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:

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_X² + F_Z² = 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.

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.

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.

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.

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%.

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.

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.