1. What is a Stepped Shaft Deflection Calculator?

Definition: This calculator estimates the deflection of a stepped shaft under a point load using the cantilever beam formula.

Purpose: It helps mechanical engineers and designers determine how much a stepped shaft will bend under applied forces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \delta \) — Deflection (meters)
• \( F \) — Applied force (Newtons)
• \( L \) — Length of shaft (meters)
• \( E \) — Young's modulus (Pascals)
• \( I \) — Moment of inertia (m⁴)

Explanation: The formula calculates the maximum deflection at the free end of a cantilever beam with a point load at the end.

3. Importance of Deflection Calculation

Details: Proper deflection analysis ensures shafts meet stiffness requirements, prevent excessive vibration, and maintain proper alignment in machinery.

4. Using the Calculator

Tips: Enter the force, shaft length, material modulus, and moment of inertia. All values must be > 0. Moment of inertia is typically very small (e.g., 10^-8 m⁴).

5. Frequently Asked Questions (FAQ)

Q1: What's a typical Young's modulus for steel shafts?
A: For steel, E ≈ 200 GPa (200 × 10⁹ Pa). For aluminum, E ≈ 70 GPa.

Q2: How do I find the moment of inertia?
A: For circular shafts, \( I = \frac{\pi d^4}{64} \), where d is diameter.

Q3: Does this work for non-stepped shafts?
A: Yes, this is the basic formula for uniform cantilever beams. For stepped shafts, you'd need to calculate each section separately.

Q4: What if my load isn't at the end?
A: Use a different formula: \( \delta = \frac{F \times a^2}{6 \times E \times I} \times (3L - a) \), where a is load distance from fixed end.

Q5: How accurate is this calculation?
A: It's theoretically exact for ideal conditions. Real-world factors like supports, distributed loads, or material imperfections may affect results.