### What is a straightening process?

### Why is wire straightened?

You know this. You process wire with WITELS-ALBERT straighteners and straightening systems, which are designed and manufactured within narrow tolerances and according to the current state of the art. Fine and good. However, are your expectations with regard to straightness or the residual curvature of the wire after the straightening process not fulfilled? Why is this so and what are the causes? Which peripheral processes, apparatus and machines have an influence on the straightening result? How is a designed straightening process evaluated and how is the selection of suitable straighteners and straightening systems determined? Which upstream and downstream equipment and machines are recommended for specific wire processing processes? Which recommendations can be given for the execution of a straightening process? The authors try to give answers to these and other questions. In addition to the theory and practice of straightening, the focus is on wire as a process material, since it has a significant influence on the result of a straightening process on an equal footing with the apparatus and machines for straightening. This guide is intended for operators who process wire on a daily basis, but also for wire manufacturers. The manufacturers of wire drawing and wire processing machines are also addressed.

### Theory

### Straightening process

Straightening units, straightening systems, straightening machines and their individual parts as well as the results that can be achieved with them are becoming more and more the focus of interest.

The necessity of straightening wire arises from the need to eliminate the curvature of the long product which it has undergone during the manufacturing process due to mechanical and/or thermal influences. As a rule, at the latest at the end of the rolling and drawing process, wire is bent, coiled or wound up by bending and thus made available in a form which is appropriate and economical for the transport of the long goods. Wire rod is widely supplied in coils. Drawn wire is available in ring or coil form, in drums or wound on spools.

For processors of wire, the process material therefore initially has a shape that does not correspond to the shape of the parts to be produced. The product specification of a bicycle spoke, a screw or a torsion spring has at least one straight segment. Without the action of external forces and moments, the curved shape of the wire continues to exist. The product specifications of the wire processors can only be fulfilled if a process provides forces and moments which lead to a change in the shape curve of the wire. The straightening process provides these forces and moments in a continuous process.

Straightening is the apparent release and elimination of stresses which the process material wire or the material to be straightened has received in the course of its manufacture due to force and moment influences.

Regardless of the geometric shape curve of the wire, the existence of longitudinal residual stresses is a fact. It is they who determine the geometric shape of the wire. Straightening with the help of straighteners, straightening systems and straightening machines changes the longitudinal residual stresses. Experience has shown that one bend or a few alternating bends are sufficient. A bend or alternate bend is simplified according to the schematic diagram.

An existing convex curvature of a wire is eliminated by bending it in the opposite direction. Under the effect of the **bending moment M_bZ**, the process material deforms elastically or elastic-plastically.

A condition for a successful straightening process is the elastic-plastic deformation of the process material cross-section, i.e. the wire is permanently deformed and does not spring back into its original shape curve. Ideally, an elastic-plastic deformation over the cross-sectional height of the wire results in a linear **strain distribution Epsilon_x** and a non-linear **stress distribution Sigma_x**. The process material wire begins to flow plastically at the inner and outer fibres or the edge zones or to deform permanently. In the core there remains an elastic part or an area which is not permanently deformed. As a result of the elastic deformation of the core and the plastic deformation of the edge zones, there is a residual stress curve over the cross-section height without the effect of the bending moment or after the springback, which determines the resulting geometric shape curve of the wire after the springback and is the initial state for the stress distribution over the cross-section height of a subsequent bend.

Alternate bending is defined as a sequence of bends, i.e. the bend described above is followed by at least one further bend, the direction of which is opposite to the previous bend.

The alternating bending is accordingly comparable with the bending back and forth of things or things in everyday life. This could be, for example, a photo that needs to be smoothed or a garden hose that cannot be laid as desired or an electrical cable that vehemently resists disappearing into the cable duct.

If the photo can be smoothed and the electrical cable permanently brought into a new shape, this is largely due to the ability of the respective material or material to allow elastic-plastic deformation. Not every material or not every material has this ability or property. The garden hose made of an elastic plastic has no potential for permanent deformation and can therefore only be laid elastically, often stubbornly.

Conditions for the elastic-plastic deformation of a wire by straightening are therefore the ability of the wire material to undergo elastic-plastic deformation. In addition, an appropriate design of the straightener, the straightening system or the straightening machine is required, which has to ensure a trouble-free sequence of bends or alternating bends and within the framework of an industrial material flow.

The design of the straightening device or straightening machine depends on the geometric and mechanical properties of the process material wire. Accordingly, a fixed or determined design of a straightener or a straightening machine determines which wires can be successfully straightened and which cannot.

Every straightener, every straightening system and every straightening machine therefore has a geometric and a mechanical straightening range which correlates with the geometric or with the mechanical properties of the process material wire. If an appropriate design of a straightener or a straightener is assumed, taking into account the mechanical properties of the process material wire, then only the **wire diameter d** or the range of diameters of the wires to be straightened according to **Equation** (**Gleichung**) **1.1** determines the success or failure of the straightening process.

The geometric **straightening range Delta** has a permissible limit for the minimum and maximum cross-sectional dimensions of the process material to be straightened. The **minimum wire diameter d_min** and the **maximum wire diameter d_max** are relevant for round wire.

