# OPC UA-based Force Control for Deep Rolling with Mechanical Tools

## Article information

## Abstract

Deep rolling can increase the service life of components under cyclic loads. This is achieved by plastic deformation of the component surface using a roller. The degree of plastic deformation depends on the rolling force. For a maximum increase in service life, the rolling force applied to the roller must stay within defined limits. When performing deep rolling using mechanical deep rolling tools, the rolling force is applied via an elastic element such as a leaf spring. The deep rolling force therefore depends on the deflection of leaf spring. It varies when the workpiece bends or has a varying diameter. These variations in the deep rolling force are not desired. They must be reduced to achieve optimum process results. To achieve this, a novel deep rolling force control for mechanical deep rolling was introduced in this paper. To control the rolling force, the force was measured with a sensory tool and machine tool axes were adjusted accordingly. The adjustment of the axes was implemented using the OPC UA standard. It is shown that this can reduce the force error during mechanical deep rolling by 90%. This ensures a constant process result and improves the mechanical deep rolling process.

**Keywords:**Mechanical deep rolling; Force control; Sensory Tool; OPC UA

## 1 Introduction

Cyclic loads lead to fatigue and are thus limiting the service life of components. A high fatigue strength of the workpiece is therefore desirable. Fatigue failures are caused by growing cracks [1]. Surface treatments are an efficient way to reduce crack growth. Commonly used processes for mechanical surface treatment are shot peening, laser shock peening and deep rolling [2]. Deep rolling is a remarkably efficient process that significantly increases the fatigue strength of components. The increased fatigue strength is achieved through three key effects [3]:

1) Smoothing of the workpiece surface, which reduces the notch effect.

2) Strain hardening in the subsurface of the workpiece.

3) Generation of residual compressive stresses on the workpiece surface, which reduce tensile stresses under load.

These combined effects can significantly increase the service life of deep rolled components by a factor of three [3,4] or even five [5]. To realize these benefits, the surface of the workpiece is plastically deformed using a roller. The extent of plastic deformation depends on the applied force on the roller. For deep rolling with mechanical tools, the resulting rolling force is influenced by the workpiece geometry. Small variances in the workpiece’s diameter can lead to changes in the actual rolling force, affecting the degree of plastic deformation and, consequently, the increase in fatigue strength [6]. This finally influences the service life of deep rolled components. In this context, Breidenstein shows a decreased fatigue strength of up to 100 MPa for a decrease of the compressive residual stress of 200 MPa [7]. Thus, the rolling force is a critical parameter for successful deep rolling. Addressing this, an approach to control the rolling force by robot was presented by Chen et al. [8]. However, for conventional mechanical deep rolling tools, there is no digital data of the rolling force. The ECOROLL AG has therefore developed a digital measuring gauge (ECOsense) [9]. This measuring gauge makes it possible to measure the spring force of a mechanical deep rolling tool. It can be used to monitor and control the surface quality of the workpiece. The spring force is a one-dimensional force, but the rolling force generated during deep rolling is two-dimensional. Therefore, this tool cannot measure the entire rolling force. To solve this problem, a force sensitive deep rolling tool was collaboratively developed by the Institute of Production Engineering and Machine Tools (IFW) and the ECOROLL AG [10]. This innovative tool enables real-time monitoring of the two dimensional rolling force during the deep rolling process. Thereby unwanted deviations from the targeted deep rolling force can be detected, the process can be stopped and faulty workpieces can be sorted out. However, some deviations of the rolling force can potentially be compensated by controlling the deep rolling force. Thereby scrap can be avoided. In this work, an approach for a novel deep rolling force control (DRFC) for mechanical deep rolling tools is presented, providing an essential contribution to the advancement of mechanical deep rolling technology.

In section 2, the general boundary conditions for mechanical deep rolling are explained. Based on that, a concept for a DRFC is introduced and the actual implementation of the DRFC is shown. After the implementation of the DRFC, the DRFC was investigated in section 3. There, the measurement results of the DRFCs dead time, the controller settings and the transfer behaviour are discussed. The results allow to evaluate the ability of the DRFC to control the rolling force and the limits of the DRFC can be derived. In section 4, the effect of the DRFC on the workpiece were investigated. Therefore, two workpieces were machined with and without DRFC. For both workpieces, the residual stress state within the workpiece was measured. This allows the final evaluation of the DRFC. Section 5 summarizes the results and provides an outlook.

