Pressure Considering Rolling Similar To Plane-Strain-Upsetting Process Calculator

Formula Used:

\[ P_r = b \times \frac{2\sigma}{\sqrt{3}} \times \left(1 + \frac{\mu_{sf} \times R \times \frac{\pi}{180} \times \alpha_b}{2(h_i + h_{fi})}\right) \times R \times \frac{\pi}{180} \times \alpha_b \]

Strip Width of Spiral Spring (b):

Flow Stress of Work Material (σ):

Frictional Shear Factor (μ_sf):

Roller Radius (R):

Bite Angle (α_b):

rad

Thickness before Rolling (h_i):

Thickness after Rolling (h_fi):

Pressure Acting while Rolling (P_r):

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1. What is Pressure Considering Rolling Similar To Plane-Strain-Upsetting Process?

This calculation determines the pressure acting during rolling operations by treating the process similar to plane-strain-upsetting. It accounts for material properties, geometric parameters, and frictional effects to estimate the required rolling pressure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_r = b \times \frac{2\sigma}{\sqrt{3}} \times \left(1 + \frac{\mu_{sf} \times R \times \frac{\pi}{180} \times \alpha_b}{2(h_i + h_{fi})}\right) \times R \times \frac{\pi}{180} \times \alpha_b \]

Where:

\( P_r \) — Pressure Acting while Rolling (Pa)
\( b \) — Strip Width of Spiral Spring (m)
\( \sigma \) — Flow Stress of Work Material (Pa)
\( \mu_{sf} \) — Frictional Shear Factor
\( R \) — Roller Radius (m)
\( \alpha_b \) — Bite Angle (rad)
\( h_i \) — Thickness before Rolling (m)
\( h_{fi} \) — Thickness after Rolling (m)

Explanation: The formula incorporates material flow stress, geometric parameters of the rolling setup, and frictional effects to calculate the pressure required during the rolling process.

3. Importance of Pressure Calculation in Rolling

Details: Accurate pressure calculation is crucial for designing rolling mills, determining power requirements, predicting roll wear, and ensuring proper material deformation without defects.

4. Using the Calculator

Tips: Enter all parameters in consistent SI units. Ensure all values are positive and physically meaningful for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the bite angle in rolling?
A: The bite angle determines the maximum possible reduction per pass and affects the friction conditions between the roll and workpiece.

Q2: How does frictional shear factor affect rolling pressure?
A: Higher friction increases rolling pressure as more force is required to overcome the resistance between the roll and workpiece surfaces.

Q3: What is flow stress and how is it determined?
A: Flow stress is the instantaneous stress required to continue plastic deformation. It depends on material composition, temperature, and strain rate.

Q4: Why is the plane-strain assumption used?
A: The plane-strain assumption simplifies the analysis by considering deformation primarily in two dimensions, which is reasonable for many rolling applications.

Q5: What are typical values for frictional shear factor?
A: Frictional shear factor typically ranges from 0.1 to 0.6, depending on surface conditions, lubrication, and material properties.