Three Kinds of Bending



Reference must be made to the peripheral areas of bending in order to give accurate information concerning bending tools. The peripheral area here refers to bending machines and how to use them for bending work. As in the saying "You can't see the describe bending tools independently of bending machines and bending forest for the trees," it is not practical to only work. However, there is no point in extending the area so broadly as to cover all items related to sheet metal bending. This "The ABC of bending tools" will, therefore, deaf with the above-mentioned subjects, concentrating on the fundamentals necessary bending tools. The fundamentals will be discussed in Chapters 1 and 2. They will be for the reader to understand referred to several times throughout the book.

Such being the case, the reader should bear with us a little further if he feels there is no description of bending tools. It may be difficult to understand these tools in the future without a thorough comprehension of the fundamentals. The reader will be convinced that he has not wasted time once he has read through this book.

1-1 Kinds of Bending
Many operators encounter inexplicable troubles throughout their daily bending operation. For example, the intended product was not produced-it lost its shape, it was out of the required dimensional tolerance, or it had scores and cracks in the bent part. Perplexed with incomprehensible troubles, some may have uttered that bending is difficult and beyond their comprehension.

Sheet metals such as steel, stainless steel, and aluminium should bend easily when pressed with a die and punch mounted in a bending machine, as long as the specified requirements are met. This bending phenomenon is recognized as quite a natural event, due to the fact that one can actually see the sheet metal bend. Then it does not seem that sheet metal bending is complicated and difficult. However, sheet metal bending is not as simple as it appears.

This chapter teaches that there are three kinds of bending. The material to be bent (hereinafter called "work") undergoes three characteristic kinds of bending in accordance with bending force application. When told there are three kinds of bending, one may wonder, "Why?" or "It can't be true." Due to the bending phenomenon appearing simple, one cannot possibly observe the work experiencing three kinds of bending while it is being bent. In fact, here is a clue to understanding the seemingly incomprehensible characteristics of sheet metal bending. Go to Top

1-2 Curve of Bending Force versus Bending Angle
As a sheet of flat work is gradually pressed with a punch and die mounted in a bending machine, the bending of the work begins according to the application of bending force. At that time, a curve is obtained by plotting the angles to which the work bends under the respective force applied. This curve shows the relationship between the bending force and the resultant bending angle (Fig. 1-1). The curve, which is also called an "S curve" due to its resemblance to the letter "S," varies greatly in shape due to the type of material.

Fig. 1-1 shows a curve of the cold rolled carbon steel (SPCC). The bending force or the tonnage required for bending a work length of I meter is taken along the Y-axis, and the bending angle 0 along the X-axis. Bending angle 0 refers to the angle to which the work is bent after forming (the product angle).

The work placed between the punch and die does not immediately bend after a bending force has been applied and the bending force will increase to a certain level. In Fig. 1-1, this increase in the bending force appears as a vertical rise in the curve. The work is known to have been pressed with approximately 6 tons of force. The work may look bent at a glance, but restores the previous shape when the bending force applied has been relieved. This is caused by the elasticity of the material. Elasticity is the quality or tendency to go back to the previous size or shape after being pulled or pressed.

As the bending force gradually increases, the bending will proceed rapidly and the bending force will reach a peak (about 10 tons) at a bend of around 130 degrees. However, the bending force begins to decrease slightly when the bend exceeds 13.0 degrees. As shown in the figure, the bending angle in this region changes remarkably with a slight difference in bending force. This is called region 1.

The required tonnage increases while the bending angle decreases below 100 degrees in the bending range. 90 bending can be performed with a bending force of approximately 12.5 tons, which is 25 percent greater than in 130 bending. The bending force that bends a material to 90 degrees is called the "required tonnage" of the material. If the material continues to be pressed, it will bend at an angle 3 or 4 degrees smaller than 90 degrees, i.e., an acute angle. This is region 2.

The acute-angled bend goes back to a 90 bend if a still greater force is exerted on it. The tonnage needed at this time corresponds to approximately 75 tons, which is about 6 times the required tonnage. In Fig. 1-1, the line steadily rising along the Y-axis in the 90 bend indicates a rapid increase in the bending force. The region in which the bending angle changes very little despite the rapid increase in bending force, is called region 3.