## 2 Rolling Force Control for Mechanical Deep Rolling

### 2.1 Basic Considerations for a Rolling Force Control for Mechanical Deep Rolling Tools

Deep rolling with mechanical tools is one variant of deep rolling. Compared to the widely used hydrostatic deep rolling, the main advantage is that no additional power or hydraulic supply is needed. The mechanical deep rolling tool can be used in lathes like a conventional turning tool, as shown in Fig. 1. Ideally, the mechanical deep rolling process is carried out directly after the turning process on the same lathe. Mechanical deep rolling is therefore easy to integrate into process chains. The main feature of the tool is a roller that is pressed against the surface of the workpiece via leaf springs. The resulting rolling force consequently depends on the deflection of the springs. However, the deflection of the leaf springs is subject to the following influences:

1) Variations of the workpiece diameter within the tolerance limits due to inaccuracy of the turning process.

2) Deflection of the workpiece caused by the deep rolling force F

_{R}.3) Positioning errors caused by an imprecise calibrated deep rolling tool or by inaccuracies of the machine tool axes.

These influences are the main disturbances to the deep rolling force. In the following the disturbances are summarized as the geometric deviation Δd (Deviation between the displaced and the non-displaced contour). The deflection of the leaf springs depends on Δd. A changing Δd in between and within machining operations leads to a force error ΔF of the resulting rolling force F_{R}.

In general, the rolling force F_{R} is a three-dimensional force consisting of the force components in x-, y- and z-direction, as shown in Fig. 1. The force F_{Y} is the tangential force on the roller. This force points in the rolling direction of the roller and it therefore corresponds to the rolling resistance. As the rolling resistance is minimal, this force component is not taken into account here. The main part of the rolling force acts in the x-z plane, therefore it is assumed that F_{R} only consists of the force components F_{X} and F_{Z}. The rolling force normal to the surface (F_{N}) of the workpiece is particularly important for deep rolling. In order to determine the normal force F_{N} from the force components F_{X} and F_{Z}, the orientation of the workpiece contour must be known. For a cylindrical workpiece, F_{N} is equal to F_{X} and F_{Z} is equal to the feed force F_{f}. In a measurement on a cylindrical workpiece, F_{X} = F_{N} = 1,000 N and F_{Z} = F_{f} = 115 N were measured. This means that the rolling force is F_{R} = √F_{X}^{2} + F_{Z}^{2} = 1,007 N. Thus, during deep rolling the feed force F_{f} is low in relation to F_{N} so that F_{R} ≈ F_{N}. It is consequently not necessary to differentiate between the value of the normal force F_{N} and the rolling force F_{R}. Therefore, only F_{R} is considered in this paper.

To achieve an increase in service life of the machined component, the rolling force F_{R} has to stay within defined limits. An unwanted variation of the rolling force is thus a problem for mechanical deep rolling. A rolling force control enables a reliable manufacturing within the desired limits and to compensate for the geometric disturbance Δd. The deep rolling force control (DRFC) considered here, is based on offsets (Off_{x} and Off_{z}) that are applied to the machine tool axes. By setting these offsets to the axes, the deflection of the leaf springs of the deep rolling tool is changed. This in turn changes the resulting rolling force. Thus, by controlling the axes offsets, the deep rolling force can be controlled.

