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Helix Angle of Screw given Torque Required in Lifting Load with Trapezoidal Threaded Screw Calculator

Helix Angle Formula:

\[ \alpha = \arctan\left(\frac{2T - (W \cdot d_m \cdot \mu \cdot \sec(15^\circ))}{(W \cdot d_m) + (2T \cdot \mu \cdot \sec(15^\circ))}\right) \]

N·m
N
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1. What is Helix Angle of a Screw?

Definition: The helix angle is the angle between the helix of the thread and a line perpendicular to the screw axis. It's crucial for determining the mechanical advantage of screw threads.

Purpose: This calculator determines the optimal helix angle when lifting a load with a trapezoidal threaded screw, considering torque, load, and friction.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \alpha = \arctan\left(\frac{2T - (W \cdot d_m \cdot \mu \cdot \sec(15^\circ))}{(W \cdot d_m) + (2T \cdot \mu \cdot \sec(15^\circ))}\right) \]

Where:

  • \( \alpha \) — Helix angle (degrees)
  • \( T \) — Torque for lifting load (N·m)
  • \( W \) — Load on screw (N)
  • \( d_m \) — Mean diameter of power screw (m)
  • \( \mu \) — Coefficient of friction (±5%)
  • \( \sec(15^\circ) \) — Secant of 15° (trapezoidal thread angle)

3. Importance of Helix Angle Calculation

Details: Proper helix angle ensures efficient power transmission, prevents self-locking when needed, and optimizes screw performance under load.

4. Using the Calculator

Tips: Enter torque, load, mean diameter, and friction coefficient (default 0.15±5%). All values must be > 0. The result is in degrees.

5. Frequently Asked Questions (FAQ)

Q1: Why is 15° used in the formula?
A: Trapezoidal threads typically have a 30° included angle, making each flank 15° from perpendicular.

Q2: What's a typical friction coefficient for screw threads?
A: For steel-on-steel with lubrication, μ≈0.15±5%. Dry conditions may increase this to 0.2-0.3.

Q3: How does helix angle affect screw performance?
A: Higher angles provide faster movement but require more torque. Lower angles offer more mechanical advantage.

Q4: What if my screw has a different thread angle?
A: Replace 15° with half your thread's included angle (e.g., 14.5° for 29° Acme threads).

Q5: Why does torque appear twice in the formula?
A: The numerator accounts for torque overcoming friction, while the denominator considers torque's effect on helix efficiency.

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