The parameters of the straightener or straightening machine as shown in **Figure 1.2** are specifically defined with regard to a fixed geometric and a fixed mechanical straightening range in order to straighten an elastic-plastic deformable wire material successfully.

For a given **roll diameter D** and a given **roll pitch T**, it is indispensable for permanent deformation of the wire with the **diameter d** to position the **straightening rolls i** specifically or to position them relative to each other in two rows alternately offset. The **a_i positions** of the **rolls i** are to be adequately ensured by the operating personnel of the straightener or straightener. Without an appropriate adjustment of the straightening rolls, the wire running from left to right through the straightener is elastically deformed at best (**Figure 1.2**). The **radius of curvature r** of the incoming wire cannot then be changed.

For the design of the **roll pitch T**, empirical values are valid taking into account the **wire diameter d** and the **roll diameter D**, which are documented in **Table** **1.1** for discrete values of the **wire diameter d** as examples.

At the interface between the straightening roller and the material to be straightened, reaction and process forces are generated which are caused by the bending moment present in the process material during deformation.

Relevant process forces of straightening are the straightening forces and the tensile forces. The straightening forces act in different directions and sizes depending on the geometric boundary conditions. They correlate with the tensile forces which, influenced by the boundary conditions, occur as forward tensile force or transport force and backward tensile force.

In order to be able to calculate the transport force required to transport a wire relative to the straightening system, the plastic deformation work performed in a straightener must be determined. For this WITELS-ALBERT uses a process simulation program which virtually maps real roll straightening processes using mathematical-physical laws.

If technological operations are upstream and/or downstream of the straightening process (**Figure 1.3**), the transport force components present in the individual operations must be taken into account when determining the total transport force. In order to achieve a high finished product quality in a processing line, it is advantageous to ensure that the transport force in the immediate vicinity of the processing line is as constant as possible. Of course, this also applies to the straightening process.

For each of the subprocesses documented in **Figure 1.3**

- unwinding,
- guiding,
- transporting,
- straightening and
- processing

is therefore desirable to ensure a constant force as far as possible in the direction of flow of the process material from left to right.

The most important straightening force on a **straightening roller i** for the design and use of a straightening unit or a straightening machine is the radial straightening force which results from the reaction forces in the x-y plane as shown in **Figure 1.2**.

The straightening rolls shall be capable of withstanding the reaction forces and shall allow the desired speed of the wire to be maintained. The range of wire speeds is wide. If speeds of less than v = 10 m/s are used in the processing of wire, speeds of up to v = 40 m/s may be encountered in the production of wire, such as drawing or rewinding.

The speed at which a wire passes through a straightening unit or a straightening machine is directly related to the rate of deformation of the process material, which corresponds to the derivation of the degree of deformation over time. Exemplary straightening tests at different speeds of the process material show that the residual curvature as well as other parameters of the straightening process do not change significantly up to a speed of approx. v = 10 m/s. The results of these tests are shown in the following. At speeds above this limit, a change in deformation occurs at identical angles of incidence.

### Process material wire

The achievement of specific geometric and mechanical parameters for a wire is the objective of the rolling process and the objective of the drawing process following the rolling process.

In the rolling mill, wire is hot rolled from a billet in several rolling passes to the minimum possible diameter of d = 5.5 mm. For a good deformation and elongation of the process material in compliance with the law of volume constancy and for a good microstructure, it is indispensable to carry out the individual passes with specifically calibrated rolls. In addition to the round calibre, the relevant calibres are the oval and the pointed calibre (diamond). The final rolling speed of modern wire rod mills is up to v = 120 m/s. At the end of a wire rod mill, a coil laying machine is used to produce the ring form, which is fanned out onto a conveyor belt to enable the design of the presentation in the form of a coil. The windings fanned out on the conveyor belt are usually cooled down specifically. Due to the fan shape, the coils overlap so that different conditions for cooling result over the length of the wire. As a result of the different cooling conditions, the wire parameters change over the wire length.

Following the rolling process, the wire is further reduced in cross-section on dry and wet drawing machines. The forming process by drawing on drawing machines is based on the active principle of the wedge, which is ensured by drawing dies or drawing hols. The wire is transported by capstans driven by actuators (**Figure 1.4**).

The transverse force required for the deformation is generated by the external drawing force being applied and, due to the inclination of the drawing beam wall and the friction between the process material and the drawing beam surface, attacks the contact surface between the process material and the drawing beam at a specific angle to the normal direction. Due to the wedge ratio resulting from the drawing angle and the friction angle, the normal force is four to seven times the drawing force. Afterwards, the deformation during drawing is mainly caused by the radial and tangential compressive stresses caused by the normal force in the material and less by the axial tensile stresses generated by the drawing force. Due to the process, longitudinal residual stresses inevitably occur in the wire. Tensile residual stresses usually occur in the core, whereas the surface layer shows compressive residual stresses. This leads to a reduction in the fatigue strength of the wire. If straightening devices are used between the capstans, the elastic-plastic alternating deformations cause a redistribution of the internal stresses, which in turn increases the fatigue strength of the wires.

