Load on Screw given Effort Required in Lifting Load with Trapezoidal Threaded Screw Calculator

Load on Screw Formula:

\[ W = \frac{P_{li}}{\left(\frac{\mu \cdot \sec(15^\circ) + \tan(\alpha)}{1 - \mu \cdot \sec(15^\circ) \cdot \tan(\alpha)}\right)} \]

Load on screw (W): N

1. What is Load on Screw Calculator?

Definition: This calculator determines the load that can be lifted by a trapezoidal threaded screw given the effort applied, friction coefficient, and helix angle.

Purpose: It helps mechanical engineers and designers analyze screw jack systems and power screw mechanisms.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ W = \frac{P_{li}}{\left(\frac{\mu \cdot \sec(15^\circ) + \tan(\alpha)}{1 - \mu \cdot \sec(15^\circ) \cdot \tan(\alpha)}\right)} \]

Where:

\( W \) — Load on screw (N)
\( P_{li} \) — Effort in lifting load (N)
\( \mu \) — Coefficient of friction (dimensionless)
\( \alpha \) — Helix angle of screw (radians)
\( \sec(15^\circ) \) — Secant of 15° (trapezoidal thread angle)

Explanation: The formula accounts for the friction in trapezoidal threads (15° thread angle) and the mechanical advantage provided by the screw's helix angle.

3. Importance of Load Calculation

Details: Proper load calculation ensures screw mechanisms can handle required loads without failure and helps determine required input effort.

4. Using the Calculator

Tips: Enter the lifting effort in newtons, friction coefficient (default 0.15 ±5%), and helix angle in radians (default 0.0785 rad ±5% ≈ 4.5°). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is 15° used in the formula?
A: Standard trapezoidal threads have a 30° included angle, making each flank at 15° from vertical.

Q2: What's a typical coefficient of friction 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 do I find the helix angle?
A: Helix angle α = arctan(lead / (π × mean diameter)), where lead is axial distance per turn.

Q4: What units should I use for the helix angle?
A: The calculator requires the helix angle in radians. 1° = π/180 radians ≈ 0.01745 rad.

Q5: Does this account for screw efficiency?
A: Yes, the formula inherently includes the screw's efficiency based on friction and helix angle.