The events that occur under the bending force in the three regions,1, 2 and 3 , are referred to as partial bending, bottoming, and coining respectively. These bending force events are the foregoing three kinds of bending. Further, partial bending and bottoming are both called air bending. Go to Top

1-3 Air Bending and Coining
In reference to basic nature, bending can be divided into two categories: air bending and coining. Air bending is a bend where air exists between the work and the die groove. As already stated, partial bending and bottoming belong to this category. These two methods of bending will be described in detail later.

Now let us compare air bending with coining in terms of economy and precision. Air bending provides the following features:

[1] Since this bending method can bend the work with relatively little force, a machine with a small capacity can be used. The cost of equipment is low, therefore, the method provides great economy.

[2] Having been influenced by springback (refer to subsection 1.4), the bending precision may not be satisfactory.

The features of coining are as follows:

[1] A machine with a large capacity must be used because this method requires a bending force which is 5 to 8 times the required tonnage in air bending. The cost of equipment is high, therefore, the method is inferior in economy.

[2] Extremely high bending precision can be obtained because springback is eliminated.

The use of air bending or coining should be decided upon according to the application and function of the product (refer to subsection1.8). Go to Top

1-4 Springback
1-4-1 Why springback occurs

Let us examine springback phenomena first. Fig. 1-2 shows a springback in V-bending by which obtuse-angled, 90, and acute angled bends are formed. In the figure, the solid lines indicate the angle during forming (ش), and the dotted lines indicate the angle after being formed ().

Here we will consider what causes springback to occur from two points of view. One view is springback considered from the stress-strain diagram, and the other view is considered from the displacement of the molecules inside the work.

In the stress-strain diagram in Fig. 1-3, as the exerted external force at point G in the plastic* region is reduced by low degrees, the amount of strain (deformation) in the work decreases gradually. It decreases parallel with the line OA (which is in the elastic region where stress is proportional to strain). When the work is totally removed from the external force, the strain reaches point X. This indicates that the work retains a certain amount of elasticity in the plastic region. In the diagram, G'X shows the amount in which the work has returned to its former condition, and OX shows the amount of permanent deformation.

To summarize the above facts, the elasticity of the work material is not eliminated even after the stress produced in the work has exceeded the yield point (The yield point is where the work gives way to stress; the plastic region lies beyond that point.). This is a cause of springback.

Fig. 1-4 is an exaggerated illustration of the molecular displacement in flat work when it is bent at an obtuse or 90 degree angle. This figure shows that the inner side of the work is compressed and the outer side is stretched. Between these sides, there is a plane which is neither compressed nor stretched. This plane is called a neutral plane or neutral axis.

When the work is bent, stresses which are opposed to each other act on the inner and outer sides of it. In general, the compressive strength of the material is far greater than its tensile strength. Exerted pressure will permanently deform the outer side of the work, but the inner side stress does not reach the yield point. Therefore, the inner side tends to go back to the former condition. Since stress is a resisting force that acts in the opposition to the exertion of the external force, a compressive stress acts outward on the inner side. This compressive stress changes into springback.

1-4-2 Positive and negative springback
You might recall the product angle if you hear the word "bending angle." This is not incorrect, but to be more exact, it should be called the "bent angle." This is because the bending angle involves the angle during formation and the already formed angle. When denotes the angle after formation and ش the angle during formation, we have -ش=A. The delta (A) is a small quantity. This A is the springback which is the angle of the small amount.

In Fig. 1-1, as already stated, the bent angle becomes 3 or 4 degrees less than 90 degrees in region . This is a phenomenon called spring-go or spring-in, which is expressed as negative A if the foregoing -ش=A is applied. In brief, a springback is +A and a spring-go or spring-in is -A. A becomes either positive or negative, depending on the bending pressure exerted.

