Ratio of Torsional Strength of Shaft with Keyway to without Keyway Calculator

Formula Used:

\[ C = 1 - 0.2 \times \frac{b_k}{d} - 1.1 \times \frac{h}{d} \]

Width of Key in Round Shaft (b_k):

Diameter of Shaft with Keyway (d):

Height of Shaft Keyway (h):

Ratio of Shaft Strength with and without Keyway (C):

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1. What is the Ratio of Torsional Strength of Shaft with Keyway to without Keyway?

The Ratio of Torsional Strength of Shaft with Keyway to without Keyway is the ratio of torsional strength of a shaft having a keyway to torsional strength of a same-sized shaft without a keyway. This ratio helps engineers understand how much the keyway weakens the shaft's torsional capacity.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C = 1 - 0.2 \times \frac{b_k}{d} - 1.1 \times \frac{h}{d} \]

Where:

\( C \) — Ratio of Shaft Strength with and without Keyway
\( b_k \) — Width of Key in Round Shaft (m)
\( d \) — Diameter of Shaft with Keyway (m)
\( h \) — Height of Shaft Keyway (m)

Explanation: The formula accounts for the reduction in torsional strength caused by the keyway, with coefficients 0.2 and 1.1 representing the relative impact of key width and height respectively.

3. Importance of This Calculation

Details: This calculation is crucial for mechanical design engineers to ensure that shafts with keyways can safely transmit the required torque without failure. It helps in proper sizing of shafts and keyways in various mechanical applications.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure that width of key and height of keyway are smaller than the shaft diameter. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical value for this ratio?
A: Typically, the ratio ranges from 0.7 to 0.95, meaning a keyway reduces torsional strength by 5-30%.

Q2: Why does a keyway reduce shaft strength?
A: The keyway creates a stress concentration point and reduces the cross-sectional area of the shaft, both of which decrease torsional strength.

Q3: Are there different formulas for different keyway shapes?
A: Yes, this formula is for standard rectangular keyways. Other keyway shapes (Woodruff, round, etc.) have different strength reduction factors.

Q4: How accurate is this formula?
A: This formula provides a good engineering approximation but actual strength reduction may vary based on material properties and manufacturing quality.

Q5: Should safety factors be applied to this calculation?
A: Yes, appropriate safety factors should always be applied to account for variations in material properties, loading conditions, and other uncertainties.