Introduction

As a typical material of ultra-high-strength steel, 42CrMo steel is widely used in high-speed heavy-duty applications due to its unique quenching depth, hardness, and good formability. It encompasses various advanced manufacturing fields, including wind turbine bearings, shield tunneling machine spindles, gears on traction locomotives, and crankshafts on heavy-duty dump trucks1,2,3. Traditionally, for shaft-like parts made of high quenchable steel, grinding is often employed as the final step in the manufacturing process after quenching and tempering. However, grinding processes require a large amount of grinding fluid, and it is difficult to complete for complex-shaped parts. With the continuous development of special processing fields, advanced manufacturing technologies such as “rolling instead of grinding” are gradually becoming popular, replacing grinding processes4,5. In order to improve the surface performance of parts, an increasing number of special processing techniques are being applied in part manufacturing, including ultrasonic shot peening6, ultrasonic rolling7, laser processing8, and wire electrical discharge machining (WEDM)9. However, ultrasonic shot peening can lead to increased surface roughness of parts, affecting their wear resistance. Laser processing is only suitable for processing materials with small thicknesses, as the energy cannot penetrate thicker metal materials, and processing surfaces may produce burrs, affecting assembly accuracy. Electrical discharge machining requires a large amount of electrical energy consumption, resulting in high costs and environmental hazards. In contrast, as one of the special processing methods, ultrasonic rolling processing technology10,11,12 is simple to operate and can process parts of any shape. By combining high-frequency vibration and static pressure loading, ultrasonic energy and static dynamic fields are applied to the surface of the part. This process does not produce chips, and the continuous contact-separation and high-frequency loading of the part’s surface by the rotatable small ball at the front end of the processing device induce intense plastic deformation inside the material, thereby forming residual compressive stress to suppress crack formation.

Cheng et al.13 conducted ultrasonic rolling processing on the inner raceways of bearing rings and found that when the amplitude was 10 μm and the workpiece rotation speed was 45 rpm, the material hardness increased from 760HV to 840HV, while the surface roughness decreased to 0.16 μm. Zhu et al.14 studied the effect of process parameters on the fatigue performance of G20Cr2Ni4A steel with surface ultrasonic rolling strengthening treatment. The results showed that without ultrasonic rolling, fatigue testing of the parts would result in material spalling with a thickness of 1 micrometer, leading to a decrease in fatigue life. In contrast, parts subjected to ultrasonic rolling would transfer fatigue cracks to deeper layers, making it more difficult for surface fatigue cracks to form, thus significantly extending fatigue life. Li et al.15 studied the effects of ultrasonic rolling on the surface properties of CuCr alloy. Parts subjected to ultrasonic strengthening treatment showed the formation of a nano-gradient layer with a depth of 300 μm on the surface, and grain refinement to 78 nm. It was found that the rolling depth had the greatest impact on surface performance. Zhu et al.16 investigated the effect of ultrasonic strengthening process on the surface integrity of TC4 titanium alloy. The results showed that under the action of ultrasonic rolling, the number of high-angle grain boundaries increased, and the hardness and residual stress of the workpiece increased with the increase of static pressure, leading to an increase in fatigue strength to 450 MPa. Ao et al.17 conducted comparative experiments on ultrasonic rolling to study the relationship between the fatigue resistance and plastic deformation degree of Ti-6Al-4 V alloy under ultrasonic rolling. It was found that with the increasing degree of plastic deformation, the material’s micro-fatigue performance significantly increased. Yu et al.18 conducted research on ultrasonic rolling strengthening modification of GH4149 alloy and obtained the influencing law of surface properties. The results showed that ultrasonic rolling significantly refined the grain size of the material’s surface, increased the number of low-angle grain boundaries, and increased the depth of residual stress layer to 0.6 mm. Xu et al.19 used ultrasonic rolling to improve the low-temperature mechanical properties of FH36 steel. It was found that ultrasonic rolling reduced the surface roughness to 0.074 μm, increased the processed hardened layer to 580 μm, and increased the dislocation density. The synergistic enhancement of these properties was the main reason for the improvement of FH36 steel’s low-temperature mechanical properties. Wu et al.20 studied the surface integrity of TiB/7050 composite materials strengthened by ultrasonic rolling. Under the action of ultrasonic rolling strengthening, the material’s fatigue life could be increased by 3.3 times, and this improvement was attributed to the increase in the depth of residual stress layer and the decrease in surface roughness. Yang et al.21 investigated the influence of ultrasonic rolling process on the formation mechanism of nano-gradient layers in GH4169 alloy steel. They characterized the processed workpiece’s cross-section using scanning electron microscopy, transmission electron microscopy, and hardness tester, and found that the material surface formed equiaxed grains with a grain size of 31.8 nm, while the hardness also significantly increased. Zhu et al.22 conducted machining experiments on G20Cr2Ni4A steel using ultrasonic rolling technology and studied the influence of process parameters on surface properties. The results showed that the surface performance of parts strengthened by ultrasonic rolling was significantly improved, with hardness increasing to 64HRC and surface roughness decreasing to 0.054 μm. Zhao et al.23 studied the effect of ultrasonic rolling on the fatigue behavior of AISI 1045 steel. They found that the surface of the strengthened parts formed a nano-layered structure after ultrasonic rolling, with residual stress reaching 453 MPa. The lower surface roughness significantly inhibited crack propagation.

