CN112257192B - One-tooth tangential integrated deviation calculation method based on actually measured tooth profile deviation - Google Patents
One-tooth tangential integrated deviation calculation method based on actually measured tooth profile deviation Download PDFInfo
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Abstract
The invention discloses a method for calculating tangential integrated deviation of one tooth of a gear based on an actually measured tooth profile deviation curve, which comprises the following steps of ideal tooth profile modeling, actual tooth profile deviation fitting, rotating and meshing the tooth profile deviation curve and the tooth profile, carrying out tangential integrated deviation calculation of one tooth, and effectively shortening calculation time and the like on the premise of ensuring calculation accuracy how to divide a rotation angle. The method aims at measuring the actual tooth profile by a gear measuring instrument only to obtain the actual tooth profile information, and further calculates the tangential integrated deviation of one tooth of the gear.
Description
Technical Field
The invention belongs to the technical field of gear precise measurement, and particularly relates to a method for calculating tangential integrated deviation of a tooth based on measured tooth profile deviation. The tooth profile is measured by a gear measuring instrument. And inputting the measured true tooth surface information into a computer to model the true tooth surface. And then, calculating the tangential integrated deviation of one tooth of the gear through processing the real tooth profile shape information through coordinate translation, coordinate rotation and the like.
Background
Gears, like shafts, bearings, etc., have a long history in human history as one kind of transmission mechanism, and are widely used in the mechanical field. The gear has the advantages of constant transmission ratio, compact structure and the like. The tangential integrated deviation of one tooth has a great influence on the stability of gear transmission, and can directly influence the vibration noise, the working precision and the like of a transmission system. The tangential integrated deviation of one tooth is taken as an important influencing factor of vibration noise, and is measured and calculated, so that the tangential integrated deviation has important significance for improving the performance of a gear box, reducing the noise of an automobile and improving the driving comfort of the automobile.
The conventional gear measuring means comprise a gear measuring center, a three-coordinate measuring machine and the like, and the measuring instruments can not directly measure projects such as tooth profile deviation, gear roughness and the like. Meanwhile, it is difficult for these instruments to directly output a tangential integrated deviation result of one tooth due to the tooth profile deviation.
Currently, one-tooth tangential integrated deviation measurement is mainly performed on a single-face meshing measuring instrument, and one-tooth tangential integrated deviation is obtained by measuring the rotation angles of two gears. However, the gear clamping precision required by the method is higher, and because the contact ratio of actual gear transmission is greater than 1, independent analysis can not be performed on a certain tooth profile. The gear global error measurement technique is capable of obtaining a one-tooth tangential integrated deviation, but requires specialized instrumentation.
Disclosure of Invention
The invention discloses a method which can realize the acquisition of a tooth tangential integrated deviation according to an actually measured tooth profile deviation curve. After that, the data can also be used for calculating parameters such as the sliding speed, the Hertz contact stress, the oil film thickness and the like of the gear through other algorithms, so that the utilization rate of the data is greatly improved. The method adopted by the invention comprises the following steps:
s1, modeling a theoretical tooth profile based on the information of the number of teeth, the modulus and the like, and taking a coordinate origin O (0, 0) as a center point of a gear A (driving wheel). By O 2 And (a cos alpha, a sin alpha) is the center point of a gear B (driven wheel, a is the center distance of two gears, alpha is the pressure angle), an ideal tooth profile model is established according to the parameters such as the number of teeth, the modulus, the pressure angle, the deflection coefficient and the like of different gears, and a theoretical involute tooth profile model is established through a parameter equation. At the intersection point T of the base circle of the gear A and the x axis 1 (r b 0) making an x-axis vertical line, wherein the vertical line is the meshing line of two gears.