The above outline for the production of wire shows that the properties and characteristics of a wire vary over its length. A discontinuous determination of the geometric and mechanical parameters, as it is realized in practice in the wire industry, only provides snapshots or a sample size, which is not representative of the properties of the process material over the length, or only slightly so, if statistical methods are taken into account.

The geometrical parameters

- wire diameter d,
- maximum curvature radius r_max,
- minimum curvature radius r_min and
- helix H

are identified by direct measurement with help of measuring devices such as calipers, micrometers and steel scales or they are calculated from measured intermediate quantities.

The **wire diameter d** is measured directly. The **radii of curvature r_max** and **r_min** follow either from the measured radii of the largest and smallest wire coils or from calculations using the intermediate values of **deflection f** and **length l** according to **Figure 1.5**. Thus, for a given **length l**, the smallest **deflection f_min** results in the maximum **radius of curvature r_max** or the **minimum** **curvature k_min** according to **Equation (Gleichung) 1.2** and the largest **deflection f_max** results in the minimum **radius of curvature r_min** or the **maximum curvature k_max** according to **Equation** (**Gleichung**) **1.3**.

**Equation (Gleichung) 1.2** and **Equation (Gleichung) 1.3** express that the **curvature k** is the reciprocal value of the **radius of curvature r**. The amount of the difference between the **maximum curvature k_max** and the **minimum curvature k_min** gives the so-called **curvature range Δk** (**Equation/Gleichung 1.4**).

With a curvature in the second dimension, the process material has a **helix H**, which is characterized by a radius and a pitch in accordance with a helical line. The difference between a wire with and without helix is illustrated humoristically in **Figure 1.6** by Willy Wire. Like the **radius of curvature r**, the **helix H **can change over the length of the wire.

If the geometric parameters of a wire are known, the mechanical parameters can be determined by the tensile test according to DIN EN 10 002. The tensile test is a static test method in which a section of wire is subjected to an increasing tensile load in the direction of its longitudinal axis. As a so-called tensile test specimen, the wire section has a certain test length which is greater than the **measuring length l**. The tensile test specimen is loaded in longitudinal direction until failure by the clamping devices of a testing machine. The **tensile force F_Z** applied by the testing machine and the **change in length Δl** of the clamped tensile specimen over the measuring length are measured during a test. Using the geometric parameters of wire diameter, measuring length and change in length over the measuring length, the results are calculated and presented in a stress-strain diagram which is characteristic for the behaviour of the wire section with respect to external tensile loading (**Figure 1.7**).

The stress-strain diagram documents the **tensile stress R** as a reaction of the material/workpiece against the applied external load as a function of **strain ϵ**, which corresponds to the quotient of the change in length over the measured length and the measured length (**Equation/Gleichung 1.5**).

The tensile stress is generated as an internal resistance force related to the **cross-sectional area A** of the wire section and is derived accordingly from the quotient of these two parameters (**Equation/Gleichung 1.6**).

With regard to the evaluation of existing and the design of new straightening processes, the following mechanical parameters are of particular interest

- technical
**yield point R_p_0,2**, **modulus of elasticity E**and**modulus of strain hardening V**.

The technical **yield point R_p_0.2** represents the stress at non-proportional elongation of 0.2% for drawn wire and identifies the limit between elastic and plastic deformation as the stress parameter. It is therefore regarded as the most important mechanical parameter for deformation processes.

The **tensile strength R_m**, prescribed for determination by various standards for the delivery conditions of wire, cannot replace the importance of the technical yield point, since the tensile strength corresponds to the stress that identifies failure by a change in cross-section. This condition, or failure under prolonged load due to fracture, is undesirable for many deformation processes. Against this background, tensile strength plays only a minor role in straightening processes.

Immediately after the start of the tensile test, the wire section or tensile specimen deforms elastically up to a specific load, i.e. there is proportionality between the change in length over the measured length and the load (**Figure 1.7**). This proportionality is known as Hooke's law, whereby the stress-strain diagram is also referred to as the elastic or Hooke's straight line. The increase of the straight line corresponds to the modulus of elasticity. If the load is reduced after purely elastic loading of the tensile specimen, the specimen returns to its original shape or length. In addition to the material, the size of the modulus of elasticity depends on the state of processing or the processes involved in production. Hot rolled steels generally have a modulus of elasticity of 210000 MPa. Drawn steel wires do not reach this value. The drawing sequence or the design of the reduction of the wire cross-section, the drawing speeds and other factors have a significant influence on the modulus of elasticity. The modulus of work hardening V is the equivalent of the modulus of elasticity in the plastic deformation range, which is characterized by non-proportionality between the change in length over the measured length and the load. The straight line from whose increase the modulus of work hardening is derived is determined using the least squares method. Experience has shown that steel wires for the **modulus of work hardening V** reach values which amount to approx. 10% to 30% of the **modulus of elasticity E**.

### Straightening units and straightening systems

The curvature of the process material determines the use of a straightening unit or a straightening system.

