Plate rolling is a common metalworking process used to produce cylindrical or conical-shaped parts from flat sheets or plates of metal. The process involves pre-bending the plate edges and then gradually bending and rolling the plate into the desired cylindrical or conical shape. The accuracy and quality of the final product depend on the proper calculations and setup of the plate rolling machine.

## Calculating for plate rolling

The first step in calculating for plate rolling is to determine the plate width, thickness, and elongation. This can be done through material testing or referencing material specifications from the manufacturer or material supplier. Once these parameters have been determined, the next step is to calculate the minimum bend radius that can be achieved without the plate cracking. This calculation is based on the yield strength and thickness of the material being rolled.

### Calculating for minimum bend radius

The minimum bend radius is calculated using the following formula:

Minimum bend radius = material thickness/maximum allowable longitudinal strain

The maximum allowable longitudinal strain can be estimated by dividing the material’s yield strength by a safety factor. The safety factor depends on various factors, including the type of material, the degree of cold work, and the degree of curvature.

### Calculating for bending force

Next, we need to calculate the bending force required to roll the plate. This force is dependent on the plate’s width, thickness, the angle of curvature, and the coefficient of friction between the plate and the rollers. The bending force can be calculated using the following formula:

Bending force = 0.33 x plate width x plate thickness x (tensile strength/minimum bend radius)

The coefficient of friction depends on several factors, such as the material’s surface finish, the contact pressure between the rollers and the plate, and any lubrication used. The coefficient of friction can be determined by conducting bench tests on various combinations of materials and lubricants.

### Calculating for rolling torque

Another critical calculation involved in plate rolling is the rolling torque required to roll the plate. This torque is based on the diameter of the rollers, the thickness of the plate, and the material’s yield strength. The rolling torque can be calculated using the following formula:

Rolling torque = (rolling force x rolling radius)/2

The rolling radius is equal to the roller diameter minus half the thickness of the plate. The rolling torque determines the amount of power required for the plate rolling machine.

### Calculating for number of passes

Finally, we need to calculate the number of passes required to achieve the desired curvature of the plate. This calculation is dependent on the plate’s thickness, width, and the desired curvature. The number of passes required can be determined using a formula known as Juravskii’s Formula:

Number of passes = 2 x (bend radius – plate thickness)/bend radius

This formula assumes that each pass results in a deformation equal to half the plate’s thickness. In practice, the deformation per pass may vary depending on the plate rolling machine’s configuration and the operator’s skill.

## How do you calculate plate bending? top 7 steps

Calculating plate bending typically involves the following steps:

### Steps 1#: Understand Plate Geometry

Begin by understanding the geometry of the plate. This includes knowing the plate’s dimensions, such as length, width, and thickness. The plate can be rectangular, circular, or have other shapes.

### Steps 2#: Identify Boundary Conditions

Determine the boundary conditions of the plate, which define how the plate is supported or constrained at its edges. Common boundary conditions include simply supported, clamped, or free edges.

### Steps 3#: Determine Loadings

Identify the external loads and moments applied to the plate. These loads can include uniform or varying distributed loads, point loads, and moments. It’s essential to know the magnitude and distribution of these loads.

### Steps 4#: Choose a Plate Bending Theory

Depending on the complexity of the problem and the accuracy required, select an appropriate plate bending theory. Common theories include:

- a. Thin Plate Theory: This theory is suitable for plates with a thickness-to-span ratio (h/l) of less than 1/20. It simplifies the equations and assumes that strains are small and that the plate remains planar.
- b. Kirchhoff-Love Plate Theory: This theory is more accurate and suitable for thicker plates. It considers both bending and stretching effects and can handle larger deformations.
- c. Finite Element Analysis (FEA): For complex geometries and loads, FEA is a numerical method that divides the plate into smaller elements to calculate deformation and stress distributions.

### Steps 5#: Solve for Plate Deflection

Apply the chosen plate bending theory to derive equations that describe the plate’s deflection. These equations may involve partial differential equations, boundary conditions, and load equations.

### Steps 6#: Calculate Deflection

Solve the derived equations for plate deflection. Depending on the method used, this may involve integration, finite element analysis software, or numerical techniques.

### Steps 7#: Check for Strength and Stiffness

Analyze the calculated deflection to ensure that it meets the strength and stiffness requirements for the specific application. Check for yield or failure criteria and ensure that the plate can safely carry the applied loads.

## Final words

Plate rolling is a complex process that involves several calculations and considerations. Accurate calculations are critical to ensure that the final product meets the desired specifications, including dimensional accuracy, mechanical strength, and surface finish. Plate rolling machines are expensive but are an essential component in many manufacturing operations. Therefore, it is essential to understand the principles involved in plate rolling and select a machine that is capable of producing the desired results.