CN109993464B - Machining parameter optimization method for reducing mounting error sensitivity of hypoid gear - Google Patents

Machining parameter optimization method for reducing mounting error sensitivity of hypoid gear Download PDF

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CN109993464B
CN109993464B CN201910334141.XA CN201910334141A CN109993464B CN 109993464 B CN109993464 B CN 109993464B CN 201910334141 A CN201910334141 A CN 201910334141A CN 109993464 B CN109993464 B CN 109993464B
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卢剑伟
王笑乐
袁博
程静
谷先广
吴勃夫
赵晓敏
姜平
董方方
夏光
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    • B23FMAKING GEARS OR TOOTHED RACKS
    • B23F5/00Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
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Abstract

The invention discloses a processing parameter optimization method for reducing the installation error sensitivity of a hypoid gear, which comprises the following steps: after geometric parameters of a large gear blank, size parameters of a gear cutting tool and machining parameters of a machine tool are given, and geometric parameters of a small gear blank and size parameters of the gear cutting tool are given, an optimal small gear machining parameter is found by establishing a mounting error comprehensive sensitivity optimization model and adopting a genetic algorithm, so that the sensitivity of the hypoid gear pair to mounting errors is reduced. The invention can judge the influence degree of different types of installation errors on the meshing performance so as to provide a theoretical basis for the control of the assembly precision during actual installation.

Description

Machining parameter optimization method for reducing mounting error sensitivity of hypoid gear
Technical Field
The invention relates to a method for optimizing machine tool machining parameters of a hypoid gear, in particular to a method for optimizing machine tool machining parameters for reducing the sensitivity degree of hypoid gear meshing quality to installation errors.
Background
The hypoid gear has the advantages of large reduction ratio, small volume and the like, is often applied to a mechanism with large load and high rotating speed, and has higher requirements on the operation stability and the silence. The good vibration noise characteristic of the gear pair is closely related to the ideal tooth surface meshing performance, and the meshing performance is influenced by the micro-topography of the tooth surface, the gear cutting processing technology and the assembling precision. At present, the tooth surface appearance design and the gear cutting machining process reach higher levels, and how to effectively reduce the influence of installation errors on the meshing performance is not well solved. The hypoid gear has complex tooth surface and is sensitive to installation errors, and the inevitable installation errors in reality can destroy an ideal meshing state to cause transmission instability, so that severe vibration and noise are generated, and further early failure of gear teeth is caused.
Liu light epitaxy provides a contact mark position parameter analysis method in the text of 'a method for determining the installation error variation range of a spiral bevel gear', and the method is used for determining the variable movement range of the installation error of the spiral bevel gear; the influence of the installation error on the meshing performance of the hyperboloid gear is researched for the contact mark and the transmission error by the royal in the text of 'the influence of the installation error on the meshing performance of the hyperboloid gear', and the method breaks through the limitation that the traditional method adjusts the field installation of the gear pair by depending on practical experience; in the analytical research on the influence of mounting errors on the tooth surface contact tracks of the spiral bevel gears, the theoretical tooth surface equation of a large gear and a small gear of the spiral bevel gears and the basic equation of tooth surface contact analysis when the mounting errors exist are deduced in the text of 'mounting error on the tooth surface contact tracks of the spiral bevel gears', the tooth surface contact analysis when the mounting errors exist is considered, and the influence of the mounting errors on contact areas is analyzed through Matlab programming from angles in which the three mounting errors act independently and the three errors act simultaneously.
The above-mentioned research about the influence of installation error to hypoid gear or spiral bevel gear meshing performance is the research developed around the influence law of installation error to gear pair meshing performance, and the meshing performance to hypoid gear pair does not carry out the analysis to different installation error sensitivities, therefore can't contrast the installation error of different grade type to the influence size of gear pair meshing performance, also can't propose the practical method of reducing hypoid gear to installation error sensitivity, consequently still exist not enoughly in engineering practical application.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides a machining parameter optimization method for reducing the sensitivity of hypoid gear installation errors so as to judge the influence degree of different types of installation errors on the meshing performance, thereby providing a theoretical basis for the control of the assembly accuracy in actual installation.