### Straightening units

Due to the arrangement of the rolls in a straightener in one plane (**Figure 1.2**), only bends in one plane, i.e. one-dimensional bends, can be influenced (**Equation/Gleichung 1.4**). Therefore, it is basically not possible to successfully process multi-dimensionally curved wire with a single straightener, provided that objectives such as the production of straight wire or the production of defined curved wire exist. The design of a unit determines the process and the achievement of an objective, taking into account that a specific straightening unit is only suitable for a given dimensional range of the process material (**Equation/Gleichung 1.1**).

These seemingly trivial connections are often not respected. It is daily practice, for example, to insert any straightening unit in any installation position into any technological line for processing wire, regardless of the level of curvature of the process material. The resulting problems, such as two-dimensional curvatures, high residual stresses and disadvantageous material properties, increase in subsequent processes to a finished product quality that no longer deserves to be called quality.

Often traditionally designed processes and grown paths of the process material are maintained, the negative consequences tolerated, although the changed state of the art or the findings suggest a different behaviour. According to the motto "The straightening unit will do the job somehow!", people act thoughtlessly and all too often suggest that the straightening unit is inadequate or unsuitable.

A thoughtless selection and a bad arrangement of a straightener are no longer up to date and are not recommended. If the arrangement remains unconsidered for the time being, then, in addition to determining the size of the straightener, the following features must be taken into account:

- number of straightening rolls
- roll adjustment principle
- quick-closing mechanism

It should be borne in mind that the technical realisation of features in a straightener is sometimes excluded. For example, it does not make sense to combine a large number of straightening rolls with the quick-closing feature, since the required closing force, especially when processing larger wire diameters, is too great and thus an adequate design and the realization of the quick-closing mechanism is not economical.

Which factors and boundary conditions influence the design as well as the necessity of the above features? There is no doubt that the geometric and mechanical parameters of the process material wire should be mentioned. In addition, there are the objectives of the straightening process, the speed of the wire, technical boundary conditions such as the available installation space, the entering height of the wire, the location of use, the availability of media such as electricity, compressed air or oil pressure. The qualification of the operating personnel and ideas for the use of a straightener as well as the interlinking with upstream and downstream processes and technical equipment also influence the design as well as the necessity of implementing the features.

Recommendations on the required number of straightening rolls are available in a very manageable form and give rise to the implementation of an alternative approach which uses the **yield point R_p_0.2** and the **range of the radius of curvature Δr** as input variables. Using **Equation/Gleichung** **1.2** and **Equation/Gleichung** **1.3**, the range of the radius of curvature follows **Equation/Gleichung 2.1**.

Fuzzy logic is used instead of a strict calculation rule with a limited validity range. A fuzzy system consists of the components fuzzification, inference and defuzzification. Both the input variables and the output variable of such a system have sharp values. However, the mechanism by which the sharp input variable is inferred from the sharp output variable is fuzzy. An application of fuzzy theory is always advantageous if the complexity of a system is large, if it is difficult to describe by mathematical correlations, or if it is non-linear and/or time-variant. With regard to the difficult possibilities of mathematically determining the number of rolls, a knowledge base consisting of the linguistic terms of the input and output variables (membership functions), the rule base as well as the inference and defuzzification mechanism is used alternatively. The knowledge introduced into the fuzzy system results from empirically gained and verbally formulated laws and is also based on results of the practical application of the virtual mapping of the straightening process using a simulation program.

**Figure 2.1** shows the structure of the fuzzy system. The input variables **Δr** and **R_p_0,2** are linked to the output variable **n**, which represents the **number of straightening rolls**, via the rule base. A sharp value for the input value range of the radius of curvature** Δr** can be determined according to **Equation/Gleichung 2.1**.

The membership functions of the input variables and those of the output variable are defined in **Figure 2.2**, **Figure 2.3** and **Figure 2.4**.

The fuzziness is shown here in particular by the fact that the respective quantities of the sizes merge into each other. A yield strength R_p_0.2 = 800 MPa is assigned to 33 % (degree of membership μ = 0.33) of the quantity very_small and to 67 % (degree of membership μ = 0.67) of the quantity small. The rule base consists of 25 rules, each of which embodies knowledge in the standardized form "IF condition 1 AND condition 2 THEN instruction 1".

The use of a suitable inference mechanism and a specific defuzzification method results in a specific transmission behavior according to the current background image (**Figure 2.5**). Thus, a sharp output variable can be generated for a set of sharp input variables at any time.

**Table 2.1** gives derived values for the **number of straightening rolls/Anzahl der Richtrollen n** for some discrete values of the input variables **yield point/Dehngrenze R_p_0,2** and **range of the radius of curvature/Bereich des Krümmungsradius Δr**. Looking at the recommendations for the number of straightening rolls, it can be seen that the required number of rolls increases proportionally with the area of the radius of curvature and the yield point. High-strength wire must therefore be processed with straighteners which have at least 11 straightening rolls. A higher number of rolls also favours geometrically advantageous forming curves of the wire to upstream and downstream processes and equipment.

In addition to the straightening range and the number of straightening rolls, the way in which the straightening rolls are positioned determines the straightening process, since the positions of the straightening rolls influence the bending operations and thus the residual curvature. WITELS-ALBERT has developed various technology levels which differ in the degree of automation. In conventional straightening technology, simple tools are used for the roll positioning. Adjustment elements equipped with a position indicator or nonius are also possible.

