Study on flow field and convective heat transfer characteristics in grinding zone of large spiral angle flow disturbance grooved wheel

In view of the high specific removal energy, high heat generation rate, low heat transfer efficiency, and easy-to-produce local high-temperature and grinding burns, new macro-structured grinding wheel forms were proposed, namely, large spiral angle grooved grinding wheels (LSG-GW, β>85°) and large spiral angle flow disturbance grooved wheels (LSDG-GW). Considering the influence of wheel parameters, groove parameters, and process parameters, an analytical model of the airflow field in the wedge area and contact area of LSG-GW was established. Analytical model of gas–liquid two-phase flow field and theoretical model of convective heat transfer coefficient distribution in heat transfer channels were established. The results showed that increasing the groove width, groove depth, and the spiral angle can reduce the pressure of the flow field in the air barrier layer and make it easier for the grinding fluid to enter the grinding contact area. The LSDG-GW further reduces the grinding fluid back flow and side flow intensity, proving that the flow disturbance structure can bring in more grinding fluid into the grinding contact area. A theoretical model for the distribution of convective heat transfer coefficient in the grinding contact area was derived, and the analysis results proved that the flow disturbance structure can significantly improve the convective heat transfer coefficient in the grinding contact area. The LSDG-GW, as a new macro-surface-structured grinding wheel, has a very promising application in the high-efficiency and high-precision grinding process of difficult-to-machine alloy materials.


Introduction
High-performance alloys have excellent characteristics such as high-temperature resistance, wear resistance, and corrosion resistance and are strategically important materials for key components to achieve high service performance under various extreme operating conditions.Among the various machining methods, precision grinding is an important method for forming high-quality functional surfaces of highperformance alloys [1,2].However, due to the grinding process' extraordinarily high specific removal energy and heat generation rate, in the face of the high mechanical properties of high-performance alloys, the low heat transfer efficiency in the grinding arc of conventional ordinary grinding wheels makes it very easy to generate local high temperatures that cause thermal damage to the surface of the workpiece [3,4].In consequence, this makes it challenging to carry out a high-quality and effective grinding procedure.Therefore, exploring the enhancement mechanism of heat transfer in the grinding arc is the core scientific problem to realize the high-quality surface grinding process for high-performance alloys.
During the grinding process, the grinding fluid is an important means of dissipating heat from the grinding arc area.The characteristics of airflow around the grinding wheel is another topic that cannot be avoided when the grinding fluid breaks through the airflow barrier to enter the grinding arc for cooling and lubrication [5][6][7][8].The flow field and convective heat transfer characteristics in the grinding area have thus been the subject of extensive theoretical and experimental research by academics both domestically and internationally.In terms of the flow field of the air barrier layer, Li [9] established a model of the effective grinding fluid flow field of coarse-grained grinding wheels.The air barrier layer flow field model and the fluid volume multiphase flow grinding fluid flow field model were established with porosity as the key parameter.The results show that the grinding wheel speed, the flow field characteristics of the air barrier layer, the grinding fluid jet velocity, and the minimum clearance of the grinding arc have a large influence on the effective flow rate in the grinding arc.Xiao [10] conducted an experimental study on the simulation of flow field and grinding performance in the grinding zone of ordered micro-grooved structured grinding wheels.The research results show that the micro-grooved structure can transport more grinding fluid into the grinding arc area, and the grinding fluid that has finished cooling is quickly carried out by the micro-grooved structure, thus promoting the flow of grinding fluid inside the grinding arc area and increasing the effective flow rate of the grinding area.The grinding area's lubrication and cooling capabilities are further boosted, and the grinding wheel's ability to hold chips is increased.It increases effective grinding fluid flow while extending grinding wheel life.In terms of convective heat transfer in the grinding area, Jin [11] conducted an experimental study on the grinding temperature under slow-feed deep-cut grinding conditions.The distribution model of convective heat transfer coefficient of grinding fluid under relevant grinding conditions was established.The results of the research show that the speed of the grinding wheel is the most important factor affecting the coefficient of heat transfer by convection of the grinding fluid on the surface of the piece and proposes an optimization strategy to achieve effective convective heat transfer with large grinding arc length.That is, CBN grinding wheels and oil-based grinding fluids are used for the grinding process.KM [12] calculated the distribution of convective heat transfer coefficients on grinding surfaces using a semi-empirical formula for cooling jets.The finite difference method (FDM) was used to simulate the temperature distribution of the shallow ground workpiece, which was further verified by experiments.The findings indicate that the influence of material removal rate must be taken into account in simulation to minimize estimation errors and that the application of grinding fluid directly onto the contact area is vital for efficient cooling.
The above studies show that surface-structured grinding wheels can bring grinding fluid into the grinding arc [13] and have unique advantages in enhancing the heat transfer performance of the grinding arc, which is a current research hotspot.Among the many types of grinding wheel surface structure, the LSG-GW has a "clear-division" contact zone and heat exchange zone.As shown in Fig. 1, the energy input during the grinding process is converted into heat in the abrasive/workpiece contact area, and the heat exchange area has a stronger grinding fluid transport capacity, thus effectively enhancing the heat exchange performance of the grinding arc area [14][15][16].In addition, the rotation of the grinding wheel will drive the lateral translation of the heat transfer zone and contact zone in the grinding arc, which helps to achieve complete cooling of the grinding fluid on the grinding surface.The preliminary findings of related studies have confirmed [17,18] that LSG-GW can significantly reduce grinding forces and grinding temperatures, which can multiply the machining efficiency and are a structured grinding wheel type with potential engineering applications.
The key to improving the heat transfer capacity in the grinding arc of LSG-GW depends on the performance of the grinding fluid transport in the heat transfer channel.Before the coolant enters the heat exchange system, it must overcome the resistance posed by the airflow field surrounding the grinding wheel and the return flow field, so the characteristics of the air flow field in the grinding area have an important influence on the heat exchange capacity of the grinding arc.The grinding fluid in the heat exchange zone of the LSG-GW exerts convective heat exchange on the grinding surface to carry away the heat generated in the contact area.However, the calculation of convective heat transfer coefficient, which can characterize the strength of heat transfer capacity in the grinding arc, has been the focus and difficulty of research [19][20][21].In addition, in terms of heat transfer performance, the latest research findings show that when the grinding fluid is ejected from the nozzle and continues to flow by inertia, the speed is gradually reduced.The flow of grinding fluid in the heat transfer channel in the grinding arc area is a non-dynamic laminar flow.Therefore, it is difficult to effectively improve the heat transfer performance in the grinding arc area by simply optimizing the grooved size [22].
Based on the above analysis, this paper proposes to prepare a disturbance structure at the bottom of the macroscopic spiral grooved of the grinding wheel to form a new type of grinding wheel structure with a disturbance grooved.As shown in Fig. 2, for fluid simulation analysis of the flow field factors affecting the heat transfer performance in the grinding arc, and based on the results of gas-liquid twophase flow field analysis, the heat transfer channel grinding liquid convective heat transfer coefficient distribution model reveals the enhancement mechanism of heat transfer performance in the grinding arc area by heat transfer channels and disturbance structures in the channels.It is important to reduce thermal damage on the grinding surface and promote the grinding process of LSDG-GW to achieve high-quality surface of high-performance alloy.

