Feasibility of Optical Flow Field Measurements of the Coolant in a Grinding Machine

Abstract

For industrial grinding processes, the workpiece cooling by metalworking fluids, which strongly influences the workpiece surface layer quality, is not yet fully understood. This leads to high efforts for the empirical determination of suitable cooling parameters, increasing the part manufacturing costs. To close the knowledge gap, a measurement method for the metalworking fluid flow field near the grinding wheel is desired. However, the varying curved surfaces of the liquid phase result in unpredictable light deflections and reflections, which impede optical flow measurements. In order to investigate the yet unknown optical measurement capabilities achievable under these conditions, shadowgraphy in combination with a pattern correlation technique and particle image velocimetry (PIV) are applied in a grinding machine. The results show that particle image velocimetry enables flow field measurements inside the laminar metalworking fluid jet, whereby the shadowgraph imaging velocimetry complements these measurements since it is in particular suitable for regions with spray-like flow regimes. As a conclusion, optical flow field measurements of the metalworking fluid flow in a running grinding machine are shown to be feasible.

1. Introduction

1.1. Motivation

Grinding is an essential manufacturing process to produce metallic parts, in which a metalworking fluid (MWF) jet is used for lubrication and cooling of the grinding zone to prevent part damage by grinding burn [1]. Several empirical experiments and simulations to characterize the cooling performance were carried out so far, whereby only an indirect optimisation of the MWF jet flow was performed [2,3,4,5,6]. Since the cooling performance is directly related to the fluid flow, in-depth knowledge of the flow field is essential for understanding the heat transfer associated with the grinding process [7,8]. However, a flow velocity field measurement of the MWF flow in a grinding machine has not been performed so far, either with or without workpiece. In addition, also the fluid concentration in the regions with MWF-air mixtures (spray) strongly influences the cooling performance, but this effect is beyond the scope of the presented investigations.

For cooling, a nozzle directs the fluid as a continuous free jet onto the rotating grinding wheel from where the MWF reaches the contact zone between wheel and workpiece. This is a highly dynamic process, which leads to a complex flow structure of the supplied fluid. In order to investigate the measurability of the MWF flow field right behind the nozzle and during the interaction with the grinding wheel, the setup used for the investigations in the present study is simplified by omitting the workpiece.

1.2. State of the Art

A general approach to investigate liquid jet shapes is shadowgraphy imaging [9], which is based on the influence of light refraction by the observed object (e.g., MWF jet) on a homogeneous background illumination. The difference in the refractive index numbers of the two phases (air and liquid) in the flow generally leads to a deflection of light at their interface. Inhomogeneities in the surface of the liquid become visible, as the evenly distributed illuminating light gets deflected differently, leading to the observation of areas with lower or higher light intensity [10,11]. The resulting camera image of the illuminated flow is called a shadowgram. Exemplarily, a shadowgram from the present study is shown in Figure 1, depicting the investigated MWF supply flow qualitatively. The image contains the entire MWF supply flow from the jet-generating nozzle to the interaction of the fluid with the rotating grinding wheel and beyond. Shadowgram-based flow investigations have already been conducted in a grinding machine. For example, Geilert et al. [12] visualised the qualitative MWF inflow field for different nozzles and volume flows but did not derive quantitative flow field information.

A quantitative velocity field measurement based on visualised turbulent structures in air flows was reported by Jonassen et al. [13] and improved by Hargather et al. [14]. Turbulent structures were used as natural flow tracers and evaluated regarding their movement during a defined period of time. For this measurement approach, the term shadowgram image velocimetry (SIV) is used here, which means tracking characteristic flow structures that are visualised with a shadowgram. However, it has to be examined if the visualisation in a grinding machine is sufficient for a quantitative velocity measurement of the MWF flow. Furthermore, it has to be checked if the correlation of the shadowgram reflects the actual MWF flow velocity. Therefore, a comparative measurement is necessary for the MWF supply flow.

As an alternative to SIV, different flow velocity measurement techniques such as Doppler-based methods or in particular the particle image velocimetry (PIV) can be taken into account. Although Doppler techniques seem to be more robust against light refractions [15], PIV is preferred here due to its less specific laser requirements. With PIV, a 2d velocity flow field is obtained by seeding the fluid with tracer particles and observing their motion with one camera. The measurement plane is defined by a light sheet illumination obtained with a double-pulse laser. Particles in the measuring plane are illuminated by the double pulse and the defined time gap between the pulses enables the determination of particle position changes (by means of cross-correlating interrogation windows in the image pairs) as well as a corresponding velocity measurement [16].

The impact of light deflection on the PIV measurement in two-phase flows depends on the surface geometry of the phase transition. For stationary liquid-air phase transitions, the systematic measurement error can be corrected by ray-tracing and mapping algorithms [17,18]. Consequently, PIV measurements in laminar two-phase flows are feasible in principle. However, the jet flow in the grinding machine typically has a randomly fluctuating liquid-air phase due to the inflow conditions with velocities up to 60 $\mathrm{m}$/$\mathrm{s}$. This leads to an increase of disturbances in the light paths of illumination and observation, resulting in an increased measurement uncertainty [19].