With developed straightening technology, which is characterized by a higher degree of automation, the straightening rolls can be positioned accurately and reproducibly in a short time. Software is an indispensable component of such an overall system.

The advantage of straighteners and straightening systems with a higher degree of automation is the possibility to adjust the straightening rolls in a defined and reproducible way. At the same time, it is possible to identify the roll positions at any time.

**Figure 2.6** documents an example of semi-automated straightening technology that processes flat wires up to 4.5 mm wide and 1.5 mm thick in two lines arranged one above the other.

The objective is the production of straightened products with a one- or two-dimensional curvature. The heart of the overall system is a PLC that automatically designs the respective straightening processes in interaction with the operator terminal, the implemented software and user inputs.

500 data sets are used and managed, each consisting of 40 individual parameters, in order to ensure that the machine can be adjusted quickly for a wide range of straightening materials and finished products.

A change in the roll positions of straighteners takes place using adjustment mechanisms which convert the rotation of an adjustment element into a translational movement of at least one straightening roll or which are based exclusively on pure translation of at least one straightening roll. Mechanisms using rotation and translation are widely used.

The relevant technical design forms for the positioning of straightening rolls are the wedge arrangement and the individual roll adjustment. In case of the wedge arrangement, as it is also the case with the semi-automated straightening technique shown in **Figure 2.6**, the rolls of at least one row are firmly applied in line on a bar, the position of which can be changed by rotation and translation. Due to the possible rotation of the bar, there is a different **roll** **pitch T** between the rolls of a straightener depending on the angle.

There are also straighteners where the rolls of one row are fixed and the rolls of the other row can be adjusted individually, as well as straighteners that have rolls that can all be positioned. The individual adjustment of all rolls of a straightener achieves the highest degree of freedom with regard to the setting options. Practice confirms the best straightening results if the amount of **roll adjustment |a_i|** according to **Figure 1.2** is reduced from the infeed to the outfeed according to an exponential function. In this way, the curvature at the infeed rolls (pre-bending zone) can be quickly and effectively reduced to a specific value which leads to the desired residual curvature at the remaining outfeed rolls (straightening zone).

The advantageous individual adjustment uses so-called motion screws or spindle mechanisms which, as gears with good self-locking properties, each translate a **torque M_iG** into a **adjustement force F_iA**. Characteristic values of such a gear are the **thread flank diameter d_iF**, the **mean pitch angle α_im** and the **friction angle ρ′_i**. The **angular velocity ω_iG** and the **spindle speed n_iG** result in the minimum **power P_i **required for the adjustment of a **roll i** according to **Equation/Gleichung 2.2**.

The **adjustment force FiA** results from the deformation of the process material in the zone of impact of the straightening **roll i** to be positioned. It corresponds to the absolute value of the **adjustment force |F_iR |**, which is correlated with reaction forces at the point of contact of the process material with the straightening roll (**Equation/Gleichung 2.3**).

To simplify the deformation of wire, only the reaction forces in the plane vertical to the roll axis (the x-y plane according to **Figure 1.2**) should be included. The consideration of the quasi-static case allows external forces and the **tangential reaction force F_it** to be neglected so that the radial reaction force at the straightening roll corresponds to the resulting straightening force (**Figure 2.7, a)**). If, moreover, the **pitch changed by ΔT **is not taken into account, the **straightening force F_iR** is formed only from the vertical component of the **resulting straightening force F_iver** (**Equation 2.4, Figure 2.7, b)**).

Equilibrium considerations considering the bending moments at the rolls (**Figure 2.7, c)**) and the pitches lead to the calculation of the **absolute value of the related straightening force |F*_iR|** according to **Equation/Gleichung 2.5**.

The use of normalized dimensionless parameters marked with an asterisk simplifies the calculation. The reference parameters for the normalized parameters are the values corresponding to the respective deformation, stress and load quantities at the limit from elastic to plastic deformation. With the** maximum elastic bending moment of the process material M_S**, into which the **yield point R_p_0.2** and the resistance moment of the circular process material enter, the related maximum bending moment at the **roll i** is calculated according to **Equation/Gleichung 2.6**.

For the **adjustment force F_iA** (**Equation/Gleichung 2.3**) or the **absolute value of the natural straightening force |F_iR|**, **Equation/Gleichung 2.7** applies.

The sum of the adjustment forces of a straightener with **n rolls** results in the **total force F_G**, which a quick-closing mechanism must provide to deform a wire (**Equation/Gleichung 2.8**). A quick-closing mechanism supports the operation of a straightener and the reproducible adjustment of the straightening rolls, e.g. when feeding a new wire which has the same characteristics as the previously used wire.

Depending on the magnitude of the **total force F_G**, specific designs are recommended for the implementation of a quick-closing mechanism for a straightener. The most common designs are those that use at least one excenter, such as those used in the ER, RS or DRS series of straighteners.

Alternatives to the excenter are motion screws or spindle mechanisms, as shown in the adjacent **Figure 2.8** (ERS series straightener). These solutions are based on the action of the wedge or use pneumatic or hydraulic cylinders.