Simulation model establishment
The air velocity and pressure within the common wheel grinding area exhibit a steady and consistent behavior that remains unchanged over time, so steady-state analysis is often used in the study.For the LSG-GW high-speed rotation process, its surrounding airflow movement is transient changes.The velocity and pressure of the ground air field at any moment and position are not stable values.Therefore, the transient analysis of the airflow field distribution when the grinding wheel rotates to different positions should be carried out.Firstly, a three-dimensional geometric model of a LSG-GW is established, as shown in Fig. 3. Considering that the rotating wall of a LSG-GW is an irregular geometry, the simulation is carried out using the multiple reference system (MRF) method.This method allows to obtain the instantaneous flow field when a large helix angle grooved grinding wheel is rotated to a specific position.Then, by rotating the LSG-GW model on the workpiece surface by 1/3, 2/3, and 1 turn, respectively, the pressure and velocity distribution of airflow in the grinding wedge can be indirectly simulated when the LSG-GW is in different transient positions.
The continuity equation of the multiple reference system model is The momentum equation of the multiple reference system model is The air flow around the grinding wheel is mainly driven by the high-speed rotation of the grinding wheel, coupled with the spiral groove on the air.The air flow around the grinding wheel is mainly driven by the high-speed rotation of the grinding wheel plus the disturbance of the air by the spiral grooves, so the air flow field in the grinding area is a kind of complex flow process characterized by strong rotation.Calculation of flow field is using the RNG k-ε turbulence model.The turbulent kinetic energy k and the turbulent dissipation rate ε are two fundamental unknown quantities.The corresponding transport equation is

Analysis of the pressure characteristics of the airflow field in the grinding zone
In order to investigate the air pressure distribution in the grinding zone of LSG-GW with different spiral angles, we used fixed spiral grooved width of 3 mm, depth of 4 mm, and wheel speed of 60 m/s.Rotation of LSG-GW with spiral angles of 86.36°, 88.18°, and 88.78° to 120°, 240°, and 360° (i.e., initial position) is relative to the initial position of the model, respectively, and simulation of grinding wheels.The cloud map of pressure distribution on its workpiece surface is viewed and organized in Table 1.
As seen in Table 1, the pressure distribution clouds of the airflow field in the grinding zone of the LSG-GW have certain similarities, showing that there is a positive pressure zone at the entrance of the wedge and ( 2) a negative pressure zone at the exit of the wedge.Near the smallest distance, the pressure difference is the most noticeable.Away from the place with the smallest gap, the pressure progressively increases to atmospheric pressure.The closer to the minimum gap, the greater the absolute value of positive and negative pressure.
The peak positive and negative pressures exist near the minimum gap.However, there are also several differences in their cloud maps of the pressure distribution of the grinding airflow field.The larger the spiral angle, the smaller the absolute value of positive and negative pressure peaks.Obviously, the lower the pressure of the airflow field in the grinding area, the better it is for the grinding fluid to break through the airflow barrier and enter the grinding arc for cooling and lubrication.If we consider the airflow field in the grinding area alone, we can get the following conclusions.The larger the spiral angle is, the less the airflow will obstruct the grinding fluid.The efficiency of heat transfer in the grinding arc area increases with the conductivity of the grooved surface.The contact area between the spiral grooved grinding wheel surface and the workpiece surface is reduced per unit time as a result of the increased spiral angle, though.It will cause the surface roughness of the ground workpiece to rise.Therefore, the impact of the spiral grooved wheel contact area and the cooling lubrication of the grinding fluid on the quality of the grinding process should be taken into consideration in the actual grinding process.The airflow field in the grinding area of LSG-GW is transient, and the reason for the transient change is that the spiral grooved constantly changes position as the grinding wheel rotates.And after analysis, it has been made clear how the spiral angle and the airflow field's pressure interact in the grinding area; i.e., the larger the spiral angle, the lower the pressure of the airflow field in the grinding zone.Therefore, in order to reduce the complexity of the model, while improving the accuracy of the analysis and making the research work more focused, the transverse motion of the heat exchange channel is not considered for the time being.At this time, the spiral grooved grinding wheel will be retired to a multi-ring grooved grinding wheel, whose grinding air velocity and pressure characteristics do not change with time.Steady-state simulation was used to investigate the effect of grooved depth and width on the grinding airflow field.Ring grooved grinding wheels can be thought of as special spiral grooved grinding wheels with a helix angle of 90° (or zero thread lift angle).Combined with Fig. 3, the spiral grooved grinding wheels with spiral angles of 86.36°, 88.18°, and 88.78° are simplified to single-ring, double-ring, and triple-ring grooved grinding wheels, respectively.The number of ring grooved and the size of the grooved are independent parameters that affect the characteristics of the grinding airflow field.Multiple rings are simply multiple replications of the effect of a single ring on airflow characteristics.Therefore, to avoid duplicating work, this part simulates and examines the impact of grooved depth and width variation on the pressure characteristics of the grinding airflow field using a single-ring grooved grinding wheel model.
The effect of grooved size on the pressure distribution in the grinding zone was investigated by single-factor analysis, as shown in Fig. 4.
From Fig. 5a, it can be seen that as the width of the trench increases, the maximum value of the pressure gradually  decreases, the absolute value of the minimum pressure also gradually decreases, and the difference between the positive and negative peak pressure decreases.It should be noted that the width of the groove should not be increased indefinitely; otherwise, the grinding quality will be reduced.This is because the larger the width of the grooved, the more air it can conduct, reducing the collection of air at the entrance of the wedge, which is reflected in the reduction of the peak positive pressure.It is simpler for the air revolving with the grinding wheel to reach the wedge area's exit through the grooves, and the air at the wedge area's departure is promptly refilled, which shows that the absolute value of the peak negative pressure is reduced.Therefore, the larger the width of the grooved, the smaller the absolute value of the positive and negative pressure peak in the grinding wedge.
The smaller air pressure in the wedge area facilitates the grinding fluid to break through the airflow barrier around the grinding wheel and reach the grinding arc area, thus providing effective cooling and lubrication.At the same time, when the groove width increases, the contact area of the grinding wheel surface decreases, and airflow restriction across the minimum gap decreases.This is the same principle as increasing the angle of the spiral brings about a weakening of the airflow field.From Fig. 5b, it can be seen that the presence of grooved on the grinding wheel surface greatly reduces the peak positive and negative pressure of the airflow field in the wedge area compared with the ordinary grinding wheel without grooved, and the greater the depth of the grooved, the smaller the absolute value of the peak positive and negative pressure of the airflow field in the wedge area.