The invention adopts the following technical scheme for solving the technical problems:
the invention discloses a processing parameter optimization method for reducing the mounting error sensitivity of a hypoid gear, which is characterized by being applied to optimizing and adjusting the processing parameters of a small wheel machine tool, wherein the optimizing and adjusting of the processing parameters of the small wheel machine tool are carried out according to the following steps:
step 1, according to the design requirements of a hypoid gear pair, setting a gear pair offset distance, a large gear blank geometric parameter, a large gear cutting tool size parameter, a small gear blank geometric parameter and a small gear cutting tool size parameter; respectively calculating machining parameters of a large wheel machine tool and machining parameters of a small wheel machine tool according to a gear machining principle corresponding to the gear cutting machine tool;
step 2, according to a large gear machining principle corresponding to the gear cutting machine tool, establishing a large gear tooth surface equation under a large gear tooth blank coordinate system by using the geometric parameters of the large gear tooth blank, the dimensional parameters of the large gear cutting tool and the machining parameters of the large gear machine tool; according to a small wheel machining principle corresponding to a gear cutting machine tool, establishing a small wheel tooth surface equation under a small wheel tooth blank coordinate system by using the small wheel tooth blank geometric parameters, the small wheel gear cutting tool size parameters and the small wheel machine tool machining parameters; according to a given gear pair offset distance, virtually assembling the large gear surface equation and the small gear surface equation to obtain a meshing gear surface equation under a meshing coordinate system;
step 3, defining four installation errors of the gear pair, including: axial error H of large wheelGAxial error H of small wheelPAxis crossing angle error sigma and offset error V; recording any one of the four installation errors as an installation error R, wherein R belongs to { H ∈ [ ]P,HGV, Σ }; setting the value range of any one installation error R of the gear pair according to the actual requirement of the installation precision;
and 4, enabling the installation error R to take K values at equal intervals in the value range, and recording the K values as { R1,R2,…,Rk,…,RKSetting other 3 errors as '0', respectively finishing the virtual assembly of the gear pair K times under the installation error R, and obtaining K meshing tooth surface equations in a meshing coordinate system under the installation error R; wherein R iskThe kth value of the installation error R in the value range is represented; k is 1,2, …, K;
step 5, respectively carrying out computer gear meshing analysis on the K meshing tooth surface equations under each mounting error according to the four mounting errors to obtain K groups of tooth surface meshing impressions and K groups of gear pair transmission error curves under each mounting error;
step 6, aiming at the tooth surface meshing imprints under four installation errors, determining four evaluation indexes for evaluating the quality of the meshing imprints, comprising the following steps of: meshing impression area S in gear tooth section coordinate systemcpTooth surface centroid position abscissa of meshing impression
Figure BDA0002038633420000021
Tooth surface centroid position ordinate of meshing impression
Figure BDA0002038633420000022
And the meshing impression azimuth angle gammacpAnd are respectively represented by formula (1), formula (2), formula (3) and formula (4); and comparing the four evaluation indexesAny one of the mounting errors is recorded as an evaluation index T,
Figure BDA0002038633420000023
the value of T is recorded as an evaluation index value fT
Figure BDA0002038633420000024
Figure BDA0002038633420000031
Figure BDA0002038633420000032
Figure BDA0002038633420000033
In the formula (1) to the formula (4), n represents the number of points into which the left side line, the right side line and the impression center line of the tooth surface meshing impression are all dispersed in the computer gear tooth meshing analysis; A. b, C is an intermediate variable, and
Figure BDA0002038633420000034
Figure BDA0002038633420000035
Figure BDA0002038633420000036
respectively representing the abscissa and ordinate of the p-th point on the left side line of the meshing impression, wherein p is 1,2, …, n-1;
Figure BDA0002038633420000037
respectively representing the abscissa value and the ordinate value of the p +1 point on the left side line of the meshing impression;
Figure BDA0002038633420000038
respectively representing the abscissa value and the ordinate value of the p-th point on the right side line of the meshing impression;
Figure BDA0002038633420000039
respectively representing the abscissa value and the ordinate value of the p +1 point on the right side line of the meshing impression;
Figure BDA00020386334200000310
respectively representing the abscissa value and the ordinate value of the p-th point on the marking center line;
Figure BDA00020386334200000311
respectively representing the abscissa value and the ordinate value of the p +1 point on the marking center line;
step 7, calculating the kth value R of the installation error RkValue f of the following evaluation index TT(Rk) And the value f of the evaluation index T without any installation errorT(0) Difference between them
Figure BDA00020386334200000312
Thereby obtaining K groups of difference values
Figure BDA00020386334200000313
Calculating the sensitivity of the evaluation index T to the mounting error R by using the formula (5)
Figure BDA00020386334200000314
Figure BDA00020386334200000315
Step 8, recording the sum of the sensitivities of the evaluation index T to the four mounting errors as STThe sum S of the sensitivities of the evaluation index T to the four mounting errorsTCarrying out weighted summation to obtain the comprehensive sensitivity CS
Using equation (6) to establish a small round of additionWorking parameters are optimized variables with minimum CSValue-targeted integrated sensitivity optimization model:
Figure BDA0002038633420000041
in formula (6), Min (C)S) The objective function value of the comprehensive sensitivity optimization model is the minimum value of the function; u. ofTA weighting coefficient that is the sensitivity of the evaluation index T to the installation error R;
step 9, selecting a group of installation error values within the value ranges of the four installation errors, completing virtual assembly of the gear pair under the selected group of installation errors, and obtaining an engagement tooth surface equation under the selected installation errors in an engagement coordinate system;
carrying out computer gear tooth meshing analysis on the meshing tooth surface equation containing the selected mounting error to obtain a tooth surface meshing impression and a gear pair transmission error curve containing the selected mounting error;
carrying out sensitivity and comprehensive sensitivity calculation on the tooth surface meshing impression containing the selected mounting error to obtain the sensitivity of four meshing performance evaluation indexes and the weighted comprehensive sensitivity;
step 10, adopting a genetic algorithm to carry out an objective function Min (C) of the comprehensive sensitivity modelS) Carrying out optimization calculation to obtain an optimal individual;
step 10.1, initialization:
taking the machining parameters of the small wheel machine tool as initial machining parameters of the small wheel machine tool to initialize a number genetic algorithm population, setting the number of individuals in the population as N, setting the iteration times of the algorithm as M, and setting the limit of an updating algebra as Q, wherein Q is less than M;
establishing N small-wheel iterative tooth surface equations of current iteration for machine tool machining parameters represented by each individual in the population according to a corresponding tooth machining principle;
step 10.2, setting effective contact areas of tooth surfaces for both the tooth surface of the large wheel and the tooth surface of the small wheel;
the effective contact area of the tooth surface is as follows: slave gearThe actual tooth surface edge of the wheel is scaled according to a set scaling factor iDMoving the formed constrained region inward;
the actual tooth flank edge comprises: a tip line, an effective root line, a large end sideline, and a small end sideline;
the scaling factor iDThe method comprises the following steps: a ratio of a tooth height of the constraining region between the addendum line and the dedendum line at the node point to an actual tooth height of the gear, and a ratio of a tooth length of the constraining region between the large end side line and the small end side line at the node point to an actual tooth length of the gear;
step 10.3, with the effective contact area of the tooth surface as constraint, respectively carrying out computer tooth meshing analysis on the large gear tooth surface equation and the currently iterated N small gear iteration tooth surface equations under the condition of selected installation errors, and calculating to obtain N groups of comprehensive sensitivities CSA value;
step 10.4, continuously performing iterative computation according to the step 10.3, and finally stopping the iterative computation until the set iteration times M or the lowest value of the comprehensive sensitivity in the continuous Q generation population is not changed, and ending the optimization process, thereby obtaining the individual with the lowest value of the comprehensive sensitivity in the final generation population as the optimal individual; and taking the machining parameters of the small gear cutting machine corresponding to the optimal individuals as the optimal machining parameters of the small gear cutting machine, so as to realize the optimal assembly of the large gear and the small gear obtained by adopting the optimal machining parameters of the small gear cutting machine according to the set relative position of the gear pair.