S2, obtaining real tooth profile information, carrying out filtering treatment on the real tooth profile information, fitting the tooth profile, and obtaining real tooth surface information of the passive gear tooth profile through measurement. It is subjected to gaussian low pass filtering. Based on the modeling result of step 1, the theoretical tooth profile S of the driven wheel 2 Rotating to the positions of two gear nodes to solve S 2 Each point is connected with T 2 Distance l of points 2 The deviation value Deltal of each point in FIG. 2 2 And/l 2 Adding to obtain L 2 . And then L is added with 2 Restoring to the tooth profile form, namely finishing fitting. Marking the tooth profile after fitting as S' 2 。
S3, realizing meshing of theoretical tooth profile of driving wheel and actual measured tooth profile of driven wheel based on algorithm
Set S 1 The intersection point of the theoretical tooth profile of the driving wheel and the meshing line is P 1 . During the rotation of the gear A, T 1 P 1 Is continuously variable. T is arbitrarily selected 1 P 1 Let S 1 Rotating to the point, and before engagement calculation starts, fitting the tooth profile S 'obtained in the step 2' 2 Rotated counterclockwise by a larger angle such that S' 2 The whole tooth profile is S 1 And below. In the subsequent calculation process, S 'is carried out' 2 Continuously rotating clockwise by a small angle. After each rotation, at two gear mesh intervals (x b2′ ，x b1 ) Delta y is calculated from the above i ＝y′ 2i -y 1i . When Deltay i > 0 for each x i When they are all true, stopping the operation, at this time r 2i I.e. the condition is fulfilled. Immediately terminate the operation, consider the two curves to be tangent at this time, output S' 2 Rotation angle theta of (2) n 。
S4 solving tangential integrated deviation of one tooth
By the method of the step 3, S 'can be solved' 2 Rotation angle theta of (2) n When meshing with two theoretical tooth profiles, the passive gear tooth profile needs to rotate by an angle theta t . Calculating the difference delta theta=theta between the two angles n -θ t The tangential integrated deviation of one tooth can be solved.
The invention provides a method for calculating tangential integrated deviation of a tooth according to an actual measured tooth profile. It is achieved that a tangential integrated deviation of a tooth can be output by measuring only the actual tooth profile of a tooth. The method can realize independent analysis of one tooth profile, and reduces the difficulty of clamping gears in the measuring process. The tangential integrated deviation of one tooth can be obtained without special instruments.
Drawings
Fig. 1 is a schematic view of two tooth profile engagement.
Fig. 2 is a graph of true tooth surface deviation after filtering.
FIG. 3 is a graph of the result of a tooth tangential integrated deviation calculation.
FIG. 4 is a flow chart of the calculation of the present invention.
In the figure: 1. addendum circle, 2, reference circle, 3, base circle, 4, root circle, 5, true tooth profile, 6, ideal tooth profile, 7, center line, 8 and meshing line.
Detailed Description
The present embodiment is further described below with reference to the accompanying drawings:
1. modeling theoretical tooth profile based on tooth number, modulus and other information
The origin of coordinates O (0, 0) is taken as the center point of the gear a (drive wheel). By O 2 And (a cos alpha, a sin alpha) is the center point of a gear B (driven wheel, a is the center distance of two gears, alpha is the pressure angle), an ideal tooth profile model is established according to the parameters such as the number of teeth, the modulus, the pressure angle, the deflection coefficient and the like of different gears, and a theoretical involute tooth profile model is established through a parameter equation. At the intersection point T of the base circle of the gear A and the x axis 1 (r b 0) making an x-axis vertical line, wherein the vertical line is the meshing line of two gears. Modeling is performed in this way, the meshing line of the two gears is perpendicular to the x-axis, and the two gears can mesh along the y-axis direction, so that convenience is brought to subsequent calculation. The positions and shapes of the two gear models, the position of the center point, the center line, etc. are shown in fig. 1.
2. Obtaining real tooth profile information, filtering the real tooth profile information, and fitting the tooth profile
i. And measuring the gear by a roughness profiler to obtain the real tooth surface information of the passive gear tooth profile. The actual tooth profile information is entered into a computer. It is subjected to gaussian low pass filtering at a cut-off wavelength of 0.5 to remove roughness information.
