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  • Mathematics and steel roll pressing

    Part 1 Making cylinders and bends by roll pressing steel

    Outcomes for Part 1(Old syllabus):

    Maths: NS4.3, NS5.2.1, PAS4.1, PAS4.4, MS4.1, MS4.2, WMS4.2, WMS4.3, WMS4.4

    ICT: enter formulae into spreadsheets, create and format spreadsheets

    Outcomes for Part 1(New syllabus):

    MA4-1WM communicates and connects mathematical ideas using appropriate terminology, diagrams and


    MA4-2WM applies appropriate mathematical techniques to solve problems

    MA4-3WM recognises and explains mathematical relationships using reasoning

    MA4-5NA operates with fractions, decimals and percentages

    MA4-12MG calculates the perimeters of plane shapes and the circumferences of circles

    ICT: enter formulae into spreadsheets, create and format spreadsheets

    (For teacher to present to students as considered appropriate could be by teaching using

    selected material from this package, or by allowing students to work through the background

    material themselves, or could be adapted as an Assessment for learning activity- see steel

    rolling a4l.doc)

    Background information

    Rolled steel is used extensively in industry.

    Steel sheet, (a few mm thick), or steel plate, (6 mm or more in thickness), is pressed into

    cylinders and cones, and steel can be pressed around specific arcs to form bends or angles. These

    are pressed to great accuracy and are then assembled to make bulk storage containers, ductwork,

    piers for oil rigs, panels for the hulls of ships, etc.

    TW Woods Construction is a heavy engineering and steel fabrication company based at Tomago,

    NSW. The gallery of photographs, (view photos here), gives a glimpse of the scope and size of

    the applications.

    The steel plates that are used in the production of these items range in thickness from 6 mm to 70


  • TW Woods has several hydraulic roll presses that are used to bend the steel plate into the

    required shape.

    The following videos show steel being pressed to form cylinders, angles and cones.

    Cylinder being pressed

    Angle being pressed

    Cone being pressed

    Note these are YouTube clips will need to have download copies saved

    We hope to get equivalent clips from TW Woods.

    Typically the finished products are accurate to within 1or 2 mm of specifications.

    During the pressing process the steel is deformed in such a way that matter is squished along

    the length from the inner surface of the steel plate to the outer surface. i.e. the inner half of the

    steel is compressed as it is forced around the roller while the outer half is stretched. The section

    of the plate that is exactly in the middle, (with regard to the thickness), is not affected.

    The length of the middle section of the steel plate is called the mean running.

    What are the implications of this?

    We know that the label that wraps around a tin of peaches is very thin. The label is actually

    printed on a rectangular sheet of paper which is then rolled to be glued to the tin. The length of

    the rectangular piece of paper is equal to the circumference of the cylindrical can.

  • The length of the label is approximately 230 mm.

    The diameter of the tin is approximately 73 mm. Confirm these results using C = d.

    For a cylinder made from thin material such as paper, cardboard, or sheet metal, the internal and

    external radii of the cylinder are virtually identical. (There is a difference, but it is so small as to

    be negligible).

    Example 1 Making a cylinder in sheet metal (1 or 2 mm thick)

  • Flues take the waste gases and smoke from a gas or wood heater and vent them outside the


    A flue is made from cylindrical sections which are joined together. Sections are typically 900

    mm or 1000 mm in length. The diameter may be from 100 mm to 305 mm (or more) depending

    on the size of the heater. The sections are rolled from sheets of stainless steel, galvanized steel,

    or copper depending mainly on the appearance required.

    Similar cylindrical components may be used in ducting for air conditioning.

    The picture shows part of the flue for a home fire place. It is

    made from rolled stainless steel. It has a diameter of 230 mm

    and is 900 mm in length.

    Find the dimensions of the rectangle of stainless steel sheet

    from which each section is made. (Allow an additional 5 mm

    on the length to allow the edges of the rolled cylinder to be

    overlapped and joined together).