The processing parameter optimization method is also characterized in that:
the small wheel machine tool machining parameters comprise: machine tool mounting root angle gammamBed position delta XBHorizontal wheel position DeltaXDVertical wheel position Δ EmRadial tool position SrAngular tool position q, tool inclination angle i, tool corner j and cutting roll ratio mcp
The method is characterized in that the effective contact area of the tooth surface is taken as constraint, and the method is that after all small wheel tooth surface equations and large wheel tooth surface equations obtained by machine tool machining parameters represented by all individuals in each generation of population are subjected to computer wheel tooth meshing analysis, if tooth surface meshing impressions obtained by the individuals exceed the effective contact area of the tooth surface, the individuals are judged to be unqualified, and the unqualified individuals are deleted from the generation of population.
Compared with the prior art, the invention has the beneficial effects that:
1. in the prior art, the size, the shape and the tooth surface position of a meshing impression are directly observed by adopting a hobbing inspection or gear tooth meshing analysis method, so that the meshing quality of a hypoid gear is judged, and the accuracy is not high. According to the method, the tooth surface meshing impression of the hypoid gear is parameterized and described in the forms of meshing impression area, the tooth surface centroid position horizontal and vertical coordinates of the meshing impression and the direction angle of the meshing impression, so that the characteristic parameters of the meshing impression are accurately represented, and the problem that the characteristic of the meshing impression cannot be accurately evaluated is solved;
2. the method adopts a single variable form to analyze the influence degrees of different types of mounting errors on the tooth surface meshing imprints one by one, and respectively calculates the sensitivity of the meshing imprints evaluation indexes of the gear pair to the different types of mounting errors, distinguishes the remarkable degree of the sensitivity degree, further finds out the mounting error category with larger influence on the meshing imprints, and provides a theoretical basis for the control of the assembly precision of the gear pair in different directions during mounting;
3. according to the method, a comprehensive sensitivity optimization model is established by adopting a weighted summation method according to the sensitivity analysis conclusion of the meshing impression evaluation indexes on different installation errors, and the meshing impression evaluation indexes can be distinguished according to different sensitivity degrees of the installation errors during optimization, so that the comprehensive optimization process of different evaluation indexes is reasonably controlled;
4. the method adopts the virtual assembly and the computer meshing analysis technology to obtain the tooth surface meshing impression and the transmission error curve, thereby avoiding the repeated trial cutting and rolling inspection processes of the gear pair in practice and reducing the trial manufacture and experiment cost; when the gear pair is designed, the influence of installation errors is reduced by optimizing processing parameters, the tolerance of the gear pair assembly link is improved, and the later cost is reduced;
5. in the optimization process of the method, the tooth surface meshing impression is restricted in an effective meshing area, so that the poor contact state of edge contact and angular contact can be avoided, the occurrence probability of failure modes of pitting corrosion and spot mark of the gear pair is further reduced, the service life of the gear pair is prolonged, and the vibration noise during meshing is reduced.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic view of the hypoid gear set installation error in the method of the present invention;
FIG. 3 is a schematic diagram of parameterized representation of meshing imprints in the method of the present invention;
FIG. 4 is a schematic view of the machining parameters of the small wheel machine to be optimized in the method of the present invention;
FIG. 5 is a schematic view of the effective meshing area of the tooth flanks in the method of the present invention;
FIG. 6a is a schematic diagram of the meshing footprint of the optimized front big gear tooth surface in the present embodiment;
FIG. 6b is a schematic view of the optimized front small wheel tooth flank meshing impression in the present embodiment;
FIG. 7a is a schematic diagram of the meshing footprint of the optimized big gear tooth surface in the present embodiment;
FIG. 7b is a schematic view of the optimized tooth flank meshing impression of the rear small wheel in the present embodiment;
FIG. 8 is a graph of objective function values of comprehensive sensitivities of various generations of populations in an iterative process of a genetic algorithm in this embodiment;
reference numbers in the figures: 1 cradle rotating speed, 2 angular cutter positions, 3 radial cutter positions, 4 cutter rotating angles, 5 cutter inclination angles, 6 cutter rotating speeds, 7 vertical wheel positions, 8 tooth blank rotating speeds, 9 horizontal wheel positions, 10 machine tool installation root cone angles, 11 bed positions, 12 meshing impressions containing installation errors on the tooth surfaces of the front large wheels, 13 meshing impressions containing no installation errors on the tooth surfaces of the front large wheels, 14 meshing impressions containing installation errors on the tooth surfaces of the front small wheels, 15 meshing impressions containing no installation errors on the tooth surfaces of the front small wheels, 16 meshing impressions containing installation errors on the tooth surfaces of the rear large wheels, 17 meshing impressions containing no installation errors on the tooth surfaces of the rear large wheels, 18 meshing impressions containing installation errors on the tooth surfaces of the rear small wheels, and 19 meshing impressions containing no installation errors on the tooth surfaces of the rear small wheels.