In summary, most simulation studies have focused solely on the ultrasonic rolling process itself. For rod-like parts, the preceding process is often turning, but little attention has been paid to simulating turning processes in previous studies. However, the initial state of the model is often crucial for establishing an accurate simulation model. In this study, by establishing a turning-ultrasonic rolling compound processing model and simulating the actual processing process, the distribution law of residual stress under different process parameters was obtained. Simultaneously, ultrasonic rolling processing experiments were conducted to verify the reliability and rationality of the simulation model, providing a new approach for the turning and ultrasonic rolling compound processing of shaft-like parts.

Simulation analysis of turning-ultrasonic rolling compound processing

Model setup and boundary conditions

As shown in Fig. 1, the turning-ultrasonic rolling compound processing simulation model was built in the ABAQUS software. The cutting tool has a front angle of 0 degrees, a back angle of 10 degrees, and dimensions of 10 mm x 10 mm. To shorten simulation calculation time and improve computational efficiency, the cutting tool was modeled using discrete rigid bodies with linear R3D4 rigid body elements, with a total of 7000 mesh divisions. The material properties of the 42CrMo steel rod are shown in Table 124, utilizing the Johnson-Cook model for material property characterization. The expression of the Johnson-Cook model is represented by Eq. 1, with the J-C parameters listed in Table 225.

$$\sigma =\left( {A+B{\varepsilon ^n}} \right)\left( {1+C\ln \frac{{{\varepsilon _1}}}{{{\varepsilon _2}}}} \right)\left( {1 - {{\frac{{T - {T_r}}}{{{T_m} - {T_r}}}}^m}} \right)$$
(1)

where A represents the yield stress at room temperature, B represents the strain hardening coefficient, C represents the strain hardening rate parameter, m denotes the thermal softening coefficient, n denotes the hardening exponent, ε1 represents the equivalent elastic strain rate, ε2 represents the reference strain rate, ε represents the equivalent elastic strain, T represents the current temperature, Tr represents the room temperature, and Tm represents the melting temperature.

Table 1 42CrMo steel properties.
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Table 2 42CrMo steel Johnson Cook model.
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Table 3 42CrMo steel J-C damage model.
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The workpiece model dimensions consist of an inner diameter of 12 mm, an outer diameter of 15 mm, and a length of 30 mm for the hollow cylinder. Mesh partitioning was performed using C3D8R linear hexahedral elements, resulting in a total of 112,098 mesh divisions for the workpiece. Local mesh refinement was applied along the machining surface within a 10 mm range along the machining direction and 0.7 mm depth from the surface into the material. The rolling ball was modeled as a discrete rigid body with a diameter of 10 mm, utilizing linear quadrilateral elements R3D4 for mesh partitioning, resulting in a total of 1388 mesh divisions. The working principle of the turning-ultrasonic rolling compound processing simulation model is as follows: firstly, turning machining is performed on the 42CrMo steel rod, followed by ultrasonic rolling simulation experiments based on the turning machining. The material removal in turning process was conducted using Johnson-Cook damage model, with the parameters shown in Table 3, where D1 to D5 represent material failure parameters. Boundary conditions were applied as follows: the cylindrical workpiece was restricted from movement and rotation along the Y and Z axes, allowing rotation only around the Z axis. The cutting tool was restricted from movement and rotation along the X and Y axes, allowing movement only along the Z axis. For the rolling ball, due to the application of ultrasonic vibration, it was restricted from movement along the Y axis and rotation along the X and Y axes, while ultrasonic vibration was applied along the X direction. Additionally, the rolling ball moved along the Z axis in the same trajectory as the cutting tool. Due to the rolling action, the rolling ball rotated around the Z axis under the driving force of the workpiece rotation. Based on this principle, two analysis steps were defined, with a total analysis time of 1 s. The turning analysis step was conducted first, with a time of 0.5 s, followed by the ultrasonic rolling processing analysis step, also with a time of 0.5 s. The analysis step is set to display dynamics. Since the cutting tool is defined as a discrete rigid body, the cutting tool’s front cutting face, primary cutting face, and secondary cutting face are set as active surfaces, while the workpiece surface is set as a passive surface. Additionally, the penalty function contact method is used. In the contact properties, the normal behavior is set to hard contact, and the tangential behavior is set to penalty contact, with a friction coefficient of 0.2 according to the actual cutting conditions.

