Stability analysis of contact spot of bevel gear and hyperbolic gear pair
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The parameters of the orthogonal hyperbolic gear pair: the axial distance E = ~85 °, the offset is not large. The average value of the derivative ds/dM does not exceed 0.02 mm/rad, and its value is small. If the offset installation accuracy does not exceed 0.01mm, the radial error and angular mounting error are related to the offset and they are also cutting the spiral bevel gear. When the previous adjustment value is used to adjust the machine tool, the tooth surface The distribution of contact spots will be different from the previous ones, usually due to machine inaccuracies. Only a more detailed study can reveal its objective reasons.
When the gear is processed, if the parameters are adjusted, the adjustment of the machine tool is related to the central helix angle, the radius of curvature rp of the cutter head bus bar or the radius of curvature of the grinding wheel. The following is an example of a gear shown in a. When machining gears, the adjustment parameters are: tool installation radius, such as installation angle qF rolling chain transmission ratio iV, hyperbolic offset private, forming line offset Li. These are determined to ensure the calculation of point contact conditions and determine the quality of feeding. It is the derivative of the gear ratio /21. The periodic error of the predetermined transmission, the average tooth line and the angle between the working lines largely influence the shape of the contact spot. All adjustments of the gears are related to each other, one of the parameters changes, and the remaining parameters are corrected.
The machine tool coordinate center Of, the gear taper apex Oi is determined by the offsets Li and Ei. If a parameter value is specified as /21, and the second parameter value varies from 0 to 180, then when the /21 constant is obtained, some closed elliptical contours (b) can be similarly obtained as constant isolines. It is close to a straight line. The two straight lines are shown together on one graph (b) and the intersection point is P distributed on the isoline of /21=constant. However, it should be noted that not all adjustments can be implemented on the machine. The b shown in b is a hyperbolic offset.
The accuracy of the transmission is evaluated by reference to the stationarity criterion, and the tolerance of the periodic error fC is specified. The upper limit of the parameter i'21 = (2n/zi) is determined, assuming that the derivative is unchanged on the meshing arc. Calculations show that such approval is not always appropriate, for example, a half-rolling drive, a hobbing pinion is a tangential motion-free mechanism, this function is a second- or third-order parabola, but in any case, the cycle error is The value corresponds to some derived value. Therefore some contours (c) should be established and all of these contours are tangent to each other at point P.
Analyze the relationship of contour bevel gear transmission. At 90 o'clock, some values ​​are obtained (busbar radius, offset EDLD is an infinite value such that the contours with /21 being constant have a hyperbolic form (d) and one of their curve clusters is tangent to each other at the same point P.
On all contours, such a point is called the envelope of the contour, but this is only theoretical. Analysis shows that when the cutter head axis coincides with the machine cradle axis, this is the degradation of the cut pinion. In fact, the pinion gear is not processed. However, mathematically this treatment satisfies the synthesis conditions, but the tooth flanks only touch a single point, and the inverse algorithm of the extended hobbing drive is used to complete the calculation. It can be concluded that the closer to the top of the gear pitch cone when machining to the P point, the worse the working line characteristics, and the greater the deviation of the gear ratio /21 from the calculated value of the meshing arc deviation.
The point of pause on the contour exposes the unevenness of the distribution point when the parameter step is constant. Introducing the parameter S (arc length), the derivative ds/ must be related to the value of the offset change and the direction of the work line. There is a section on the contour shown that does not change much with the change of the angle M. However, if the offset change is small, the other adjustment parameters change little. Now, the specific example is used to illustrate the problem.
There are installation errors. In the above range, the change of the hobbing chain transmission ratio is small, and therefore, the total error has only a rounding error of about 0.025 mm and introduces a tool forming radius error and a cutter pulsation. Further analysis shows that with the decrease of the forming radius difference, the derivative ds/dM is reduced by adding the instantaneous contact area of ​​the cutter teeth. Therefore, the integration of other original conditions is actually realized only by the adjustment and adjustment, and the installation error is further aggravated. The gear ratio/21 error obtained at this time is small, and the angle M is substantially changed, and the change value is 1 to 2°. Sometimes, if the helix angle is 35 or more, the edge contact phase occurs in the meshing.
Third, the conclusion that under certain conditions contact speckle instability has its objective characteristics, see.
The stability phenomenon is obvious, which is caused by the hyperbolic gear parameters, the adjustment is complicated, and the transmission ratio changes greatly.
Compared with the hobbing processing scheme, the semi-rolling processing scheme has unsatisfactory contact spots and poor meshing quality, so it should be used as little as possible.