Torque To Angle Calculator

Torque To Angle Formula:

\[ \theta = \frac{T}{K} \times \frac{360}{2 \pi r} \]

Angle (θ):

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1. What is the Torque To Angle Formula?

The Torque To Angle formula calculates the angular displacement (θ) resulting from applied torque (T) given the torsional stiffness (K) and radius (r). This calculation is essential in mechanical engineering for determining rotational movement in various systems.

2. How Does the Calculator Work?

The calculator uses the Torque To Angle formula:

\[ \theta = \frac{T}{K} \times \frac{360}{2 \pi r} \]

Where:

\( \theta \) — Angle in degrees
\( T \) — Torque in Newton-meters (Nm)
\( K \) — Stiffness in Newton-meters per degree (Nm/deg)
\( r \) — Radius in meters (m)

Explanation: The formula calculates the angular displacement by dividing the applied torque by the torsional stiffness and scaling by the geometric factor that converts radians to degrees considering the radius.

3. Importance of Angle Calculation

Details: Accurate angle calculation from torque is crucial for designing mechanical systems, analyzing rotational motion, determining fastener tightening specifications, and ensuring proper operation of rotating machinery.

4. Using the Calculator

Tips: Enter torque in Nm, stiffness in Nm/deg, and radius in meters. All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is torsional stiffness?
A: Torsional stiffness (K) is a measure of resistance to twisting or rotational deformation, expressed as the torque required to produce a unit angle of twist.

Q2: When is this calculation typically used?
A: This calculation is used in mechanical engineering applications such as bolt tightening, shaft design, torsion spring analysis, and rotational system design.

Q3: How does radius affect the angle calculation?
A: The radius directly influences the angular displacement - larger radii result in smaller angular displacements for the same applied torque and stiffness.

Q4: What are typical units for these measurements?
A: Torque is typically measured in Nm, stiffness in Nm/deg or Nm/rad, radius in meters, and angle in degrees or radians.

Q5: Are there limitations to this formula?
A: This formula assumes linear elastic behavior and may not accurately predict angles for materials that exhibit non-linear behavior or when dealing with large deformations.