Fig. 1
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Simulation model diagram of turning-ultrasonic rolling compound processing.

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Turning analysis of 42CrMo steel

To efficiently conduct turning-ultrasonic rolling compound processing simulation experiments within a limited number of trials, an orthogonal experimental design was adopted, comprising four factors with four levels each, totaling 16 simulation experiments. The machining parameters are presented in Table 4, where the ultrasonic frequency is set to 28 kHz, spindle speed ranges from 50r/min to 200r/min, feed rate ranges from 0.05 mm/r to 0.2 mm/r, static pressure ranges from 500 N to 800 N, and amplitude ranges from 7 μm to 10 μm. Parameters for turning preprocessing include a cutting speed of 800 m/min, a cutting allowance of 0.2 mm, and a feed rate of 0.1 mm/r. The Von-Mises stress is utilized to represent the variation of residual stresses.

Table 4 Ultrasonic rolling orthogonal experiment.
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As shown in Fig. 2, the machining status of Von-Mises stress under turning conditions at different time frames is illustrated. This stage consists of 200 analysis steps, and Fig. 2a and i display selected frames from the 10th to the 200th frame, representing the distribution of Von-Mises stress from the beginning to the end of the turning process. As shown in Fig. 2a, the workpiece undergoes elastic deformation under the compressive action of the cutting tool at the 10th frame of the turning analysis step. The Von-Mises stress is distributed radially from the center of the contact area between the tool and workpiece. At the central contact position, Von-Mises stress reaches 1454 MPa, but chip formation has not yet occurred. As shown in Fig. 2b, plastic deformation begins as the shear stress applied by the tool exceeds the yield limit of the workpiece at the 50th frame, initiating chip formation. However, the formed chips are short, and the machining process is not fully stable yet. The maximum Von-Mises stress remains at the contact point between the tool tip and the workpiece, increasing from 1454 MPa to 1486 MPa. As shown in Fig. 2c, the Von-Mises stress continues to increase to 1476 MPa at the 60th frame, but the discontinuous chip formation process leads to poor surface quality after turning, reducing tool life and causing irregular vibration, affecting surface quality. Figure 2d, illustrates the maximum Von-Mises stress increases from the initial 1454 MPa to 1486 MPa at the 110th frame. Uniform chip formation begins, and the turning process becomes continuous, reducing tool wear and heat generation, and improving surface quality. Figure 2e and i represent the stress distribution from the 130th to the 200th frame. The maximum Von-Mises stress decreases and stabilizes at 1478 MPa. The cutting force decreases, the turning process stabilizes, and excessive wear and deformation of the tool and workpiece are avoided. The machining temperature stabilizes, continuously forming a cycle of elastic deformation, plastic deformation, fracture, and separation, resulting in uniform and consistent chip formation on the tool front face and good surface quality on the workpiece.

Fig. 2
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Von-Mises stress diagram of turning process at different time steps.

