Effect of initial base circle radius G0 When calculating the rack and pinion profile curve, one parameter is the base circle radius Gi. After trial calculation, we get an empirical formula for calculating Gi: Gi=G0[1-sin(0.6Ai)]. This formula is mainly used for the tooth profile of a general Logix rack. It can be known from the formula that Gi is affected by two parameters, one is the initial base circle radius G0, and the other is the pressure angle Ai. G0 is the initial value, and the change of Gi is affected by Ai because if Gi=G0 does not change, the degree of bending of the tooth shape is affected. Given the correction factor of Ai, the degree of bending of the tooth profile can be adjusted. When the values ​​of A0 and D are constant, the value of G0 affects the degree of tooth profile bending of Logix racks. As the G0 increases, the tooth profile of the rack will become straighter, whereas the tooth profile of the rack will become more curved as G0 decreases. Therefore, for a rack with a large modulus, a larger G0 value should be taken. Conversely, a rack with a smaller modulus should take a smaller G0 value.
According to a program compiled by Borland C 5.0, different parameters D are input. In the case of a starting pressure angle of 40 and a maximum pressure angle of 350, Table 1 is obtained. It shows the relationship between the number of D and NP points, D The smaller the value, the larger the number of NP points. When D is 0.0010, the number of NP points can reach tens of thousands, and the larger the number of NP points, the more points where the relative curvature of the gear is zero when meshing, the less time between relative sliding of the gears, and the relative rolling time. The more, the less the wear of the tooth surface, the longer the life and load carrying capacity of the gear. As long as the initial pressure angle and the maximum pressure angle, as well as the relative pressure angle, are given, the number of NP points on the gear tooth profile can be known.
It can be found that the number of NP points is only related to A0, D and Amax, regardless of the initial base circle radius G0. It is the effect of the change of D on the tooth profile. It can be seen from the figure that the change of D can cause the change of the tooth shape. By analyzing the rack coordinate formula, it can be found that the number of NP points is determined after the given maximum pressure angle. Under the given law, the radius of the base circle Changes also occur, but the number of NP points determines the radius of variation of the base circle radius, and the radius of curvature Qmk=6ki=1rbi(D-Di) of each point is determined by the radius of the base circle of each NP point. The smaller the D is, the more the number of NP points is, the larger the radius of the base circle is, and the larger the radius of curvature Qmk is, so the curve is more curved.
In addition to the basic parameters of the Involute rack, the Logix rack has a larger initial pressure angle A0 and a more curved tooth profile. The smaller the value of the relative pressure angle D is, the better the meshing performance of the gear is. However, the value of the relative pressure angle should be reasonably selected for the convenience of manufacturing.
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