The use of cylinders to apply the closing force, as documented in **Figure 2.9** (ERS H series levelers), ends the technical category of straighteners. Directive 2006/42/EC declares an assembly of connected parts as machinery if it is equipped or intended to be equipped with a drive system other than directly applied human or animal power and if at least one part is movable. Semi-automated straightening technology as shown in Figure 2.6, which uses actuators to position straightening rollers, also complies with the scope of the aforementioned Machinery Directive, which applies to the EU states and the EFTA states of Iceland, Liechtenstein, Norway and Switzerland.

As partly completed machinery within the meaning of Directive 2006/42/EC, straightening machines are supplied without guards and without controls. A Declaration of Incorporation in the customer's national language and Assembly Instructions in an EU language are prepared for each straightening machine and enclosed with the delivery. Straightening machines have a machine marking and carry a machine plate without CE marking (**Figure 2.10**). The machine plate documents the address of the manufacturer, the machine designation, the machine number, the wire diameter range, the power and the maximum pressure, the weight of the machine as well as the year of manufacture.

The assembly instructions inform about the conditions which must be fulfilled by the partly completed machinery to be assembled correctly to form with other parts a complete machinery without impairing the safety and health of persons. Each assembly instruction contains information and instructions on the following topics:

- Information, safety and residual risks
- Characteristics and data
- Setting up
- Handling and use
- Servicing, cleaning and maintenance
- Decommissioning, disassembly and disposal

The intended use of any partly completed machinery is to be assembled or completed with other partly completed machinery (e.g. guards and controls, whether or not they separate) to form a functional and complete machinery. The instructions and conditions given in the assembly instructions must be observed and ensured for the completion or installation of the incomplete machinery in a complete machinery. Accordingly, the assembly instructions must be read and understood before completion or installation of the incomplete machinery and before commissioning. In the event of incomprehension or uncertainty in understanding the assembly instructions, the manufacturer's authorized documentation representative named in the installation declaration for the incomplete machinery must be consulted in writing and in detail. The communication process following the interview must be documented and conducted with the aim of achieving complete understanding. The system and process control of the incomplete machinery is determined by the electrics, hydraulics, pneumatics, hardware, software, protective devices, peripheral elements of the complete machinery, upstream and downstream machinery, user specifications, etc. The communication process following the interview must be documented and with the aim of creating a complete understanding. The Machinery Directive 2006/42/EC as well as pending standards and legal bases apply to the design of these subsystems and machines as well as to possible user specifications which must not lead to an impairment of the safety and health of persons. The designer and the operator of the complete machinery or plant in which an incomplete machinery of WITELS-ALBERT GmbH is installed are responsible for compliance with and consideration of these standards and legal bases. The **adjustment force F_iA** according to **Equation/Gleichung 2.3** causes the mechanism for roll adjustment to spring out. If an appropriate straightener or straightener is designed, the spring deflection is negligibly small. A low spring deflection or sufficient rigidity is considered a quality feature for straighteners and straightening machines, as it is also responsible for the exact securing of the roll positions under load. Nevertheless, it is sometimes advisable not to use the upper limit of the given straightening range of a straightener or a straightener, especially if wire with a high **yield point R_p_0.2** is to be processed and wear is to be minimized.

In case of doubt, the manufacturer must always be consulted when selecting the size of a straightener or a straightening machine. Depending on the parameters of the process material wire described at the beginning and other influencing factors, the manufacturer will carry out the necessary calculations and make the selection considering the results of the calculations.

### Straightening systems

Multidimensionally curved wire, as shown in **Figure 1.6** on the left, is straightened with a straightening system. A straightening system consists of at least two straighteners. Each straightener manages the elastic-plastic deformation of the process material wire in a specific plane. Accordingly, at least one straightener has horizontal roll axes and at least one remaining second straightener of the straightening system has vertical roll axes, i.e. there is an angle of 90° between the straightening planes of such a straightening system. The orientation of the roll axes (horizontal or vertical) correspond to the axis around which the respective bends are realized in the plane. Depending on the series of straighteners, connecting angles or bottom plates are used to design a straightening system (**Figure 2.12**).

The connecting bracket offers the advantage of a simple or uncomplicated installation of the straightening system, since only one straightener has to be screwed firmly to a bracket or similar and the remaining straightener of the straightening system is held overhung over the connecting bracket. The design of the connection bracket with two retaining plates and a rotationally symmetrical intermediate piece with an internal hole for the wire to pass through enables, in contrast to the version with a bottom plate, the simple implementation of alternative straightening systems consisting of more than two straighteners and/or enabling the implementation of differentiated angles between the straightening planes. For example, so-called straightening chains consisting of three or four straighteners are conceivable.

Base plates are particularly recommended for straighteners or straightening systems that process wire with a diameter greater than 15 mm. Due to the higher mass of these larger devices and systems, a stable substructure is required. **Figure 2.13** illustrates the dimensions that straighteners can assume.

Special cases are straightening systems consisting of straighteners with identical orientation of the roller axes. An example documents **Figure 2.14**. A killing set TR 3-1.5, a straightener ER 9-1.5 and a helix straightener HR 3-1.5 are mounted one behind the other in the throughfeed direction.