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Finite element analysis of ultrasonic rolling on 42CrMo steel

Figure 3 illustrates the distribution of residual stress in 42CrMo steel rods after ultrasonic rolling under different static pressures. It can be observed that the residual stress increases with increasing static pressure. When the static pressure reaches 800 N, the Von-Mises stress reaches its maximum value of 1316 MPa, with evenly spaced stress concentration zones appearing on the sample surface along the feed direction of the rolling ball. Conversely, when the static pressure is 500 N, the Von-Mises stress is only 1123 MPa, and no stress concentration areas appear on the sample surface. This is because the static pressure at this level is insufficient to induce appropriate plastic deformation in the workpiece, thus failing to enhance the surface properties. As the static pressure increases from 600 N to 700 N, areas of significantly increased residual stress gradually appear on the workpiece surface, with the residual stress increasing from 1240 MPa to 1299 MPa. This is due to the intensified plastic deformation within the material as the static pressure increases, resulting from the increased impact force under the action of static pressure. When the static pressure decreases, the residual stress also decreases significantly, indicating that the impact energy brought by ultrasonic vibration is insufficient to induce severe plastic deformation on the material surface. Meanwhile, ultrasonic rolling strengthening results in a “peak shaving and valley filling” effect, which flattens the tool marks left by previous turning processes, leading to a significant increase in residual stress. However, when the static pressure is too low, the kinetic energy brought by ultrasonic impact cannot press the part surface absolutely smooth, thereby introducing higher residual compressive stress. In fact, ultrasonic rolling processing is a metal flow effect without chip formation. It transfers the accumulated metal at the protruding positions to the concave positions through ultrasonic vibration and impact, resulting in a mirror-like surface finish. It is also a surface finishing technique that introduces beneficial residual compressive stress to suppress crack initiation while achieving an absolutely smooth surface, significantly enhancing the surface properties and extending the service life of the components. The objective of researching ultrasonic rolling processing technology to increase residual compressive stress in components is to maintain their excellent performance under harsh operating conditions. The static pressure influences the residual stress within 42CrMo steel by altering the degree of plastic deformation on the material’s surface. Increasing the static pressure during ultrasonic rolling can significantly enhance the residual compressive stress on the surface layer of the part while also deepening the affected layer of residual compressive stress. This ensures that both the surface and internal regions of the material are subjected to the strengthening effects of ultrasonic rolling. Conversely, when the static pressure is reduced, the force exerted by the rolling ball decreases, leading to insufficient plastic deformation, resulting in lower residual compressive stress. Moreover, the reduced residual compressive stress does not extend its influence to deeper regions, thereby diminishing the impact range and distribution depth of the residual stress. When the static pressure is excessively high, residual tensile stress may even form at deeper layers. This occurs because, when the static pressure exceeds the plastic deformation limit, residual tensile stress is generated within the material to maintain stress balance.

Fig. 3
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Residual compressive stress diagram of turning process at different static pressures.

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Fig. 4
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Residual compressive stress diagram of turning process at different amplitudes.

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Figure 4 depicts the distribution of residual stress under different amplitudes. From the Von-Mises stress graph, it can be observed that the energy applied by ultrasonic rolling to the rolling ball radiates from the contact area towards the feed direction. With increasing amplitude, evenly spaced stress concentration areas appear on the workpiece surface. When the amplitude is 10 μm, the residual stress reaches its maximum value of 1352 MPa. However, the phenomenon of “crushing” appears in the upper right corner of the graph, leading to excessive deformation of the mesh and the appearance of stress concentration areas nearby. In other words, although increasing the amplitude generates greater residual stress on the surface of the component, it can lead to fatigue failure of the already processed surface. The yield strength of 42CrMo steel is insufficient to withstand the impact energy brought by ultrasonic vibration, resulting in excessive deformation and failure of the component surface. Additionally, it is worth noting that excessive increase in amplitude can lead to failure modes such as re-cracking and defects on the surface of the component after ultrasonic rolling strengthening, significantly reducing the fatigue resistance and service life of the component. This is because excessively large amplitudes increase the impact force of the rolling ball, significantly increasing the instability of the ultrasonic processing system. Conversely, when the amplitude is 7 μm, the residual stress is only 1243 MPa. Furthermore, it is found that increasing the amplitude from 9 μm to 10 μm results in a larger increase in residual stress (94 MPa) compared to increasing the amplitude from 7 μm to 8 μm. The increase in amplitude leads to intensified plastic deformation on the material surface, and the higher amplitude also causes the rolling ball to penetrate deeper into the workpiece. Therefore, the increase in amplitude significantly affects the distribution of residual stress. Both excessively large and small amplitudes fail to produce good strengthening effects on the workpiece surface, while an amplitude of 9 μm results in better surface effects, with a residual stress of 1288 MPa. Amplitude affects the variation in residual compressive stress by influencing the degree of plastic deformation on the material’s surface. When the amplitude increases, the impact force and kinetic energy exerted by the rolling ball on the workpiece surface also increase, leading to a higher residual compressive stress value and a deeper affected layer of residual compressive stress. An appropriate amplitude will result in a uniform distribution of residual compressive stress within the material, significantly enhancing the surface properties. However, when the amplitude is too low, the energy and impact generated by the amplitude are insufficient to create uniform and consistent residual compressive stress within the material. Conversely, if the amplitude is too high, it may lead to the formation of microcracks on the workpiece surface, which can reduce the fatigue resistance of the part during service. Therefore, selecting the correct amplitude is crucial for enhancing the effectiveness of residual compressive stress induced by ultrasonic rolling and achieving good surface quality.

