Recovery Torque In Fully Plastic Case Calculator

Fully Plastic Recovery Torque Formula:

\[ T_{f\_rec} = -\left(\frac{2}{3} \pi r_2^3 \tau_0 \left(1 - \left(\frac{r_1}{r_2}\right)^3\right)\right) \]

Outer Radius of Shaft (r₂):

Yield Stress in Shear (τ₀):

Inner Radius of Shaft (r₁):

Fully Plastic Recovery Torque (T_{f_rec}):

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1. What is Fully Plastic Recovery Torque?

Fully Plastic Recovery Torque is the equal and opposite torque to the fully plastic applied torque in a shaft. It represents the torque required to recover the shaft from its fully plastic state to its original configuration, considering the material's yield stress in shear.

2. How Does the Calculator Work?

The calculator uses the Fully Plastic Recovery Torque formula:

\[ T_{f\_rec} = -\left(\frac{2}{3} \pi r_2^3 \tau_0 \left(1 - \left(\frac{r_1}{r_2}\right)^3\right)\right) \]

Where:

\( T_{f\_rec} \) — Fully Plastic Recovery Torque (N·m)
\( r_2 \) — Outer Radius of Shaft (m)
\( \tau_0 \) — Yield Stress in Shear (Pa)
\( r_1 \) — Inner Radius of Shaft (m)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: The formula calculates the recovery torque based on the shaft geometry and material properties, accounting for the hollow section when applicable.

3. Importance of Recovery Torque Calculation

Details: Accurate recovery torque estimation is crucial for designing shafts that can withstand plastic deformation and return to their original state, ensuring structural integrity and safety in mechanical systems.

4. Using the Calculator

Tips: Enter outer radius and yield stress in shear in meters and Pascals respectively. Inner radius must be less than outer radius. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What does negative torque value indicate?
A: The negative sign indicates that the recovery torque acts in the opposite direction to the applied plastic torque.

Q2: How does inner radius affect the recovery torque?
A: A larger inner radius (hollow shaft) reduces the recovery torque since there's less material to resist deformation.

Q3: What is yield stress in shear?
A: Yield stress in shear is the stress at which a material begins to deform plastically under shear loading.

Q4: Can this formula be used for solid shafts?
A: Yes, for solid shafts set inner radius (r₁) to 0, which simplifies the formula.

Q5: What are typical applications of this calculation?
A: This calculation is used in mechanical engineering for designing shafts, torsion members, and other components that may experience plastic torsion.