Analysis of the velocity characteristics of the airflow field in the grinding zone
The MRF simulation method was used to obtain the vector diagram of the velocity distribution of the airflow field in the grinding area when the LSG-GW with different spiral angles rotated to different positions, which is organized as shown in Table 2.The spiral grooved width is also set to 3 mm, the depth is 4 mm, and the grinding wheel speed is 60 m/s.From Table 2, it can be seen that the maximum value of airflow velocity in the grinding zone of LSG-GW occurs near the minimum gap; i.e., the high-speed rotating grinding wheel at the smallest spacing has the most impact on the air in the grinding area.However, their velocity distribution vector diagrams of the grinding airflow field also differ in several ways.The larger the spiral angle, the lower the workpiece surface airflow velocity.This is because the spiral grooved on the grinding wheel surface is equivalent to increasing the minimum clearance between the grinding wheel and the workpiece, and the larger the spiral angle is, the larger the minimum clearance is.The minimum clearance rises, the air on the workpiece's surface that is impacted by the high-speed rotating grinding wheel will become smaller, indicating that the airflow speed is decreasing, and the airflow speed near the wall of the grinding wheel is roughly equal to the speed of the grinding wheel.At the same time, the minimum clearance between the grinding wheel and the workpiece increases, the total amount of air that can be conducted per unit time increases; i.e., the air flow between the entrance and the exit of the grinding wedge increases, which is also conducive to increasing the effective flow of grinding fluid, thus improving the heat transfer performance of the grinding arc.
In order to study the inlet return flow in the wedge area, a spiral grooved wheel with a spiral angle of 86.36°, which   areas, respectively, which make its two-dimensional velocity vector diagram, as shown in Fig. 6.
As can be seen in Fig. 6, no return flow occurs within a distance of one grinding wheel radius around the minimum gap at the entrance of the wedge, both in the contact and non-contact zones.The return flow phenomena appear away from the minimal gap, although the strength is not very strong.Therefore, by placing the grinding fluid nozzle within one wheel radius of the minimum clearance, the effect of the return flow of air from the grinding zone on the entry of the grinding fluid into the grinding arc is considered to be negligible.
In order to further study the air flow direction in the grinding area, a Z = 0 plane airflow tracing diagram was made as shown in Fig. 7.
As can be seen from Fig. 7, a significant portion of the air flows in the direction of the grinding wheel width before the minimum clearance in the grinding arc is reached.And the air flowing to the right side of the grinding wheel in the diagram is obviously more; that is, the flow direction is consistent with the direction of rotation of the helix.This indicates that the spiral grooved throws the air out of the grinding zone to both sides of the grinding wheel, suppressing the return flow phenomenon.In addition, according to the air velocity vector diagram of the workpiece surface in Table 2, it can also be concluded that the air flow on both sides of the grinding wheel is a non-negligible part of the air flow in the grinding zone.It is also an important reason why there is no significant return flow within the wedge.

Experimental study of the flow field in the grinding area
On the basis of the simulation study, the velocity measurement experiments of the flow field of the air barrier layer and the return flow field in the grinding area are carried out to verify the feasibility and validity of the created flow analysis model.
The experimental platform used in this experiment is M7130A horizontal axis moment table surface grinder.The motor parameters are shown in Table 3.
White corundum grinding wheels are used, with a quantity for 4. Of these, three are LSG-GWs; one is ordinary grinding wheel.All grooved wheels have a groove depth of 5 mm.For convenience of description, the grinding  Combined with the demand for airflow field measurement in the grinding area, SW6086 thermal anemometer was selected for the wind speed detection device.The anemometer adopts a hot-wire sensor, which is suitable for high-precision wind speed measurement, and the technical parameters are shown in Table 4.
In order to study the effect of spiral grooves on the airflow velocity in the grinding area, LSG-GW with different structural parameters and ordinary grinding wheels with the same diameter and width were prepared.Measurement of return flow velocity at the inlet of the wedge and wind velocity at the outlet of the wedge with the SW6086 thermal anemometer.
Make the grinding wheel and table surface fit and leave a very small gap (≤ 0.5 mm) and the experiment clockwise rotation of the grinding wheel and table stationary, as shown in Fig. 9.
At the entrance of the wedge area, keep the wind speed probe always in the center section of the grinding wheel.
Starting at 40 mm from the minimum clearance, gradually moving away from the minimum clearance, measurements are taken and recorded every 5 mm, ending at 160 mm from the minimum clearance.Obtain the relationship between return flow velocity and minimum gap distance.Adjust the grinding wheel speed, and study the relationship between the return flow velocity and the grinding wheel speed.At the exit of the wedge area, the wind speed probe was fixed at a distance of 40 mm from the minimum clearance, and the wind speed change of the LSG-GW, and the ordinary grinding wheel with different structural parameters was measured and recorded at this position.The experimental conditions and experimental parameters are shown in Table 5.
Considering the special characteristics of transient changes in the airflow field in the grinding area of LSG-GW, all measurement positions in the experimental program were recorded five times, and the average value was taken as the airflow velocity at that position.Measurements were taken to record the magnitude of the inlet airflow velocity in the wedge area of grinding wheels 1, 2, 3, and 4, and all the data were organized into a point and line plot, as shown in Fig. 10.
As can be seen from Fig. 10, in the wedge area, the air velocity decreases from 40 to 100 mm from the inlet to the minimum gap.The inflection point occurs at 100 mm, after which the air velocity increases and then continues to decrease.In the interval of 40 mm ~ 100 mm, the direction   of air velocity is the same as the rotation direction of the grinding wheel, i.e., positive airflow.The airflow velocity in the wedge area of the No. 2 wheel in this interval is the highest, followed by the No. 1 and No. 3 wheels, and the No. 4 wheel is the smallest.This indicates that the grooves are holding more air to reach the entrance of the wedge.In close proximity to the minimum gap, the airflow speed of the LSG-GW is large, which is conducive to the use of airflow to promote the smooth grinding fluid into the grinding arc to complete the cooling effect.In the 100 mm position, an airflow velocity inflection point appeared.Then the airflow velocity continues to reduce.The directions of the airflow and the rotation of the grinding wheel are opposite which is the return flow.The airflow velocities in the wedge area of the four sets of grinding wheels in this interval do not differ much and are all at a low level.This indicates that the intensity of the return flow at the entrance of the wedge area is low, and a large amount of air flows to both sides of the grinding wheel.It does not show the strong return flow phenomenon in the two-dimensional airflow field analysis model, which is in good agreement with the established three-dimensional flow field analysis results in the grinding area.From Table 6, comparing grinding wheels 1, 2, and 4, the greater the width of the spiral groove, the greater the velocity of the airflow at the exit of the wedge area.Comparing grinding wheels 2, 3, and 4, the greater the spiral angle, the greater the exit air velocity in the wedge area.The outlet air velocity in the wedge area of LSG-GW is significantly higher than that of an ordinary wheel without grooves.It shows that the grooves have a strong conductive effect on the air in the grinding area.The inlet air to the wedge area is more likely to reach the outlet of the wedge area through the grooves with larger gaps, which results in a weaker return flow in the grinding area and a lower intensity of the airflow field.This also facilitates the conduction of the grinding fluid.