### 2.2 Implementation of the DRFC

To control the axes offsets of the machine tool, an interface for data exchange in between the machine tool and an external control PC is needed. Here, OPC UA is used. OPC UA is a widely used and approved standard to read and write machine tool data. For example, an OPC UA server is included as standard in the Siemens Sinumerik controls 828D/840D sl since version 4.94. The usability of an OPC UA based DRFC is therefore potentially high. The overall control strategy for the OPC UA based DRFC is shown in Fig. 2. As described, the shown DRFC adjusts the machine tool axes position by applying offsets. Thereby the rolling force F_{R} is controlled to match the target force F_{T}. The DRFC was realized on a machine tool of the type DMG MORI CTX beta 800 TC. The machine control on this machine tool is a Siemens Sinumerik 840D sl. Within the Sinumerik, an adjustment of the machine tool axis offset is allowed. Via the Sinumerik variable $AA_OFF offset can be set to the machine tool axes. In process, the variable $AA_OFF can be changed by synchronized actions. Within a synchronized action the axes offset $AA_OFF is set to the value of a Sinumerik GUD (Global User Data) variable of type SYG_IU. This type of GUD variable is capable of synchronized actions. In addition, the GUD variable can be changed via OPC UA from an external PC to control the axes offset. On the other hand, the rolling force was measured by the sensory deep rolling tool. The force measurement of the tool is based on strain gauges. The tool has integrated electronics that transmit the strain gauge data wirelessly via MQTT (Message Queuing Telemetry Transport) to the external control PC. There the rolling force is calculated from the strain gauge data. Since the rolling force is available and the axes offset can be written, a force control can be realized. For the rolling force control a PID-controller was used. It controls the axes offsets corresponding to the measured rolling force. The parameters of the PID-controller were adjusted experimentally on the machine tool, taking into account the step response of the controller (Further details in section 3.2). After setting the parameters of the PID-controller, a deep rolling force control (DRFC) was available.

## 3 Investigation of the DRFC

### 3.1 Dead Time of the DRFC

OPC UA is an approved standard. However, the transfer rate of OPC UA is limited and a high dead time occurs. In a first investigation, the actual dead time Δt of the DRFC was measured according to Fig. 3.

The time Δt in between the write command for the offset Off and the response of the rolling force F_{R} was therefore measured over 100 repetitions. In addition to the dead time of OPC UA, the dead time of the wireless data transmission of the tools force data via MQTT is included in the overall dead time Δt. For the machine tool CTX 800 used here, an average dead time of 0.45 s was determined and at maximum a dead time of up to 3 s occurred. Considering the high dead time, control operations are no typical use case for OPC UA. Thus, the potentials of an OPC UA based force control for mechanical deep rolling are not known. The DRFC was therefore initially investigated independently of the actual machining of a workpiece.

### 3.2 Setting the PID-Controller

After measuring the dead time, the influence of different settings of the PID-controller was investigated. The setting parameters for a PID-controller are the proportional gain factor K_{P}, the integral gain factor K_{I} and the derivative gain factor K_{D}. In Fig. 4, the response of the controller to a step in the target force F_{T} is shown. For this experiment, the deep rolling tool was positioned directly above the workpiece surface. This means that the measured rolling force F_{R} without additional offset is 0 N. The target force was then changed from F_{T} = 0N to F_{T} = 400 N and the resulting rolling force was measured. Different parameter settings of the controller were tested and compared in the experiment. Regardless of the parameters selected, the rolling force F_{R} increases with a delay to the target force F_{T}. The delay corresponds to the dead time of about 0.45 s measured in section 3.1. First K_{I} and K_{D} were kept at 0 and the proportional gain K_{P} was gradually increased. Measurement M01 shows the response of the controller for K_{P} = 0.2. With this setting, there is a clear tendency to oscillate and a further increase in K_{P} is not possible since the controller tends to become unstable at a higher K_{P}. Nevertheless, the distance to the target force is still very large at over 200 N. The reason for the instability of the controller at a higher K_{P} is the high dead time measured in section 3.1. To avoid overshooting, K_{P} was reduced to 0.1 and an integral gain of K_{I} = 0.005 was added (M02). The integral gain leads to a slowly increasing rolling force until the target force is reached. To reach the target force faster, K_{I} was increased further until the target force was overshot (M03). Overshooting is not desirable in deep rolling, as a rolling force higher than the target force can damage the surface of the workpiece. Therefore, K_{I} was reduced until overshoot no longer occurred (M04). Finally, the derivative gain K_{D} was added (M05). The derivative gain K_{D} dampens the response. This allows K_{I} to be increased without the controller overshooting. M05 shows the system response for this final setting, which was then used for all further experiments. With this parameter setting, the target force is reached after about 2.5 s without overshooting. To summarize, it can be said that the main part of the control deviation is compensated by the integrating term of the controller. This means that the PID controller used here essentially behaves like an I-controller.

