When using the milling head to connect the milling groove to the milling machine, the formula for calculating the gear ratio of the hanging wheel is:
i = z1/z2 × z3/z4 = 40P/L = 40P/Dπcotβ
In this formula, i represents the gear ratio between the indexing head spindle and the table's longitudinal feed screw. Z1 and z3 are the number of teeth on the driving gears, while z2 and z4 are the number of teeth on the driven gears. The constant 40 refers to the number of divisions. P is the pitch of the workpiece, which is 6mm in this case. L is the lead of the workpiece, D is the outer diameter, and β is the spiral angle of the groove.
For example, when milling a small lead spiral groove on an X5032 vertical milling machine with a lead L = 9mm, the calculation becomes:
i = z1/z2 × z3/z4 = 40P/L = (40 × 6)/9 = 26.6667
However, there is no pre-set gear combination that matches this ratio. According to the hanging wheel table, the maximum and minimum ratios are 14.4000 and 0.06944, respectively. This means the effective lead range is from 16.67 mm to 3456 mm. Since L = 9 mm falls outside this range, it cannot be processed directly.
To solve this issue, a dual indexing head system can be used. A second indexing head is installed between the first indexing head and the longitudinal feed screw of the milling machine table. The output shaft of the first indexing head is connected to the input of the second using a Z to Zb gear. The second indexing head acts as a speed multiplier, increasing the ratio by 40. The first indexing head is used for clamping and indexing the workpiece. During operation, it is essential to manually rotate the handle of the first indexing head to move the table longitudinally. Motorized feeding must be avoided, as it could damage the worm gear pair of the second indexing head.
After this modification, the new formula for the hanging wheel ratio becomes:
Ii = Z1/Z2 × Z3/Z4 = P/L × Za/Zb = P/Dπcotβ × Za/Zb
Normally, when processing standard leads, the gear ratio Za:Zb is 1:1, so the formula simplifies to:
I = Z1/Z2 × Z3/Z4 = 6/L = 6/Dπcotβ
For small leads, the gear ratio is changed to 1:2, resulting in:
Ii = Z1/Z2 × Z3/Z4 = 3/L = 3/Dπcotβ
These calculated ratios can then be used to find the appropriate gear combinations.
Now, let's calculate the hanging wheel ratio for a small lead workpiece.
Solution: According to the formula, the hanging wheel ratio is:
i = Z1/Z2 × Z3/Z4 = 6/L = 6/9 = 0.6667
Checking the hanging wheel table, a possible combination could be: Z1/Z2 × Z3/Z4 = 100/90 × 60/100
For more details on the X5032 vertical milling machine, visit: X5032 Vertical Milling Machine
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