Detailed Description
In the embodiment, the method for optimizing the machining parameters for reducing the sensitivity of the hypoid gear installation error is applied to optimizing and adjusting the machining parameters of a small wheel machine tool, wherein the sensitivity of the installation error refers to the sensitivity of the meshing performance of a gear pair to the installation error; the machining parameters of the small wheel machine tool comprise: machine tool mounting root angle Δ EmBed position delta XBHorizontal wheel position DeltaXDVertical wheel position Δ EmRadial tool position SrAngular tool position q, tool inclination angle i, tool corner j and cutting roll ratio mcpAs shown in fig. 4. The optimized adjustment of the machining parameters of the small wheel machine tool is carried out according to the following steps:
step 1, according to the design requirements of a hypoid gear pair, setting a gear pair offset distance, a large gear blank geometric parameter, a large gear cutting tool size parameter, a small gear blank geometric parameter and a small gear cutting tool size parameter; according to the Gleason machining principle adopted by the gear cutting machine tool, the machining parameters of the large wheel machine tool and the small wheel machine tool are respectively calculated, and the machining parameters of the small wheel machine tool are used as the initial machining parameters of the small wheel machine tool for initializing the population in the genetic algorithm. The gritson hypoid gear pair is the most common gear system form in the automotive hypoid gear pair in China, so the invention is taken as an example, but the invention is not only limited to the gritson gear system gear processing;
step 2, establishing a large gear tooth surface equation under a large gear tooth blank coordinate system by using the geometric parameters of the large gear tooth blank, the dimensional parameters of the large gear cutting tool and the processing parameters of the large gear machine tool according to the corresponding large gear processing principle of the gear cutting machine tool; according to the corresponding small wheel machining principle of the gear cutting machine tool, a small wheel tooth surface equation under a small wheel tooth blank coordinate system is established by utilizing the geometric parameters of the small wheel tooth blank, the dimensional parameters of the small wheel gear cutting tool and the machining parameters of the small wheel machine tool. The equation of the tooth surface of the large wheel and the equation of the tooth surface of the small wheel are radial vector and normal vector mathematical equations of points on the tooth surface, can be used for obtaining the tooth surface point cloud three-dimensional coordinates of the large wheel and the small wheel, and can express the real tooth surface of the gear according to the equation of the tooth surface. And virtually assembling a large gear surface equation and a small gear surface equation according to the given gear pair offset distance to obtain a meshing gear surface equation under a meshing coordinate system. The virtual assembly refers to assembling a large gear surface equation and a small gear surface equation into a meshing coordinate system by adopting a coordinate transformation method according to the preset offset distance of a gear pair and the right-hand rule of a Cartesian coordinate system. The original large and small gear blank coordinate system origin is located at the meshing coordinate system origin, the X-axis direction of the original axis of the large gear is parallel to the Y-axis of the meshing coordinate system, the X-axis direction of the axis of the small gear is along the X-axis of the meshing coordinate system, and the distance between the axes of the large and small gears is an offset distance. Respectively rotating a big gear tooth surface equation and a small gear tooth surface equation by a certain angle to ensure that radial vectors of the big gear tooth surface and the small gear tooth surface at a calculation reference point under a meshing coordinate system are equal, and the meshing transmission ratio at the calculation reference point is equal to the theoretical transmission ratio when the gear pair is designed;
step 3, as shown in fig. 2, defining four installation errors of the gear pair includes: axial error H of large wheelGAxial error H of small wheelPAxis crossing angle error sigma and offset error V; any one of the four installation errors is recorded as an installation error R belonging to the { H ∈ RP,HGV, Σ }; according to the actual requirement of the installation precision, the value range of any installation error R of the gear pair is set, for example: hGTaking +/-0.3 mm; hPTaking +/-0.3 mm; v is plus or minus 0.3 mm; taking +/-0.3 degrees;
and 4, enabling the installation error R to take K values at equal intervals in the value range, and recording the K values as { R1,R2,…,Rk,…,RKSetting other 3 errors as '0', respectively finishing the virtual assembly of the gear pair K times under the installation error R, and obtaining K meshing tooth surface equations in a meshing coordinate system under the installation error R; wherein R iskThe kth value of the installation error R in the value range is represented; k is 1,2, …, K;
step 5, aiming at four installation errors, respectively carrying out computer gear meshing analysis (TCA, Tooth contact analysis) on K meshing Tooth surface equations under each installation error to obtain K groups of Tooth surface meshing impressions and K groups of gear pair transmission error curves under each installation error;
