Calculating Maximum Load and Factor of Safety for a Single Square-Thread Power Screw

What are the steps to determine the maximum load that can be borne by a single start square threaded power screw according to von Mises failure theory?

Steps to Determine Maximum Load of a Single Square-Thread Power Screw

1. Calculate the Major Diameter (D) of the Screw: The major diameter of the screw is given as 50mm. 2. Calculate the Frictional Diameter (Df) of the Collar: The frictional diameter of the collar is 1.25 times the major diameter of the screw, which can be calculated as: Df = 1.25 * D 3. Calculate the Mean Diameter (dm) of the Screw: The mean diameter is the average diameter of the screw threads and is calculated using the formula dm = D - (0.5 * p), where p is the pitch of the screw. 4. Calculate the Torque (T) Required to Overcome Friction in the Collar: The torque can be calculated using the formula T = (F * Df * µ) / 2, where F is the axial load applied to the screw and µ is the coefficient of friction. 5. Calculate the Equivalent Stress (σ) in the Screw Using von Mises Failure Theory: The equivalent stress can be calculated as σ = (16 * T) / (π * dm²). 6. Calculate the Maximum Load (P) that can be Borne by the Power Screw: The maximum load can be determined using the formula P = (π * dm² * σ_yield) / 4, where σ_yield is the yield stress of the material. 7. Calculate the Factor of Safety (FS) for the Power Screw: The factor of safety is calculated as FS = σ_yield / σ. By following these steps and plugging in the given values, we can determine the maximum load that can be borne by the single square-thread power screw and the factor of safety according to von Mises failure theory.

The maximum load that can be borne by the power screw is calculated to ensure a factor of safety of 2 using von Mises failure theory. By following the steps outlined above and substituting the values provided, we can calculate the maximum load and the factor of safety for the single start square threaded power screw. Given: - Major Diameter (D) = 50mm - Pitch (p) = 8mm - Coefficient of Friction (μ) = 0.08 - Frictional Diameter of Collar (Df) = 1.25 * D - Yield Stress (σ_yield) = 240 MPa Now, let's calculate the maximum load and factor of safety: 1. Calculate the major diameter: D = 50mm 2. Calculate the frictional diameter of the collar: Df = 1.25 * 50 Df = 62.5mm 3. Calculate the mean diameter of the screw: dm = D - (0.5 * p) dm = 50 - (0.5 * 8) dm = 50 - 4 dm = 46mm 4. Calculate the torque required to overcome friction: T = (F * Df * μ) / 2 5. Calculate the equivalent stress in the screw: σ = (16 * T) / (π * dm²) 6. Calculate the maximum load that can be borne by the power screw: P = (π * dm² * σ_yield) / 4 7. Calculate the factor of safety for the power screw: FS = σ_yield / σ By plugging in the values and following the calculations, we can determine the maximum load and the factor of safety for the single square-thread power screw based on the given parameters.

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