    Using C = d, we find the circumference of the cylinder to be 230 which is 723 mm (to the

    nearest mm).

    Now we need to add on the 5 mm joining allowance.

    The stainless steel sheet would need to be cut to a length of 728 mm and a width of 900 mm.

    However, for a cylinder made from steel which is 60 mm thick, or even 6 mm thick, the

    difference between the internal and external radii cant be ignored.

    When the thickness is 6 mm or more it is called plate steel rather than sheet steel.

    Example 2 Pressing a cylinder from steel plate

  • Suppose that we have to make a cylinder from 60 mm steel

    plate such that the cylinder has a height of 1500 mm and

    external radius of 900 mm. (Note that in the manufacturing

    industry lengths are expressed in mm.)

    It is most important to have the steel plate cut very accurately, (within 1 mm), to the correct

    length and width before it is pressed. The pressing process cant be adjusted to correct any errors

    in the dimensions of the plate if we press an incorrectly sized plate we will get an incorrectly

    sized cylinder.

    We know that the steel plate will have to be 60 mm thick and 1500 mm wide, but how long must

    it be?

    It appears that the length of the plate will have to be equal to the outside circumference of the

    cylinder C = 2 r = 2 900 = 5655 mm (correct to the nearest mm).

    If we act on this calculation and cut a sheet of 60 mm thick steel into a rectangle of length 5655

    mm by 1500 mm, then roll it, we will get a cylinder of the correct height but the radius will be


    Why? In the rolling process the outside material is stretched as it is rolled, which means that the

    outer circumference will be more than 5655 mm, which then means that the external radius will

    be greater than 900 mm.

    1500 mm 1800 mm

    60 mm

  • How do we solve the problem? We must work with a length measurement that does not change

    during the rolling process, i.e. we must work with the mean running.

    Step 1 Calculate the radius of the mean running

    The radius of the circle produced with the mean running as its circumference is (900 30) mm or

    870 mm. This was obtained from the formula RM = RE T, where RM is the radius of the

    mean running, RE is the external radius and T is the thickness.

    This was calculated by subtracting half of the thickness from the external radius.

    Which explanation is better for the target students?

    (Note that people in trades usually work with diameters rather than radii worth discussing with

    students using calipers etc you measure diameter, not radius).

    Step 2 Calculate the circumference of the mean running, which is the required length to cut

    Using C = 2 RM we obtain C = 2 870 = 5466 mm (correct to the nearest mm).

    Now we know that the 60 mm thick steel plate has to be cut to a length of 5466 mm and a width

    of 1500 mm.

    Example 3 Pressing a cylinder from steel plate

    We are required to manufacture a cylinder from plate steel.

    The dimensions of the cylinder are:

    height 800 mm

    inside diameter 1200 mm

    wall thickness 70 mm

    Find the dimensions of the steel plate to be used.

    Step 1 The mean radius is 635 mm.

    Note that when working with inside units, RM = RI + T. (i.e. the radius of the mean running

    is the interior radius plus half the thickness).

    Step 2 Length required = circumference of mean running

    = 2 635

    = 3990 mm

  • The steel required is 3990 mm long, 800 mm wide and 70 mm thick.

    A video of entire process (order specs to cutting to pressing to welding) at TW Woods will be


    Example 4 Pressing a bend (angle) from steel plate

    Thin materials like paper or cardboard can be folded along a line to form any required angle.

    Steel plate cant be folded along a line to form an angle. It has to be pressed and will produce the

    required bend around a circular arc. This is shown in the following picture.

    This pic from Jorgensen Metal Rolling site, do we acknowledge copyright. Would prefer to get

    something similar from TW Woods.

    We need to be familiar with some specific terminology, as shown in the following diagram.

  • A combination of these two videos might be useful to present and explain the terminology,and to

    explain why the bend angle is equal to the angle at the centre of the circular arc.

    Terminology used in bending

    Bend angle and angle at centre

    Suppose that we have to make a righ