Optimization method of calculating the edge size of hob gear hob by computer

July 14, 2022

As shown in Fig. 1, after the hob shaving, the amount of edge trimming is δ, and the trimming height is ft. In normal circumstances, as long as the processing conditions can be satisfied, the shaving edge angle αd and trim edge height ft of the gear after shave should be made as large as possible (but when the modulus mn ≤ 3, ft is preferably not more than 0.5). It can be seen that the determination of trim size is a two-parameter optimization problem. The author took the following optimization steps when compiling the computer program for calculating the edge size:

Fig. 1 Gear tooth tip repair edge

(1) For the initial assignment, for the shaved top gear trimming edge δ and the trimming edge height ft, as indicated on the drawing sheet, the required values are entered; if not shown on the drawings, the modulus mn and the number of teeth may be used. z is reasonably assigned to a larger initial value, such as mn=2, z=30, then δ=0.3, ft=0.45. For the trim angle αd, αd=30° can be stipulated.
(2) As shown in Figure 2, from ft and αd to calculate the height of the cutting edge on the cutting edge starting point to the top of the tooth hd, and determine whether hd ≥ 1.95mn is established, if it is not established, then step by step by 0.01 decrement ft recalculated . This cycle runs until ft is not less than 0.3.

Figure 2 Hob repair starting point

(3) After the ft is determined, the α d is incremented by 1′′ until the calculated amount of gear crowning δ satisfies the requirement. At this time, αd is the maximum trim angle, as shown in FIG. 3 .
(4) According to hd and αd obtained hob tooth root groove width Wi (see Figure 3).

Figure 3 seeking the maximum repair angle

(5) Judging whether the width Wi Width of the tooth root groove obtained satisfies Wi ≥ W (W is the minimum groove width for repairing the tooth root arc R2). If Wi is too small, it can be solved as follows: 1 If ft > 0.35, we can continue decrementing ft in increments of 0.01, while αd remains constant, ie reducing both ft and δ to increase Wi, as shown in Figure 4. 2 If ft ≤ 0.35, only reduce αd to increase Wi, as shown in Figure 5. However, it should be noted that W is also changing at the same time due to the change of αd. Obviously, when αd decreases, δ also decreases accordingly. Therefore, when αd decreases to 30° and Wi still cannot meet the requirement of Wi≥W, in order to avoid that δ is too small, R2 should be appropriately reduced.

Fig. 4 Constant edge angle αd

Figure 5 Reduce the trim angle αd

(6) Finally determine αd and calculate δ.
In the above optimization process, the lower limit of circulation is limited. In fact, as long as the parameters and dimensions of the gear are properly designed, there will be no situation where the lower limit of circulation can not meet the optimization condition. If this happens, it means that the gear does not need to Make repairs.

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