For PIV measurements in fluctuating refractive index fields in air, the systematic measurement error has been determined and partially corrected [20,21]. Approaches for measuring and correcting the measurement errors of randomly fluctuating surfaces of the liquid-air phase transition have been proposed, but these are either too slow [22] or only feasible for changes in the scale of micrometers [23]. Hence, PIV measurements of the MWF flow in a grinding machine have not been studied yet. In particular, the applicability of PIV to measure the free jet flow in a grinding machine needs to be examined.

1.3. Aim and Outline

For this reason, the article investigates the measurability of the MWF flow velocity field in a grinding machine with SIV and PIV for various volume flows. For the quantification of the velocity field of the continuous free MWF jet between nozzle and grinding wheel, SIV and PIV are applied and studied to serve as complementary measurement techniques to evaluate the usability of flow characteristics as flow tracers. For the MWF flow behind the interaction zone with the grinding wheel, the droplets of the MWF are used for a respective velocity field measurement with SIV.

The measurement approaches for the velocity field of the MWF flow with SIV and PIV are explained in Section 2. Section 3 gives details about the experimental setup, which is implemented in a grinding machine. The flow field measurement results are shown and discussed regarding the measurement feasibility in Section 4. At first, SIV and PIV measurements of the supply flow are compared. Subsequently, measurements of the MWF flow in interaction with the grinding wheel are presented and assessed regarding the measurability of the MWF flow field. The article closes with a summary and an outlook in Section 5.

2. Measurement Approach

In order to measure the flow velocity field with optical measurement techniques, flow characteristics must be visualised, from which the fluid motion can be derived. As shown in Figure 1, the flow gets torn up into droplets after interaction with the grinding wheel. There, the appearing droplets are unambiguously allocated in the shadowgram imaging, so that their movement can be observed with high-speed measurements and an SIV measurement approach. The 2d displacement field behind the interaction with the grinding wheel is calculated with a cross-correlation of consecutive images captured at the times $t_1$ and $t_2$ [24]. For this purpose, the obtained images are divided into interrogation areas for each and the cross-correlation function

$$\begin{array}{c}\hfill cc(\Delta \tilde{x},\Delta \tilde{y})=\sum _{\tilde{x}}^{}\sum _{\tilde{y}}^{}{I}_1(\tilde{x},\tilde{y})·I_2(\tilde{x}+\Delta \tilde{x},\tilde{y}+\Delta \tilde{y}),\end{array}$$

(1)

is evaluated, with $I_1$ and $I_2$ as the image intensity at $t_1$ and $t_2$, respectively, over the image position $(\tilde{x},\tilde{y})$. The displacement $(\Delta \widehat{\tilde{x}},\Delta \widehat{\tilde{y}})$ of the cross-correlation maximum from the origin represents the displacement of the imaged particles or flow structures between the consecutive images. The velocity field is thus calculated by dividing the displacement from each interrogation area by the time interval $t_2-t_1$ between the considered images.

In contrast to the MWF behaviour after the wheel interaction, the situation for the MWF supply flow and its interaction with the grinding wheel is different. The MWF exiting the nozzle and hitting the grinding wheel is a continuous liquid free jet that forms structures on the surface due to friction with the stagnant surrounding air [25], which leads to local changes in the free jet surface. The appearing inhomogeneities on the surface represent characteristic flow structures and are visualisable with the shadowgraphy method. When applying SIV, these surface structures are used as flow tracers for a velocity determination (analogue to the image processing in the regions after the interaction with the grinding wheel). The occurrence of the surface structures mainly depends on the outlet shape of the nozzle, the fluid properties of the MWF (with respect to the fluid properties of the surrounding air) and the fluid velocity at the outlet. One important characteristic quantity is the Reynolds number

$$\begin{array}{c}\hfill Re=\frac{v_{\sup }·d_{\mathrm{h}}}{\nu }\end{array}$$

(2)

with $v_{\sup }$ as the supply flow velocity, $d_{\mathrm{h}}=\frac{4·w·h}{2w+2h}$ the hydraulic nozzle outlet diameter, w and h the width and height of the rectangular nozzle outlet and $\nu$ the kinematic viscosity of the MWF. As a theoretical value for the supply flow velocity $v_{\sup }$ at the nozzle exit, the continuity equation yields the approximation

$$\begin{array}{c}\hfill v_{\sup ,\mathrm{theo}}\approx \frac{Q}{w·h}\end{array}$$

(3)

with Q as the provided volume flow. As classified by McNaughton and Sinclair [26], liquid jet properties can be derived from the Reynolds number. For $1000<Re<3000$, the liquid jet remains laminar after exiting the nozzle for a certain length and is named a semi-turbulent jet. For Reynolds numbers above 3000, the jet is considered fully turbulent with turbulent structures immediately after the nozzle outlet. On the other hand, for pipe flows, the laminar–turbulent transition point is given at the critical Reynolds number around 2300 and the clearly turbulent flow region is above 4000 [27]. Note that the cited Reynolds numbers are for round nozzle exit, so that the findings can be applied to the studied rectangular nozzle orifice only to a certain extent. However, since the surface structures depend on the flow conditions, their usability as flow tracers must be analysed for Reynolds numbers covering laminar, laminar to turbulent transitional and fully turbulent jet regimes regarding possible differences in the results of the SIV flow field measurements.

