Experimental study on surface roughness processed by ultrasonic surface rolling process

In order to explore the formation principle of microscopic morphology of the lower surface of USRP, USRP theoretical analysis and processing experiments are carried out. Firstly, the spatial motion trajectory of tool head by USRP is established to reveal formation principle of surface morphology. Additionally, this experiment employs a single-factor experimental design method. The influence law of process parameters and surface roughness is obtained. The results show that the workpiece speed affects the circumferential machining density of the part, and the feed speed affects the axial density of the part. Surface roughness initially decreases and subsequently increases with rising amplitudes and static pressure. It gradually rises with improvement of feed rate and rotational speed. This provides a new way to adjust the surface topography of USRP in the future.

1. Introduction 42CrMo steel is a common material for manufacturing wind power bearing rings, which has high strength, hardness, and wear resistance.However, wind turbines are often exposed to high and cold environments, and the working conditions are particularly harsh.Therefore, the surface strengthening of wind turbine-bearing ring materials has been the focus of researchers [1][2][3].A plastic processing process with a simple structure and effective structure is proposed: ultrasonic surface rolling process (USRP).It can significantly reduce surface roughness of wind-turbine bearing ring material, enhancing fatigue resistance of parts, and thus extend the service life.Scholars have conducted plenty of studies about USRP.Liu et al. [4].carried out the ultrasonic rolling test of Ti-6Al-4V material, and the results indicated a significant increase in hardness and residual stress of components after USRP treatment.Wu et al. [5] investigated the friction properties of GCr15 with varying textures after USRP processing and found that the friction reduction performance under the cross-texture shape was the best.Meng et al. [6] simulated and experimented with USRP on 5140 steel and found that USRP can prepare textures on the surface of parts.The parts processed by USRP have significantly improved the residual stress [7], microhardness [8], microstructure [9], mechanical properties [10], and so on.In summary, most of the research focuses on aluminum alloys, titanium alloys, stainless steel, etc.In contrast, 42CrMo steel is rarely studied, and even less is the surface roughness formation mechanism of 42CrMo steel processed by ultrasonic roll extrusion.USRP can significantly reduce surface roughness and reduce friction between parts, thereby greatly improving part life.This paper analyzes and experiments on surface roughness of specimen treated by USRP and provides a new idea on surface morphology mechanism of components processed by USRP.

Analysis of the spatial motion trajectory of tool head on USRP
USRP is mainly completed by tool head in the ultrasonic rolling extrusion device.Similarly, fast oscillation applied to exterior of workpiece is also realized by rolling the ball.Therefore, to study the contact process between tool head and surface of specimen, it is necessary to analyze motion relationship between tool head and the outside of specimen.It is manifest that rule of ultrasonic extrusion processing that while tool head is fed along the axle of workpiece, it hits the part's surface with high-frequency vibration in the vertical direction.The motion relationship formula is shown in Equation (1).

/ r S vf <
(1) where S is half the distance between adjacent centers of the rolling ball during USRP, v denotes speed of tool head, fr represents vibration frequency.
The theoretical microscopic peak height of ultrasonic rolling-strengthened surface is shown in Equation (2).

∋ (
where Rh is the theoretical microscopic peak height, and A stands for amplitude.t represents movement time of tool head, φ is the phase angle, R2 denotes radius of tool head, and S stands for half distance between adjacent centers of tool head on USRP.Equation ( 1) can be substituted into Equation (2), as shown in Equation (3).