Simulation model building
When analyzing the gas-liquid two-phase flow field in the grinding arc, the air and grinding fluid are insoluble in each other, so the VOF model is used.In order to study the effect of the flow structure on the flow state and effective flow rate of the grinding fluid which is in the grinding arc area heat transfer channel, the spoiler structure was further designed.Create a cylindrical spoiler structure with a base diameter of 2 mm, a height of 2 mm, and a number of 50 uniformly distributed in the bottom of the grooved of a   Figure 12 shows the three-dimensional geometric model of the gas-liquid two-phase flow field in LSDG-GW.The grinding fluid ejected by the nozzle enters the grinding arc as the grinding wheel rotates for cooling, lubrication, and chip cleaning during the grinding operation, so the grinding fluid nozzle is placed at the entrance of the wedge area.The width of the grinding fluid nozzle is equal to the width of the grinding wheel.This setting is mainly to avoid underestimating the effect of the spiral grooved on grinding fluid conduction due to insufficient fluid supply.

Analysis of grinding fluid flow state
The key structural parameters of LSG-GW include spiral angle, grooved width, and grooved depth, which are independent of each other in their influence on the flow state of grinding fluid.Therefore, the simulation conditions such as grooved width 3 mm, grooved depth 4 mm, and grinding process parameters were kept consistent by using the single-factor analysis method.The study is done on how spiral angle affects the flow status of grinding fluid, with fixed grinding wheel circumferential speed of 30 m/s and grinding fluid injection speed of 1 m/s, using the middle injection, and obtained rendering of the volume fraction distribution of grinding fluid in the gas-liquid two-phase flow field in the grinding arc of LSG-GW with different spiral angles, as shown in Fig. 13.
As a comparison, a rendering of the volume fraction distribution of the fluteless plain wheel grinding fluid for the same grinding process parameters was obtained, as shown in Fig. 14.Figures 13 and 14 show that in order to break through the airflow barrier, grinding fluid is released from the nozzle at a specific speed, combined with the surrounding air and directed at three different locations.First is to enter the grinding arc area to complete the cooling and lubricating effect on the workpiece.Second, the airflow in the grinding area is thrown to both sides of the grinding wheel due to the side drain effect.Third, the backflow of grinding fluid is caused by not breaking the airflow barrier.The side drainage and reflux of grinding fluid will reduce the effective utilization rate of grinding fluid, so efforts should be made to improve the flow of grinding fluid into the grinding arc.In order to observe the flow of grinding fluid inside the grinding arc area, the tangential method is used in the grinding wheel width direction.Five sections with Z = −15 mm, Z = −7.5 mm, Z = 0, Z = 7.5 mm, and Z = 15 mm are created, respectively.Through these sections, the minimum gap and the volume fraction distribution of the grinding fluid in the heat exchange channel can be clearly observed, as shown in Fig. 15.
From Fig. 15, it can be seen that after the grinding fluid breaks through the airflow around the grinding wheel and enters the grinding arc, it exists in the minimum gap between the grinding wheel and the workpiece and in the heat exchange channel.To complete convective heat transfer to the workpiece surface, the heat exchange channel can move a lot of grinding fluid into the grinding arc area.Ordinary grinding wheel wedge area entrance has some reflux.No significant backflow was found in the wedge area of the LSG-GW.The main reason is the relatively low intensity of the airflow field in the latter grinding arc area, and the location of the grinding fluid nozzle is chosen in an area largely unaffected by the return flow.Therefore, there is no backflow caused by the grinding fluid failing to break through the airflow barrier on the grinding wheel surface.
The grinding fluid may not all fit through the narrowest gap or heat exchange channel, even if there is no reflux.The reason is that the grinding fluid will be affected by the airflow leakage around the grinding wheel and flow to both sides of the grinding wheel.In order to study the flow pattern of grinding fluid in the width direction of the grinding wheel, the volume distribution plot of grinding fluid in the X = 0 plane (minimum clearance cross-section) for LSG-GW with different spiral angles and ordinary grinding wheels were plotted separately, as shown in Fig. 16.
As can be seen in Fig. 16, the grinding fluid exists in two parts.One exists within the gap formed by the grinding wheel and the workpiece, including the minimum gap and the heat exchange channel, which is for the effective flow.The second is on both sides of the grinding wheel, and this part of the grinding fluid fails to enter the grinding arc area for cooling, which is an ineffective flow.As the spiral angle increases, the contact area between the grinding wheel and the workpiece decreases, the heat dissipation area of the grinding surface increases, the effective flow into the heat exchange channel of the grinding arc increases, and the grinding fluid is distributed more evenly in the direction of the grinding wheel width.Moreover, the spiral grooved constantly changes position as the grinding wheel rotates; i.e., the heat exchange channel moves across the width of the grinding wheel.This will result in the grinding fluid completely cooling the grinding surface.The effective flow rate of conventional grinding wheels, in contrast, is plainly much lower.Firstly is that there is no heat exchange channel for the transport of grinding fluid plus.Secondly, a large amount of grinding fluid is affected by the highpressure airflow field and fails to enter the grinding arc area and is thrown out of the sides of the grinding wheel.
After the analysis of the effect of grooved depth on the number of grinding fluid integrals, it is known that with the increase of grooved depth, the flow rate of transportable grinding fluid in the heat exchange channel gradually increases.Further investigation reveals that the grinding fluid actually adheres to the bottom of the groove or the surface of the grinding wheel as opposed to the workpiece surface as it enters the grinding arc.This results in some of the grinding fluid entering the grinding arc but not actually cooling the workpiece.Furthermore, after the depth of the grooved increases to a certain level, the driving ability of the bottom of the grooved to the grinding fluid gradually decreases.This results in a low flow rate of grinding fluid on the workpiece surface in the non-contact area, and the convective heat transfer capability of the grinding fluid to the workpiece surface is not strong.For this purpose, disturbance structure was prepared at the bottom of the grooved of the wheel with a helix angle of 86.36°, a grooved width of 3 mm, and a grooved depth of 4 mm to form a large helix angle disturbance grooved grinding wheel.The disturbance structures are evenly distributed.
Figure 17 shows the cloud plot of the grinding fluid integration number in LSDG-GW with a disturbed flow structure.From the diagram, it can be seen that the disturbance structure has a driving effect on the transport of grinding fluid in the heat exchange channel.The flow disturbance structure quickly transports the grinding fluid after it has finished cooling, encouraging the flow of grinding fluid inside the grinding arc, increasing the effective grinding fluid flow inside the grinding arc, and aiding in improving the grinding arc's capacity for heat transfer.In order to further clarify the flow trajectory and velocity of the grinding fluid inside the grinding arc area under the effect of the disturbed flow structure, a two-dimensional velocity vector diagram of the grinding fluid was made, as shown in Fig. 18.
Figure 18a and b show the trajectory of the grinding fluid in the heat transfer channel without/with the action of the disturbance structure, respectively.The diagram shows that when there is no disturbed flow structure, the trajectory of the grinding fluid in the heat exchange channel is regular and steady.The parts flow in layers, and there is no lateral mixing.Under the action of the disturbance structure, the original motion state is disturbed, and irregular and unstable trajectory of the grinding liquid in the heat exchange channel appears.The grinding fluid flow speed is greatly increased, and a high turbulent kinetic energy flow field is formed in the heat exchange channel.

