A helical compression spring made of ASTM A227 hard drawn steel wire used essentially for static loading is made to support a maximum load of 150N. Given that robust linearity is 0.2.
The correct answer and explanation is :
To solve this problem involving a helical compression spring, we need to calculate the spring’s stiffness (spring constant) and ensure that it can handle the maximum load while adhering to the given condition of robust linearity.
Given Information:
- Maximum load (F) = 150 N
- Robust linearity (θ) = 0.2
- Material: ASTM A227 hard-drawn steel wire (commonly used for static loading in compression springs)
Spring Constant (k):
The spring constant is a measure of how stiff the spring is, which determines the force needed to compress it a given distance. It is calculated using Hooke’s Law: F=k×ΔxF = k \times \Delta x
Where:
- FF is the force (150 N),
- kk is the spring constant (which we need to find),
- Δx\Delta x is the displacement (compression or elongation) of the spring.
The term “robust linearity” refers to the ratio of the maximum load that the spring can handle without exceeding its elastic limit. It’s typically a factor that quantifies the allowable strain (deformation) within the spring without causing permanent damage or failure.
Given that the robust linearity is specified as 0.2, it suggests that the spring should be designed such that the load does not exceed this factor of its maximum displacement, indicating the proportion of the maximum load that can still yield elastic deformation without causing permanent deformation.
The robust linearity suggests that the maximum compression (Δx) the spring can experience, based on the given load, is: Δx=Fkandk=FΔx\Delta x = \frac{F}{k} \quad \text{and} \quad k = \frac{F}{\Delta x}
Given robust linearity as 0.2, the spring displacement must align with a safe design load under this factor. Therefore, the spring constant kk is derived by calculating the maximum allowable displacement of the spring under the maximum load. Based on the properties of ASTM A227 steel wire, the spring’s ability to handle these loads is a crucial element for ensuring durability and functionality.