In order to realise PIV and SIV measurements in a grinding machine, the proposed measurement arrangement is schematically depicted in Figure 2. For SIV, a diffuse background light source is used to illuminate the fluid, and a high-speed camera on the opposite side records the resulting shadowgram over time. Note that with this arrangement no depth information in z-direction is acquired and a superposition of flow structures from different depths of the fluid cannot be separated and disturbs the detectability.

The MWF supply flow is generated by a nozzle with a rectangular orifice shape, resulting in a liquid jet shape based on the orifice geometry as shown in Figure 3. The liquid free jet has the basic shape of a sheet with a thickness and width in the same scale as the orifice shape. However, due to the surface tension the liquid is tapering by time which leads to an increased rounded cross-section at the outer edges. According to the liquid jet geometry, the visualisation result depends on the perspective. For the top view, an observation of the jet over the width w through its thickness h is made. With the side view, an observation is made through the entire jet width w. Comparing the measurement results from top and side view, the perturbations caused by the volumetric illumination of the shadowgraphy can be discussed qualitatively with respect to the geometry of the free jet. Measurements with top view result in observations through a thin jet volume. Due to the small volume, a 2d flow geometry can be assumed. Accordingly, the surface structures represent practically the entire flow of the fluid. In addition, almost no superposition of the characteristic flow structures from different depths occurs. However, for flow measurements in interaction with the grinding wheel, images must be taken from the side of the grinding wheel in z-direction (as shown in Figure 2). A superimposed observation of the characteristic flow structures from different depths is then expected, which results in possible misallocation and a reduced detectability of the flow structures. Therefore, it is necessary to determine the impact of the volumetric observation on the measurement. For this purpose, observations of the MWF jet’s top and side view are performed and the measurements are compared with each other.

Finally, the movement of the flow characteristics must be examined in relation to the flow velocity. To accomplish this, the velocity of the free jet is determined with a standard PIV system, i.e., with a pulsed laser and a camera in both perspectives, see Figure 2. Difficulties in illuminating and observing the flow tracer particles due to the effect of light refraction are expected, which increase with number and intensity of the flow structures. To ensure that PIV measurements of the MWF free jet are feasible, measurements are carried out for different jet flow conditions. First, a laminar free jet flow without unsteady surface structures is used to proof the general PIV measurement feasibility. Afterwards, measurements are performed on a laminar-turbulent transient flow, with faint flow structures present, which also allows SIV flow measurements. A comparison of the absolute measurement uncertainties for the laminar and transient case will reveal the impact of the flow-induced uneven surface.

3. Experimental Setup and Signal Processing

3.1. Grinding Machine with Optical Access

The measurements are conducted in a surface grinding machine of the type Micro-Cut A8 CNC manufactured by the company ELB. The MWF is supplied in the x-direction of the used coordinate system through a nozzle with a specific profile according to Rouse et al. [28,29] (see Figure 3a) onto the grinding wheel surface. The distance between the nozzle orifice and the point of impact on the grinding wheel is 120 mm. The used metal working fluid is CUT MAX 902-10 with a density of $0.82$ $\mathrm{k}\mathrm{g}$/${\mathrm{m}}^3$ and dynamic viscosity of 11 ${\mathrm{mm}}^2$/$\mathrm{s}$ at a temperature of 40 ${}^{\circ }\mathrm{C}$. The MWF has not been diluted and is a visually transparent yellow-golden liquid with a refractive index number of $1.44575\pm 0.00018$. The used volume flow is measured with an oval wheel meter with an accuracy of ±$0.5$ L/min.

For the MWF supply, two different orifice sizes were used with a common width of 20 $\mathrm{m}$$\mathrm{m}$ and the used coordinate system has its origin at the centre of the nozzle orifice. For investigations focusing on the free jet, a nozzle with an orifice height $h=$ $2.3$ mm is used. For MWF flow measurements with the grinding wheel, the nozzle height $h=$ $0.9$ mm is applied to achieve higher flow velocities (relevant for industrial applications) for the same volume flows. The used experimental parameters for the measurements focussing on the supply flow can be seen in

Table 1. Experimental parameter for the volume flow Q, theoretical flow velocity $v_{\sup ,\mathrm{theo}}$, Reynolds number $Re$ and expected flow state for measurements on the supply flow with nozzle width of $w=20$mm and height of $h=2.3$mm.