Figure 2 represents the deviation of the true tooth profile from the theoretical tooth profile at various points of the tooth profile. When the real tooth profile is fitted with the theoretical tooth profile, the theoretical tooth profile S of the driven wheel is based on the modeling result of the step 1 2 Rotating to the positions of two gear nodes to solve S 2 Each point is connected with T 2 Distance l of points 2 Then only the deviation value Deltal of each point in FIG. 2 is needed 2 And/l 2 Adding to obtain L 2 . And then L is added with 2 Restoring to the tooth profile form, namely finishing fitting. Marking the tooth profile after fitting as S' 2 。
3. S is arranged for realizing meshing of theoretical tooth profile of driving wheel and actual measured tooth profile of driven wheel based on algorithm 1 The intersection point of the theoretical tooth profile of the driving wheel and the meshing line is P 1 . During the rotation of the gear A, T 1 P 1 Is continuously variable. The change interval is (T) 1 A，T 1 E) Wherein T is 1 The points represent the points of intersection of the meshing line with the base circle of gear a, a being the start of the meshing of the two gears and E being the end of the meshing of the two gears. T is arbitrarily selected 1 P 1 Let S 1 Rotating to the position to perform subsequent engagement calculation; before engagement calculation starts, fitting the tooth profile S 'obtained in step 2 (ii)' 2 Rotated counterclockwise by a larger angle such that S' 2 The whole tooth profile is S 1 And below. In the subsequent calculation process, S 'is carried out' 2 Continuously rotating clockwise by a small angle. After each rotation, at two gear mesh intervals (x b2′ ，x b1 ) Delta y is calculated from the above i ＝y′ 2i -y 1i . Wherein x is b2′ Is S' 2 Abscissa at tooth tip, x b1 Is S 1 And the abscissa at the tooth tip. Set S 1 The coordinates of the upper point are (x i ，y 1i ) Let S' 2 The coordinates of each point on the table are (x i ，y′ 2i ). In S' 2 In the clockwise rotation process, three conditions are sequentially generated as shown in the formula (1). Wherein Δy i The detailed calculation method of (2) is as shown in the formulas (2) to (6).
Δx＝x b1 -x b2′ (4)
Δy i ＝y′ 2i -y 1i ，i＝1，2，...，n (6)
Where a is the center-to-center distance of the two gears. θ n The rotation angle is α, and the pressure angle is α. a×cos (α) and a×sin (α) each represent S' 2 The abscissa and ordinate of the rotation center. r is (r) 2i Representative will S' 2 After rotating a certain angle, S' 2 Coordinates of the above points. Deltax represents S after each rotation 1 Tooth vertex abscissa and S' 2 The difference in the abscissa of the upper tooth vertex. X is x i Representative is that, in the meshing calculation section (x b2′ ，x b1 ) Sequentially taking values. X to be taken i Respectively brought to S 1 And S' 2 Solving for the corresponding y 1i And y' 2i . Then calculate each x i Corresponding delta y i . When Deltay i > 0 for each x i When they are all true, stopping the operation, at this time r 2i I.e. the condition is fulfilled. When engaged computing x on interval i The value is dense enough, S' 2 Is sufficiently small, once y 'no longer occurs' 2i -y 1i In case of < 0, the operation is terminated immediately, the two curves are considered to be tangent, and S 'is output' 2 Rotation angle theta of (2) n 。
In the calculation process, if the rotation angle is divided too finely at one time, the calculation amount of the useless calculation part is greatly increased, and the calculation cost and the time cost are greatly increased. For this case, a larger rotation angle interval is selected, and a rough interval of a target angle is found first. This interval is then further subdivided. Therefore, the calculation accuracy can be improved on the premise of reducing the calculation cost and the time cost as much as possible.
4. Solving tangential integrated deviation of one tooth
Under the method described in the step 3, S 'can be solved' 2 Rotation angle theta of (2) n . Meanwhile, the same method can be used for solving the angle theta of the passive gear tooth profile required to rotate when two theoretical tooth profiles are meshed t . At this time, the difference Δθ=θ between the two angles can be solved n -θ t And then carrying out certain unit conversion operation to solve the tangential integrated deviation of one tooth. The calculation result is shown in fig. 3.