Figure 5 shows the distribution of residual stress at different specimen speeds. Figure 5a and d represent the distribution of residual stress at specimen speeds of 50r/min, 100r/min, 150r/min, and 200r/min, respectively. It can be observed that as the specimen speed increases, the residual stress gradually decreases. When the specimen speed is 200 r/min, the residual stress is at its minimum, with a value of 1316 MPa. Conversely, when the speed is 50r/min, the residual stress reaches 1321 MPa. It can be seen that the influence of specimen speed on residual stress is smaller than that of static pressure and amplitude, as the change in residual stress caused by changes in speed is smaller. As the specimen speed increases, the area of the workpiece affected by the impact of the rolling ball decreases, leading to reduced plastic deformation of the material and more unprocessed areas along the Z-axis of the workpiece. Therefore, it can be seen from Fig. 5d that the unimpacted area of the workpiece is smaller at this time, with only a small part of the ultrasonic rolling impact area. When the rotational speed decreases, the rolling balls form continuous strengthening zones along the circumferential direction. Under the combined effect of lower feed speed and lower workpiece rotational speed, overlapping strengthening zones are formed in the circumferential direction of the workpiece. This increases the frequency of impacts of the rolling balls on the surface of the workpiece per unit time, thereby significantly enhancing the residual stress on the workpiece surface. However, when the rotational speed increases, it leads to an increase in rolling force and processing temperature, resulting in phenomena such as wear and burning of the rolling tool head. This often has an opposite effect on improving the surface properties of the components strengthened by ultrasonic rolling process. Therefore, it is important to choose the workpiece rotational speed in ultrasonic rolling process reasonably. A higher workpiece rotational speed reduces the residual compressive stress while also thinning the affected layer of residual stress, leading to a decrease in surface quality and negatively impacting the uniform distribution of residual stress within the part. Conversely, when the workpiece rotational speed is lowered, the contact time between the rolling ball and the workpiece increases, resulting in a more uniform distribution of residual compressive stress on the material surface. This extended contact time also generates a greater plastic deformation layer, thereby creating higher residual compressive stress. However, it can be observed that excessively low rotational speeds lead to a decrease in strengthening efficiency. In practical engineering applications, it is essential to carefully select the combination of workpiece rotational speed and other process parameters to effectively enhance the residual compressive stress and surface quality of the part.

Fig. 5
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Residual compressive stress diagram of turning process at different rotational speeds.

