Calculation of the theoretical strip width

Method according to DIN standard 6935

The prerequisites to be observed regarding material and radius allowed for this method are outlined in DIN standard 6935. The standard is valid for bended pieces of flat steels that are to be used in general mechanical engineering and structural steel engineering. The elongation in a bending zone will be calculated with a non-dimensional correction factor K that will have a value between 0 and 1. The factor indicates the difference between neutral line and centre line of an arc element and, thus, allows for a calculation of the neutral line.
Depending on the ratio between inner radius/material thickness (ri/so) the calculation will be subdivided into several methods which will result in different values for the gauge factor.

Calculation according to VDI guideline 3389 (sheet #3)

The VDI guideline no. 3389 offers standard values for the calculation of the effective length for workpieces with a bending angle of 90 degrees (bending by wedge-shaped tool). These standard values are the result of long-term statistics.
Besides standard values for tool design the VDI guideline 3389 offers a formula for the calculation of the length of unfolding.
The effective length for an angle of 90 degrees is, thus, calculated on the basis of the length of the two inner sides and an add-up value of x. Contrary to the DIN definition, the add-up value will depend on bending radius ri, material thickness s and material characteristics. The guideline contains empirically determined values for 11 materials.
You are free to define in-house tables of materials at this point. Thus, you may integrate additional (e.g. your in-house) material diagrams.

Calculation according to Proksa

The calculation method according to Proksa applies to roll-forming to shape and it is subdivided into three methods. Their choice depends on the ratio of inner radius/material thickness. The result of the calculation formulas defined by Proksa will be the lengthening D b in the bending area caused by the shaping process.
In the second sub-method (ri/so between 0.1 and 5) the "specific material thickness" S (=current material thickness/original material thickness) will be used. The calculation of this specific material thickness S is executed via a differential equation defined by Proksa.
Due to the possibility to numerically solve the non-linear differential equation according to Proksa this method of calculating the material thickness is especially apt for EDP devices.

Calculation according to Bogojawlenskij

The method to calculate the material width according to Bogojawlenskij is based on values delimited by trial and error. The measured values have mainly be determined by angle and U-profile. For this calculation method as well, the value of D b has to be calculated for each individual bending area.

In-house calculation methods

In addition, the system provides the possibility to modify all values manually (interactively) during the computer dialogue, e.g. for material add-ups in case of special tool design. User-defined formulas for the calculation of the unbended length may also be "stored" in the program. Thus, in-house standards or calculation methods may be integrated into the program system without any problem.

Application in a computer program system

The user may easily transfer the above methods for the calculation of the effective length to the sheet metal profile sections designed by CAD. The only condition will be the profile geometry stored in the computer. For calculation run - in additon to the CAD-depiction - a file will be created which records all intermediate results (gauge factors, add-up, etc.) and profile data. The lengths calculated for the not-lengthened line of the individual arc elements will automatically be stored in the data base.

General approach In order to guarantee the accurate dimension of a profile to be produced within given tolerance limits, a calculation of the coil stock width with maximum accuracy will be necessary. For sheet metal profiles the coil stock width is identical to the length of unfolding (unbentlength). Basically the calculation of the coil stock width is based on the following factors. Due to the shaping and the material constriction in the bending area caused by it, there will be an elongation of the sheet metal width in case of a given retention in volume.
	In order to produce an arc element with a defined opening angle and an average arc length of b , a length compensating element has to be deducted. The compensation element corresponds to the lengthening of the final profile (D b). The value for the coil stock width (length of unfolding) of any profile will consequently result from the length of unfolding of the final profile minus the total of lengthening in the bending areas.
The previous model depiction gives an idea of D b lengthening of a bending area. We assume for straight elements that they will not be reshaped during the profiling process. There are different calculation methods to determine the modification in length in the bending areas which are based on different physical mathematical approaches. The COPRA -system will contain all methods listed here in a methods database. By pressing a key the chosen method will be applied.