Then what are the conditions that cause a negative springback or spring-go? Let us ex- amine the process of V-bending (Fig. 1-5). (a)

During V-bending, the work inserted between the punch and die changes its state from (a) to (b) and then to (c) under the bending force. The work at that time can be regarded as a continuum that contains positive factors (springback) and negative factors (spring-go).

Additionally, it can be considered that (c) these positive and negative factors are not constant, but show their qualities of being positive or negative while changing in accordance to the force applied. Therefore, the (d) springback or the spring-go will occur on the work, depending on the way bending force is applied to the work. Go to Top

1-5 Bottoming
The term "bottoming" comes from the verb "bottom" which means "to reach the bottom." This bending technique is also called "bottom pressing" or "bottom striking" at the production site. Bottoming, one type of air bending, is most widely used because it can accurately bend the work with relatively low tonnage.

In Fig. 1-6, t stands for the sheet thickness, V for the 'V-width (shoulder width of a V-die), and ir for the inside radius of the bend. The desirable, proper V-width varies with sheet thickness. Table 1-1 shows the relationship between the sheet thickness and the V-width in bottoming. This table shows the optimum standards in which the coefficient of the V-width becomes greater as the sheet thickness increases. However, one should note that the V-width should also be determined by taking the flange length and inside radius of the product into consideration. The method of determining the V-width will be described in a later chapter.

Table 1-1 Relationship between Sheet Thickness (t) and V-width

Sheet thickness

0.5-2.6 mm

3.0-8 mm

9-10 mm

12 mm or more






The inside radius in bottoming has been experimentally clarified to be approximately 1/6 of the V-width, i.e., ir=V/6. So ir can be determined by substituting the V-width obtained from Table 1-1 into this equation. For example, if the V-width is 6 times the sheet
thickness, the inside radius equals the sheet thickness (ir = t). Further, if V=12t, then ir=2t. From these examples, the inside radius ir is known to vary from It to 2t with the sheet thickness.

When the inside radius (ir) is equal to t (ir=t), it is called the standard ir. For example, in the case of t=l mm, bending at the standard ir can be accomplished with a die of V=6 mm. Similarly, if t=1.6 mm, then a die of V=10 mm will produce the same result. Many products are bent at the standard ir.

Bending accuracy in bottoming is influenced by springback. The most widely used countermeasure is to offset springback by bending the work an additional amount equal to the springback. This is the reason tooling for 90 bending is available in such V-groove angles as 90, 88, 85, and 80. The 90 V-tooling has no allowance for springback, but in practice the product angle can be finished at 90 degrees by applying bending force while simultaneously keeping good balance between springback and spring-go.

In the tooling used for bottoming, the punch tip and die V-groove must be of the same angle. This is an essential condition to obtain satisfactory precision of the product. (This subject will be described in detail later.) Go to Top

1-6 Partial bending
The name "partial bending" comes from the fact that the work partially contacts the tooling in three places during bending (A, B and C in Fig. 1-7). Partial bending is typical air bending.

This bending method is characterized by a wide range of bending angles which can be selected freely. For instance, in partial bending using a 30' punch and a 30' V-die, the work can be bent at any angle between 30 and 180 degrees. Partial bending is convenient, thus, it is widely used, following bottoming.

The V-width in partial bending should be 12 to 15 times the sheet thickness to achieve precision. Fig. 1-8 explains the reason. Bending precision refers to bending angle variation, which is theoretically related with the depth of the punch into the die.

In Fig. 1-8, Vb is the V-width used in bottoming and Vp is the V-width used in partial bending; Vp is approximately two times greater than Vb. When the depth of the punch into the die is constant, Op (the range in which the angles vary in forming with the partial bending V-width) is small in comparison to op. This means the range of bending angle variation is smaller in Vp than in Vb. During partial bending, the use of a larger V-width than that in bottoming results in good precision.

However, even if the V-width is increased, partial bending remains inferior in bending precision to bottoming. For that reason, a bottoming type of tooling should be used when high precision is required. The bottoming type of tooling are the punch and die in which springback (AO) is considered to suit the required angle of the product. Go to Top

1-7 Coining
You might think it is unusual that a bending method is called "coining." Coining comes from the word coin that means "metal money" and "making metal into coins." In spite of mass production, each piece of coin is made with almost no variation in shape and size. From this, the name "coining" seems to have been applied to this bending method whereby accurate bends are obtained.