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Figure 6 illustrates the distribution of residual stress at different feed rates, representing feed rates of 0.05 mm/r, 0.1 mm/r, 0.15 mm/r, and 0.2 mm/r, respectively. As the feed rate increases, the residual stress gradually decreases. When the feed rate is 0.05 mm/r, the residual stress reaches its maximum value of 1302 MPa, while when the feed rate increases to 0.2 mm/r, the residual stress decreases to 1297 MPa. Compared with the influence of static pressure, amplitude, and speed on residual stress, the influence of feed rate on residual stress is minimal, with a change range of only 5 MPa. On one hand, when the feed rate decreases, the areas of the rolling ball’s action on adjacent areas of the material are brought closer, equivalent to the same area being repeatedly rolled twice, resulting in significantly increased plastic deformation and thus increased residual stress. On the other hand, the analysis step time is only set to 0.5 s, and the influence of the feed rate on residual stress is not significant within smaller time intervals. When the feed speed increases, the moving speed of the rolling balls in the direction of workpiece feeding accelerates, which differs from the situation with lower feed speed. In this case, there is no overlapping zone between adjacent positions of the rolling balls. In other words, more un-strengthened areas appear along the feeding direction of the rolling balls. Instead of applying ultrasonic impact to induce severe plastic deformation of the workpiece, the rolling balls directly leave at higher feed speeds, resulting in the coexistence of strengthened and un-strengthened areas. Similarly, when the feed speeds are 0.15 mm/r and 0.2 mm/r, the maximum residual stress is both 1297 MPa. However, the minimum residual stress value at 0.15 mm/r is 26.03 MPa, which is higher than the residual stress value of 24.99 MPa at 0.2 mm/r. It can be seen that when the feed speed exceeds 0.15 mm/r, the maximum residual stress tends to stabilize, indicating that beyond this limit, the maximum residual stress reaches equilibrium, forming an overall stable stress equilibrium field, with only local stress values changing. Therefore, feed rate affects the formation of residual compressive stress by altering the contact time between the rolling ball and the workpiece surface as well as the degree of plastic deformation induced by ultrasonic rolling. When the feed rate decreases, the contact time between the rolling ball and the workpiece increases, allowing the impact force and ultrasonic energy generated by the rolling process to fully act on the surface of the part. Additionally, the ultrasonic energy and kinetic energy can penetrate deeper into the material, forming a uniform plastic deformation layer, resulting in higher residual compressive stress and a deeper affected layer of residual stress. Similarly, a lower feed rate provides the part with sufficient time for elastic recovery and stress relaxation, leading to a more uniform distribution of residual compressive stress. Conversely, when the feed rate increases, the contact time between the rolling ball and the workpiece is shortened, which is insufficient to produce a uniform plastic deformation layer, leading to reduced residual compressive stress. However, an excessively low feed rate can also reduce processing efficiency. In practical engineering applications, it is crucial to select the feed rate carefully according to the actual processing needs to effectively enhance residual compressive stress.

Fig. 6
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Residual compressive stress diagram of turning process at different feed rates.

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Therefore, it can be seen that the rotational speed, feed rate, static pressure, and amplitude affect the distribution of residual stress by influencing the degree of plastic deformation. The static pressure and amplitude have a greater impact on residual stress, while the rotational speed and feed rate have a smaller impact on residual stress. However, it is also important to note that excessive amplitude can lead to surface wear and crushing, resulting in adverse effects on the surface properties of the components strengthened by ultrasonic rolling. Similarly, setting the feed speed too low will significantly prolong the ultrasonic rolling process, causing a noticeable decrease in strengthening efficiency. Therefore, to achieve higher residual compressive stress under the action of ultrasonic rolling, the amplitude and static pressure should be set as large as possible, while the rotational speed and feed speed should be adjusted to be as small as possible. Such process parameters result in greater residual compressive stress generated on the surface of the workpiece by the ultrasonic rolling process, thereby extending its service life while improving its surface properties.

Ultrasonic rolling process experiment

Materials

The experiment employed a 42CrMo steel rod that underwent quenching and fine machining, with a diameter of 30 mm and a length of 300 mm. The machining parameters for fine machining were as follows: cutting speed of 800 m/min, depth of cut of 0.2 mm, and feed rate of 0.1 mm/r. The microstructure of the rod consists of martensite.