Q in L/min	${\mathit{v}}_{\mathbf{sup},\mathbf{theo}}$ in m/s	Re	Flow State
14.9	5.40	2024	laminar
26.6	9.64	3614	transient
39.4	14.26	5349	turbulent

and for the flow-tool interaction in

Table 2. Experimental parameter for the volume flow Q, theoretical flow velocity $v_{\sup ,\mathrm{theo}}$, Reynolds number $Re$ and expected flow state for measurements on the fluid-tool interaction with nozzle width of $w=20$mm and height of $h=0.9$mm.

Q in L/min	${\mathit{v}}_{\mathbf{sup},\mathbf{theo}}$ in m/s	Re	Flow State
16.0	14.78	2313	laminar
26.6	24.63	3856	transient
37.2	34.48	5399	turbulent

. The used grinding wheel has a radius of 200 mm and rotates with a circumferential velocity of 25 m/s. To provide access for the optical components into the grinding chamber, the protective acrylic glass window that closes the grinding chamber is removed and replaced with a transparent foil. Viewing windows are cut into the foil to achieve an undisturbed observation of the volume flows. Work safety is ensured by an external protective housing, which additionally grants laser safety.

For investigating solely the MWF supply flow at first, an interaction with the grinding wheel is prevented by moving it out of plane in z-direction. In order to determine the top view of the MWF free jet flow, the nozzle is rotated by 90° instead of reassembling the optical measurement setup. Finally, the nozzle is placed in its original position and the MWF flow interacting with the rotating wheel is studied.

3.2. Optical Setup

The optical setup is shown in Figure 2. It is realised according to the scheme illustrated in Figure 4. A light-emitting diode (LED) panel is installed as a diffuse background illumination on the rear wall within the working area of the grinding machine for flow visualisation with shadowgraphy. It provides an illumination of 2400 $\mathrm{lm}$ in neutral white (colour temperature 4300 $\mathrm{K}$). The distance from the LED panel to the centre of the grinding wheel is 250 mm. For the observation, a high-speed camera of the type Pro Y4 from the company Integrated Design Tools Motion is located at a distance of $z=$ 60 mm to the centre of the grinding wheel with the camera axis orientated in z-direction. A spatial resolution of 125 μm/px is achieved with the 105 mm F2,8 EX macro objective from the company Sigma and the shadowgrams are recorded with a repetition rate of $13.700$ $\mathrm{Hz}$ and an exposure time of 50 μs. The exposure time is short enough to capture quasi-stationary images of the flow details.

To obtain PIV measurements of the MWF supply, polyamid seeding particles with an average size of 50 μm and a density of $1.03$ $\mathrm{g}$/${\mathrm{cm}}^3$ are filled into the MWF tank of the grinding machine. To illuminate the seeded flow, a frequency-doubled pumped Nd:YAG pulsed laser at a wavelength of 532 $\mathrm{n}$$\mathrm{m}$ with a maximum energy per pulse of 200 $\mathrm{m}$$\mathrm{J}$ and a pulse length of 10 $\mathrm{n}$$\mathrm{s}$ of the type Evergreen from the company Quantel is used. A double pulse repetition rate of 15 $\mathrm{Hz}$ is used with a time separation per pulse between 70μs to 100 μs, which is adjusted according to the flow velocity. The laser light sheet has a width of approximately 50 $\mathrm{m}$$\mathrm{m}$ with a sheet thickness of 1 mm. It illuminates the free MWF supply jet between the positions 50 mm to 100 mm along the x-axis and is placed in the centre axis of the free jet. The laser beam is guided into the grinding machine with a light-guiding arm, which provides the necessary flexibility and protection from contaminating MWF for the optical components. The necessary optics to form a laser light sheet are installed in the grinding machine and protected by a housing to avoid unwanted contamination by MWF droplets. For particle imaging a $5.5$ $\mathrm{M}$$\mathrm{px}$ sCMOS camera of the type Zyla from the company Andor with a 50 $\mathrm{m}$$\mathrm{m}$ focal length objective of the type Planar T* 1.4/50 from the company Zeiss is used. The camera is positioned at a distance of $z=$ 60 $\mathrm{c}$$\mathrm{m}$ to the MWF jet, observing in z-direction and images are taken with a spatial resolution of 80 μm/px. For a reduction of disturbing ambient light, a bandpass filter with a central wavelength of 532 $\mathrm{n}$$\mathrm{m}$ and FWHM bandwidth of 4 $\mathrm{n}$$\mathrm{m}$ is used.

3.3. Image Enhancement and Cross-Correlation Algorithm

For the velocity field calculation, the captured images for SIV and PIV are visually enhanced and analysed with the software DynamicStudio, developed by the company Dantec Dynamics. The image enhancement process uses a spatial median and a top-hat image filter for eliminating noise in the images. For increasing the detectability of the particles, the Sobel operator is used to highlight horizontal intensity changes and to eliminate visible stationary flow structures from the edges. The velocity field is then calculated with an adaptive PIV algorithm with an overlap of 75% for an interrogation area size of 32 px × 32 px. For the velocity field determination for a certain set of cooling parameters (e.g., MWF volume flow, nozzle height), 1000 single measurements are taken for SIV and 350 for PIV. For each of these measurement series the averaged velocity field is calculated after automated outlier deletion with a range validation to minimize the residual impact of measurement outliers. Additionally, the standard deviation of the measurements is determined as a measure of the random measurement deviation.

