CN106369139B - A kind of Machining of Near-Hyperboloid Gear parameter acquiring method meeting high order driving error - Google Patents
A kind of Machining of Near-Hyperboloid Gear parameter acquiring method meeting high order driving error Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 57
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- 230000005540 biological transmission Effects 0.000 claims description 86
- 244000309464 bull Species 0.000 claims description 41
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/17—Toothed wheels
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/08—Profiling
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Abstract
The present invention relates to a kind of Machining of Near-Hyperboloid Gear parameter acquiring methods for meeting high order driving error, comprising the following steps: 1) the initial manufacture parameter of gear wheel and pinion gear in hypoid gear is obtained according to existing tooth surface design method；2) the pinion gear teeth millet cake that the gear wheel flank of tooth is selected and is conjugated with it is calculated according to initial manufacture parameter, and obtains the Machine-settings with the pinion gear flank of tooth of gear wheel conjugation；3) according to preset high order driving error curve, obtain the new pinion gear flank of tooth, using the pinion gear flank of tooth and it is above-mentioned obtained in gear wheel conjugation the pinion gear flank of tooth obtain pinion gear correction of the flank shape face；4) according to preset contact trace and Contact Ellipse half-breadth, the pinion gear correction of the flank shape face obtained to step 3) is adjusted, and obtains the pinion gear correction of the flank shape face for meeting default high order driving error curve and preset exposure trace；5) flank of tooth high-order error reverse method is utilized, pinion gear is calculated and adds the corresponding Machine-settings of the new flank of tooth behind correction of the flank shape face.
Description
Technical Field
The invention relates to a hypoid gear machining parameter obtaining method meeting high-order transmission errors, and belongs to the field of gear manufacturing.
Background
Hypoid gears are one of the most important transmission parts in transmission systems, and are widely used in products such as automobiles, aircrafts, ships and warships. The transmission performance of hypoid gears is mainly related to the transmission error curve and the contact footprint of the gear pair. Improper placement of the gear contact footprint can cause offset loading and stress concentrations. The transmission error is the difference between the actual and theoretical rotational angles of the large gear, which reflects the speed and displacement changes in the gear transmission. For a pair of meshing gear pairs, meshing impacts are generated when the relative speed is abruptly changed. The transmission error curve is plotted as a function of pinion rotation angle, with the slope representing the change in gear relative speed. The speed difference between adjacent transmission error curves at the switching points causes the gear teeth to be engaged, thereby generating impact.
In order to improve the performance of the hypoid gear, Litvin and the like propose that impact and installation errors can be absorbed by using a parabola-shaped rotation error, Stadtfeld proposes a fourth-order transmission error curve after researching a symmetrical parabola-shaped transmission error curve, and considers that the parabola-shaped transmission error can cause impact of tooth replacement due to larger relative speed when tooth replacement is carried out, and the fourth-order transmission error can reduce the impact caused by the relative speed when the tooth replacement is carried out. Relevant researches on the fourth-order transmission error are carried out by domestic and foreign scholars, and the main problems in the researches comprise that: the transmission error curve actually obtained by the design method has a larger difference with the expected curve; only the design of transmission error is carried out and the control on the tooth surface contact footprint is neglected; some methods are lack of contact print pre-control and actual result comparison although contact print control is carried out, and the print control effect cannot be explained; some are only applicable to fourth order transmission error curves.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a method for obtaining tooth surface machining parameters of a hypoid gear pinion, which can reduce a hypoid gear high-order transmission error.
In order to achieve the purpose, the invention adopts the following technical scheme: a hypoid gear machining parameter obtaining method meeting high-order transmission errors comprises the following steps: 1) obtaining initial processing parameters of a large gear and a small gear in a hypoid gear according to the existing tooth surface design method; 2) calculating a pinion tooth surface point completely conjugated with the bull gear and a pinion tooth surface point according to the initial processing parameters, and acquiring machine tool processing parameters of the pinion tooth surface completely conjugated with the bull gear; 3) obtaining a new pinion tooth surface according to a preset high-order transmission error curve, and obtaining a pinion modification surface only meeting the preset high-order transmission error curve by utilizing the pinion tooth surface and the pinion tooth surface which is completely conjugated with the bull gear and is obtained in the step 2); 4) adjusting the pinion shaping surface obtained in the step 3) according to a preset contact print and a half width of a contact ellipse to obtain a pinion shaping surface meeting a preset high-order transmission error curve and a preset contact print; 5) and calculating a pinion adding step 4) by utilizing a tooth surface high-order error reverse solving method to obtain the machine tool machining parameters corresponding to the new tooth surface after the pinion shaping surface meeting the preset high-order transmission error curve and the preset contact print.