Analysis of factors influencing the effective flow rate of grinding fluid
The effective grinding fluid flow in the grinding zone of LSG-GW includes the grinding fluid flow through both the minimum gap and the heat exchange channel.The circumferential speed of the grinding wheel is 30 m/s, and the injection speed of the grinding fluid is 1 m/s.Using the middle injection, the effective flow of the grinding arc area of the LSG-GW with different structural parameters was obtained as shown in Table 7, Table 8, and Table 9.From Table 7, Table 8, and Table 9, it can be seen that the effective flow and effective flow rate of grinding fluid in the grinding arc area increased to different degrees as the spiral angle, grooved width, and depth increased.However, the grinding wheel construction characteristics significantly affect the augmentation of the effective flow rate of grinding fluid, with the spiral angle having the biggest impact and the grooved width and depth having a relatively minor impact.This is because the increase in effective grinding fluid flow in the grinding arc of LSG-GW is due to the increased flow of grinding fluid in the heat transfer channel.While the spiral angle changes, the contact area of the grinding wheel surface changes most obviously, and the number of heat exchange channels increases, thus significantly increasing the effective flow of grinding fluid in the grinding arc area.
With a wheel circumferential speed of 30 m/s and a nondisturbing structure, the effective flow rate of the grinding fluid and the effective flow rate with the grinding fluid jet speed at different nozzle positions are shown in Fig. 19.
From Fig. 19, it can be seen that as the grinding fluid jet speed increases, the effective flow rate of grinding fluid at all three jet positions gradually increases.However, at a jet speed of 1.5 m/s, the effective flow rate of grinding fluid  decreases instead.The reason for this phenomenon is that by increasing the grinding fluid jet speed, the supply flow increases more relative to the effective flow.According to the definition of effective flow rate, the effective flow rate will show a decreasing trend.This demonstrates that raising the supply of grinding fluid flow rate aids in improving the effective flow rate, but after growing to a certain point, the waste of grinding fluid increases, which is in direct opposition to the idea of green machining.At the same time, different nozzle positions have a great influence on the effective flow rate of grinding fluid and the effective rate, with the middle jet having the best effect, the upper jet having the second best effect, and the lower jet having the worst effect.This is because the middle and upper jets are used, on the one hand, the influence of the return flow from the grinding area on the grinding fluid jet is effectively avoided, and on the other hand, it is easier for the grinding fluid to enter the grinding arc area by the airflow in the direction of grinding wheel rotation.When the lower jet is employed, the effective flow of grinding fluid and the effective flow rate are both at their lowest, and the air resistance required to enter the grinding arc is at its highest.
Figure 20 shows the effective flow and effective flow rate fluctuation curves for various grinding wheel circumferential velocities when the nozzle is positioned in the middle of the jet and there are no obstruction structures.From Fig. 20a, it can be seen that the larger the circumferential speed of the grinding wheel, the lower the effective flow rate in the grinding arc.This is because the strength of the airflow barrier on the surface of the grinding wheel increases with the increase of the circumferential speed of the grinding wheel, and the strength of the return flow field at the entrance of the wedge zone also increases, which makes it difficult for the grinding fluid to enter the grinding arc zone and reduces the effective flow.At the same time, the increase of grinding fluid jet speed helps grinding fluid break through the airflow barrier on the grinding wheel surface, which is expressed as an increase of effective flow.From Fig. 20b, it can be seen that the effective flow rate of grinding fluid shows the same trend of increasing and then decreasing as in Fig. 20b.This phenomenon shows that in order to analyze the cooling  Figure 21 shows the variation curves of the effective flow rate of grinding fluid and effective flow rate with the jet speed when the grinding wheel circumferential speed is 30 m/s, and the central jet is used with/without disturbing flow structure.From Fig. 21a, as can be observed, the scrambling structure considerably increases the effective flow rate of the grinding fluid in the grinding arc area.The more pronounced the improvement in the effective flow is, the higher the grinding fluid jet speed is.This is because the disturbance structure is designed to increase the effective flow rate by increasing the flow rate of the grinding fluid in the heat transfer channel.When the jet velocity is 0.5 m/s, too little grinding fluid breaks through the airflow barrier and enters the grinding arc area, and the enhancing effect of the disturbance structure cannot be brought into full play.A significant amount of grinding fluid is transported in the heat exchange channel when the injection speed is 1.5 m/s.The flow of grinding fluid in the heat exchange channel is further accelerated under the influence of the disturbed structure, and the flow through the grinding arc area per unit time is significantly increased.From Fig. 21b, it can be seen that the effective flow rate in the grinding arc area of the LSG-GW with the disturbed flow structure is almost the same as that at 1 m/s at the grinding fluid injection speed of 1.5 m/s, while the effective flow rate of the grinding fluid starts to decrease without the disturbed flow structure.
This indicates that the scrambled structure increases the effective grinding fluid flow rate at the same grinding fluid supply flow rate, which helps achieve rapid heat transfer in the grinding arc area while reducing grinding fluid waste.