Claims (1)
1. A tooth tangential integrated deviation calculation method based on actual measurement tooth profile deviation is characterized by comprising the following steps: comprises the following steps of the method,
s1, modeling a theoretical tooth profile based on tooth number and modulus information;
taking a coordinate origin O (0, 0) as a gear A, namely a center point of the driving wheel; by O 2 (acos alpha, asin alpha) is the center point of the driven wheel, namely the gear B, a theoretical tooth profile model is established according to the tooth number, the modulus, the pressure angle and the deflection coefficient parameters of different gears, and a theoretical involute tooth profile model is established through a parameter equation; at the intersection point T of the base circle of the gear A and the x axis 1 (r b 0) making an x-axis vertical line, namely, an meshing line of two gears; a is the center distance of two gears, and alpha is the pressure angle;
s2, obtaining real tooth profile information, carrying out filtering treatment on the real tooth profile information, and fitting the tooth profile;
acquiring real tooth surface information of the passive gear tooth profile through measurement; inputting the real tooth profile information into a computer and carrying out Gaussian low-pass filtering with the cut-off wavelength of 0.5 so as to remove roughness information; based on the modeling result of S1, the theoretical tooth profile S of the driven wheel 2 Rotating to the positions of two gear nodes to solve S 2 Each point is connected with T 2 Distance l of points 2 The deviation value Deltal of each point is calculated 2 And/l 2 Adding to obtain L 2 The method comprises the steps of carrying out a first treatment on the surface of the And then L is added with 2 Restoring the tooth profile form, and finishing fitting;marking the tooth profile after fitting as S' 2 ；
S3, meshing of a theoretical tooth profile of the driving wheel and an actual measured tooth profile of the driven wheel is achieved based on an algorithm;
theoretical tooth profile S provided with driving wheel 1 The intersection point with the meshing line is P 1 The method comprises the steps of carrying out a first treatment on the surface of the During the rotation of the gear A, T 1 P 1 Is continuously variable; t is arbitrarily selected 1 P 1 Let S 1 Rotating to this point, the fitted tooth profile S 'obtained in S2 is then followed by engagement calculation' 2 Rotated counterclockwise by a larger angle such that S' 2 The whole tooth profile is S 1 The lower part; will S' 2 Continuously rotating clockwise by a small angle; after each rotation, at two gear mesh intervals (x b2′ ，x b1 ) Delta y is calculated from the above i ＝y′ 2i -y 1i The method comprises the steps of carrying out a first treatment on the surface of the When Deltay i > 0 for each x i When they are all true, stopping the operation, at this time r 2i I.e. the condition is satisfied; immediately terminate the operation, consider the two curves to be tangent at this time, output S' 2 Rotation angle theta of (2) n ；x b2′ Is S' 2 Abscissa at tooth tip, x b1 Is S 1 An abscissa at the tooth tip; y is 1i 、y′ 2i Respectively S 1 And S' 2 The ordinate of each point; r is (r) 2i Representative will S' 2 After rotating a certain angle, S' 2 Coordinates of each point;
s4, solving a tangential integrated deviation of one tooth;
solving for S 'through S3' 2 Rotation angle theta of (2) n The method comprises the steps of carrying out a first treatment on the surface of the When two theoretical tooth profiles are meshed, the angle theta of the passive gear tooth profile required to rotate is obtained by the same method as S3 t The method comprises the steps of carrying out a first treatment on the surface of the Calculating the difference delta theta=theta between the two angles n -θ t The tangential integrated deviation of one tooth can be solved.
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| CN113063589B (en) * | 2021-03-18 | 2023-07-04 | 重庆青山工业有限责任公司 | Gear microscopic error vibration prediction method based on neural network |
| CN113283029B (en) * | 2021-05-21 | 2023-11-21 | 北京工业大学 | Method for acquiring envelope shape on actual tooth profile based on iterative filtering |
| CN113591238B (en) * | 2021-07-19 | 2024-03-22 | 北京工业大学 | Gear tangential integrated deviation calculation method based on gear point cloud data |
| CN113819874B (en) * | 2021-09-01 | 2024-04-02 | 宜昌长机科技有限责任公司 | Method for checking speed ratio and speed ratio crowned tooth sector machining precision |
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