step 6, determining and judging the meshing imprints of the tooth surfaces under the four installation errorsFour evaluation indexes of scar quality include: meshing impression area S in gear tooth section coordinate systemcpTooth surface centroid position abscissa of meshing impression
Figure BDA0002038633420000071
Tooth surface centroid position ordinate of meshing impression
Figure BDA0002038633420000072
And the meshing impression azimuth angle gammacpAnd are respectively represented by formula (1), formula (2), formula (3) and formula (4); and any one of the four evaluation indexes is recorded as an evaluation index T,
Figure BDA0002038633420000073
the value of T is recorded as an evaluation index value fT
Figure BDA0002038633420000074
Figure BDA0002038633420000081
Figure BDA0002038633420000082
Figure BDA0002038633420000083
In the formula (1) to the formula (4), n represents the number of points into which the left side line, the right side line and the impression center line of the tooth surface meshing impression are all dispersed in the computer gear tooth meshing analysis; A. b, C is an intermediate variable, and
Figure BDA0002038633420000084
Figure BDA0002038633420000085
Figure BDA0002038633420000086
respectively representing the abscissa and ordinate of the p-th point on the left side line of the meshing impression, wherein p is 1,2, …, n-1;
Figure BDA0002038633420000087
respectively representing the abscissa value and the ordinate value of the p +1 point on the left side line of the meshing impression;
Figure BDA0002038633420000088
respectively representing the abscissa value and the ordinate value of the p-th point on the right side line of the meshing impression;
Figure BDA0002038633420000089
respectively representing the abscissa value and the ordinate value of the p +1 point on the right side line of the meshing impression;
Figure BDA00020386334200000810
respectively representing the abscissa value and the ordinate value of the p-th point on the marking center line;
Figure BDA00020386334200000811
respectively represents the abscissa value and the ordinate value of the p +1 th point on the trace in the impression. As shown in fig. 3, the coordinate system of the cross section of the gear tooth is a coordinate system which takes the actual root line of the gear as an x-axis, takes the design origin of the gear as an origin o, and is vertical to the x-axis and points to the outside of the gear in the axial cross section;
step 7, calculating the kth value R of the installation error RkValue f of the following evaluation index TT(Rk) And the value f of the evaluation index T without any installation errorT(0) Difference between them
Figure BDA00020386334200000812
Thereby obtaining K groups of difference values
Figure BDA00020386334200000813
Calculating the sensitivity of the evaluation index T to the mounting error R by using the formula (5)
Figure BDA00020386334200000814
Figure BDA00020386334200000815
Step 8, recording the sum of the sensitivities of the evaluation index T to the four mounting errors as STThe sum S of the sensitivities of the evaluation index T to the four mounting errorsTCarrying out weighted summation to obtain the comprehensive sensitivity CS
Establishing a small wheel machining parameter as an optimization variable by using the formula (6), and taking the minimum CSValue-targeted integrated sensitivity optimization model:
Figure BDA0002038633420000091
in formula (6), Min (C)S) The objective function value of the comprehensive sensitivity optimization model is the minimum value of the function; u. ofTIs a weighting coefficient for evaluating the sensitivity of the index T to the mounting error R.
Figure BDA0002038633420000092
Are weighting coefficients of four evaluation indexes. And the numerical value of each weighting coefficient is set according to the sequence of the sensitivity values of the four evaluation indexes to the installation error calculated from the big to the small and the corresponding weighting coefficient value is set manually according to the principle of the big to the small. For example: if the sensitivity values are arranged in the order from large to small:
Figure BDA0002038633420000093
the weighting coefficients can be artificially set to:
Figure BDA0002038633420000094
Figure BDA0002038633420000095
the set of values is given artificially, satisfies the corresponding magnitude order and
Figure BDA0002038633420000096
the principle of (1) is as follows;
step 9, selecting a group of installation error values within the value ranges of the four installation errors, for example: hGTaking 0.17 mm; hPTaking-0.22 mm; v is 0.11 mm; taking the sigma to be-0.15 degrees, completing virtual assembly of the gear pair under the condition of containing the selected group of installation errors, and obtaining an engagement tooth surface equation under the condition of containing the selected installation errors in an engagement coordinate system;
performing computer gear tooth meshing analysis (TCA) aiming at a meshing tooth surface equation containing the selected mounting error to obtain a tooth surface meshing impression and a gear pair transmission error curve containing the selected mounting error;
carrying out sensitivity and comprehensive sensitivity calculation on the tooth surface meshing impression containing the selected mounting error to obtain the sensitivity of four meshing performance evaluation indexes and the weighted comprehensive sensitivity;
step 10, adopting a genetic algorithm to synthesize an objective function Min (C) of a sensitivity modelS) Carrying out optimization calculation to obtain an optimal individual; the problem of selecting the machine tool machining parameters is converted into the problem of reducing the comprehensive sensitivity objective function value of the installation error for solving, so that the complicated machine tool machining parameter adjusting process can be avoided.
