Force Analysis of Metal Sheet in Bending Operation on Sheet Bending Machine

DOI : 10.17577/IJERTV4IS010115

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Force Analysis of Metal Sheet in Bending Operation on Sheet Bending Machine

1Mr. Nitin P. Padghan

Research Scholar, Department of Mechanical Engg.

Priyadarshini College of Engineering, Nagpur:19

2Mr. Prafulla D. Deshpande

Assistant Professor, Department of Mechanical Engg.

Suryodaya college of Engineering &Technology, Nagpur

3Dr. C. N. Sakhale

Associate Professor, Department of Mechanical Engg.

Priyadarshini College of Engineering, Nagpur:19

Abstract In the three roller bending machine, the three rollers rotate. Bending can be done in both sheet metal and bars of metal. For designing a three roller bending machine, it is required to calculate the exact force for bending. Based on this force, the machine parameters and motor power are decided. Various factors that should be considered while calculating this force are material properties, width, and thickness, number of passes, bending radius, force developing mechanism and link. To analyses the force and power for motor the designer takes the help of analysis software. The cost of software for analysis is high. So there is requirement to find simple formula. In this paper the various theories regarding bending are reviewed, formulae for force and power calculation are collected and finally a case study is taken where we have put together all the results of these formulae.

Keywords Bending force, bend radius, material thickness and

width, Number of passes.


Roller bending process can be used to deform a sheet or plate to hollow shapes of constant (i.e. cylindrical, elliptical) or varying cross sections like cone frustum. Cylindrical and conical shells are the basic components used for the various engineering applications like cylindrical tanks, boiler chambers, heat exchanger shells, pressure vessels, tunnels, etc. The process can be performed using many materials such as carbon and alloy steels, aluminum alloys and titanium alloys. Rolling machines with both three and four rolls are indispensible to the production of cylinders with various curvatures. The rolling process is usually performed by a three roll bending machine often called as pyramid type, because of the peculiar arrangement of the three rollers. The entire process of the roll bending may be divided into three steps: namely,

  1. Positioning of blank sheet or plate.

  2. Lowering of the center roller.

  3. Feeding of the plate.

    In the very first step, a flat blank sheet is fed into the machine by two rotating side rollers until the sheet is properly positioned. In the second step, center roller is displaced downward causes bending of the sheet. In the final step, two side rollers rotate again, so that the sheet is bent continuously.

    The rolling process always began with the crucial operation of pre bending both ends of the sheet. This operation eliminated flat spots when rolling a fall cylindrical shape and ensured better closure of the seam. The success of three roller bending process heavily depends on the experience and skill of the operator.

    Figure 1 shows the six stages of three roller sheet bending operation sequence for fixed bottom roller gap.

    Fig. 1: Three Roller Sheet Rolling Sequence for Fixed Bottom Roller Gap

    Top roller load required to bend the plate is the function of various parameters viz. sheet thickness, sheet width, sheet material property, shell diameter to be rolled, center to center distance between bottom two rollers, displacement of top roller, etc.


      Features of Three Roller Rolling Machine: The upper roll on 3-roll plate bending machine is fixed. The two ends of upper roll are controlled by PLC. The two lower roll can move up and down in arc way around fixed roller. It can finish pre-bending and rolling by feeding once. The three rollers are driving rollers. They can prevent skidding while rolling thin steel plates. Three roller rolling machine is controlled by micro-machine and has digital display. Compared with four roller plate bending machine, the structure of three roller plate rolling machine is compact and

      multiple. It is economical and practical for rolling thin and medium plates.It features clear and precise operation, high efficiency, reliability and competitiveness.



      Among different plate bending machines, three roller plate rolling machine possesses the maximum structure and driving modes. The structure, price and application of three roller rolling machine will be different owing to the roller position change.

      Fig 2.3 Roller sheet bending machine CAD Model.

      It involve the study of present 3 roller sheet bending machine.. In this we will first identify the mechanical element will find out the dimension of the machine component from vidarbha Industry.

      9. Forces analysis of metal sheet by analytical method.

      Bending force analysis of metals sheet during bending operation by software approach .


Calculations Of Gear Drive:

Fig 4.Power Transmission System for rolling machine

  1. FOR DRIVE 1 :-

    1. Pd1 = Pr x K1

      Where, Pd = Design power Pr = Rated power

      K1 = Load Factor, table XVI 2, D.D. Book there are 5% power losses

      Pr = 0746 5 0.95

      [Motor used of 5HP] Pr = 3.5435 KW

      Pd1 = 3.5435 1.2

      [load factor K1 = 1.25for medium shocks ]