4. Measurement Results

The impact of optical distortions on flow measurements of the MWF jet is discussed in Section 4.1. In Section 4.2, the PIV measurement is shown to be feasible for a laminar MWF jet flow. The PIV measurement is further used as a reference to determine the flow behaviour of the characteristic flow structures of a laminar–turbulent transient flow used for SIV, which is studied in Section 4.3. After the measurability of the MWF supply flow velocity is clarified, complete flow field measurements in interaction with the grinding wheel are conducted with SIV and the results are presented in Section 4.4.

4.1. Impact of Optical Distortions on MWF Jet Flow Measurements

To examine the influence of light refraction on both measuring methods for different inflow conditions qualitatively, raw images are captured with the PIV and the shadowgram imaging system for the volume flows 14.9 L/min, 26.6 L/min and 39.4 L/min, resulting in a laminar, transient and turbulent flow respectively. The resulting images are shown in Figure 5.

For the lowest volume flow of $14.9$ L/min (Figure 5a,b) a laminar free jet without temporally varying structures results. Considering the top view, a smooth centre area is visible and light refractions occur only at the cylindrical edges. In the range of 40 mm to 120 mm of the x-axis, the scattered light of the seeding particles is visible and in the side view, the originally round particles are observed significantly distorted due to the curved jet surface and appear as ellipses (see red circle). So in both views, the particles can be identified, which allows for the calculation of their velocities with PIV via cross-correlation algorithms. Since almost no characteristic flow structures can be observed, a SIV velocity measurement is not possible.

At an increased volume flow of $26.6$ L/min (Figure 5c,d), faint turbulences of the transient flow in form of waves are present on the free jet geometry. These structures follow the flow direction and are visible in the shadowgraphy, which principally enables a SIV velocity evaluation.

Due to the surface structures, further light refractions occur in the illumination with the laser light section for PIV, visible at 90 mm of the x-axis. However, the occurring light refraction is not significant and the particles are still observable. An evaluation with PIV seems therefore still possible. The comparison of the velocity measurement with SIV (based on flow structures) and PIV (based on seeding) in Section 4.3 will reveal, if the characteristic flow structures reflect the flow velocity.

For the flow rate of $39.4$ L/min (Figure 5e,f), a fully turbulent flow with more intense surface structures on the MWF appear. Due to the dominant surface inhomogeneities, total reflections occur in parts of the wave structures. The influence of the total reflections is a major obstacle for the PIV measurement technique. If total reflections occur, the laser light does not enter the MWF and no particles are illuminated. In addition, the reflections are significantly brighter than the scattered light from the particles, which reduces their visibility. As a result, a velocity evaluation based on the motion of the particles without further adjustment is no longer feasible, since mainly the wave structures are visualised. The existing turbulent structures are distinguishable in the shadowgraph picture and their size increases with the distance to the nozzle orifice in x-direction. As a consequence, velocity measurements with PIV and SIV are feasible, but both are based on the motion of wave structures.

4.2. Feasibility of PIV to Measure the Laminar MWF Flow Velocity $v_{\sup }$

PIV velocity field measurements are taken for top and side view of the laminar MWF supply flow with a flow rate of $14.9$ L/min. The average 2d velocity fields and their corresponding uncertainties for jet positions from x = 40 mm to 120 mm according to top and side view are shown in Figure 6. The flow directions are indicated by the vector directions and the background displays the colour-coded magnitude of the 2d flow field $v_{\sup }$ in m/s.

The measurement from the top view reveals a homogeneous velocity field along the x-axis. In the middle area from y = −5 mm to 5 mm the velocity is constant along the whole x-axis at $5.55$ m/s. In contrast, the bottom edge of the flow (y =−5 mm to −10 mm) shows a systematically lower velocity of $5.4$ m/s. This difference in the measurement can be caused by the cylindrical edge, which is responsible for possible light deflections. To exclude systematic measurement errors due to light deflection, the following analysis focuses on the homogeneous range from y = −5 mm to 5 mm.

The uncertainties of the measurements increase, when the signal-to-noise ratio decreases due to poor illumination. The area from x = 60 mm to 100 mm is well illuminated and shows a standard deviation of $0.2$ m/s for the velocity magnitude. In the poorer illuminated region, the standard deviation increases to $0.6$ m/s. Hence, PIV measurements of the laminar MWF supply flow are achieved with a standard deviation of approximately 4% in the well illuminated region despite the difficult measurement conditions regarding accessibility and the influence of light refraction.