Since OPC UA and MQTT are used for the controller, an exact feedback loop time cannot be guaranteed. Due to the slow response of the controller, it is not negatively affected by small variations in the feedback loop time. However, as measured in section 3.1, the dead time can be up to 3 s in some exceptional cases. To ensure that the controller does not override even in cases where the feedback loop time is much longer, the PID controller has been extended to include an “On-change function”. This function checks whether the offset written by the controller has been written to the machine tool after 0.5 s at the latest. If the offset has not been changed during this time, control is interrupted until the value has been written.

### 3.3 Ramp Response of the DRFC

A PID-controller is capable to compensate all static disturbances by its integral term. Nevertheless, for a dynamically changing disturbance, a tracking error ΔF of the rolling force remains. For deep rolling, the disturbances are the variances in the geometry of the workpiece, respectively geometric deviations Δd. The remaining tracking error ΔF depends on the rate of change of the geometric deviation V_{d/t}. As shown in Fig. 5 a geometric deviation Δd occurs between the displaced contour of the workpiece and the non-displace contour. This type of deviation can be caused by a deflection of the workpiece as a result of the rolling force. During machining, the geometric deviation decreases as the deflection of the workpiece is less close to the chuck. V_{d/t} thus depends on the machining time Δt and the geometric deviation Δd. To investigate the influence of V_{d/t} on the residual tracking error ΔF of the deep rolling force F_{R}, different V_{d/t} were applied to the deep rolling tool while using the DRFC. In an experiment, a defined V_{d/t} was achieved by applying a ramp function to the deep rolling tool through the movement of the machine tool axis. V_{d/t} is thereby equivalent to the gradient of the ramp. The resulting ΔF depending on V_{d/t} is show in Fig. 5. A linear correlation was determined. At a change of the deviation of 1 mm/min the remaining deep rolling force error ΔF is about 35 N. This error is relatively high considering the low change rate of the deviation of only 1 mm/min. The reason for that is the high dead time within the DRFC. To achieve a stable behaviour of the DRFC despite the dead time, the parameters of the PID-controller must be set conservative. This leads to a slow response time of the controller. However, deep rolling does not require a high dynamic of the controller. A typical machining time is approx. 1 min and the deviations that actually occur on the workpiece in production are small (<< 1 mm). That means the V_{d/t} in production is usually much lower than 1 mm/min and the tracking error of the force is thus less than 35 N. The sensory deep rolling tool is suitable for deep rolling forces up to 4,000 N meaning that the relative tracking error for a ramp response of the DRFC is less than 1%.

### 3.4 Step Response of the DRFC

The ramp response of the DRFC shows the response for disturbances with constant change rates. Additionally, the step response of the DRFC was investigated. The step response of the DRFC for a disturbance was measured according to the experimental setup shown in Fig. 6. Therefore, a workpiece with a step in diameter of 0.05 mm was machined and deep rolled afterwards. Without DRFC, the step in diameter leads to a step of 109 N in the resulting rolling force F_{R}. The DRFC reduces this initial force error to 56 N. Additionally the DRFC reduces the remaining mean error of 83 to 3 N after a settling time of 3 s. Only a residual force noise of ±15 N around the target force remains. Furthermore, the step response allows to evaluate the stability of the DRFC. The step disturbance covers a broad frequency band. Thus, potential natural frequencies of the DRFC are excited by the step disturbance. Since the system response of the DRFC has no dominant oscillation and the oscillations that occur are quickly dissipated, the behaviour of the DRFC can be classified as stable.

