Math Problem Statement
A helical compression spring is made of music wire. The spring has to support a load of 150 N. Due to space limitations, the outer diameter of the spring should not exceed 25 mm, the solid length should not to exceed 40 mm, and the free length of the spring is not to exceed 100 mm. Allowable shear stress for music wire is 800 MPa and G = 81000 N/mm2
Solution
To design a helical compression spring made of music wire under the given conditions, we will follow standard spring design calculations. Here's the process:
Known Data:
- Load (P) = 150 N
- Outer diameter (Do) ≤ 25 mm
- Solid length (Ls) ≤ 40 mm
- Free length (Lf) ≤ 100 mm
- Allowable shear stress (τ) = 800 MPa = 800 N/mm²
- Modulus of rigidity (G) = 81,000 N/mm²
Step
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Spring Mechanics
Shear Stress
Modulus of Rigidity
Hooke's Law
Formulas
Solid length (Ls) = Na * d
Shear stress (τ) = (8 * P * D) / (π * d^3)
Spring constant (k) = G * d^4 / (8 * D^3 * Na)
Deflection (ΔL) = P / k
Theorems
Hooke's Law
Torsional Stress Theory
Suitable Grade Level
College-Level Engineering
Related Recommendation
Helical Compression Spring Design for 150 N Load with Space Constraints
Calculate Shear Stress, Deflection, and Factor of Safety for a Helical Spring
Determine Diameter of a Steel Wire Under Tensile Load with Stress and Elongation Limits
Minimum Spring Compression to Prevent Block from Falling (110 N/m Spring and 0.42 Static Friction)
Calculate Spring Compression of a 10.9 kg Weather Rocket at Rest