All straighteners shown above serve the purpose of influencing the **curvature range Δk** according to **Equation/Gleichung 1.4**. However, the helix straightener HR 3-1.5 fulfils an additional task which consists in influencing the **helix H** according to **Figure 1.6**. This is achieved by the special design of the straightener, which is characterised by two fixed straightening rolls and one middle straightening roll, which can be positioned or adjusted both radially and axially. Due to the possible axial adjustment of a straightening roll and the fact that all straightening rolls of the helical straightener are provided with a circumferential recess, which places the process material in a geometrical constrained position, a torsional deformation can be impressed on the wire in continuous operation, which leads to an influencing of the **helix H**. The straightening roll can be positioned radially as well as axially.

### Practice

Added value is achieved through cost-effective roller straightening processes.

### Alternative objectives

In addition to the already explained necessity of the straightening process to produce straight wire, there are alternative objectives.

For example, it is common to use straighteners and straightening systems to apply a back tension to the process material wire. The back tension can become so large that a change in length of the wire results. The elongation of the wire is associated with an increase in the yield point of the process material. As a result of tensile deformation in continuous operation, wire rod stretched accordingly has a modified stress-strain diagram which differs significantly from the stress-strain diagram of a wire rod.

Even in the field of strand production by simple stranding, wires are subjected to a defined back tension by rolls arranged offset in two rows in order to preform all the individual wires involved in the joining process and to produce a first-order helix line that is as identical as possible. This means that the individual wires only have a very limited ability to spring back and try to leave the strand connection. **Figure 3.1** shows a VR series preform unit with preform rolls arranged on three discs. The number of preform rolls is determined by the strand design or the number of individual wires to be preformed. The pitch or distance between the inlet and outlet discs of the preforming unit is proportional to the lay length of the strand. In order to be able to use a preforming unit for as many strand products as possible, the pitch is adjustable in a specific range. The preforming rolls of the preforming unit shown in **Figure 3.1** can be adjusted centrally by twisting the central disk, thus ensuring elastic-plastic deformation of the wires.

If, after the joining process, the strand is postformed with at least one straightening system, the remaining elastic stresses are converted into plastic deformations. The stresses of postforming, which is also known as the *Pawo* process, result from a combination of stretching and straightening of the process material strand. Primarily the process stands for the superposition of tensile and bending stresses and secondarily for the superposition of compressive and torsion stresses. Depending on the strand diameter or also on the diameter of a strand composite (rope), postforming units have smaller or larger dimensions. **Figure 2.13** shows the largest model of a postforming unit ever produced by WITELS-ALBERT GmbH.

As a rule, two to four postforming units are arranged one behind the other in a processing line after the stranding point in the direction of travel, whereby the elastic stresses of the process material are converted into plastic deformations in at least two planes.

A higher number of deformation planes are also used in the production of welding wire. For example, straightening systems consisting of three straightening units are increasingly used for rewinding or winding wire. The infeed side and the central straightener of such a straightening system are used to straighten the curvature of the process material wire in the curvature range and to eliminate the helix. The task of the straightening unit on the outlet side of the straightening system is to produce the constant residual curvature desired by the user of the welding wire. It is required because it supports the design of a stable welding process and produces a good outer and inner seam pattern.

The behaviour of a wire section under tensile load (**Figure 1.7**, **Equations/Gleichungen 1.5** and **1.6**) at room temperature has already been explained. If an elastic-plastic deformation occurs due to tensile loading, which is illustrated by a permanent change in length, the original technical yield point increases. Colloquially it is said that the wire section or the material becomes stronger or harder. This hardening can continue if the wire section is permanently extended by repeated tensile stress. If, on the other hand, the first tensile stress is followed by compressive stress, i.e. deformation in the opposite direction, this can lead to softening, which manifests itself in a reduction in the technical yield point.

The elastic-plastic alternating bending of the straightening process softens many wire materials in the same way. Tensile tests on steel wire samples before and after straightening processes prove this and show a softening between 5 % and 10 %.

On steel wires with a low carbon content, on the other hand, hardening is observed, as it also occurs during the alternating bending of copper.

### Installation arrangement

The optimal integration of straighteners and straightening systems into a production line is of great importance. If the design of a straightening process primarily depends on the geometric and mechanical parameters of at least one wire, the integration into a production line depends on the periphery and the upstream and downstream processes, machines and equipment.

Although the processes upstream and downstream of a straightening process can be very diverse, rules for integration can be derived for all variants.

It is absolutely necessary to ensure the zero line. The term zero line expresses the fact that the tools involved in the processes of a processing line are positioned in relation to defined geometric boundary conditions in such a way that a process material of specific dimensions is only touched, i.e. no deformations occur in the areas of influence of the tools. Excluded from this are unavoidable interruptions, e.g. in the form of deflections of the process material. The positioning of the tools, including those of a straightening device or system, must always be defined starting from the zero line, so that any tool positions can be reproducibly set at any time.

Even if the zero line is guaranteed, theoretically an infinite number of further possibilities follow for the application of a straightener or straightening system, since a rotation around the zero line, a rotation around the normal vector to the zero line as well as a shift in the direction of the process material is conceivable.

