**1 ****Introduction**

Since the load on the plate roll bending machine is large, so the requirement for the parts strength is high.

In addition, due to the fierce competition in the market, it is urgent to reduce the cost of the plate rolls, so it is imperative to design the machine accurately and reliably.

For the design calculation of the roll bending machine, the force analysis of the rolling machine is required first, and the result is the original parameters of the design of each part of the rolling machine.

And the calculation of driving power of the main drive system is the necessary parameter for designing the main drive system and selecting the motor.

Therefore, the calculation of the force analysis and driving power of the plate rolling machine is very important to the design of the roll bending machine.

In this post, the calculation of the force capabilities of symmetrical three-roll bending machine is one of the methods, the other types of plate rolling machine can take it for reference.

**2 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:

In the above formula,

B, δ – The maximum width and thickness of rolled steel sheet (m)

σ_{s}- Material's yield limit (kN • m^{-2})

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 F_{2 }on the roll plate can be obtained via the formula:

In the above formula,

θ – The angle between defiled line *OO*1 and *OO*2,

α – Lower roller center distance (m)

*d*_{min} – Min diameter of plate rolling (m)

*d*_{2}* – *Lower roller diameter (m)

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 0.5d_{min}, in order to simplify the calculation , the above equation can be changed to:

According to the force balance, the pressure force F_{1}, which is generated by the upper roller, acting on the rolling plate is:

**3. 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 T_{n1} and the friction torque T_{n2}.

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

The ratio is equal to the power of deformation torque T_{n1}, namely:

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Therefore,
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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:

In the above formula:

*f* – Coefficient of rolling friction, take *f* = 0.008m

*μ* – Coefficient of sliding friction, take *μ *= 0.05-0.1d_{1},

d_{2} – Upper roller & lower roller diameter (m)

D_{1}, D_{2} – Upper roller & lower roller neck diameter (m)

The size is not yet accurate in the design phase, the value can take D_{i} = 0.5d_{i} (i=1, 2). The lower roller drive torque T equals the sum of the deformation torque T_{n1} and the friction torque T_{n2}.

**3.2 Lower roller driven power**

Lower roller driven power is:

In the above formula:

*P* – Driven power (m • KW)

*T* – Driven force moment (KN • m)

n_{2} – Lower roller rotation speed (r • min^{-1}), n_{2}=2*V*/d_{2} (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*.

GuilhermeFebruary 15, 2018 at 1:35 amHello,

Where did you get all these formulas from? I currently making a report for my school project and my advisor teacher is asking for the formulas references so I can apply them.

MachineMfgFebruary 18, 2018 at 9:34 amfrom experts in this field.

DudeFebruary 25, 2018 at 12:44 pmWhen showing your calculations for lower roller drive moment (3.1), your calculations appear to drop the V term (rolling speed) with no explanation. The units work out after dropping the term, but not before. Can you explain where this term is used during this step? Equation 5 does not have a clear path from what is shown above it. Thank you

Abdul Bilal AhnedMay 1, 2018 at 3:11 pmThe rolling speed is the speed of sheet

manzoor ahmadApril 30, 2018 at 5:21 pmsir i need calculation for 1 inch metal sheet rolling

Aniket Vijay WaghSeptember 7, 2018 at 2:13 pmWhat’s the minimum rolling diameter of sheet

MachineMfgSeptember 8, 2018 at 8:10 pmthis is determined by the upper roller diameter

Govind RaoNovember 30, 2018 at 1:23 pmI would like to bend 100mm X 100mm X 1900 dia ring could you help me with the calculations

MachineMfgNovember 30, 2018 at 4:20 pmYou can refer to the calculation formula in this article.

zvodretiluretDecember 1, 2018 at 9:44 pmThis really answered my problem, thank you!

kishoreDecember 3, 2018 at 6:11 pmthank you so much sir this article really helped me

MachineMfgDecember 3, 2018 at 8:16 pmGlad it can help you.

ChandrakntJanuary 6, 2019 at 1:15 amI want to buy maschine sustainable to bend 25 mm thick and 150 mm max size

MachineMfgJanuary 6, 2019 at 8:27 amKindly check your email to check our reply.

rohan gaiikwadJanuary 26, 2019 at 6:20 pmexplain the eqn.(1) pls.

MachineMfgJanuary 28, 2019 at 11:50 amDo you understand it now?

rohan gaiikwadFebruary 17, 2019 at 5:12 pmWhere is the explanation for eqn.1 did you sent it on my email ? i cant see it in my inbox.

plz send the explanation of formulas to my email – [email protected]

plz sir it is very important for me.

HenryMay 22, 2019 at 3:24 pmdo you have the same explanation for 2 roll plate bending machine (with urethane (rubber) roll) ?

MachineMfgMay 29, 2019 at 3:31 pmCurrently, we didn’t write this for 2 roll plate bending machine. Will take this into consideration.