Methods

The ultrasonic rolling experiment was conducted on the HK30F-HKD micro-energy processing equipment manufactured by Shandong Huayun Technology Co., Ltd. The ultrasonic strengthening device was fixed on the lathe tool post using bolts. Due to the large size of the ultrasonic strengthening device, a specially extended center tip was used for centering and supporting the 42CrMo steel rod. The lathe selected for the experiment was the ZAK4085D1 CNC lathe manufactured by Shanghai Kerong Equipment Co., Ltd. The ultrasonic power supply is 520 W. The 42CrMo steel rod was rotated at high speed with the assistance of a hydraulic chuck, as shown in Fig. 7. The process parameters input into the FANUC CNC system were the same as those for simulation. The micro-energy switch and coolant switch were turned on, the ultrasonic frequency is set at 28 kHz. And the amplitude was set using the micro-energy equipment control panel within the range of 7 μm to 10 μm. The static pressure was set using the pressure gauge at the end of the orange tube connected to the air compressor of the micro-energy equipment, with a range of 500 N to 800 N. The workpiece speed was set from 50r/min to 200r/min, and the feed rate was set to 0.05 mm/r, 0.1 mm/r, 0.15 mm/r, and 0.2 mm/r, respectively. The speed and feed rate were set using the CNC program of the FANUC system. A special fully synthetic lubricant was used for cooling. To compare the differences between the established turning-ultrasonic rolling simulation model and the ultrasonic rolling experiment, residual stress measurements were performed using an xstress3000 stress analyzer. Each segment of the processed area after ultrasonic rolling was divided into cubes (3D dimensions of 10 mm x 10 mm x 10 mm) on a Wire Electrical Discharge Machining (WEDM). The polished parts were polished with sandpaper ranging from 500 grit to 2000 grit, followed by fine polishing using W3.5 diamond polishing paste on a polishing machine. Corrosion was performed using a 4% nitric acid alcohol solution for 5 s. After corrosion, the parts were cleaned with anhydrous ethanol and air-dried. Once everything was prepared, residual stress measurements were conducted using the xstress3000 stress analyzer. The Xstress3000 stress analyzer is manufactured by Stresstech OY in Finland. The sin 2φ method is used to measure residual stress, with measurement angles set to 0 degrees and 45 degrees. The measurement voltage is set to 30 kV, and the measurement current is set to 7 mA. Cu target is used to irradiate the sample surface, with an irradiation area of 1 mm2. Each set of experimental parameters is measured three times to obtain an average value, reducing experimental error.

Fig. 7
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Ultrasonic rolling processing experiment diagram.

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Comparison between experimental results and simulation results

Figure 8 shows the comparison between the experimental results and simulation results of the ultrasonic rolling process. To reduce the influence of simulation errors and measurement errors, each set of experimental results is measured three times to obtain the mean and standard deviation for comparison, thereby reducing errors. The maximum relative errors between the simulated and experimental values of residual stress after ultrasonic rolling are 12.76%, 8.8%, 12.9%, and 15.06%, respectively. The experimental results indicate that residual stresses gradually decrease with increasing rotational speed and feed rate. Conversely, an increase in amplitude and static pressure leads to an upward trend in residual stresses. Similarly, experimental results also reveal the same pattern as simulated results: with increasing static pressure and amplitude, the residual stress undergoes significant variations. However, the influence of rotational speed and feed rate on residual stress is relatively minor, with smaller variations observed. However, it is noticeable that the experimental results are significantly higher than the simulation results. This disparity can be attributed to the assumption made in the simulation model, where the cutting tool and rolling ball are treated as discrete rigid bodies. In actual machining processes, the cutting tool and rolling ball experience wear and heat generation, causing the heat from the workpiece surface to transfer to the machining tools. Consequently, the simulated values are notably higher than the experimental values. Nevertheless, overall, both the experimental and simulation results exhibit a similar trend in the variation of residual stresses. This consistency demonstrates good agreement between the experimental and simulation results, indicating that the established simulation model for combined turning and ultrasonic rolling possesses high precision and accuracy. The consideration of turning conditions in the ultrasonic rolling simulation model enhances its reliability, enabling the simulation of actual ultrasonic rolling processes.

Fig. 8
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Comparison of simulation and experimental results of ultrasonic rolling under different process parameters.

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Conclusions

This study employed ABAQUS software to establish a simulation model for the turning process of 42CrMo steel, followed by simulations of ultrasonic rolling processes. Additionally, experimental ultrasonic rolling strengthening tests were conducted to verify the accuracy and reliability of the simulation model. The following conclusions were drawn:

  1. (1)

    During the simulation of turning for 42CrMo steel, the cutting forces and cutting temperatures gradually stabilized, while the chip underwent processes such as elastic deformation, plastic deformation, fracture, and separation. These findings provide a more precise simulation model for subsequent ultrasonic rolling processes.

  2. (2)

    The residual stress variation obtained from the simulation of combined turning and ultrasonic rolling closely matched the results of experimental ultrasonic rolling tests. This consistency validates the accuracy of the simulation model and offers a new approach for simulating the combined turning and ultrasonic rolling of shaft components.

  3. (3)

    To enhance the residual stress on the material surface after ultrasonic rolling, it is advisable to increase the static pressure and amplitude as much as possible while conducting ultrasonic rolling at lower rotational and feed speeds. However, excessive amplitude may damage the surface of the workpiece, necessitating the selection of appropriate process parameters for ultrasonic rolling strengthening.