Subsequently, the measurements of top and side views are compared to identify systematic influences of light refraction. Unlike the top view, the measurements from the side view show a linear decreasing velocity from $5.6$ m/s to $5.4$ m/s with a constant standard deviation of $0.2$ m/s. For better illustration of the flow velocity along the x-axis, the average along the y-axis is calculated and displayed in Figure 7 for the top view and the side view. The average velocities along the x-axis are displayed as a solid line and their standard deviation as the coloured background.

The top view shows a constant average velocity of $v_{\sup }=$ $5.55$ m/s without any significant changes along the x-axis. In comparison, in the side view at first a small increase from $5.6$ m/s to $5.64$ m/s is measured, until it decreases almost linearly to $5.4$ m/s. The differences in the velocity are attributed to the observation of seeding particles through the curved surface of the cylindrical edges. Due to light deflections, a systematic position deviation between the observed and original position of the tracer particles occurs, which leads to systematic measurement deviations for the position and thus also for the velocity. Although the side view measurements are systematically affected by light refraction, the differences between the measurements of both views are mostly smaller than $0.1$ m/s. Therefore, flow field measurements on the laminar MWF supply flow with PIV for top and side view are feasible.

4.3. Verification of SIV

To determine how the movement of the characteristic flow structures relates to the flow velocity, SIV and PIV measurements on the MWF supply flow are compared with each other and with the theoretically expected velocities $v_{\sup }$. For this purpose, the flow rate of $26.6$ L/min is used, which sets the MWF supply flow in a laminar to turbulent transient state. Minor characteristic flow structures are present, which allow measurements with SIV, and PIV provides plausible measurement results, since the seeding particles are still detectable. Similar to the analysis in Section 4.2, the 2d velocity fields of PIV and SIV for both views are determined.

In Figure 8a the average velocity fields of PIV and SIV from the top view are shown for the range x = 20 mm to 120 mm. The velocity fields of both measurements are in agreement and show a homogeneous flow field around $9.5$ m/s. It is noticeable that the PIV measurement indicates lower velocities at the lateral edges, which is caused by the refraction of light at the cylindrical geometry. On the other hand, the measurement with SIV in the positions x = 20 mm to 50 mm and z = 0 mm to −10 mm shows a slightly lower velocity.

In Figure 8b, the top view mean velocities and their standard deviations for the area without the cylindrical edge geometries (z = −5 mm to 5 mm) for PIV and SIV are displayed. The velocities are well matched and have a maximum deviation of $0.1$ m/s. A slight increase of the velocity in the range of x = 20 mm to 80 mm from $9.5$ m/s to $9.75$ m/s is noticeable, until the velocity remains constant. The increase of the velocity is within the measurement uncertainties caused by random measurement deviations and therefore no statements about a systematic deviation can be made. The standard deviation is almost constant for both measurements and amounts to $0.3$ m/s for PIV and $0.6$ m/s for SIV, respectively.

The measurements for the side view of the MWF supply flow are shown in Figure 8c. The flow field of the PIV measurement is in the range of 9.8m/s to 9.5m/s, whereas the SIV measurement is systematically $0.3$ m/s lower with velocities in the range of 9.5m/s to 9.2m/s. The mean velocities along the y-direction and their standard deviations are displayed in Figure 8d. Neglecting the offset of $0.3$ m/s, the curves of the velocities are almost identical for both measurements, with a standard deviation of $0.3$ m/s for PIV and $1.0$ m/s for SIV, respectively. It is expected that the offset results from the MWF flow controller of the grinding machine. The flow has to be stopped after each measurement and the flow controller has an estimated flow standard deviation of $0.5$ L/min, resulting in a velocity standard deviation of $0.18$ m/s. Nevertheless, the higher standard deviation of SIV shows the limitations of the measurements based on the characteristic flow structures. The superposition of characteristic structures from different planes provides a less precise measurement with SIV but still ensures velocity measurements from the MWF supply flow with standard deviations around $10.8$% in the side view.

To compare the measurement conditions with respect to the feasibility of PIV and SIV, the globally averaged velocities for the MWF supply volume flows of $14.9$ L/min and $26.6$ L/min are listed in

Table 3. Calculated and theoretical free jet velocities with standard deviations for PIV and SIV measurements of the MWF free jet.

$\mathit{Q}\mathbf{in}\mathbf{L}/\mathbf{min}$	View	${\mathit{v}}_{\mathbf{sup}}$ (PIV)	${\mathit{v}}_{\mathbf{sup}}$ (SIV)	${\mathit{v}}_{\mathbf{sup},\mathbf{theo}}$
14.9	top	($5.56\pm 0.20$) m/s	-	5.40 m/s
	side	($5.54\pm 0.17$) m/s
	rel. error	3.1–3.6%
26.6	top	($9.57\pm 0.33$) m/s	($9.62\pm 0.59$) m/s	9.60 m/s
	side	($9.63\pm 0.33$) m/s	($9.33\pm 1.01$) m/s
	rel. error	$3.6$%	6.1–10.8%