Convective heat transfer coefficient distribution of heat transfer channel fluid
During the grinding process, the contact zone and the heat exchange zone are alternately arranged and move laterally within the grinding arc, and the heat transferred into the workpiece within the contact zone is then transferred into the adjacent heat exchange zone again.In other words, the next time the grinding process occurs, the grinding fluid in the heat exchange zone removes the heat produced in the contact area from the grinding arc, as shown in Fig. 22.Most of the time while grinding, the grinding depth is much smaller than the grinding wheel's diameter, resulting  in a very narrow grinding arc, so the grinding arc length is assumed to be a straight line with a length of l c .Furthermore, the grinding wheel grooved spiral angle (β>85°) is large, so the flow of grinding fluid in the heat exchange channel is considered to be two-dimensional.Then the convective heat transfer problem of the fluid in the heat transfer channel in the grinding arc area is simplified to a two-dimensional fluid out-swept flat plate model on the grinding arc length l c .The grinding fluid in the heat exchange zone face to the heat of grinding is the heat generated in the contact zone.
Figure 23 shows the formation and development of the flow boundary layer when the grinding fluid flows along the workpiece surface with velocity u ∞ , the starting section is the laminar flow area, and the flow velocity of the grinding fluid near the workpiece surface is relatively low.The boundary layer eventually thickens and transforms into a turbulent state with erratic motion trajectories as the flow advances.The flow rate of the grinding fluid suddenly increases close to the workpiece surface.
Newton's cooling equation is the basic formula for calculating the convective heat transfer coefficient(CHTC) h for a unit area with In which: q = heat flow density, W/m 2 .h = convection heat transfer coefficient, W/(m 2 •K).T w = solid surface temperature, K. T ∞ = fluid mainstream temperature, K. Within the thin layer close to the surface of the workpiece, there is where κ is the thermal conductivity of the fluid and T y | | |y=0 is the gradient of fluid temperature change in the y-direction at the adjoining wall.At the workpiece surface location, in conjunction with Eqs. ( 5) and ( 6), the heat flow density into the grinding fluid can be expressed by the following equation: i.e., get Equation ( 8) relates the convective heat transfer coefficient of the heat transfer surface to the temperature field of the fluid.For a given grinding fluid, the thermal conductivity κ is a known constant, and the grinding fluid temperature T ∞ is considered to be the room temperature.The surface temperature of the workpiece in the grinding arc is T w which is uniformly distributed along the grinding direction by simplifying the consideration.Therefore, it is also important to acquire the temperature gradient of the grinding fluid in the depth direction of the grooved at the surface of the workpiece against the wall in order to solve the fluid convection heat transfer coefficient in the heat transfer channel of the grinding arc.
First, determine the grinding arc length l c .If the grinding wheel diameter d s is 200mm and the grinding depth a e is 0.1mm, then the grinding arc length l c can be calculated by the following equation: In order to obtain the convective heat transfer coefficient at any coordinate position on the surface of the workpiece, first, the grinding arc length is discretized in the x-direction, (7)  and the discretization step dx is set to 0.01 mm.Then, any x coordinate corresponds to a workpiece surface temperature, thermal boundary layer thickness, flow boundary layer thickness, and convective heat transfer coefficient.When calculating the convective heat transfer coefficient of the fluid in the grinding arc of an ordinary grinding wheel, it is generally considered that the flow speed of the grinding fluid in the grinding arc is equal to the grinding speed v s .LSG-GW has a "clear-division" contact zone and heat exchange zone.The flow rate of the grinding fluid on the bottom fluid side of the grooved is nearly equal to the grinding speed v s when seen from the direction of the depth of the grooved in the heat transfer zone.The flow speed of the grinding fluid on the fluid side of the workpiece surface is considered to be the flow speed at the grinding fluid nozzle.
The flow volume from the grinding fluid nozzle is 500 mL/s, and the cross-sectional area is 100 mm, according to which the injection velocity of grinding fluid; i.e., the inlet velocity of the heat transfer channel in the grinding arc area, v max , is 5 m/s.The Reynolds number with the grinding arc length l c as the characteristic length is calculated as Critical Reynolds number Re c is the Reynolds number when the grinding fluid on the workpiece surface changes from laminar flow to turbulent flow.For the flow of twodimensional fluid outwardly swept solid surface, the critical Reynolds number is generally taken as 5×10 5 .
The water-based grinding fluid and oil-based grinding fluid were selected to cool the grinding arc area, respectively, and their thermophysical properties and kinematic characteristics are shown in Table 10.
Bringing the data in Table 10 into Eq.( 10), the maximum Reynolds number is 2.28×10 5 , which is lower than the critical Reynolds number Re c .That is, regardless of whether a water-based grinding fluid or an oil-based grinding fluid is used, the flow is laminar in the grinding arc length l c .The grinding fluid therefore flows in the heat exchange channel in the grinding arc area in a nondynamic laminar flow with a gradually decreasing speed after being ejected from the nozzle due to inertia.The flow speed of grinding fluid in the heat exchange channel of the grinding arc is uniformly reduced, and the outlet flow speed v min is reduced to half of the inlet flow speed.
Then the mainstream speed v of the grinding fluid at any coordinate x of the workpiece surface can be expressed as where Δv is the velocity difference between any two adjacent discrete points x(i) and x(i+1).
According to the boundary layer theory, the thickness δ of the flow boundary layer at the heat transfer channel entrance x from the grinding arc area can be calculated according to the following equation: The thickness of the thermal boundary layer δ t at the heat transfer channel entrance x from the grinding arc area is >where Pr = a is called the Planter number.The discrete x-direction of the workpiece surface is completed, and the mainstream velocity of the grinding fluid at any x position and the thickness of the flow boundary layer and the thickness at the thermal boundary are determined.Discretized the grooved depth direction, i.e., the y-direction, to determine the velocity and temperature variation of the grinding fluid within the boundary layer in the y-direction.
Since the thickness of the boundary layer is an order of magnitude smaller than the depth of the trench, it is chosen to be discretized by a fixed number of copies.The thickness of the flow boundary layer and the thickness of the thermal boundary layer can be used to compute the discrete step, which will perform the dispersion in the y-direction.
The number of discrete parts is set to 200, because the thickness of the thermal boundary layer and the thickness of the flow boundary layer are not equal in most cases, it is necessary to discretize the velocity problem and the temperature problem in the y-direction separately, and both are calculated with the maximum boundary layer thickness.The maximum boundary layer thickness in this context refers to the thickness of the boundary layer reached by the grinding fluid at the exit of the heat transfer channel in the grinding arc because the flow in the heat transfer channel in the grinding arc is laminar.For a two-dimensional, steady-state, boundary layer type problem with no internal heat source, the differential control equations for the flow and temperature fields can be expressed as follows: Conservation of mass equation: According to the characteristics of the heat transfer channel flow field in the grinding arc area, the fixed solution condition is given as where u ∞ is the mainstream speed of grinding fluid on the surface of the workpiece in the heat exchange channel.
Solving Eq. ( 17) according to the above fixed solution conditions, the variation of the grinding fluid velocity within the flow boundary layer in the y-direction can be expressed as where μ is the dynamic viscosity of the grinding fluid and dp dx can be determined by Bernoulli's equation for an ideal fluid outside the boundary layer: In the heat transfer channel in the grinding arc area, the definite solution condition is obtained according to the meaning of the thermal boundary layer: According to Eqs. ( 16) and ( 18) and ( 21), the following equation can be inversed: A simplification of the above equation yields the equation for the fluid temperature T in the thermal boundary layer as The fluid temperature outside the thermal boundary layer is the mainstream grinding fluid temperature T ∞ .The corresponding thermal boundary layer thickness δ t can be calculated from Eq. ( 13) for any x position on the surface of ( 19) u = 1 dp dx the workpiece.Then all the discrete points in the y-direction will be circulated to find the fluid temperature T (x,y) corresponding to any (x,y)position in the heat exchange channel.
In the heat transmission channel in the grinding arc area, the temperature distribution of the grinding fluid within the fluid-side boundary layer of the workpiece surface is depicted in Fig. 24.From Eq. ( 23), we can obtain the temperature T (x,y) within the fluid-side boundary layer of the workpiece surface.Take the temperature T (x,1) corresponding to the first discrete point in the y-direction on the fluid side of the workpiece surface and the workpiece surface temperature T w .According to the definition, the temperature gradient of the grinding fluid at the workpiece surface can be calculated by the following equation: Combining equation Eqs. ( 8), ( 12), ( 13), (23), and (24), the convective heat transfer coefficient h x of the grinding fluid in the heat transfer channel of the grinding arc is calculated as According to the equation, which is based on a simplified model, the convective heat transfer coefficient h x is primarily influenced by the flow rate of the grinding fluid via the heat transfer channel, the length of the grinding arc, and the thermophysical parameters and motion characteristics of the fluid itself.And the workpiece surface temperature T w is eliminated in the calculation; i.e., the convective heat transfer coefficient h x is not directly related to the workpiece surface temperature T w .The related study [23] has also confirmed that the convective heat transfer coefficient h x is little affected by the workpiece surface temperature T w when the workpiece surface temperature T w is lower than the grinding fluid boiling temperature; i.e., the grinding fluid cools the grinding arc area effectively.Only when the surface temperature of the workpiece, T w , is greater than the boiling point of the grinding fluid, it will lead to vaporization of the grinding fluid and cannot achieve effective cooling, h x = 0.
The distribution curve of convective heat transfer coefficient of grinding fluid in the heat transfer channel of grinding arc can be calculated from Eq. (25), as shown in Fig. 25.
From Fig. 25, it can be seen that the convective heat transfer coefficient of the grinding fluid in the heat transfer channel of the grinding arc is not a constant value.Water-based grinding fluids have a greater convective heat transfer coefficient than oil-based grinding fluids, and the trend is basically the same for both.The distribution curve can be divided into 3 10 The grinding fluid's convective heat transfer coefficient is much lower than the strong convective heat transfer interval, yet it varies only little.Large grinding arc lengths can be effectively cooled thanks to the ability to maintain a rather steady convective heat transfer capacity.It is the primary time for convective heat exchange.From Eq. ( 25), it can be seen that the convective heat transfer coefficient h x is closely related to the mainstream speed u ∞ of the grinding fluid on the workpiece surface.Therefore, the inlet velocity v max of the heat exchange channel in the grinding arc area is set to 1 m/s, 3 m/s, and 5 m/s respectively, and the reduction of the mainstream velocity of the grinding fluid in the heat exchange channel is analyzed and processed.The relationship between the mainstream speed of grinding fluid and convective heat transfer coefficient is shown in Fig. 26.
From Fig. 26, it can be seen that the convective heat transfer coefficient increases by gradually increasing the mainstream speed of the grinding fluid on the surface of the workpiece in the heat transfer channel.In comparison to the main convective heat transfer zone, the convective heat transfer coefficient is clearly improved in the strong convective heat transfer zone.It is clear that the primary element impacting the convective heat transfer coefficient is the flow rate of the grinding fluid in the heat transfer channel.Improving convective heat transfer coefficient is the key to improved heat transfer efficiency.The flow rate of the grinding fluid in the channel has the biggest impact on the convective heat transfer coefficient of the heat transfer channel in the grinding arc.Therefore, in order to further enhance the heat transfer performance in the grinding arc, it is necessary to focus on increasing the flow rate of the grinding fluid in the heat transfer channel.With a single spiral grooved heat exchange channel, the flow speed of grinding fluid on the workpiece surface is gradually reduced, resulting in a rapid decrease in its heat exchange capacity.Disturbance structure at the bottom of the grooved helps to create local turbulence, resulting in a significant increase in the flow rate of the grinding fluid in the heat transfer channel.On the fluid side of the workpiece surface, the speed of the grinding fluid increases to match the grinding speed.Additionally, it is assumed that the fluid in the grinding arc's heat transfer channel is in turbulent flow due to the short laminar flow segment.
When the grinding fluid is in turbulent motion, the differential control equations of the flow and temperature fields can be expressed as where ν t denotes the turbulent viscosity and a t denotes the turbulent thermal diffusivity.
It can be seen that the momentum and energy equations in Eq. ( 26) are extremely similar in form.Therefore, Eq. ( 26) is introduced dimensionlessly into (26)

