# Establishment of force model for gear shaft of feed box of C6136A lathe

Before determining the speed of the gear shaft of the feed box, the speed of the main shaft must be determined, because it is transmitted to the gear shaft through the main shaft, three-star gear and change gear. The gear shaft needs to bear the maximum torque, the speed should be controlled at the minimum, and the spindle speed should also be the minimum.

When the motor power of the gear shaft of the feed box is constant, the feed speed is small; when the feed rate is large, the gear shaft of the feed box bears large load, resulting in large deformation of the gear shaft of the feed box. Therefore, this paper selects the low-speed branch of feed box gear shaft transmission, C6136A lathe has a total of eight speeds, from 42 R / min to 980 R / min in equal proportion sequence distribution, select the speed between 42 R / min and 980 R / min, find the lowest speed of feed box gear shaft transmission when full power is transmitted, then we can know the maximum torque of feed box gear shaft. Based on this, the mechanical model of gear shaft transmission of feed box is established.

Figure 1 is the main drive power and torque characteristic diagram of C6136A machine tool, where n represents the shaft speed, T represents the torque, and P represents the power. The calculated speed NC of spindle refers to the lowest speed when the spindle transmits full power. Tmax is the maximum torque of the shaft. Pmax is the maximum power of the shaft. When n ≥ NC, the spindle transmits full power, and t decreases with the increase of speed, which is the constant power working range; when n ≤ NC, t = Tmax, and P decreases with the decrease of speed, which is the constant torque working range. For general machine tools such as lathe, milling machine and specialized machine tools such as planer, the calculated speed of these machine tools is based on the empirical formula: NC = Nmin φ Z / 3-1 obtained from the investigation, analysis and measurement in the process of use. Where NC is the calculated speed of the machine tool, Nmin is the lowest speed of the machine tool, φ is the common ratio between the machine tool speeds, and Z is the number of machine tool speeds. nmin= 10r/min，φ = 1.25，Z = 8。 The calculated speed NC of C6136A machine tool is 10 × 1.25 = 50R / min.

Through the calculation of transmission ratio, I = NC / N2 = 8.18 and N2 = 6R / min can be obtained.

Figure 2 shows the expanded view of C6136A feed box, in which the front and rear supports of the feed box are long supports. The lowest transmission speed is in the low-speed transmission group, so the power is transmitted to the gear shaft through the pinion on the change gear and the big gear 36:90 on the gear shaft.

Figure 2 torque calculation formula of machine tool feed box is as follows: T = 9 550p / NC. Where t is the torque of the spindle drive, unit n · m, P is the calculated power of the shaft, unit kW, NC is the calculated speed of the spindle R / min. The motor power of 7.5kW is brought into the formula, and the efficiency is 0.9.

T1=T2=9 550P/nc =9 550×4.4×0.9 /6 = 6 303 (N·m)。 The direction is shown in Figure 3.

When the speed of gear shaft is set to 6R / min to transmit feed, the transmitted power is transmitted to the gear shaft through the gear with 90 teeth and diameter of 135mm. Through the simulation process and TT, the tangential force is deduced as follows: FT1 = 6303n · M / 0.675m = 9337 (n) axial force: FT1 = 6303n · M / 0.675m = 9337 (n): 