Feed Axis Calculations

Torque

1. Z: Thrust 1500 N + dead weight 60 kg × 9.81 = 589 N, totaling 2,089 N. T = 2,089 × 5 / (2π × 0.9) = 1.85 N·m (excluding acceleration and friction)
2. Horizontal: 100 kg × 0.5 m/s² = 50 N. T = 50 × 5 / (2π × 0.9) = 0.044 N·m (excluding guideway friction)

The 8 N·m for Z and 3 N·m for horizontal are holding torques, which drop with spindle speed. Check the values at 600 rpm on the torque-speed curve (unverified).

Spindle Speed

• Rapid traverse 3 m/min: 3000 / 5 = 600 rpm
• Feed for φ12: 0.07 × 1250 = 87.5 mm/min, 87.5 / 5 = 17.5 rpm. Watch out for low-speed pulsation

Z-axis Length

With a stroke of 150, the effective length of the screw is stroke 150 + nut 100 + margin, so the distance between the supports is about 320, and the overall length is about 380.

Critical Speed (Rail Direction)

1. Root diameter 13.2 mm (temporarily using the value for THK BIF1605): I = π × 13.2⁴ / 64 = 1,490 mm⁴, A = 137 mm²
2. Span between supports 900 mm, fixed-supported, λ = 3.927
3. ω = λ² / l² × √(E I / (ρ A)) = 15.42 / 0.81 × 16.86 = 321 rad/s = 3,066 rpm
4. With a safety factor of 0.8, it is 2,453 rpm. Since we operate at 600 rpm, there is no problem

Buckling

• For Z, a span between supports of 320 or less is on the safe side using the value for 350. Z, span between supports 350, fixed-supported: P = 2 π² E I / L² = 49 kN. Operating load is about 2 kN
• Sufficiently large compared to the total of downward thrust and dead weight

Axial Rigidity (Z)

1. Screw: E A / L = 205,000 × 137 / 350 = 80 N/µm
2. Nut: 44 kgf/µm × 9.81 = 432 N/µm (TBI table)
3. Bearing: 100 N/µm (assumed)
4. Total: 1 / (1/80 + 1/432 + 1/100) = 40 N/µm. At 1500 N, this is 0.037 mm

Since this is in the feed direction, it does not affect hole position, but affects blind hole depth.