The method for acquiring the initial processing parameters of the large gear and the small gear in the step 1) is a Gleason method, and the acquired initial processing parameters comprise theta1、φ1、θ2、φ2、And v12。
The process for acquiring the machine tool machining parameters of the pinion tooth surface completely conjugated with the bull gear in the step 2) is as follows:
obtaining a big gear tooth surface point r according to the formula (1)2And normal n2Obtaining a pinion tooth surface point r according to equation (2)1And normal n1；
Wherein, theta1And phi1Respectively representing the cutter angle and the cradle angle, theta, during pinion machining2And phi2Respectively representing the cutter head corner and the cradle corner when the large gear is machined;
by using the formula (3) and the formula (4), the coordinates of the tooth surface points of the pinion gear completely conjugated with the bull gear are obtainedAnd normal directionWith equation (5), the difference curved surface △ R of the pinion gear fully conjugate with the bull gear and the pinion gear tooth surface obtained from equation (2) is obtained as follows:
wherein,andrespectively being pinion angleAnd pinion initial position angle;andrespectively a bull gear corner and a bull gear initial position corner; v. of12The relative speed of the pinion and the bull gear;
and (3) calculating the machining parameters of the tooth surface of the pinion which is completely conjugated with the bull gear by using the hypoid gear tooth surface error reverse solving method for the differential curved surface △ R.
The process of obtaining the pinion profile in the step 3) is as follows:
the formula (6) is a general form of a high-order transmission error curve
Wherein,for high order transmission error values, asIs the coefficient of the high-order transmission error curve, and q is the highest order of the high-order transmission error curve;
according to the horizontal and vertical coordinates of the extreme points in the preset high-order transmission error curve, listing the position equation and the extreme value equation of each extreme point, thereby solving the coefficient a of the high-order transmission error curves；
And then, obtaining the pinion gear surface point meeting a preset high-order transmission error curve with the large gear by using the formula (4) and the formula (6)And obtaining a modification surface sigma of the pinion by using an equation (8) according to the tooth surface point and the pinion tooth surface point which is completely conjugated with the bull gear and is obtained in the step 2)1：
The process of obtaining the pinion shaping surface meeting the preset high-order transmission error curve and the preset contact print in the step 4) is as follows:
taking a two-dimensional projection diagram after the modification surface is projected to a plane, wherein a contact trace in the diagram is divided into 3 sections, one section is an addendum part, the other section is a dedendum part, and a straight line connecting the addendum part and the dedendum part is also provided;
wherein L is1Defining the design contact half width as b for the distance from the point to the contact trace in the two-dimensional projection diagram, and modifying the point by using the modification quantity as ∑2Using equation (10) to convert ∑2And the modification part sigma obtained in the step 3)1And adding to obtain a final modified surface sigma:
Σ＝Σ1+Σ2。 (10)
the tooth surface high-order error reverse solving method adopted in the step 5) is a roll ratio correction method, the tooth surface error reverse solving is carried out by using the method, the corresponding pinion machining parameters after the trimming surfaces are overlapped are calculated, and finally the machining parameters of the pinion meeting the preset high-order transmission error curve and the contact footprint are obtained.
Due to the adoption of the technical scheme, the invention has the following advantages: 1. the actually obtained high-order transmission error curve is well matched with the curve preset by a designer. 2. The obtained tooth surface contact print is well matched with the preset position of a designer. 3. The method is suitable for designing any-order transmission error curve and can be used for designing higher orders.
