representing that the machined parameters increment of length or distance can get 0.01mm, for representing that the machined parameters increment of angle can get 0.01rad, can 0.001 be got for nondimensional machined parameters increment.
The type of bevel gear making parameter and quantity are different according to the difference of the type of gear and processing mode used, also the correlation parameter of cutting pinion cutter used or emery wheel is comprised in machined parameters, to process the slope knife half spread out method of hypoid gear, the machined parameters that steamboat adds man-hour comprises: horizontal position of wheel, workhead offset, Installing machine tool root angle, berth, radial, angle cutter spacing angle, tilt child's hair twisted in a knot-childhood, swivel angle, rolls totally 11, ratio, cutter radius and tool-tooth profile angle.
5) first round machined parameters selection is carried out, determine first adjustment variable: successively using each machined parameters as variable, to step 4) this machined parameters sensitivity coefficient vector sum step 3 of obtaining) the actual measurement Gear shape process error vector that obtains carries out simple linear regression analysis, least square approximation mode is adopted to solve (only as example, be not limited to this) linear regression coeffficient of this machined parameters, and calculate the coefficient of determination of this machined parameters; Contrast the coefficient of determination of each machined parameters, get the maximum machined parameters of the coefficient of determination as first adjustment variable.Calculate theoretical residual error now, if meet error correction requirement, then determine to get the maximum machined parameters of this coefficient of determination and carry out error correction as the linear regression coeffficient of adjustment variable, this machined parameters as error transfer factor amount; If theoretical residual error does not meet error correction requirement, then proceed next step.
The mathematical model of simple linear regression analysis is expressed as:
findα
j
min(||e+α
js(ζ
j)||
2)(6)
In formula, α
jrepresent the linear regression coeffficient of a jth machined parameters, namely machined parameters ζ
jadjustment amount.
Error correction requires to set according to actual needs, and as required, the maximum residual error of flank of tooth point is less than certain specified rate, or requires 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 using except first adjustment variable except residue machined parameters and step 5) determine as first adjust variable machined parameters together with as variable, binary linear regression analysis is carried out to their sensitivity coefficient vector sum actual measurement Gear shape process error vector, solve the linear regression coeffficient that the first adjustment variable combines with each machined parameters of residue respectively, and calculate the coefficient of determination of each machined parameters combination; Contrast each machined parameters combination the coefficient of determination, get the coefficient of determination maximum time machined parameters combination in residue machined parameters as second adjustment variable.Calculate theoretical residual error now, if meet error correction requirement, then determine to get step 5) machined parameters determined carries out error correction as linear regression coeffficient when the second adjustment variable, their combinations as error transfer factor amount as the first adjustment variable, this machined parameters determined; If theoretical residual error does not meet error correction requirement, then proceed next step.
The mathematical model of binary linear regression analysis is expressed as:
findα
f，α
j
min(||e+α
fs(ζ
f)+α
js(ζ
j)||
2)(7)
s.t.j≠f
In formula, ζ
ffor the machined parameters as first adjustment variable, α
fand α
jfor linear regression coeffficient.
7) carry out N and take turns machined parameters selection, determine N number of adjustment variable: successively using except front N-1 adjustment variable except residue machined parameters with as front N-1 adjust variable N-1 machined parameters together with as variable, the linear regression analysis of N unit is carried out to their sensitivity coefficient vector sum actual measurement tooth surface error vector, solve the linear regression coeffficient that front N-1 adjustment variable combines with each machined parameters of residue respectively, and calculate the coefficient of determination of each machined parameters combination; Contrast each machined parameters combination the coefficient of determination, get the coefficient of determination maximum time that residue machined parameters as N number of adjustment variable.Calculate theoretical residual error now, if meet error correction requirement, then determine that getting this N number of machined parameters carries out error correction to linear regression coeffficient when N number of adjustment variable, their combinations as error transfer factor amount as first; If theoretical residual error does not meet error correction requirement, but select the N number of machined parameters as adjustment variable to reach the adjustment variables number upper limit, then get this N number of machined parameters equally and carry out error correction to linear regression coeffficient when N number of adjustment variable, their combinations as error transfer factor amount as first; Otherwise proceed next round machined parameters to select.
In above-described embodiment, the tooth top of the Edge Distance tooth surfaces of bevel gears of quadrilateral mesh, tooth root and large small end border 3-5mm on the flank of tooth.