      Pd1 = 4.4293 KW

    2. Tooth load (Ft) =

      where Vp Pitch line velocity Vp = rw

      Fig 3.3 roller sheet bending machine form vidharbha Industry


      1. Productivity analysis of manually operated and power operated sheet bending machine

      2. Modelling of metal sheet bending machine.

      3. Simulation of sheet metal bending machine with different materials.

      4. Forces analysis of metal sheet by analytical method.

      5. Bending force analysis of metals sheet during bending operation by software approach .

      6. Productivity analysis of manually operated and power operated sheet bending machine

      7. Modelling of metal sheet bending machine.

      8. Simulation of sheet metal bending machine with different materials.

        = d/2×2×N1

        Vp = 1093.27 m/s Ft = Pd1/Vp

        Ft = 4.051 N

        Module , m = ==6.470 mm where , d = Pitch diameter

        T = No. of teeth

    3. Dynamic load, (Fd) = Where,

C = Deformation factor , table XVI D.D. book e = Error in profile mm fig. 16. 1 D.D. book

b = Face width of gears

Fd 4.051 211093.275900 0.068 75

211093.27 5900 0.068 75 4.051

Fd = 29872.41 N.

We know thatFd = 29872.41 N.



2 1

1 2

N 17


W 3

2900 23


iii) 2


N2 = 2143.4 rpm


    Calculation of load & stress acting on the sheet

    42840.4 34663 12

    48 196 103 1250 103

    2 = 31.279 mm

    1. for t3 = 15mm

      4 169 103 1250 153

      W = 4EI/ RL


      1. W3

        550 3466 12

        E = Modulus of elasticity of compression I = Moment of inertia of sheet.

        W3 = 144586 N

        144586 625 7.512

        R = Radius of curvature L = Length of sheet

      2. b3

        1250153 12


        1. t1=5mm

      b =1250 mm


      i) W1 = 4EI / RL

      E = 196 x 103MPa or N.mm2


      I =


      b3 = 1927.81 N/mm2

      iii) 3=Wl3/48EI

      144586 34663 12

      48 196MU3 1250 153

      3=29.873 mm

    2. t4 = 20mm

    4 196 103 1250 203

    R = Radius of curvature L = Length of sheet.n

    1. W4

      550 3466 12

      4 196 103 1250 53



      W4 = 342723.51 N


      342723.51 625 10 12

      550 3466 12

      W = 5355.05 N

    2. b

    1250 203


    ii) Bending shress.


    b4 = 2570.42 N/mm2

    342723.51 34663 12

    b1 I

    iii) 4 48 196 103 1250 203

    M = Bending moment

    Y = Perpendicular distance of the neutral cassis

    b 5355.05 625 2.5 12

    4 =26.231 mm

    e)t5 = 25mm

    4 196 103 1250 253


    1250 53

    = 642.60 N/mm2

    i) W4

    550 3466 12

    iii) Deflection of sheet at mid span to obtain required radius

    W5 = 669381. 34 N

    of curvature –



    b 669381.3 625 12.5 12


    1250 253



    669381.3 34663 12

    5355.05 34663 12

    48 196 103 1250 53

    iii) 5 48 196 103 1250 253

    5 = 22.54 mm

    Materials are used for force analysis are as follows

    b) for t2

    1. W2

      = 10mm

      41 961103 1250 103

      550 3466 12

      1. Aluminum alloy

      2. Copper alloy

      3. Stainless steel

      4. Gray cast iron

      5. Magnesium alloy

      W2 = 42840.40 N

    2. Bending shress. MY

    b2 I


    42840.40 625 5 12

    2 1250 103

    b2 = 1285.21 N/mm2

    Thickness of sheet used practically varies from 5mm to 25 mm. The experimental performed on sheet having dimensions ( 1250 x 3466) mm . The power gained by upper roller through different gear drive system and this load is applied on the sheet. A sheet passes through between the upper and lower roller the sheet goes

    bend. This process is continue till the required result is obtained.

    The stress induced on the sheet is calculated by the analytically as well as virtually using analysis software.

    For virtual analysis CAD MODEL is generated in creo parametric 2.0 and converted into iges format and call into the ANSYS workbench for structural analysis.

  2. RESULTS For thickness 5mm:




    Standard Deviation ()

    t = 5 mm



    Deformation (mm)



    Aluminum Alloy




    Copper Alloy




    Gray Cast Iron




    Magnesium Alloy




    Stainless Steel



    Table No.1: Analytical Calculation


    After performing actual experiment force calculation and fem analysis on metal sheet at different materials, we conclude that the force which required for bending the sheet is found by virtually it is tested in terms of factor of safety as well as material safety while bending operation.

    On the basis of the results and its analysis, following conclusion can be drawn. From the results analysis for constant radius of curvature (R) ,constant dimensions by changing the material, load(W) increases as the value of modulus of elasticity(E) increases ie Load is directly proportional to the modulus of elasticity. From the results analysis and calculations we can conclude that for same material keeping dimensions constant change in radius of curvature(R) changes the value of load(W) .As radius of curvature(R) increases the load(W) value also increases. From the results analysis and calculations , for same radius of curvature (R) and material if thickness varies from 5 mm to 25 mm ,it directly affects the value of load(W) ie. Load increases as the thickness changes in increasing order. Required surface finish of cylinder or any circular product is directly affected by skilled labour as they lowered the top roller with the help of power screw in some extent.


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