The step response allows a general evaluation of the dynamic behaviour of the DRFC and the DRFCs stability. More in-depth information about the dynamic behaviour of the DRFC can be provided by a disturbance frequency response. However, due to the low dynamic bandwidth of the DRFC, no complete interference frequency response was measured. Only the cutoff-frequency was determined by a sinusoidal excitation of the DRFC with different frequencies by deep rolling an eccentric workpiece. Thereby a 3-dB cutoff-requency at 0.2 Hz was determined. Disturbances as they occur from an eccentric workpiece (for example 16.7 Hz at 1,000 RPM), can thus not be reduced by the DRFC.

Besides the disturbance response of the DRFC the control behaviour is of interest. The reference variable for the DRFC is the target force F_{T}. In this work the target force is assumed to be constant. Thus, the reference frequency response wasn’t investigated here.

### 3.5 DRFC in Two Dimensions

For the determination of the main characteristics of the DRFC, only rolling forces in the x-direction were considered. As shown in Fig. 2, the DRFC can control both the x- and the z-axis of the machine tool. In a next step, the DRFC was investigated with deep rolling forces acting simultaneously in the x and z directions. This means that a two-dimensional DRFC is required. A workpiece as shown in Fig. 7 with two radii of 10 mm was manufactured and deep rolled afterwards. The radii lead to a slowly changing direction of the rolling force F_{R}. The rolling force changes from almost complete x-direction to an equally distributed force in x- and z-direction and back to complete x-direction of the force. To achieve a two-dimensional force control, the returned offset from the PID-controller is separated into the x- and z-direction according to the direction of the currently acting rolling force. Thereby the target force F_{T} is achieved as a combination of the forces F_{X} and F_{Z}. The measurement results in Fig. 7 show a maximum deviation of 65 N from the target force during the uncontrolled deep rolling process. During the controlled process the deviation is reduced to 54 N. Here the effect of the DRFC appears to be small. The reason for this is that vibrations occur in the radius during deep rolling. These vibrations are caused by a change of the contact geometry and the surface quality within the radius. The vibrations have a frequency much higher than the cutoff-frequency of the DRFC. Thus, they cannot be compensated. Despite this, the mean force for the uncontrolled process is 274 N and for the controlled process 299 N. The target force is 300 N. The error in the mean force is reduced from 26 to 1 N. Thus, the DRFC is capable to control a two-dimensional force as well.

## 4 Effect of DRFC on Resulting Residual Stress in the Workpiece

After section 3, the DRFC’s limits in controlling the deep rolling force are known. However, the effect of the deep rolling process on the workpiece with and without DRFC has not yet been analysed. In further experiments two specimen were machined as shown in Fig. 8. The machined workpieces were then analysed with regard to the service life-increasing residual stress σ at the surface.

To investigate the effect of a geometric disturbance Δd on the residual stress, a conical workpiece was manufactured as shown in Fig. 9. The diameter of the conical workpiece changes from d_{d} = 46 to 46.2 mm. Thereby an increasing disturbance Δd is achieved. As in section 3.3, this kind of disturbance can be caused by the bending of the Workpiece. The measurement results without DRFC show an increasing deep rolling force corresponding to the disturbance Δd. The rolling force is rising from 650 to 1,030 N over the length of the workpiece. After deep rolling the residual stress σ at the surface (information depth max. 5.5 μm) was measured with an x-ray diffractometer of type Seifert XRD 3003 TT. Three measurement points were selected along the machined path. The measured residual stress is decreasing from σ_{ax} = −331 MPa (axial) at the first measurement point, over σ_{ax} = −481MPa at the second point to σ_{ax} = −525 MPa. Overall, a small geometric disturbance of Δd = 0.1 mm leads to a change in the achieved residual stress of Δσ_{ax} = 194 MPa. For components with a high dynamic load this can significantly reduce the service life. Thus, to ensure a certain service life, the residual stress must be kept within defined limits. A constant residual stress level is potentially achieved by the DRFC. To prove this, the conical workpiece was deep rolled a second time with the DRFC.

