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How to Calculate Load and Power for Symmetrical 3-Roll Plate Bending Machine

Key takeaways:

1. The design of plate roll bending machines necessitates a precise force analysis and calculation of driving power to ensure the machine's components can withstand the substantial load during operation, which is crucial for both performance reliability and cost-effectiveness in a competitive market.

2. Key parameters in the force analysis include the calculation of maximum torque required for cylinder rolling, accounting for the yield limit of the material and a reinforcement coefficient to adjust for material deformation, as well as the supporting and pressure forces acting on the plate during the rolling process.

3. Determining the driving power for the lower roller—the primary driver in the plate rolling process—requires the summation of deformation torque and friction torque, with factors such as rolling and sliding friction coefficients, roller dimensions, and transmission efficiency playing a significant role in the accurate calculation of the motor's power requirements.


The load on plate roll bending machines is substantial, so the strength of its parts must be high.

Furthermore, with intense competition in the market, reducing the cost of plate rolls is crucial. This means that the machine must be designed with accuracy and reliability.

In order to design the roll bending machine, it is necessary to first perform a force analysis of the rolling machine, which provides the original parameters for designing each part of the machine.

The calculation of the driving power of the main drive system is also important for designing the main drive system and selecting the motor.

As a result, calculating the force analysis and driving power of the plate rolling machine is critical to the design of the roll bending machine.

This post provides one method for calculating the force capabilities of a symmetrical three-roll bending machine, and other types of plate rolling machines can use it as a reference.

Force Analysis

2.1 Maximum torque required for a cylinder rolling

When the plate rolling machine is working, the steel sheet should be rolled into the steel pipe.

At this time, the stress of the material has reached the yield limit.

Therefore, the bending stress distribution on the tube section is shown below the figure (b), and the bending moment M of the section is:

Maximum torque required for cylinder rolling

In the above formula,

  • B, δ – The maximum width and thickness of rolled steel sheet (m)
  • σs – Material’s yield limit (kN m-2)
Stress distribution of roll bending

Fig.1 Stress distribution of roll bending

When considering the deformation of the material, there is reinforcement, and the reinforcement coefficient K is introduced to modify the equation (1), namely:


In the above formula,

  • K – reinforcement coefficient, the value can be K = 1.10~1.25, when the result for δ/R is big, then take the biggest value.
  • R – Neutral layer’s radius of the rolling plate (m)

2.2 Force Condition

When rolling steel plate, the force condition is shown as below figure. According to the force balance, the supporting force Fon the roll plate can be obtained via the formula:

supporting force F2

In the above formula,

  • θ – The angle between defiled line OO1 and OO2,
The angle between defiled line
  • α – Lower roller center distance (m)
  • dmin – Min diameter of plate rolling (m)
  • d2Lower roller diameter (m)
Force analysis of roll bending

Fig.2 Force analysis of roll bending

Considering that the thickness of the plate δ is far less than the minimum diameter of the rolling tube, the radius R of the neutral layer is around 0.5dmin, in order to simplify the calculation, the above equation can be changed to:


According to the force balance, the pressure force F1, which is generated by the upper roller, acting on the rolling plate is:


Calculation of driving power

3.1 Lower roller drive moment

The lower roller of the plate rolling machine is the driving roller, and the driving torque on the lower roller is used to overcome the deformation torque Tn1 and the friction torque Tn2.

In the process of steel plate rolling, the deformation capabilities stored in AB section of the steel plate (see Fig 1a and Fig 2) is 2Mθ, the costed time is 2θR/V (V is rolling speed).

The ratio is equal to the power of deformation torque Tn1, namely:

deformation capabilities ratio


The friction torque includes the rolling friction torque between the upper and lower roller and the steel plate, and the sliding friction torque between the roller neck and the shaft sleeve, which can be calculated as follows:

Tn2 value

In the above formula:

  • f – Coefficient of rolling friction, take f = 0.008m
  • μ – Coefficient of sliding friction, take μ = 0.05-0.1d1,
  • d2 – Upper roller & lower roller diameter (m)
  • D1, D2 – Upper roller & lower roller neck diameter (m)

The size is not yet accurate in the design phase, the value can take Di = 0.5di (i=1, 2). The lower roller drive torque T equals the sum of the deformation torque Tn1 and the friction torque Tn2.

lower roller drive torque T

3.2 Lower roller driven power

Lower roller driven power is:

Lower roller driven power

In the above formula:

  • P – Driven power (m • KW)
  • T – Driven force moment (KN • m)
  • n2 – Lower roller rotation speed (r • min-1), n2=2V/d2 (V is rolling speed)
  • η – transmission efficiency, η=0.65-0.8

The power of the main motor can be obtained from the value of P.

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32 thoughts on “How to Calculate Load and Power for Symmetrical 3-Roll Plate Bending Machine”

  1. Sir,
    I made a 3 roller machine of bed length 3600mm, But when tried for bending the center part of the sheet did not bend . The diameter of 3 shafts is 58mm. Thicknes of the sheet is1.6mm., Kindly guide me through this issue

  2. dear sir,
    I want to know that what is the distance between two rollers of sheet rolling machine. because I am traying to make one sheet rolling machine. so please guide me the distance between two rollers( bottom) . my roller dia is 120mm all three rollers.

  3. Sir, how we can decide the roller diameter if we want to make the pipe of 25 to 50 mm dia.from 1.5- 2 mm sheet thickness,and also please tell us about other design calculations like speed of roller, bottom roller distance etc..

  4. Chris Phimister


    Is the lower roller drive torque for each roller, or is it the sum of both together? i.e. if the calculation result is 30Nm, is that 30Nm per shaft, or 15Nm each for a total of 30Nm?

    Does having the top roller driven as well affect the torque requirement?

    Thank you,

  5. Amit Madhogaria

    I need help with the calculations and design of a plate bending machine for our personal use.
    Would you be interested in drawing the correct specifications for us on consultancy basis.

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