. The measurements with PIV have an almost constant standard deviation of $3.6$%, regardless of the view or the used volume flow. The SIV measurement of the top view has a $0.3$ m/s increased standard deviation of $0.6$ m/s ($6.1$%). Deformations of the characteristic flow structures explain the increased standard deviation for SIV. The deformation of the structures produces a sum of two velocity components: the motion of the entire structure plus the velocity of the deformation at its edges. The combination of the two velocity components increases the standard deviation while maintaining the mean value consistent. For the measurement of the side view, the standard deviation of SIV increases further by additional $0.4$ m/s to $1.0$ m/s ($10.8$%). This is caused by the superposition of the flow characteristics resulting from the observation along the width of the MWF flow. The structures from different depths cannot be distinguished from each other and a misallocation of the structures results in outliers which increases the calculated standard deviations. This assumption is confirmed by the unchanged standard deviation for PIV, where the observation of particles is reduced to the plane of the laser light sheet. This demonstrates that the PIV measurement provides a more precise flow measurement, but the SIV is an effective alternative.

Although the measurement with SIV is less precise than PIV, especially for the side view, the velocity fields of the MWF supply flow measured by PIV and SIV are nevertheless consistent within the limits of the measured standard deviations. In addition, the confidence intervals of the measured velocities for both measurement methods also agree with the theoretically expected velocities. This confirms the assumption of the applicability of the characteristic flow structures of the MWF supply flow for a velocity measurement.

4.4. Flow Field with Rotating Grinding Wheel

For the flow field measurements with the fluid-tool interaction, the MWF flow was generated with volume flows of 16.0 L/min, 26.6 L/min and 37.2 L/min with a nozzle outlet height of $h=0.9$mm. With SIV, a velocity field calculation of the flow before, with and after interaction is achieved based on the visualised flow structures. As a measure for the supply condition of the grinding process, the velocity ratio $R=\frac{v_{\sup }}{v_{\mathrm{g}}}$ of the MWF supply flow $v_{\sup }$ to the circumferential velocity of the grinding wheel $v_{\mathrm{g}}=$ 25 m/s is used. Currently, a range of R ≈ $0.8-1.0$ is assumed to be adequate for a sufficient MWF supply condition [7]. To obtain the quantitative MWF supply velocity $v_{\sup }$ from the SIV measurements, the flow structures in the homogeneous area of x = 80 mm to 110 mm are used (see Figure 9a). The velocity ratios R range from 0.496 to 1.04 and are listed in

Table 4. Measured flow velocities of the MWF supply flow $v_{\sup }$ and velocity ratio R for the used volume flows Q and added theoretical nozzle heights $h_{\mathrm{theo}}$ to discuss the deviation to the theoretical MWF supply flow velocities $v_{\sup ,\mathrm{theo}}$.

$\mathit{Q}\mathbf{in}\mathbf{L}/\mathbf{min}$	${\mathit{v}}_{\mathbf{sup}}\mathbf{in}\mathbf{m}/\mathbf{s}$	$\mathit{R}=\frac{{\mathit{v}}_{\mathbf{sup}}}{{\mathit{v}}_{\mathbf{g}}}$	${\mathit{v}}_{\mathbf{sup},\mathbf{theo}}\mathbf{in}\mathbf{m}/\mathbf{s}$	${\mathit{h}}_{\mathbf{theo}}\mathbf{in}\mathbf{mm}$
$16.0$	$12.4\pm 1.3$	$0.496\pm 0.052$	$14.78$	$1.075$
$26.6$	$19.1\pm 1.8$	$0.764\pm 0.072$	$24.63$	$1.116$
$37.2$	$26\pm 2.8$	$1.04\pm 0.11$	$34.48$	$1.192$

together with the measured and theoretical MWF supply flow velocities. To depict the results, the calculated average velocities are plotted in Figure 9 as colour-coded vectors in the corresponding shadowgram image.

To present the capabilities of SIV regarding the flow field of a grinding process, the determined flow fields are discussed qualitatively and quantitatively in relation to the MWF supply conditions. With the impact of the MWF on the grinding wheel at x = 120 mm, the flow splits in two parts. One part of the flow adheres to the surface of the grinding wheel and the other gets deflected. The adherent flow gets accelerated to the circumferential velocity of the grinding wheel until it loses adherence due to centripetal forces. This results in differences in velocity between the adherent and deflected flows, which can be seen in a sheared flow in the area of x = 180 mm to 280 mm and y = −20 mm to 0 mm. An increase in the velocity field in this area is observed for the volume flows of $16.0$ L/min ($R=0.50$) and $26.6$ L/min ($R=0.76$).

For the volume flow of $37.2$ L/min ($R=1.04$), the jet velocity is higher than the circumferential velocity of the grinding wheel, which leads to a different characteristic in the visualised flow field and its velocity field. In the region of x = 180 mm to 280 mm and y = −30 mm to −10 mm, a droplet structure is observable, which appears to be the deflected supply flow. Despite the interaction with the grinding wheel, the MWF is largely coherent and moves with a velocity above the circumferential velocity. The investigations indicate that for a velocity ratio $R=1.04>1$, most of the MWF gets deflected instead of entrained into the grinding process. This observation matches the fact that above a certain flow rate, no further increase in heat dissipation can be achieved [7]. A fluid dynamical change, which might describe this phenomenon, is explained by the qualitative visualisation of the flow, as well as the calculated quantitative flow field.