Drawings
FIG. 1 is a schematic view of a pinion gear fully conjugate with a bull gear as obtained in the present invention;
FIG. 2 is a schematic illustration of the 4 th order transmission error curve employed in summary 3 of the invention;
FIG. 3 is a schematic view of the projection of a modified surface onto a parametric plane contact footprint control in the present disclosure 4;
FIG. 4 is a schematic view of the half-width control of the contact ellipse projected by the profile surface onto the parametric plane in accordance with the present invention 4;
FIG. 5 shows a modified face Σ for the pinion in step 3 of the present invention1；
FIG. 6 illustrates a final profile Σ of the pinion gear in step 4 of the present embodiment;
FIG. 7 is a graph comparing high order transmission errors in step 5 of an embodiment of the present invention;
FIG. 8 is a comparison of contact prints of the pinion gear at step 5 of the embodiment of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
The invention provides a method for acquiring tooth surface processing parameters of a hypoid gear pinion, which comprises the following steps:
1) initial machining parameters of a gearwheel and a pinion in a hypoid gear are obtained according to existing tooth surface design methods (e.g. Gleason method, reference gear handbook, second edition), said initial machining parameters including theta1、φ1、θ2、φ2、And v12。
2) Calculating a gear surface point of a bull gear and a gear surface point of a pinion gear completely conjugated with the gear surface point according to the initial processing parameters, and obtaining the machine tool processing parameters of the gear surface of the pinion gear completely conjugated with the bull gear, wherein the specific process comprises the following steps:
according to the formula (1), the big gear tooth surface point r can be obtained2And normal n2The pinion tooth surface point r can be obtained according to the formula (2)1And normal n1
Wherein, theta1And phi1Respectively representing the cutter angle and the cradle angle, theta, during pinion machining2And phi2Respectively representing the cutter head corner and the cradle corner when the large gear is machined.
In order to completely conjugate the obtained pinion tooth surface and the bull gear tooth surface obtained according to equation (1), it is necessary to satisfy the transmission ratio equation (3) and the meshing equation (4).
The transmission ratio equation:
wherein,andrespectively a pinion rotation angle and a pinion initial position rotation angle;andthe turning angle of the big gear and the turning angle of the initial position of the big gear are respectively.
Meshing equation:
wherein v is12The relative speed of the pinion and the bull gear.
By using the formulas (3) and (4), the coordinates of the tooth surface points of the pinion gear completely conjugated with the bull gear can be obtainedAnd normal directionWith equation (5), a differential curved surface △ R of the pinion gear fully conjugate with the bull gear and the pinion gear surface obtained from equation (2) can be obtained:
the differential surface △ R can be used for calculating the machine tool machining parameters of the pinion tooth surface completely conjugated with the bull gear by utilizing a hypoid gear tooth surface error reverse calculation method, and FIG. 1 shows the pinion tooth surface completely conjugated with the bull gear.
3) Obtaining a new pinion tooth surface according to a preset high-order transmission error curve, and obtaining a pinion shaping surface only meeting the preset high-order transmission error curve by using the pinion tooth surface and the pinion tooth surface which is completely conjugated with the large gear and is obtained in the step 2), wherein the specific process is as follows:
the formula (6) is a general form of a high-order transmission error curve
Wherein,for high order transmission error values, asAnd q is the coefficient of the high-order transmission error curve, and the highest order of the high-order transmission error curve.
FIG. 2 is a 4 th order transmission error curve, where C2The point is a middle point, C1And C3Two peaks on either side. Lambda [ alpha ]1,λ2,λ3The abscissa values, δ, corresponding to the 3 points, respectivelyc1,δc2,δc3The ordinate values correspond to the 3 points, respectively. The 5 unknowns in equation (6) can be based on the positional equations of these three points and C1And C3Equation of extreme value of points, see formula (7)
All the term coefficients in the formula (6) can be obtained by the formula (7).
By using the formula (4) and the formula (6), the pinion tooth surface point meeting the preset high-order transmission error curve with the large gear can be obtainedAnd obtaining a pinion shaping surface sigma by using a formula (8) according to the tooth surface point and the pinion tooth surface point which is obtained in the step 2) and is completely conjugated with the bull gear1
4) Adjusting the pinion shaping surface obtained in the step 3) according to a preset contact print and a half width of a contact ellipse to obtain the pinion shaping surface meeting a preset high-order transmission error curve and the preset contact print, wherein the specific process is as follows:
as shown in fig. 3, it is a two-dimensional projection of the modified surface projected on a plane. The contact traces are divided into 3 segments, where K1K2And K3K4The slope of the straight line CL is k for the tooth crest and the tooth root portionsslope. For the 3 sections of contact traces, if the falling point on the modification surface is on the 3 sections of straight lines, no correction is carried out, and for the rest points on the modification surface, the modification surface is corrected according to the preset contact half width.
As shown in fig. 4, for point P on the profile surface1If the preset contact half width is defined as b, the correction amount of the point modification is represented by formula (9)
Wherein L is1Is the distance of the point to the contact trace within the two-dimensional projection.
