Core Diameter Of Screw Given Unit Bearing Pressure Calculator

Core Diameter of Screw Formula:

\[ d_c = \sqrt{d^2 - \frac{4 \times W_a}{S_b \times \pi \times z}} \]

Nominal Diameter of Screw (d):

Axial Load on Screw (Wₐ):

Unit Bearing Pressure for Nut (S_b):

Number of Engaged Threads (z):

Core Diameter of Screw (d_c):

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1. What is Core Diameter of Screw?

The core diameter of a screw is defined as the smallest diameter of the thread of the screw or nut. It represents the diameter at the root of the threads and is a critical parameter in mechanical engineering design.

2. How Does the Calculator Work?

The calculator uses the core diameter formula:

\[ d_c = \sqrt{d^2 - \frac{4 \times W_a}{S_b \times \pi \times z}} \]

Where:

\( d_c \) — Core diameter of screw (m)
\( d \) — Nominal diameter of screw (m)
\( W_a \) — Axial load on screw (N)
\( S_b \) — Unit bearing pressure for nut (Pa)
\( z \) — Number of engaged threads
\( \pi \) — Mathematical constant pi (≈3.1416)

Explanation: This formula calculates the minimum required core diameter to withstand the given axial load while maintaining acceptable bearing pressure on the engaged threads.

3. Importance of Core Diameter Calculation

Details: Accurate core diameter calculation is essential for ensuring screw strength, preventing thread stripping, maintaining proper load distribution, and ensuring the longevity of threaded connections in mechanical assemblies.

4. Using the Calculator

Tips: Enter nominal diameter in meters, axial load in newtons, unit bearing pressure in pascals, and number of engaged threads. All values must be positive numbers with engaged threads being at least 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between nominal diameter and core diameter?
A: Nominal diameter is the largest diameter of the screw thread, while core diameter is the smallest diameter at the root of the threads.

Q2: Why is unit bearing pressure important in screw design?
A: Unit bearing pressure determines the contact stress between screw and nut threads, affecting wear resistance and preventing thread deformation.

Q3: How does the number of engaged threads affect the core diameter?
A: More engaged threads distribute the load over a larger area, allowing for a smaller core diameter while maintaining the same bearing pressure.

Q4: What are typical unit bearing pressure values for different materials?
A: Unit bearing pressure varies by material combination, typically ranging from 10-30 MPa for steel-steel pairs and 5-15 MPa for steel-bronze pairs.

Q5: When should this calculation be used in engineering design?
A: This calculation is crucial when designing power screws, lead screws, jack screws, and other applications where screws carry significant axial loads.