It is noticeable that the theoretically expected velocities $v_{\sup ,\mathrm{theo}}$ are significantly higher than the measured $v_{\sup }$. The reason for this cannot be clearly traced back. It is assumed that the 3D-printed resin nozzle expands with respect to the volume flows. Increasing the flow rate also increases the pressure inside the nozzle, which can lead to possible expansion of the orifice. To substantiate the assumption, theoretical heights of the nozzle are calculated from Equation (3) for the respective measured velocities and are added to Table 4. Considering the increase of the theoretical outlet opening that matches the measured flow velocities, small geometric deviations of the nozzle in the range of 0.175 mm to 0.292 mm might cause the difference in theoretical and measured supply velocities. Even though this study uses a special kind of nozzle, a measurement of the inflow condition is recommended for an accurate determination of the velocity ratio R. It should be noted that the velocity is evaluated at a distance of 80 mm to 110 mm instead of directly at the nozzle’s outlet. Although the velocity decreases with distance, as shown in Figure 8d, this is a minor effect that can be neglected.

A measurement limitation currently remains in the area of the first interaction of the MWF supply jet close to the grinding wheel (compare with the area of interaction as shown in Figure 1). The shape of the flow has changed in comparison to the free jet but is not yet torn apart into droplets. The flow is opaque and no flow structures are detectable. The two present flows in this area (deflected and entrained) are subsequently torn into droplets. The further the flow is apart from the grinding wheel, the more the flow separates into droplets. The detectability of the droplets and thus also the evaluability of the flow field increases steadily with the distance to the grinding wheel. Therefore, the obtained velocities before and after the interaction are plausible, and flow structures which are assignable to the flow fields and fluid dynamic phenomena like a shear layer are obtainable, whereas the flow velocity close to the grinding wheel is difficult to obtain with shadowgram imaging.

5. Conclusions and Outlook

In this study, the feasibility of optical measurements of the MWF flow in a grinding process is investigated for a simplified setup without workpiece. For this purpose, two different measurement methods (SIV and PIV) were implemented in a grinding machine. The majority of the presented flow field measurements is based on characteristic flow structures, which are visualised with shadowgraphy and used as flow tracers for SIV. The validity of this method is shown by comparison measurements of the supply flow with PIV reference measurements.

The standard deviations for the velocity measurements of the MWF free supply jet are determined from the measurement series, neglecting outliers. For PIV, a maximum standard deviation of 4% results, independent of the measurement arrangement. In comparison, the measurements for SIV showed a maximum standard deviation of 6% for the top view and 11% for the side view, respectively. The superposition of visualized fluid structures in different depths, combined with the change in shape of these structures, results in a significantly increased random deviation, especially in the side view. Nonetheless, the measurement results provide a first impression of the MWF flow, in particular of the average flow velocity, which is one of the most important parameters for the grinding process. In addition, the use of a theoretical velocity from the continuity equation is confirmed. Furthermore, the velocity measurements offer the possibility to detect unforeseen (e.g., pressure-related) geometric deviations of the nozzle geometry by a comparison of the theoretical and the measured velocity fields.

Systematic measurement deviations of the supply flow velocity are revealed, necessitating further investigations in order to provide an appropriately resolved measurement of the MWF supply flow behaviour along the jet axis. Measurement deviations are most likely contributed by the light deflection at the curved surface of the liquid-air phase transition.

The measured velocity flow fields after the interaction with the grinding wheel are verified by the plausibility of the visualised flows. The velocity changes that occur as a result of the interaction at the grinding wheel agree in magnitude and direction with the circumferential velocity of the grinding wheel. Only the flow in direct contact with the grinding wheel is not measurable due to the absence of visualisable fluid structures. Further research on the measurability of the flow in relation to the illumination conditions is therefore recommended.

The obtained results prove the feasibility of quantitative SIV-based flow velocity field measurements for the MWF supply flow as well as for the MWF flow after the grinding wheel interaction. This is a key step to the future understanding of the connection between the cooling properties of fluid dynamics and thus, to the ongoing development of optimised cooling in the grinding process.

In future investigations, the influence of a workpiece on the measurability of the flow directly in front of and behind the interaction zone has to be examined. For this purpose, a grinding setup with variable grinding gap will be used. When the fluid interacts with the grinding gap, not all of the fluid is coupled into the cooling process and the non-coupled portion bounces off the workpiece and tool. This results in a highly atomised backflow that affects the observation of the flow, and its impact on the flow measurement has to be determined. Furthermore, investigations to estimate the local mean fluid concentrations in the droplet regions of the MWF flow field are of interest, since the concentrations also influence the cooling performance. For this purpose, an approach to determine the concentrations from the captured shadowgram image intensities in the droplet regions will be tested.