Adding the small gear shaping surface obtained in the step 3) and the shaping part of the shaping surface obtained according to the preset contact trace and the contact half width in the step 4) by using an equation (10) to obtain a final small gear shaping surface sigma meeting a preset high-order transmission error curve and a preset contact footprint:
Σ＝Σ1+Σ2 (10)
5) and calculating a pinion adding step 4) by utilizing a tooth surface high-order error reverse solving method to obtain the machine tool machining parameters corresponding to the new tooth surface after the pinion shaping surface meeting the preset high-order transmission error curve and the preset contact print. The tooth surface high-order error inverse calculation method can specifically adopt a roll ratio correction method.
The effect of the present invention will be described below by way of a specific example. A hypoid gear pair is taken, the machining process is gear grinding, and the design parameters of the gear pair are shown in the table 1.
TABLE 1 hypoid gear basic parameter table
1) A group of tooth surface initial processing parameters are obtained by utilizing a Gleason method, and the processing parameters of the corresponding large gear and the corresponding small gear are shown in a table 2 and a table 3.
TABLE 2 initial design scheme for large wheel machining parameters
| Vertical knife position (mm) | 123.5533 |
| Horizontal knife position (mm) | 96.3544 |
| Horizontal wheel position (mm) | -1.6070 |
| Machine tool mounting root cone angle (°) | 74.7683 |
TABLE 3 initial design scheme small wheel processing parameters
| Concave surface | |
| Basic cradle angle (°) | 60.3220 |
| Vertical wheel position (mm) | 18 |
| Horizontal wheel position (mm) | 0.7360 |
| Machine tool mounting root cone angle (°) | -4.5273 |
| Radial knife position (mm) | 151.2363 |
| Roll ratio | 5.4328 |
| Bed (mm) | 14.1914 |
| Knife angle (°) | 151.1859 |
| Angle of inclination (degree) | -17.6359 |
| Outer knife (convexity)Inner knife) nose radius (mm) | 149.0029 |
2) According to the initial processing parameters and the formula (1) and the formula (2)
The tooth surface point r of the pinion gear completely conjugated with the bull gear can be obtained1And normal n1。
According to the transmission ratio equation formula (3) and the meshing equation formula (4), the coordinates of the tooth surface points of the pinion which are completely conjugated with the bull gear can be obtainedAnd normal directionThe differential surface △ R of the pinion fully conjugate with the bull gear and the pinion tooth surface obtained according to the equation (2) can be obtained by using the differential surface equation (5), and the machining parameters of the pinion tooth surface fully conjugate with the bull gear can be calculated by using the differential surface △ R by using a hypoid gear tooth surface error back-solving method, and are shown in table 4.
TABLE 4 pinion machining parameters fully conjugate with bull gear
3) According to the general form of the preset high-order transmission error curve
Wherein,for high order transmission error values, asAnd q is the coefficient of the high-order transmission error curve, and the highest order of the high-order transmission error curve.
The abscissa of 3 points is takenλ2＝0，Corresponding ordinate δc1＝0，δc2＝-1.2×10-5，δc3＝-0.88×10-6The 5 unknowns in equation (6) can be based on the positional equations of these three points and C1And C3Equation of extreme value of point, see formula (7)
The coefficients of the high-order transmission error curve can be obtained by the following equation (7), which is shown in Table 5.
TABLE 5 higher order Transmission error Curve coefficients
| a0 | -1.2e-5 |
| a1 | 3.9615e-6 |
| a2 | 1.2149e-4 |
| a3 | -2.6292e-5 |
| a4 | -3.2262e-4 |
According to the formula (4) and the formula (6), the pinion tooth surface point meeting the preset high-order transmission error curve with the large gear is obtainedAnd according to the tooth surface point and the pinion tooth surface point which is completely conjugated with the bull gear and is obtained in the step 2), obtaining a gear modification surface sigma which only meets a preset high-order transmission error curve by using a formula (8)1See fig. 5.
4) Using the contact trace shown in FIG. 3, take the straight line CL slope kslopeWhen the contact half width b is 0.2 as 1.45, and the drop point on the modified surface is on the 3-segment straight line, no correction is made, and the remaining points on the modified surface are expressed by the formula (9)
Correcting the shape correction surface according to the formula (10)
Σ＝Σ1+Σ2 (10)
And finally obtaining a pinion shaping surface sigma meeting the preset high-order transmission error curve and the preset contact footprint, which is shown in figure 6.