∋ (
Due to ∂Rh / ∂R > 0, it can be seen that Rh is a subtraction function with respect to R, indicating that the larger the diameter of tool head is, the smaller peak of surface convex after strengthening will be.The excessive diameter of the rolling ball will cause irregular vibration of the process system.Therefore, during actual USRP process, the diameter of rolling ball should be appropriately increased under the premise of ensuring that the entire process system has sufficient rigidity.
Due to Rh / ∂S > 0, it can be seen that Rh is positively correlated with S, and S is negatively correlated with fr.Thus, Rh will decrease with the increase of fr, and the peak height of the theoretical bulge after strengthening decreases.The ultrasonic frequency vibration process of the rolling ball can successfully evade tearing of the surface material by the reinforced tool head in conventional rolling extrusion.A more ideal surface quality can be obtained.
Therefore, in this USRP experiment, the ultrasonic frequency is designated as 20 kHz, and radius of the rolling ball is 10 mm.It is clear from the above analysis that the surface of the part at high frequency and large radius will produce lower surface roughness and ideal surface quality.
When ultrasonic rolling reinforced workpiece, the reinforced surface can be treated as the outer circular surface of a regular cylinder.The polar graph system (R, θ, Z) is instituted from crosssectional direction.
When the reinforced workpiece rotates once, the number of cycles of tool head relative to workpiece vibration can be expressed as Equation ( 4), which can be decomposed into a positive integer and a fraction.
where n represents spindle speed, Δ denotes spindle speed, and ε is the spindle speed.
The vibration of tool head relative to specimen in time domain is shown in Equation ( 5).The phase offset of tool head relative to vibration of sample is shown in Equation ( 6).where Rc(t) is the vibration displacement of the rolling ball, A represents ultrasonic amplitude, fr denotes vibration frequency, t stands for vibration time, φ is phase offset, and ε is the spindle speed.In a complete ultrasonic rolling strengthening process, the feed rate and rotational speed remain unchanged.Spindle rotation number of the rolling strengthening process is shown in Equation (7).
where N stands for the number of spindle rotations, n represents rotational speed, f denotes feed rate.
The average linear velocity of the tool head relative to workpiece can be acquired from rotational speed of the workpiece, as shown in Equation ( 8).
2 60 where v is the average linear velocity, R represents radius of the rolling ball, and n denotes rotational speed.
The cylindrical workpiece is divided in radius direction of the end face circle.The number of cylindrical workpieces divided in the circumferential direction is obtained, as depicted in Equation ( 9).
where NP is the number of cylindrical workpieces divided along the circumferential direction, Y is the total segmentation length, ΔY is the length segmentation interval, R2 represents radius of the rolling ball, and Δθ denotes angle segmentation interval.Therefore, the entirety of trajectory nodes is expressed in Equation ( 10).
where Nt stands for total amount of trajectory points, N denotes the count of spindle rotations, NP represents the quantity of cylindrical workpieces divided along the circumferential direction, n denotes rotational speed, R2 stands for radius of the rolling ball, and ΔY is the length segmentation interval.
In the strengthening process, the rolling ball does the feed movement parallel to the outer axis of the workpiece while rolling freely on the outer circular surface.Because the ultrasonic frequency vibration of the luffing rod is transmitted to the rolling ball, the rolling ball is subjected to highfrequency simple harmonic vibration along the circumferential direction at a relatively stable frequency.According to the above segmentation method, the trajectory equation of the rolling ball on the three coordinate axes in the polar coordinates is shown as Equation (11). 2 ( ) s i n () where Rc(j) is the vibration displacement of the rolling ball relative to specimen, A denotes vibration amplitude, fr represents vibration frequency, j stands for natural number, which can be equal to 0, 1, 2..., Nt, ΔY is the length segmentation interval, v is the average linear velocity, φ is the phase offset, θc(j) is the trajectory displacement along the θ axis, Y is the total segmentation length, Zc(j) is the trajectory displacement along the Z axis, f is the feed rate.
Equation ( 11) is the path of tool head with sinusoidal movement along the surface of the reinforced material and the trajectory of the feed movement under the action of the feed force.The coupling form of the three equations can represent the three-dimensional trajectory of the rolling ball in whole process.
Similarly, if Equation (11) can be converted to the k Spatial reference system, the trajectory equation of the ultrasonic rolling ball on k-th section can be expressed as Equation (12).
where Rt(i, k) represents vibration movement of the kth cross section after conversion along the R axis, A is the vibration amplitude, C is the replacing value in the discrete equation of rolling ball relative to workpiece vibration, k is the constant, i is the natural number, which can be equal to 0, 1, 2 ..., NP is the number of cylindrical workpieces divided along the circumferential direction, and φ is the phase offset.θt(i, k) is the feeding displacement of the kth cross section after conversion along the θ axis, Δθ is the length segmentation interval along the θ axis, Zt(i, k) is the feeding displacement of the kth cross section after conversion along the Z axis, ΔZ is the length segmentation interval along the Z axis.
Equation ( 13) illustrates the calculation of C.
where C is the replacing value in the discrete equation of rolling ball relative to workpiece vibration, fr is the vibration frequency, ΔY is the length segmentation interval, v is the average linear velocity, n is the rotational speed, NP is the number of cylindrical workpieces divided along the circumferential direction.
The calculation of ΔZ is shown in Equation ( 14).
where ΔZ is the length segmentation interval along the Z axis, f is the feed rate, ΔY is the length segmentation interval, and Y is the total segmentation length.
The above polar equation is converted into an equation in a Cartesian coordinate system (Y, Z, R).