Then
The boundary conditions are given for Eq. ( 28): Discretize the grinding arc length l c in the x-direction with a discrete step of 0.01 mm.The grinding arc length l c is then replaced by the discrete point x(i).It may be approximated by assuming that t a t = Pr = 1 .After, correct it to obtain the solution result when Pr≠1.When Pr = 1, since all variables in Eq. ( 28) are dimensionless quantities, u * and Θ should have exactly the same solution, and then The relationship between the Nusser number Nu x and the local drag coefficient c f at any x(i) position on the grinding arc length l c is obtained: From Fig. 27, it can be seen that the distribution of the high turbulent kinetic energy heat transfer channel grinding fluid convective heat transfer coefficient driven by the scrambled trench structure can be divided into two curves for the strong convective heat transfer zone and the main convective heat transfer zone.After creating the flow disturbance structure at the bottom of the groove, the convective heat transfer coefficient is raised by more than 2.2 times in comparison to the typical big spiral angle grooved heat transfer channel.The main convection heat transfer zone has a more significant increase in heat transfer capacity.
Figure 28 shows the distribution of convective heat transfer coefficient of water-based grinding fluid with grinding speed driven by the scrambled trench structure with high turbulent kinetic energy heat transfer channel.
The graph shows that the convective heat transfer coefficient increases with the increase of grinding speed.However, in the actual grinding process, the grinding speed and the macro-convective heat transfer coefficient of the grinding fluid do not always maintain a positive correlation [21].This is because as grinding speed increases, grinding temperature rises as well, and when the temperature above the boiling point of the grinding fluid, the grinding fluid's macro-convective heat transfer coefficient decreases instead.
Based on the grinding wheel structure parameters and grinding process parameters, a three-dimensional analysis model of the airflow field in the grinding area of LSG-GW driven by parameters was established, and the factors influencing the pressure and velocity distribution of the airflow field were studied.The minimal space between the grinding wheel and the workpiece is indirectly increased by spiral grooves, which reduces airflow velocity on the workpiece surface.The increased air flow between the inlet and outlet of the grinding wedge also contributes to the conduction of the grinding fluid.The larger the spiral grooved width, depth, and spiral angle on the grinding wheel surface, the lower the pressure of the airflow field in the grinding arc, and the stronger the weakening ability of the grinding airflow field.The air in the grinding arc flows in the direction of the grinding wheel width before the minimum clearance is reached, effectively suppressing the return flow at the entrance of the wedge.
A numerical analysis model of the gas-liquid two-phase flow field in the wedge area-grinding arc area was established based on the distribution characteristics of the gas barrier flow field and the return flow field in the grinding area of LSG-GW.The grinding fluid will be obstructed by the airflow around the grinding wheel when it enters the grinding arc.However, the reflux and side leakage phenomenon in the grinding area of LSG-GWs is significantly less than that of non-grooved ordinary grinding wheels, because a large amount of grinding fluid is transported inside the heat exchange channel.Additionally, the effective flow of grinding fluid in the heat exchange channel gradually increases with the increase in spiral angle, grooved width, and depth.A high-turbulence heat transfer channel flow field is created at the bottom of the grooved by the disturbance structure inside the grinding arc.The effective flow volume in the grinding arc area is significantly increased, which helps to reduce thermal damage on the grinding surface and improve the quality of the grinding surface.
Based on the characteristics of the gas-liquid two-phase flow field distribution in the grinding zone of LSDG-GW, the convective heat transfer coefficient distribution of the grinding fluid acting on the workpiece surface in the heat transfer channel with/without the disturbed flow structure is modeled respectively.According to the convective heat transfer strength, the distribution curve of the grinding fluid's convective heat transfer coefficient in the heat transfer channel can be split into strong convective heat transfer interval and main convective heat transfer interval.The flow speed of grinding fluid in the heat transfer channel is the main factor affecting the convective heat transfer coefficient in the grinding arc.The flow disturbance structure at the bottom of the grooved makes the flow rate of grinding fluid in the heat exchange channel increase significantly, the convective heat transfer coefficient increases significantly, and the range of strong convective heat transfer zone increases significantly, further enhancing the heat transfer performance in the grinding arc area.
Aiming at the high specific removal energy and heat generation rate of high-performance alloys in the grinding process, resulting in localized high temperatures causing thermal damage to the surface of the workpiece, a solution was proposed to the practical engineering problem.It has certain application prospects in the high-efficiency and high-precision grinding process of difficult-to-machine alloy materials.