In above-described embodiment, for eliminating some stochastic errors, for gear general measure 3-5 flank of tooth, using after gained tooth surface error is averaged as final measurement.
In above-described embodiment, the machined parameters number upper limit being elected to be adjustment variable needs to determine according to actual error correction, and for generalized case, the selected machined parameters number upper limit of suggestion is no more than 3, and namely N is less than or equal to 3.
The present invention can be widely used in the Gear shape process error correction of various bevel gear.Below to be applied to the Gear shape process error correction of a hypoid gear steamboat concave surface, illustrate using method of the present invention:
This hypoid gear adopts the processing of slope knife half spread out method, and its basic parameter comprises:
| Title | Numerical value | Title | Numerical value |
| Large tooth number | 37 | Little tooth number | 9 |
| Modulus | 11.49mm | The bull wheel face width of tooth | 61mm |
| Offset | 26mm | Crossed axis angle | 90° |
| Steamboat design helix angle | 43.65° | Mean pressure angle | 22.5° |
| Bull wheel pitch cone angle | 73.87° | Steamboat pitch cone angle | 15.99° |
The initial manufacture parameter of this hypoid gear steamboat concave surface comprises:
| Machined parameters title | Machined parameters initial value |
| Angle cutter spacing/° | 60.3220 |
| Workhead offset/mm | 18.0000 |
| Horizontal position of wheel/mm | 0.7360 |
| Installation root angle/° | -4.5273 |
| Radial/mm | 151.2363 |
| Roll ratio | 5.4328 |
| Berth/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 Figure 2, select a lateral tooth flank of this hypoid gear steamboat concave surface, this flank of tooth evenly divides one to be had 9 row along tooth length direction, has the quadrilateral mesh of 5 row along tooth depth direction, amounts to formation 45 net points, is numbered these 45 net points; The tooth top of this flank of tooth of grid Edge Distance, tooth root and large small end border 3-5mm.
These 45 net points are projected on the shaft section of this hypoid gear, becomes the subpoint on shaft section.
With the shaft staggered point of this hypoid gear for true origin, X-axis is Gear axis direction, Y-axis is gear radial direction, planar two dimensional coordinate system is set up in the shaft section of this hypoid gear, the two-dimensional coordinate of each net point in shaft section two-dimensional coordinate system is determined, i.e. the two-dimensional coordinate of subpoint by interpolation method.
According to the two-dimensional coordinate of each subpoint, solving equation group (1), calculates the tooth surface parameters of each net point; The tooth surface parameters of net point is substituted into the tooth surface equation of this hypoid gear steamboat concave surface, solve the theory three-dimensional coordinate of these flank of tooth net points under gear coordinate system and flank of tooth normal vector.
Select gear measuring center, under the three-dimensional coordinate of flank of tooth net point under gear coordinate system and flank of tooth normal vector are transformed into the surving coordinate system of this gear measuring center, obtain the theory three-dimensional coordinate of flank of tooth net point under this surving coordinate system and flank of tooth normal vector; Gear measuring center is adopted to record the actual three-dimensional coordinate of net point under surving coordinate system and flank of tooth normal vector.
According to the theory three-dimensional coordinate of net point under surving coordinate system and flank of tooth normal vector and actual three-dimensional coordinate and flank of tooth normal vector, calculate the actual measurement Gear shape process error of each net point; According to the numbering of 45 net points, the actual measurement Gear shape process error amount of gained 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 net points is write as the vector of 45 × 1, be actual measurement Gear shape process error vector.
On the machined parameters initial value basis of this hypoid gear steamboat concave surface, respectively small sample perturbations is applied to each machined parameters, wherein, for representing that the machined parameters increment of length or distance can get 0.01mm, for representing that the machined parameters increment of angle can get 0.01rad, can get 0.001 for nondimensional machined parameters increment, each only to a machined parameters applying disturbance, other machined parameters remain unchanged.
After applying disturbance to a certain machined parameters, calculate the disturbance three-dimensional coordinate of flank of tooth net point according to machined parameters now, flank of tooth point disturbance three-dimensional coordinate and error when being undisturbed between theory three-dimensional coordinate, be the Gear shape process error of this machined parameters disturbance; Set up the sensitivity coefficient vector of this machined parameters to Gear shape process error further.