The actual trajectory equation of the rolling ball is shown in Equation
where Rt(i, k) is the vibration displacement of the kth cross-section in Cartesian coordinates, A is the vibration amplitude, C is the re placing value in the discre te equation of rolling ball re lative to workpiece vibration, k is the constant, i is the natural number, which can be equal to 0, 1, 2 ..., NP is the number of cylindrical workpieces divided along the circumferential direction, φ is the phase offset.Yt(i, k) is the feeding displacement of the kth cross section after conversion in Cartesian coordinates, and ΔY is the length segmentation interval.Zt(i, k) is the feeding displacement of the kth cross section after conversion in Cartesian coordinates, and ΔZ is the length segmentation interval along the Z axis.
According to Equation (15), the surface roughness under USRP treatment can be calculated.When the feed rate of the rolling ball is 30 mm/min, and rotational speed of reinforced workpiece is 100 revolutions per minute, the processing of parts is very intensive.There are more machining areas of the same length.While the rotational speed is 600 r/min with a feed rate of 60 mm/min, trajectory of the rolling ball is a little sparser.There is much less machining area per unit length.The density of ultrasonic rolling strengthening is evidently influenced by both the feed rate of the rolling ball and the rotational speed of the reinforced workpiece.It can increase the machining density of the reinforced test piece by lowering the feed rate along the busbar direction.Diminishing the speed of the reinforced workpiece can increase the impact times of the rolling ball turn, thereby improving the processing density.However, the decrease in feed speed and workpiece speed will lead to too low processing efficiency, so the processing parameters should be selected by considering the strengthening effect and processing efficiency in USRP.

Materials and methods
This experiment uses quenched and turned 42CrMo steel bar stock.The initial roughness measures 1.1 μm, with an initial hardness of 630 HV.The USRP experiment is conducted using the ZAK4085D1 CNC lathe.This experiment employs a single-factor experimental design method.The USRP process parameters are outlined in Table 1, while the USRP experimental setup is illustrated in Figure 1.Table 1.Single factor experiment.The ultrasonic generator is activated, with a frequency of 20 kHz, adjusting to amplitude value that needs to be set.At the same time, the machine speed and feed rate are adjusted in Table 1, and static pressure is slowly applied.The impact device has a ruler at the end of it.Its static pressure principle is 1 mm, equivalent to 50 N, and each section length is processed by oil-cooled.

Results
The experimental results depicted in Figure 2 illustrate that when the static pressure is 300 N, the surface roughness is the lowest, and its value is 0.483 μm.However, as the spindle speed increases, surface roughness is higher, and the minimum value of 0.406 μm occurs when the spindle speed is 100 r/min.While the feed rate continues to increase, so does the surface roughness.This is consistent with the theoretical analysis part of the first section.When the feed rate is reduced, the processing density of the part in the axial direction can be increased, and the surface of the part can be rolled evenly.When the speed is reduced, the number of rolling times in the circumferential direction can be increased so that the processing density is greatly increased.As the amplitude increases, there is an observed tendency for surface roughness to initially decrease, followed by an increase.Therefore, in order to obtain better surface quality, the rotational speed and feed rate should be lower.

Conclusions
In this study, the formation mechanism of USRP surface micromorphology is studied theoretically and experimentally.The study explores the influence of USRP process parameters on surface roughness and draws the following conclusions: (1) The motion state of the rolling ball under USRP in space is analyzed, which found that the workpiece speed affects the circumferential machining density of the part.In contrast, the feed speed affects the axial machining density of the part.
(2) USRP experiments are carried out.The research revealed that surface roughness exhibits a pattern of initially decreasing and then increasing with increasing static pressure and amplitude, while it consistently rises with higher feed rates and spindle speeds. 2

Figure 1 .
Figure 1.USRP experiments.A total of 20 sections are processed, each section is 5 mm long with a 2 mm interval between them.The ultrasonic generator is activated, with a frequency of 20 kHz, adjusting to amplitude value that needs to be set.At the same time, the machine speed and feed rate are adjusted in Table1, and static pressure is slowly applied.The impact device has a ruler at the end of it.Its static pressure principle is 1 mm, equivalent to 50 N, and each section length is processed by oil-cooled.

Figure 2 .
Figure 2. Different process parameters in Ra.(a) Different static pressures in Ra; (b) Different spindle speed in Ra; (c) Different feed rates in Ra; (d) Different amplitudes in Ra.