Step 10.1, initialization:
and (3) taking the small wheel machine tool processing parameters obtained in the step (1) as small wheel machine tool initial processing parameters for initializing a number genetic algorithm population, setting the number of individuals in the population as N, setting the iteration times of the algorithm as M, and setting the updating algebra limit as Q, wherein Q is less than M. The updating algebra limit is defined as that if the lowest value of the comprehensive sensitivity in the continuous Q generation population is not updated in the optimization process, the iterative computation process is stopped, and the optimization is finished;
establishing N small-wheel iteration tooth surface equations of current iteration for machine tool machining parameters represented by each individual in the population according to the Gleason machining principle;
step 10.2, setting effective contact areas of tooth surfaces for both the tooth surface of the large wheel and the tooth surface of the small wheel;
the effective contact area of the tooth surface is as follows: according to a set scaling coefficient i from the actual tooth surface edge of the gearDMoving the formed constrained region inward;
the actual tooth flank edge comprises: a tip line, an effective root line, a large end sideline, and a small end sideline;
scaling factor iDThe method comprises the following steps: a ratio of a tooth height of the tooth top line and the tooth bottom line of the constraining region between the nodes to an actual tooth height of the gear, and a ratio of a tooth length of the large end side line and the small end side line of the constraining region between the nodes to an actual tooth length of the gear;
step 10.3, with the effective contact area of the tooth surface as constraint, respectively carrying out computer gear tooth meshing analysis (TCA) containing selected installation errors on the large gear tooth surface equation obtained in the step 2 and N small-gear iteration tooth surface equations of the current iteration, and calculating to obtain N groups of comprehensive sensitivities CSThe value is obtained. Taking the effective contact area of the tooth surface as constraint, namely after performing computer wheel tooth meshing analysis on all small wheel tooth surface equations and large wheel tooth surface equations obtained by machine tool machining parameters represented by all individuals in each generation of population, if tooth surface meshing impressions obtained by the individuals exceed the effective contact area of the tooth surface, judging the individuals to be unqualified, and deleting the unqualified individuals from the generation of population;
step 10.4, continuously performing iterative computation according to the step 10.3, and finally stopping the iterative computation until the set iteration times M or the lowest value of the comprehensive sensitivity in the continuous Q generation population is not changed, and ending the optimization process, thereby obtaining the individual with the lowest value of the comprehensive sensitivity in the final generation population as the optimal individual; and the machining parameters of the small gear cutting machine corresponding to the optimal individuals are used as the optimal machining parameters of the small gear cutting machine, so that the optimal assembly of the large gear and the small gear obtained by machining according to the optimal machining parameters of the small gear cutting machine according to the set relative position of the gear pair is realized.
Example (b):
taking a pair of hypoid gear pairs with an offset distance of 38mm as an example, the number of teeth of a large gear is 7, the number of teeth of a small gear is 36, basic geometric parameters are shown in table 1, machining parameters of the large gear machine tool calculated according to the Gleason method are shown in table 2, and initial machining parameters of the small gear are shown in table 10.
TABLE 1 hypoid gear pair geometry parameters
Figure BDA0002038633420000101
Figure BDA0002038633420000111
TABLE 2 bull wheel processing parameters
Figure BDA0002038633420000112
Fig. 1 is a general flow chart of the method of the present invention, and fig. 2 is a schematic diagram of the mounting error of a hypoid gear pair in the method of the present invention, and the mounting error quantity parameter of the gear pair is given according to table 3. FIG. 3 is a schematic diagram illustrating parameterized meshing impressions of the method of the present invention, where the optimized meshing impression of the front bull gear tooth surface is shown in FIG. 6a, and includes a meshing impression 12 under the condition of installation error on the optimized front bull gear tooth surface and a meshing impression 13 under the condition of no installation error on the optimized front bull gear tooth surface; the tooth flank meshing impressions of the small wheel are shown in fig. 6b and include an impression 14 under the condition of mounting error on the optimized front small wheel tooth flank and an impression 15 under the condition of no mounting error on the optimized front small wheel tooth flank. The parameters of the meshing impressions without mounting error and with mounting error before optimization, which are respectively calculated according to the calculation formulas of the meshing impression area, the centroid position and the direction angle, are shown in tables 4 and 5.
TABLE 3 installation error quantity parameter
Figure BDA0002038633420000113
TABLE 4 meshing impression parameters without mounting errors before optimization
Figure BDA0002038633420000121
TABLE 5 meshing footprint parameters including mounting errors before optimization
Figure BDA0002038633420000122
Defining the mounting error H separatelyP,HGThe range of V is [ -0.3, +0.3]mm, the variation range of sigma is [ -0.3, +0.3]deg. The gear pair meshing analysis containing the installation error is completed, and the sensitivity coefficient of the impression before optimization to the installation error in each direction, which is obtained by comparing the variation condition of each parameter of the meshing impression, is shown in table 6.
TABLE 6 sensitivity coefficient of meshing impression to mounting error in each direction before optimization
Figure BDA0002038633420000123
And (3) optimizing by adopting a genetic algorithm, wherein the population size is determined to be 40, namely, each generation of population contains 40 individuals, and the iteration number is determined to be 100, namely, the iteration is performed for 100 times at most. Comparing sensitivity coefficients of the impressions to the anisotropic errors, selecting the weighting parameters as
Figure BDA0002038633420000124
Namely, the weighting coefficient of the centroid of the meshing impression is 0.2, the weighting coefficient of the centroid of the meshing impression is 0.175, the weighting coefficient of the area of the meshing impression is 0.275, and the weighting coefficient of the orientation angle of the meshing impression is 0.35.
Fig. 4 is a schematic diagram of machining parameters of a small wheel machine tool to be optimized, including an angular tool position 2, a radial tool position 3, a tool rotation angle 4, a tool inclination angle 5, a vertical wheel position 7, a horizontal wheel position 9, a machine tool installation root cone angle 10, a bed position 11, a cradle rotation speed 1, a cutter head rotation speed 6 and a gear blank rotation speed 8. The effective meshing area of the tooth flanks during optimization is shown in fig. 5.