Successively disturbance is applied to all machined parameters, calculate the Gear shape process error of each machined parameters disturbance, and set up the sensitivity coefficient vector of each machined parameters.
Specification error correction requires: for residual error, require that the residual error maximal value of net point is no more than 2 μm; The upper limit of setting Choice and process parameter is 3.
Carry out first round machined parameters selection: successively using each machined parameters as variable, simple linear regression analysis is carried out to each machined parameters sensitivity coefficient vector sum actual measurement Gear shape process error vector, solve the linear regression coeffficient of each machined parameters, and calculate the coefficient of determination of each machined parameters; Contrast the coefficient of determination of each machined parameters, show that the maximum machined parameters of the coefficient of determination of linear regression is " berth ", the coefficient of determination is 0.9572, therefore selects " berth " as first adjustment variable.When selection " berth " is as adjustment variable, when its linear regression coeffficient is as adjustment amount, the theoretical residual error maximal value of linear regression is 10.1 μm, does not meet the demands, and therefore needs to carry out second and takes turns selection.
Carry out second take turns machined parameters select: successively by the machined parameters except " berth " together with " berth " as variable, binary linear regression analysis is carried out to their sensitivity coefficient vector sum actual measurement Gear shape process error vector, solve the linear regression coeffficient that " berth " combines with each machined parameters of residue respectively, and calculate the coefficient of determination of each combination; Contrast the coefficient of determination of each machined parameters combination, show that coefficient of determination when " radial " and " berth " being combined is maximum, the coefficient of determination is now 0.9951, therefore selects " radial " as second adjustment variable.Variable is adjusted as first adjustment variable, " radial " as second using " berth ", linear regression coeffficient during their combinations is as adjustment amount, the maximal value of theoretical residual error is now 3.4 μm, does not still meet the demands, and therefore needs to carry out third round selection.
Carry out the selection of third round machined parameters: successively by the machined parameters except " berth " and " radial " together with " berth " and " radial " as variable, ternary linear regression analysis is carried out to their sensitivity coefficient vector sum actual measurement Gear shape process error vector, solve the linear regression coeffficient that " berth " and " radial " combines with each machined parameters of residue respectively, and calculate the coefficient of determination of each combination; Contrast the coefficient of determination of each machined parameters combination, show that coefficient of determination when " cutter tilt " and " berth " and " radial " being combined is maximum, the coefficient of determination is now 0.9955, therefore selects " cutter tilt " as the 3rd adjustment variable.Variable, " radial " is adjusted as second adjustment variable, " cutter tilt " as the 3rd adjustment variable as first using " berth ", linear regression coeffficient during their combinations is as adjustment amount, the maximal value of theoretical residual error is now 3.6 μm, does not still meet the demands; But selected machined parameters quantity reaches the upper limit, therefore no longer carries out next round selection.
Final selection " berth ", " radial " and " cutter tilt " are as adjustment variable, linear regression coeffficient when they combine is 0.2951 ,-1.9655 and-0.0150 respectively, and therefore the adjustment amount of three machined parameters is respectively 0.2951mm ,-1.9655mm and-0.0150rad.Adopt the machined parameters machining gears detect revised actual Gear shape process error again after adjustment, 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 |
Visible, revised actual Gear shape process error, within 10 μm, reaches desirable correction effect.
The various embodiments described above are only for illustration of the present invention; wherein the structure of each parts, setting position and connected mode etc. thereof all can change to some extent; every equivalents of carrying out on the basis of technical solution of the present invention and improvement, all should not get rid of outside protection scope of the present invention.