5) And reversely solving the pinion profile surface meeting the preset high-order transmission error curve and the preset contact mark by using a roll ratio correction method, and obtaining machining parameters of the pinion which meets the preset high-order transmission error and the contact mark after the profile surface is superposed, wherein the machining parameters are shown in a table 6.
TABLE 6 pinion machining parameters meeting Preset high order Transmission error and contact footprint
And calculating and analyzing the pinion obtained by the processing parameters to obtain a high-order transmission error curve and a contact print, and comparing the high-order transmission error curve and the contact print with a preset condition. In fig. 7 it can be seen that the high order transmission error curve differs from the preset value by a maximum of 5 μ rad. In order to see the contact footprint more clearly, the calculation result is projected onto a two-dimensional projection plane of the tooth surface of the pinion, the contact footprint is shown in fig. 8, in the plane, the horizontal axis is the tooth width direction, the vertical axis is the tooth height direction, the point a is a point on the preset contact trace, and the point B is a point on the actually obtained contact trace. In fig. 8, the maximum deviation between the point on the intended contact trace and the point on the actually obtained contact trace in the multi-tooth meshing region in the tooth width direction is 0.547mm and 0.84% of the tooth width, the maximum deviation in the tooth height direction is 0.277mm and 1.76% of the average tooth height, and the distance between the two points is 0.617 mm. In the single-tooth meshing region, the maximum deviation of the actually obtained trace in the tooth root portion from the preset trace in the tooth width direction was 0.89mm, accounting for 1.37% of the tooth width, and the maximum deviation in the tooth height direction was 0.601mm, accounting for 3.81% of the average tooth height. The reason why the error is larger in this portion than in the multi-tooth meshing region is that there is a residual error in the tooth surface error back-calculation performed in step 5), which is larger in the large-end root portion than in the remaining portion. In the figure, the point C is the position of the end point of the major-semiaxis of the preset contact ellipse, the point D is the position of the end point of the major-semiaxis of the actually obtained contact ellipse, the semimajor axis of the preset contact ellipse is 7.875mm, the major-semiaxis of the actually obtained contact ellipse is 7.743mm, and the error is 1.68% of the preset value. In summary, the high-order transmission error and the contact imprint obtained by the method meet the preset requirements, the maximum high-order transmission error is 5 μ rad different from the preset value, and the maximum semi-major axis and the maximum preset value of the contact trace and the contact ellipse are 3.81%.
The method adopted by the invention can well meet the requirements of designers, improves the transmission performance of the hypoid gear, overcomes the defect of poor matching degree of other methods, and also overcomes the defect that other methods do not control contact marks. Meanwhile, the method can be popularized to any order, and only the coefficient item in the formula (6) is modified.
The above embodiments are only for further detailed description of the object, technical solution and advantages of the present invention, and are not intended to limit the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. A hypoid gear machining parameter obtaining method meeting high-order transmission errors comprises the following steps:
1) obtaining initial machining parameters of a large gear and a small gear in a hypoid gear according to the existing Gleason tooth surface design method;
2) calculating a pinion tooth surface point completely conjugated with the bull gear and a pinion tooth surface point according to the initial processing parameters, and acquiring machine tool processing parameters of the pinion tooth surface completely conjugated with the bull gear;
3) obtaining a new pinion tooth surface according to a preset high-order transmission error curve, and obtaining a pinion modification surface only meeting the preset high-order transmission error curve by utilizing the pinion tooth surface and the pinion tooth surface which is completely conjugated with the bull gear and is obtained in the step 2);
4) adjusting the pinion shaping surface obtained in the step 3) according to a preset contact print and a half width of a contact ellipse to obtain a pinion shaping surface meeting a preset high-order transmission error curve and a preset contact print;
5) and calculating a pinion adding step 4) by utilizing a tooth surface high-order error reverse solving method to obtain the machine tool machining parameters corresponding to the new tooth surface after the pinion shaping surface meeting the preset high-order transmission error curve and the preset contact print.