By the alternating arrangement of the rolls of a straightener in one plane and the objective of realizing (n-2) effective bending operations with n straightening rolls, a first constraint results, including the curvature of the incoming process material, which restricts each of said rotations to a specific angle. If this constraint is taken into account, there are a total of eight different possibilities for arranging a straightener or straightening system as shown in **Figure 3.2**. Accordingly, an application must be carried out in such a way that the axis of the first straightening roll arranged in the transport direction of the process material is parallel to the axis of the spool/coil or deflection roll, for example, upstream, and both axes are on the same side with respect to the zero line. Instead of an upstream spool/coil or pulley, an adequately curved process material can be used.

The exact arrangement of the straightening process in the direction of the process material follows from a second constraint which defines the **distance A** (**Equation/Gleichung 3.1**) to a process upstream of the straightening process.

Adherence to the **distance A** marked in **Figure 3.2** results in a constant straightening quality over the long term. If the distance A, which is determined under consideration of the **diameter of the coil D_coil**, is not respected, the process material not yet freed of its curvature has the possibility of twisting both before and in the straightener or straightening system. The moment vectors of the bending operations taking place are stochastically aligned and lead to disadvantageous deformations as well as to variable and poor straightening quality.

The VIMEO video introduces all eight relevant VW variants. The first straightener of a straightening system in the direction of throughfeed is always correctly arranged depending on the direction of throughfeed of the wire, the spool or coil axis and the direction of rotation of the spool or coil! This is how it is done!

### Adjustment of the straightening rolls

The straightening rolls of a straightener or straightening system must be set relative to each other in order to enable a change in the process material properties such as residual curvature or straightness or the residual stresses and strength due to alternating deformation. The adjustment is the absolute position of a straightening roll in relation to the specific zero line.

In practice, the effort to achieve a defined straightening quality is the subjective modification of the settings of the adjustable straightening rolls of a straightener or straightening system by trial and error under constant visual contact with the straightened process material. The adjustment based on trial and error is often carried out without knowledge of the geometric and mechanical characteristics of the process material or wire. Causes of variations in the straightening quality at a specific adjustment such as different material properties or differences in the geometric dimensions of the material to be straightened are not recognized and there is no determined influence on the quality. On the other hand, there are modern processing methods for the process material and the desire for complicated product geometries in high quality. The previous procedure is therefore unacceptable, not least because of the personnel and time intensity and the material expenditure.

There are as many philosophies on roll adjustment as there are straighteners in use. Based on mathematical-physical models for the alternating deformation of process materials, a helpful objective adjustment instruction can be derived which is of a qualitative character and is characterized by the fact that larger adjustments are realized in the front area of a straightener, the so-called pre-bending zone, in order to effectively eliminate the initial curvatures of the process material. This produces a maximum curvature, which is reduced to the desired residual curvature by the alternating deformations in the subsequent straightening zone, which is characterized by smaller roll adjustments.

As an alternative to the qualitative adjustment recommendation of straighteners and straightening systems described above, WITELS-ALBERT uses results that provide a virtual image of the roll straightening process. The roll positions are determined quantitatively and a priori by simulating the wire straightening process. The simulation is based on a theoretical model for the elastic-plastic alternating bending of a process material and the relationship between bending moment and curvature, which can be determined for each bending operation performed in the straightener. Thus the **curvature of the material to be straightened k(x)** can be determined, which leads to the calculation of the **roll positions a_i = y(x)** by numerical integration of the second order differential equation valid for deformation by bending (**Equation/Gleichung 3.2**). The requirements for a process simulation are the knowledge of the properties of the process material as well as of the geometric boundary conditions of the respective straightener.

### Service How2Straight.com

Given the large variety of applications for straighteners, the diversity of types and models, and the varying objectives of differentiated straightening processes, it is often desired that the simulation process can be moved directly into the wire manufacturing or processing environment. The operators themselves should be given the tools to calculate the required positions of the rolls. To address the complexity of process simulation, a web-based service has been developed, which produces results that allow even an inexperienced operator to determine roll positions, so that a defined level of production quality can be achieved.

How2Straight.com is a new and simple we-based service, which uses unit libraries containing information about the roll positions to produce straight steel wire having a round cross-sectional geometry. It has the advantage that it can be used without change in case there is a need for creating and implementing new libraries or improving existing ones.

How2Straight.com calculates and visualizes the roll adjustment data considering the specified process material properties (wire diameter, yield point, modulus of elasticity) and the individual type of roll straightening unit. The user interface provides appropriate input fields and buttons for this purpose. It is normally quite straightforward to determine or look up the properties of the process material.

All adjustments, which have been calculated and visualized on the user interface, should be made on the straightening unit using the individual process material zero line as a starting point. The term process material zero line means that the straightening rolls are positioned in relation to defined geometric conditions on the unit in such a way that a process material of a specific dimension is only touched, but no deformation takes place in the area influenced by the rolls. Whether conventional or semi-automatic straightening equipment is being used is irrelevant. Using the How2Straight.com data in the daily routine of setting up roll straightening units saves labor, time, energy and process material. For the first time the service How2Straight.com opens up the possibility to eliminate the empirical or trial and error roll adjustment method.