Claims (10)
1. a 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, obtain the flank of tooth point of this tooth surface shape feature of a series of expression, calculate the theory three-dimensional coordinate of these flank of tooth points under gear coordinate system and flank of tooth normal vector;
2) select a kind of measuring equipment, calculate the flank of tooth dot information of flank of tooth point under this measuring equipment, according to flank of tooth dot information, adopt measuring equipment to measure actual three-dimensional coordinate and the flank of tooth normal vector of flank of tooth point;
3) according to the theory three-dimensional coordinate of flank of tooth point and flank of tooth normal vector and actual three-dimensional coordinate and flank of tooth normal vector, calculate the actual measurement Gear shape process error of flank of tooth point, set up actual measurement Gear shape process error vector;
4) successively respectively small sample perturbations is applied to each machined parameters of bevel gear, calculate the Gear shape process error that each machined parameters small sample perturbations produces at flank of tooth point place, set up the small sample perturbations Gear shape process error vector of each machined parameters, and set up the sensitivity coefficient vector of each machined parameters further;
5) first round machined parameters selection is carried out, determine first adjustment variable: successively using each machined parameters as variable, simple linear regression analysis is carried out to this machined parameters sensitivity coefficient vector sum actual measurement Gear shape process error vector, solve the linear regression coeffficient of this machined parameters, and calculate the coefficient of determination of this machined parameters; Contrast the coefficient of determination of each machined parameters, get the maximum machined parameters of the coefficient of determination as first adjustment variable; Calculate theoretical residual error now, if meet error correction requirement, then get the maximum machined parameters of this coefficient of determination and carry out error correction as the linear regression coeffficient of adjustment variable, this machined parameters as error transfer factor amount; If theoretical residual error does not meet error correction requirement, then proceed next step;
6) carry out second and take turns machined parameters selection, determine second adjustment variable: successively using except first adjustment variable except residue machined parameters with as first adjust variable machined parameters together with as variable, binary linear regression analysis is carried out to their sensitivity coefficient vector sum actual measurement Gear shape process error vector, solve the linear regression coeffficient that the first adjustment variable combines with each machined parameters of residue respectively, and calculate the coefficient of determination of each machined parameters combination; Contrast each machined parameters combination the coefficient of determination, get the coefficient of determination maximum time machined parameters combination in residue machined parameters as second adjustment variable; Calculate theoretical residual error now, if meet error correction requirement, then get the combination of this machined parameters and carry out error correction as linear regression coeffficient when first, second adjustment variable, their combinations as error transfer factor amount; If theoretical residual error does not meet error correction requirement, then proceed next step;
7) carry out N and take turns machined parameters selection, determine N number of adjustment variable: successively using except front N-1 adjustment variable except residue machined parameters with as front N-1 adjust variable N-1 machined parameters together with as variable, the linear regression analysis of N unit is carried out to their sensitivity coefficient vector sum actual measurement tooth surface error vector, solve the linear regression coeffficient that front N-1 adjustment variable combines with each machined parameters of residue respectively, and calculate the coefficient of determination of each machined parameters combination; Contrast each machined parameters combination the coefficient of determination, get the coefficient of determination maximum time that residue machined parameters as N number of adjustment variable; Calculate theoretical residual error now, if meet error correction requirement, then determine that getting this N number of machined parameters carries out error correction to linear regression coeffficient when N number of adjustment variable, their combinations as error transfer factor amount as first; If theoretical residual error does not meet error correction requirement, but select the N number of machined parameters as adjustment variable to reach the adjustment variables number upper limit, then get this N number of machined parameters equally and carry out error correction to linear regression coeffficient when N number of adjustment variable, their combinations as error transfer factor amount as first; Otherwise proceed next round machined parameters to select.
2. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 1, is characterized in that, described step 1) in flank of tooth discretize and calculate flank of tooth point theory three-dimensional coordinate and flank of tooth normal vector under gear coordinate system and comprise the following steps:
1. on the flank of tooth, evenly divide the grid of some, grid vertex is flank of tooth point;
2. by flank of tooth spot projection on the shaft section of bevel gear, become the subpoint on shaft section;
3. with the shaft staggered point of bevel gear for true origin, X-axis is Gear axis direction, and Y-axis is gear radial direction, sets up planar two dimensional coordinate system in shaft section, calculates the coordinate of subpoint under this two-dimensional coordinate system;
4. according to the two-dimensional coordinate of subpoint, the tooth surface parameters of the flank of tooth point corresponding with this subpoint is calculated;
5. the tooth surface parameters of flank of tooth point is substituted into the tooth surface equation of this bevel gear, calculate theory three-dimensional coordinate under gear coordinate system of flank of tooth point and flank of tooth normal vector.
3. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 2, is characterized in that, described step 5. in the tooth surface equation of bevel gear be:
In formula, θ and
for tooth surface parameters, r represents the three-dimensional coordinate of flank of tooth point under gear coordinate system, and n represents the flank of tooth normal vector of flank of tooth point under gear coordinate system.
4. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as described in claim 1 or 2 or 3, is characterized in that, described step 3) calculating flank of tooth point surveys Gear shape process error and actual measurement Gear shape process error vector computing formula is:
In formula, r
iwith
be respectively the theory of i-th flank of tooth point and actual three-dimensional coordinate; n
ibe the theoretical flank of tooth normal vector of i-th flank of tooth point, e
ibe the actual measurement Gear shape process error of i-th flank of tooth point, e is the actual measurement Gear shape process error vector of institute's geared surface point on the flank of tooth.
5. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 4, it is characterized in that, described step 4) in the computing formula of Gear shape process error vector of the Gear shape process error that produces at flank of tooth point place of machined parameters small sample perturbations and machined parameters small sample perturbations be:
In formula, ζ
jrepresent the initial value of a jth machined parameters, Δ ζ
jrepresent the small sample perturbations of a jth machined parameters, r
i(ζ
j) represent the theory three-dimensional coordinate of i-th flank of tooth point, r
i(ζ
j+ Δ ζ
j) represent the three-dimensional coordinate after i-th flank of tooth point disturbance, n
irepresent the theoretical flank of tooth normal vector of i-th flank of tooth point,
gear shape process error when representing jth machined parameters generation small sample perturbations, i-th flank of tooth point produced, ε
jrepresent the Gear shape process error vector of a jth machined parameters generation small sample perturbations time institute geared surface point;
The computing formula of the sensitivity coefficient vector of each machined parameters is:
In formula, s (ζ
j) represent machined parameters ζ
jand the sensitivity coefficient vector between Gear shape process error.
6. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as described in claim 1 or 2 or 3 or 5, is characterized in that, described step 5) in the mathematical model of simple linear regression analysis be:
findα
j
min(||e+α
js(ζ
j)||
2)
In formula, α
jrepresent the linear regression coeffficient of a jth machined parameters, namely machined parameters ζ
jadjustment amount.
7. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 6, is characterized in that, described step 6) in the mathematical model of binary linear regression analysis be:
findα
f，α
j
min(||e+α
fs(ζ
f)+α
js(ζ
j)||
2)
s.t.j≠f
In formula, ζ
ffor the machined parameters as first adjustment variable, α
fand α
jfor linear regression coeffficient.
8. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 2, is characterized in that, the tooth top of the Edge Distance tooth surfaces of bevel gears of grid, tooth root and large small end border 3-5mm on the described flank of tooth.
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, it is characterized in that, described N is not more than 3; Type and the processing mode of the type of described machined parameters and quantity and gear match.
10. a kind of tooth surfaces of bevel gears mismachining tolerance modification method as claimed in claim 9, it is characterized in that, described step 4) in machined parameters apply small sample perturbations refer on the basis of this machined parameters initial value increase a fractional increments, wherein, for representing that the machined parameters increment of length or distance gets 0.01mm, for representing that the machined parameters increment of angle gets 0.01rad, 0.001 is got for nondimensional machined parameters increment.
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Cited By (14)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105538035A (en) * | 2015-12-24 | 2016-05-04 | 广东省自动化研究所 | Precise machining equipment and method for metal parts |
| CN107133405A (en) * | 2017-05-09 | 2017-09-05 | 清华大学 | Consider the spiral bevel gear flank of tooth loading performance optimization method of teeth bending strength |
| CN108274081A (en) * | 2017-02-14 | 2018-07-13 | 中国航发哈尔滨东安发动机有限公司 | A kind of deformation-compensated processing method of spiral bevel gear |
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| CN110300936A (en) * | 2017-02-16 | 2019-10-01 | 克林格伦贝格股份公司 | For designing and processing the method and corresponding machining tool and software of gear |
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Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103927428A (en) * | 2014-05-09 | 2014-07-16 | 清华大学 | Bevel gear dislocation quantity finite element computing method with multi-factor influences taken into account |
-
2015
- 2015-05-18 CN CN201510252788.XA patent/CN105069271B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103927428A (en) * | 2014-05-09 | 2014-07-16 | 清华大学 | Bevel gear dislocation quantity finite element computing method with multi-factor influences taken into account |
Non-Patent Citations (2)
| Title |
|---|
| GUO Y ET AL.: "Stiffness matrix calculation element bearings using a finite element/contact of rolling mechanics model", 《MECHANISM AND MACHINE THEORY》 * |
| 王小椿 等: "螺旋锥齿轮的齿面测量及机床加工参数修正", 《机械工程学报》 * |
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