The optimized parameters of the meshing imprints without installation errors and with installation errors are shown in tables 7 and 8, the sensitivity coefficient of the meshing imprints to the mounting errors in each direction is shown in table 9, and the optimized parameters of the small wheel machining are shown in table 10.
TABLE 7 optimized meshing footprint parameters without mounting errors
Figure BDA0002038633420000131
TABLE 8 optimized meshing footprint parameters with mounting errors
Figure BDA0002038633420000132
TABLE 9 sensitivity coefficient of optimized meshing footprint to mounting error in each direction
Figure BDA0002038633420000133
TABLE 10 optimization of front and rear small wheel processing parameters
Figure BDA0002038633420000134
Figure BDA0002038633420000141
The optimized big gear tooth surface meshing impression is shown in FIG. 7a and comprises: the optimized tooth surface of the big wheel is provided with a meshing impression 16 under the condition of installation error, and the optimized tooth surface of the big wheel is provided with a meshing impression 17 without installation error; the small wheel flank meshing impression is shown in fig. 7b and comprises: the optimized small wheel tooth surface has meshing impression 18 under the condition of installation error, and the optimized small wheel tooth surface has meshing impression 19 under the condition of no installation error. Comparison with fig. 6a and 6b shows that the change in impression of the tooth flanks of the large and small wheels after optimization is less pronounced than before optimization for the same installation error. From table 9, it can be seen that 11 of the 16 sensitivity parameters were all decreased, with a maximum decrease of 9.35%, and the remaining 5 sensitivity were increased, but none of them was large, with a maximum amplitude of 4.83%, and overall, the overall sensitivity of the meshing impression of the gear pair to mounting errors was decreased. The overall engagement region is located within a predetermined effective engagement region, proving effective for constraining the rational engagement region. The population comprehensive sensitivity target value iteratively calculated by the genetic algorithm is shown in fig. 8, and the optimal individual objective function value can be converged to a preset value after 100 times of iterative calculation, so that the genetic algorithm adopted by the method is proved to be feasible and efficient.

Claims (1)

1. A machining parameter optimization method for reducing the sensitivity of hypoid gear installation errors is characterized by being applied to optimizing and adjusting the machining parameters of a small wheel machine tool, and the optimization and adjustment of the machining parameters of the small wheel machine tool are carried out according to the following steps:
step 1, according to the design requirements of a hypoid gear pair, setting a gear pair offset distance, a large gear blank geometric parameter, a large gear cutting tool size parameter, a small gear blank geometric parameter and a small gear cutting tool size parameter; respectively calculating machining parameters of a large wheel machine tool and machining parameters of a small wheel machine tool according to a gear machining principle corresponding to the gear cutting machine tool; the small wheel machine tool machining parameters comprise: machine tool mounting root angle gammamBed position delta XBHorizontal wheel position DeltaXDVertical wheel position Δ EmRadial tool position SrAngular tool position q, tool inclination angle i, tool corner j and cutting roll ratio mcp
Step 2, according to a large gear machining principle corresponding to the gear cutting machine tool, establishing a large gear tooth surface equation under a large gear tooth blank coordinate system by using the geometric parameters of the large gear tooth blank, the dimensional parameters of the large gear cutting tool and the machining parameters of the large gear machine tool; according to a small wheel machining principle corresponding to a gear cutting machine tool, establishing a small wheel tooth surface equation under a small wheel tooth blank coordinate system by using the small wheel tooth blank geometric parameters, the small wheel gear cutting tool size parameters and the small wheel machine tool machining parameters; according to a given gear pair offset distance, virtually assembling the large gear surface equation and the small gear surface equation to obtain a meshing gear surface equation under a meshing coordinate system;
step 3, defining four installation errors of the gear pair, including: axial error H of large wheelGAxial error H of small wheelPAxis crossing angle error sigma and offset error V; recording any one of the four installation errors as an installation error R, wherein R belongs to { H ∈ [ ]P,HGV, Σ }; setting the value range of any one installation error R of the gear pair according to the actual requirement of the installation precision;
and 4, enabling the installation error R to take K values at equal intervals in the value range, and recording the K values as { R1,R2,…,Rk,…,RKSetting other 3 errors as '0', respectively finishing the virtual assembly of the gear pair K times under the installation error R, and obtaining K meshing tooth surface equations in a meshing coordinate system under the installation error R; wherein R iskThe kth value of the installation error R in the value range is represented; k is 1,2, …, K;
step 5, respectively carrying out computer gear meshing analysis on the K meshing tooth surface equations under each mounting error according to the four mounting errors to obtain K groups of tooth surface meshing impressions and K groups of gear pair transmission error curves under each mounting error;
step 6, aiming at the tooth surface meshing imprints under four installation errors, determining four evaluation indexes for evaluating the quality of the meshing imprints, comprising the following steps of: meshing impression area S in gear tooth section coordinate systemcpTooth surface centroid position abscissa of meshing impression
Figure FDA0002842465530000011
Tooth surface centroid position ordinate of meshing impression
Figure FDA0002842465530000012
And the meshing impression azimuth angle gammacpAnd are respectively represented by formula (1), formula (2), formula (3) and formula (4); and any one of the four evaluation indexes is recorded as an evaluation index T,
Figure FDA0002842465530000013
the value of T is recorded as an evaluation index value fT
Figure FDA0002842465530000014
Figure FDA0002842465530000021
Figure FDA0002842465530000022
Figure FDA0002842465530000023