2. The method for acquiring the machining parameters of the hypoid gear meeting the high-order transmission error as claimed in claim 1, wherein the method comprises the following steps: the method for acquiring the initial processing parameters of the large gear and the small gear in the step 1) is a Gleason method, and the acquired initial processing parameters comprise theta1、φ1、θ2、φ2、And v12；
Wherein, theta1And phi1Respectively representing the cutter angle and the cradle angle, theta, during pinion machining2And phi2Respectively representing the cutter head corner and the cradle corner when the large gear is machined;andrespectively a pinion rotation angle and a pinion initial position rotation angle;andrespectively a bull gear corner and a bull gear initial position corner; v. of12The relative speed of the pinion and the bull gear.
3. The method for acquiring the machining parameters of the hypoid gear meeting the high-order transmission error as claimed in claim 2, wherein the method comprises the following steps: the process for acquiring the machine tool machining parameters of the pinion tooth surface completely conjugated with the bull gear in the step 2) is as follows:
obtaining a big gear tooth surface point r according to the formula (1)2And normal n2Obtaining a pinion tooth surface point r according to equation (2)1And normal n1；
Wherein, theta1And phi1Respectively representing the cutter angle and the cradle angle, theta, during pinion machining2And phi2Respectively representing the cutter head corner and the cradle corner when the large gear is machined;
by using the formula (3) and the formula (4), the coordinates of the tooth surface points of the pinion gear completely conjugated with the bull gear are obtainedAnd normal directionWith equation (5), the difference curved surface △ R of the pinion gear fully conjugate with the bull gear and the pinion gear tooth surface obtained from equation (2) is obtained as follows:
wherein,andrespectively a pinion rotation angle and a pinion initial position rotation angle;andrespectively a bull gear corner and a bull gear initial position corner; v. of12The relative speed of the pinion and the bull gear;
and (3) calculating the machining parameters of the tooth surface of the pinion which is completely conjugated with the bull gear by using the hypoid gear tooth surface error reverse solving method for the differential curved surface △ R.
4. The method for acquiring the machining parameters of the hypoid gear meeting the high-order transmission error as claimed in claim 3, wherein the method comprises the following steps: the process of obtaining the pinion profile in the step 3) is as follows:
the formula (6) is a general form of a high-order transmission error curve
Wherein,for high order transmission error values, asIs the coefficient of the high-order transmission error curve, and q is the highest order of the high-order transmission error curve;
according to the horizontal and vertical coordinates of the extreme points in the preset high-order transmission error curve, listing the position equation and the extreme value equation of each extreme point, thereby solving the coefficient a of the high-order transmission error curves；
And then, obtaining the pinion gear surface point meeting a preset high-order transmission error curve with the large gear by using the formula (4) and the formula (6)And obtaining a modification surface sigma of the pinion by using an equation (8) according to the tooth surface point and the pinion tooth surface point which is completely conjugated with the bull gear and is obtained in the step 2)1：
5. The method for acquiring the machining parameters of the hypoid gear meeting the high-order transmission error as claimed in claim 1, wherein the method comprises the following steps: the tooth surface high-order error reverse solving method adopted in the step 5) is a roll ratio correction method, the tooth surface error reverse solving is carried out by using the method, the corresponding pinion machining parameters after the trimming surfaces are overlapped are calculated, and finally the machining parameters of the pinion meeting the preset high-order transmission error curve and the contact footprint are obtained.
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| TWI646441B (en) * | 2017-12-07 | 2019-01-01 | 正修學校財團法人正修科技大學 | Design method and product of preset fourth-order transmission error of face gear |
| CN108115217B (en) * | 2017-12-13 | 2019-02-19 | 长安大学 | A kind of Machining Spiral Bevel Gear method based on high-order driving error |
| CN108470102B (en) * | 2018-03-21 | 2021-10-22 | 西安科技大学 | Small wheel tooth surface design method and machining method for meshing performance pre-control |
| TWI672448B (en) * | 2019-01-07 | 2019-09-21 | 正修學校財團法人正修科技大學 | Design method of point contact cosine helical gear transmission mechanism of fourth-order transmission error |
| CN109977579B (en) * | 2019-04-03 | 2022-09-13 | 合肥工业大学 | Machine tool machining parameter optimization method for improving hypoid gear meshing quality |
| CN109993464B (en) * | 2019-04-24 | 2021-04-06 | 合肥工业大学 | Machining parameter optimization method for reducing mounting error sensitivity of hypoid gear |
| CN112211985A (en) * | 2020-11-04 | 2021-01-12 | 北京航空航天大学 | Bidirectional shape-modifying design method for contact trace controllable face gear shape |
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