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Among the individual errors of the gear, the tooth profile error has the greatest influence on the noise. In general, the larger the tooth profile error, the greater the noise, but there is no simple proportional relationship between the two. Studies have shown that (1), the magnitude of the noise is not only related to the size of the tooth profile error, but also depends on the shape of the tooth profile. Figure i is a comparison of the noise generated when the three gears with the same tooth profile error and different tooth shapes mesh with the standard gear. It can be seen from the figure that the tooth shape is different, and the noise can be different by about 10 db. Among them, the gear with the convex tooth shape has the lowest noise, which is an ideal tooth shape. However, the concave tooth shape is subjected to two impacts in one engagement due to the tooth teeth, and the noise is the largest, which is to be avoided in production. When shaving with a standard shaving cutter, the machined gear teeth are generally concave in shape due to the shaving mechanism. For this purpose, an anti-deformation method is generally used to grind the shaving cutter into a concave shape so that a gear having a convex tooth shape can be machined. In the case of grinding the teeth, the concave tooth shape of the convex tooth-shaped irregular tooth shape in the tooth root of the tooth R does not generate a concave tooth shape. However, in the production practice, it is found that the gears processed by the grinding teeth have better tooth shape and better tooth shape, but the noise is not necessarily low. Sometimes the tooth shape error value is large, but the noise is actually worse. low. The magnitude of the noise is not only related to the value of the tooth profile error, the shape of the tooth profile, but also to the matching of the tooth profile error direction.
1 The concept of the integrated tooth profile error of the gear pair Under normal circumstances, the tooth profile error curve generated during the grinding of the tooth is generally linear, that is, the pressure angle deviation occurs. In order to express the tooth shape pressure angle error, the author supplements the tooth shape error as follows: when the tooth root is convex, the tooth shape error is represented by a negative sign; when the tooth top is convex, the tooth shape error is represented by a positive sign. If the tooth shape error is -0.012, the tooth profile error value is 0.012. The tooth profile error curve is that the tooth root is slightly convex, that is, the pressure angle is too large. On the contrary, the tooth profile error is +0.012, indicating that the tooth profile group is active. Tooth shape error driven gear tooth error gear pair auxiliary gear 2, test spare parts: the drive wheel speed 1000rpm, the distance 300mm error value is 0.012, the tooth profile error curve is slightly convex, the pressure angle is small, as shown by the dotted line in the figure Represents the standard involute tooth profile and the solid line represents the true tooth profile).
Production practice shows that the noise generated when a pair of gears mesh with each other is not only related to the tooth profile error of the gear, but also related to the tooth shape pressure angle error direction; when the tooth profile error is the same, the drive wheel pressure angle is slightly smaller The driven wheel pressure angle is advantageous for reducing noise. In practice, the author has tested a pair of spur gears with a modulus of 2.5 mm, a pressure angle of 20., a number of teeth of Z53/Z35, and a design accuracy of 7 in a headstock of a lathe. Table 1. It can be seen from Table 1 that the tooth profile errors of the two sets of gears are equal in magnitude, but the transmission noise group 2 is significantly lower than the group 1, and the difference between the two is 4db. The difference lies in the active of the group 1. The direction of the tooth profile error is that the tip of the tooth is negative and the pressure angle is too large, and the direction of the tooth profile of the group 2 is positive and the pressure angle is small. It can be seen that the guiding significance in the production is the size of the tooth profile error of a pair of gears and the matching of the error direction. Therefore, the author puts forward the concept of the gear tooth pair integrated tooth profile error.
Table 1 The influence of tooth size error and direction on noise The so-called gear pair integrated tooth shape error refers to the comprehensive error of the pressure angle of a pair of meshing gears, and defines the gear pair integrated tooth shape error as a pair of meshing gears to The pressure angle deviation of the driving wheel when the moving wheel pressure angle is the reference. When the pressure angle error directions of the two gears are the same, the value is the difference between the two gear pressure angle errors; when the pressure angle errors of the two gears are opposite, the value is the sum of the two gear pressure angle errors. The symbol definition of the gear pair integrated tooth profile error is the same as the tooth profile error symbol specification of the aforementioned single gear. When the driving wheel pressure angle is greater than the driven wheel pressure angle, the gear pair integrated tooth shape error is a negative value; when the driving wheel pressure angle is smaller than the driven wheel pressure angle, the gear pair integrated toothed pair of gears is driven by a pair of gears. The sign of the tooth profile error tooth profile error of the driven wheel is as specified above.
If the gear tooth error is +0.005, the gear tooth pair integrated tooth profile error of group 1 gear is -0.016 (=(-0.011)-(+0.005)), the drive wheel pressure angle is larger than the driven wheel; and the group 2 gear gear The secondary integrated tooth profile error is +0.006 (=(+0.011)-(+0.005)), and the drive wheel pressure angle is slightly smaller than the driven wheel pressure angle.
2 Gear pair integrated tooth profile error and noise gear pair integrated tooth profile error have great influence on gear transmission noise. The key to affect gear gear noise is the integrated tooth profile error of the gear pair of a pair of meshing gears, instead of the tooth profile of a single gear. error. Because the gears are engaged with another pair of gears of comparable precision, rather than meshing with the standard gears as in the usual manufacturing inspection gears. Therefore, it is necessary to consider not only the size of a pair of gear tooth shapes, but also the matching of the error direction, that is, the comprehensive tooth shape error of the gear pair. Just as the hole and the shaft are matched, not only the tolerance but also the size should be considered. The direction of the deviation is the same. As shown in Table 1, although the tooth profile error values ​​of the single gears of the two groups of gears are equal, the tooth profile error of the two gears in group 1 is opposite, and the corresponding tooth profile error of the gear pair is also large and negative. However, the tooth shape error directions of the two gears in group 2 are the same, and the corresponding gear tooth profile error is small and positive, so the gear pair transmission noise of group 1 is significantly higher than that of group 2, and the two sets of gear teeth are engaged. The transmission noise of the elastically deformed gear differs by 4 db. The wrong pound is positive 5, that is, the total curved shape of the gear pair is the sum of the deformation of the lining wheel teeth of the meshing wheel is the main; The reason why the first page of winter is caused is that when the driving wheel pressure angle is slightly smaller than the driven wheel pressure angle and the gear pair comprehensive tooth shape error is small and positive, the base of the driving wheel is slightly larger than the driven wheel. . As shown, when the tooth is engaged, the top of the driving wheel is in contact with the root of the driven wheel, and the elastic deformation of the tooth causes the base of the driving wheel to be slightly reduced, while the base of the driven wheel is slightly increased. The elastic deformation of the teeth during the engagement is composed of two parts: the bending deformation and the contact deformation of the teeth. It can be seen from the figure that the bending deformation of the gear teeth mainly occurs on the driving wheel when the teeth are engaged, and the bending deformation of the driving wheel teeth when the teeth are engaged reduces the base joint. The contact deformation reduces the base of the driving wheel and increases the base of the driven wheel. The master-slave tooth 7) circuit implementation of the function fi and can be seen from Table 3, the implementation of any three-variable function requires only one three-variable universal logic gate and a small number of inverters need up to two), the wiring scheme given in this paper The minimum number of inverters is required.
The wiring sequence table gives the order in which the variables are connected. The connection to the inputs of constants 0 and 1 is not affected.
+) The look-up table design method is generally applicable to the following functions of four variables. For a function of four or more variables, its superiority is lost due to the exponential increase of the number of functions represented by the corresponding classification.