The results for deep rolling the conical workpiece with the DRFC are shown in Fig. 10. The target force was set to 900 N. With the DRFC the residual deviation from the target force is approximately 6 to 7 N. This deviation corresponds to the tracking error that can be estimated according to Fig. 5. Here a deviation Δd of 0.1 mm over a length of 90 mm occurs. With the rolling feed f_{w}, the rolling speed v_{w} and the workpiece diameter of d_{d} = 46 mm the processing time for a length of 90 mm is 0.58 min. Thus, the calculated V_{d/t} is 0.17 mm/min and the corresponding tracking error is 6.6 N. The estimation of the tracking error according to Fig. 5 therefore provides good results. In comparison to the uncontrolled deep rolling process the force error is reduced considerable by more than 90%. The measurement of the residual stress shows that the variation of the achieved residual stress is reduced as well. The previously measured variation of 194 MPa is reduced to 28 MPa. It can therefore be concluded that the effectiveness of the DRFC in terms of constant residual stresses is achieved.

## 5 Conclusions

The positive effects of deep rolling on the service life of components depends on the correct deep rolling force. If the force is too low, compressive residual stresses will not be achieved within the workpiece. This leads to a reduced service life. Conversely, if the force is too high, the surface of the workpiece is damaged and the service life is reduced as well. For mechanical deep rolling the rolling force varies due to geometric variations of the workpiece. To reduce the variation of the rolling force and to achieve constant compressive residual stresses within the workpiece, a deep rolling force control (DRFC) for mechanical deep rolling was introduced in this work. Mechanical deep rolling is usually performed on conventional lathes. To control the deep rolling force on the machine tool, OPC UA is used. Via OPC UA the offsets of the machine tool are controlled by a PID-controller. It was shown, that the DRFC can reduce the mean force error to 3 N for static disturbances. Finally, the effect of the DRFC on the compressive residual stresses within the workpiece was investigated. The variance of the residual stress was reduced from 194 MPa to 28 MPa for a sample workpiece. Thus, the DRFC is able to keep the resulting residual stress within a narrow range.

Here the target force was assumed to be constant. A constant target force leads to constant residual stresses, as long as the contact surface between the roller of the deep rolling tool and the surface of the workpiece is constant. If a radius is deep rolled, the contact surface changes. Thus, the target force has to be adjusted for constant residual stresses. This effect was not considered here and will be investigated in future works. The long-term target is to achieve constant residual stresses independent of the workpiece geometry.

## Acknowledgements

These are results of the cooperation project “Process-monitored and controlled mechanical deep rolling” (ZF4810001LP9/ ZF4070523LP9). It is funded by the Federal Ministry of Economics and Climate Protection (BMWK) as part of the Central Innovation Program for SMEs (ZIM) and is supervised by the Working Group of Industrial Research Associations (AiF). The ECOROLL AG thanks for the productive cooperation in this project and the IFW thanks for the financial support.

#### List of Symbols

F_{R}

Rolling Force

F_{X}

Rolling Force in x-direction

F_{Y}

Rolling Force in y-direction

F_{Z}

Rolling Force in z-direction

F_{N}

Rolling Force Normal to the Surface of the Workpiece

F_{f}

Rolling Force in Feed Direction

F_{T}

Target Force

ΔF

Force Error (Delta between F_{R} and F_{T})

Δd

Deviation between the Displaced and the Non-displaced Contour

Off_{x}

Offset to the Machine Tool x-axis

Off_{z}

Offset to the Machine Tool z-axis

$AA_OFF

Offset Parameter on Siemens Sinumerik 840 d sl

SYG_IU

GUD-variable for Synchronized Action on Siemens Sinumerik 840 d sl

Δt

Dead Time

K_{P}

Proportional Gain of the PID-controller

K_{I}

Integral Gain of the PID-controller

K_{D}

Derivative Gain of the PID-controller

v_{d/t}

Rate of Change of Geometric Deviation Δd

f_{w}

Feed

v_{w}

Rolling Speed

d_{r}

Roller Diameter

d_{d}

Workpiece Diameter

σ

Residual Stress

## References

## Biography

**Prof. Dr.-Ing. Berend Denkena** is Professor and Executive Director of the Institute of Production Engineering and Machine Tools of the Leibniz University Hannover, Germany.

**Jan Berlin** is Research Assistant in the Department of Machine Tools and Controls at the Institute of Production Engineering and Machine Tools of the Leibniz University Hannover, Germany.