Coining provides two advantages: (1) very high bending precision and (2) the capability of reducing the inside radius to as small as possible. Fig. 1-9 shows the work and tooling in the final stage of coining, from which you can see the punch tip is imbedded into the work. This penetration of the punch tip, together with a high pressure produced by the punch and die V-groove, eliminates springback. This is the reason coining requires a bending force 5 to 8 times greater than bottoming.

The V-width in coining is smaller than in bottoming, preferably 5 times sheet thickness. One reason for this is to reduce the amount of the punch tip penetration into the work by decreasing the ir (you will recall ir is 1/6 of the V-width). Another reason is to increase the V-die's surface pressure by making its V-groove area smaller.

If coining is performed in a V-width close to that of bottoming, the punch tip penetration will increase as much as the ir increases, requiring an additional bending pressure. Also, since the V-groove area becomes larger, it is inevitable that the surface pressure will drop. It should be noted that these factors will act like a brake upon satisfactory coining.
In coining, the angles of the punch tip and die V-groove should be made equal to the required angle of the product. For instance, in the case where a 90' bend is to be formed, a 90' punch and 90' die should be used without considering springback.

As previously explained, high tonnage is needed to perform coining. The limit of the sheet thickness bendable by coining is governed by the machine's capacity; it also varies with the amount of pressure the upper beam can withstand. Accordingly, consideration should be given to this point in determining the bending limit. The tolerable pressure of an upper beam is usually guaranteed by the tonnage per unit length. Bending pressure for coining a 1.6 mm thick cold rolled carbon steel is 75 tons of bending pressure per meter and a 2 mm thick cold rolled carbon steel is approximately 115 tons per meter. So the bending thickness limit is 2 mm, because, in general, the tolerable pressure of the upper beam of the press brake is approximately 100 tons per meter. Go to Top

1-8 Arrangement of Three Types of Bending
As stated in subsection 1.3, it is necessary to select the proper bending method in accordance with the application and function of the product. Do not determine the merits and demerits of the three bending methods, but use them properly in order to make the most of the advantages of each.

For example, if an NC press brake and acute-angled tooling are used, partial bending will permit products having acute-angled, 90', and obtuse-angled bends to be formed continuously from the first to the last bend.

The demand for higher bending accuracy is becoming greater. In the late 1960's in Japan, excellent sheet-metal working machines, such as shearing machines, punch presses, and press brakes became popular. The appearance of quality punches and " dies followed. With such background circumstances, accuracy of finishing made remarkable progress, and sheet-metal working machines superseded part of the jobs of machine tools such as the milling machine, drilling machine, and lathe.

Speaking of the bending accuracy at that time, it was at an age of "1 mm" in terms of general, nominal tolerance. With the present technical level, "0.2 mm" is an acceptable standard of tolerance, which tends to rise as high as "0.l mm." Such being the case, the bending accuracy today is required to be 10 times as precise as that of twenty years ago. In other words, we have entered an age in which bending accuracy must equal the accuracy achieved in coining, and in that sense, coining must be taken into consideration.

As already stated, bottoming is the most widely used method of bending because it achieves relatively high precision. Due to the high economy in the cost of equipment, bottoming will continue to play a significant part in material bending. The serious problem in bottoming is the easy occurrence of springback. However, we have now accumulated so much technical knowledge on springback and can apply it to tooling designs. That is to say, countermeasures against springback have advanced so much that bottoming can be performed with ease and confidence.

The present situation of the three types of bending has been outlined. Table 1-2 shows the important points from the description I comparing these three methods. Each method should be understood properly through this table and used in bending work.

Table 1-2 A Comparison of Three Types of V-Bending

Type of bending



Bending angle dispersion

Surface precision


Partial bending




Forms surface with large curvature radius

Range of bending angle can be selected freely.






Good precision is obtainable by using relatively little tonnage.






Very good precision is obtainable. The tonnage required is 5-8 times that required in bottoming



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