In the formula (1) to the formula (4), n represents the number of points into which the left side line, the right side line and the impression center line of the tooth surface meshing impression are all dispersed in the computer gear tooth meshing analysis; A. b, C is an intermediate variable, and
Figure FDA0002842465530000024
Figure FDA0002842465530000025
Figure FDA0002842465530000026
respectively representing the abscissa and ordinate of the p-th point on the left side line of the meshing impression, wherein p is 1,2, …, n-1;
Figure FDA0002842465530000027
respectively representing the abscissa value and the ordinate value of the p +1 point on the left side line of the meshing impression;
Figure FDA0002842465530000028
respectively representing the abscissa value and the ordinate value of the p-th point on the right side line of the meshing impression;
Figure FDA0002842465530000029
respectively representing the abscissa value and the ordinate value of the p +1 point on the right side line of the meshing impression;
Figure FDA00028424655300000210
respectively representing the abscissa value and the ordinate value of the p-th point on the marking center line;
Figure FDA00028424655300000211
respectively representing the abscissa value and the ordinate value of the p +1 point on the marking center line;
step 7, calculating the kth value R of the installation error RkValue f of the following evaluation index TT(Rk) And the value f of the evaluation index T without any installation errorT(0) Difference between them
Figure FDA00028424655300000212
Thereby obtaining K groups of difference values
Figure FDA00028424655300000213
Calculating the sensitivity of the evaluation index T to the mounting error R by using the formula (5)
Figure FDA00028424655300000214
Figure FDA00028424655300000215
Step 8, recording the sum of the sensitivities of the evaluation index T to the four mounting errors as STWill evaluate toSum S of sensitivities of the target T to four mounting errorsTCarrying out weighted summation to obtain the comprehensive sensitivity CS
Establishing a small wheel machining parameter as an optimization variable by using the formula (6), and taking the minimum CSValue-targeted integrated sensitivity optimization model:
Figure FDA0002842465530000031
in formula (6), Min (C)S) The objective function value of the comprehensive sensitivity optimization model is the minimum value of the function; u. ofTA weighting coefficient that is the sensitivity of the evaluation index T to the installation error R;
step 9, selecting a group of installation error values within the value ranges of the four installation errors, completing virtual assembly of the gear pair under the selected group of installation errors, and obtaining an engagement tooth surface equation under the selected installation errors in an engagement coordinate system;
carrying out computer gear tooth meshing analysis on the meshing tooth surface equation containing the selected mounting error to obtain a tooth surface meshing impression and a gear pair transmission error curve containing the selected mounting error;
carrying out sensitivity and comprehensive sensitivity calculation on the tooth surface meshing impression containing the selected mounting error to obtain the sensitivity of four meshing performance evaluation indexes and the weighted comprehensive sensitivity;
step 10, adopting a genetic algorithm to carry out an objective function Min (C) of the comprehensive sensitivity modelS) Carrying out optimization calculation to obtain an optimal individual;
step 10.1, initialization:
taking the machining parameters of the small wheel machine tool as initial machining parameters of the small wheel machine tool to initialize a number genetic algorithm population, setting the number of individuals in the population as N, setting the iteration times of the algorithm as M, and setting the limit of an updating algebra as Q, wherein Q is less than M;
establishing N small-wheel iterative tooth surface equations of current iteration for machine tool machining parameters represented by each individual in the population according to a corresponding tooth machining principle;
step 10.2, setting effective contact areas of tooth surfaces for both the tooth surface of the large wheel and the tooth surface of the small wheel;
the effective contact area of the tooth surface is as follows: according to a set scaling coefficient i from the actual tooth surface edge of the gearDMoving the formed constrained region inward;
the actual tooth flank edge comprises: a tip line, an effective root line, a large end sideline, and a small end sideline;
the scaling factor iDThe method comprises the following steps: a ratio of a tooth height of the constraining region between the addendum line and the dedendum line at the node point to an actual tooth height of the gear, and a ratio of a tooth length of the constraining region between the large end side line and the small end side line at the node point to an actual tooth length of the gear;
step 10.3, with the effective contact area of the tooth surface as constraint, respectively carrying out computer tooth meshing analysis on the large gear tooth surface equation and the currently iterated N small gear iteration tooth surface equations under the condition of selected installation errors, and calculating to obtain N groups of comprehensive sensitivities CSA value; the method is characterized in that the effective contact area of the tooth surface is taken as constraint, after calculation wheel tooth meshing analysis is carried out on all small wheel tooth surface equations and large wheel tooth surface equations obtained by machine tool machining parameters represented by all individuals in each generation of population, if tooth surface meshing impressions obtained by the individuals exceed the effective contact area of the tooth surface, the individuals are judged to be unqualified, and the unqualified individuals are deleted from the generation of population;
step 10.4, continuously performing iterative computation according to the step 10.3, and finally stopping the iterative computation until the set iteration times M or the lowest value of the comprehensive sensitivity in the continuous Q generation population is not changed, and ending the optimization process, thereby obtaining the individual with the lowest value of the comprehensive sensitivity in the final generation population as the optimal individual; and taking the machining parameters of the small gear cutting machine corresponding to the optimal individuals as the optimal machining parameters of the small gear cutting machine, so as to realize the optimal assembly of the large gear and the small gear obtained by adopting the optimal machining parameters of the small gear cutting machine according to the set relative position of the gear pair.
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