Fig. 2
Fig. 2 Schematic diagram of LSDG-GW and flow disturbance structure in the grooved

Fig. 5
Fig. 5 Effect of trench size on pressure distribution

Fig. 6
Fig. 6 Inlet velocity vector diagram of wedge area

Fig. 7
Fig. 7 Tracing of airflow movement in the grinding zone

Fig. 10
Fig. 10 Relation between airflow velocity and distance from minimum clearance

Fig. 12
Fig. 12 Three-dimensional geometric model of gas-liquid two-phase flow field

Fig. 14 Fig. 15
Fig. 14 Distribution of grinding fluid integration number in the gasliquid two-phase flow field of a fluteless ordinary grinding wheel

Fig. 16
Fig. 16 Cloud plot of the distribution of the minimum clearance grinding fluid integration number

Fig. 17
Fig.17 Cloud plot of liquid integration number for LSDG-GW

Fig. 19
Fig. 19 Effective flow of grinding fluid and effective flow rate at three nozzle positions

Fig. 20
Fig. 20 Effective flow and effective flow rate at different circumferential speeds of grinding wheels

Fig. 21
Fig. 21 Effective flow and effective flow rate of grinding fluid with/without disturbance structures

Fig. 22
Fig. 22 Partial view of the grinding arc of a LSG-GW

Fig. 23
Fig. 23 Formation and development process of flow boundary layer Conservation of momentum equation: Energy conservation equation: For the two-dimensional fluid out-swept plate model, the momentum conservation equation for steady-state flow of grinding fluid, i.e., the Navier-Stokes equation, can be simplified as >where, in the equation: u = mainstream speed of grinding fluid in x-direction, m/s.ρ = density of grinding fluid, kg/m 3 .ν = kinematic viscosity of grinding fluid, m 2 /s.p = grinding fluid pressure, Pa.

3 TFig. 24
Fig. 24 Fluid temperature distribution on the surface of the workpiece (i.e., thermal boundary layer) to the convective heat transfer intensity.The first stage is in the vicinity of the heat exchange channel inlet, approximately in the range of x=0~0.2lc .The convective heat transfer coefficient of the grinding fluid has a process of dramatic change from large to small, but overall, the convective heat transfer coefficient is at a high level and is in the strong convective heat transfer range.The second stage is approximately in the range of x = 0.2 l c ~lc interval.

Fig. 25
Fig. 25 Distribution of fluid convection heat transfer coefficient in the heat transfer channel in the grinding arc area

Fig. 26
Fig. 26 Relationship between the mainstream speed of grinding fluid and convective heat transfer coefficient

Fig. 27
Fig. 27 Effect of the disturbance structure on the convective heat transfer coefficient of the grinding fluid in the heat transfer channel

Table 1
Cloud map of pressure distribution on the surface of workpiece grinding with LSG-GW

Table 2
Vector diagram of velocity distribution of airflow field in the grinding zone of LSG-GW

Table 3
Grinder motor technical parameters angle of 89° and grooved width of 2 mm is named No.1; the grinding wheel with spiral angle of 89° and grooved width of 4 mm is named No.2; the grinding wheel with spiral angle of 87° and grooved width of 4 mm is named No.3; ordinary grinding wheel is named No. 4, as shown in Fig.8.
Fig. 8 LSG-GW and ordinary GWs wheel with spiral

Table 4
Technical parameters of anemometer

Table 5
Experimental conditions and experimental parameters

Table 6
Wind speed at the exit of the wedge

Table 7
Effective flow in the arc area at different spiral angles (grooved width 3 mm, depth 4 mm)

Table 9
Effective flow in the arc area at different grooved depths (helix angle 86.36°, grooved width 3 mm)