Investigations on the Effect of Fluid Jet to Wheel Speed Ratio on Specific Grinding Energy

Abstract

The use of metalworking fluid (MWF) in surface grinding is essential, but its supply contributes notably to the process energy demand. This study investigates the effect of the fluid jet to wheel speed ratio q_s on specific grinding energy and associated CO₂ emissions. Experiments with grinding wheels of different grit sizes (F60–F120) were conducted at cutting speeds of 35 and 60 m/s. Critical specific material removal rates Q’_{w, crit} were determined by taper grinding, with the onset of grinding burn identified by Barkhausen noise analysis. Based on these values and the grinding wheel width, specific process energies e_total were derived from grinding, pump, and machine base load. F120 wheels showed no systematic dependence of Q’_{w, crit} on q_s, whereas for coarser F80 and F60 wheels, decreasing q_s from 1.0 to 0.6 increased Q’_{w, crit} by 13–27% at 35 m/s and decreased it by 33–35% at 60 m/s. The most efficient process (F60, 35 m/s, q_s = 0.6) required 152.8 J/mm³, the least efficient (F120, 60 m/s, q_s = 0.8) 333.1 J/mm³. Because CO₂ emissions scale with e_total, the relative differences in energy directly indicate relative differences in CO₂ output. An illustrative case study shows that adjusting q_s alone (F80, 35 m/s) lowers annual emissions from 0.284 t to 0.206 t, a reduction of approximately 27%. These findings highlight the influence of q_s on grinding efficiency and process energy demand.

1. Introduction

Grinding typically represents the final machining step for hardened mechanical components, such as shafts and gears, where any damage must be strictly avoided due to the high part value. During this operation, the workpieces are exposed to a combined thermomechanical load, with heat generation being the dominant factor [1,2]. Consequently, thermal alterations may develop in the subsurface, commonly manifesting as tempering zones [3]. These phenomena, generally referred to as grinding burn, can induce tensile residual stresses, hardness reductions due to tempering, or, in some cases, hardness increases caused by phase transformations and re-hardening at the surface [4,5,6,7]. Such changes can significantly impair functional properties, including wear resistance, and may lead to premature component failure in service [8,9]. In current industrial practice, thermal effects are commonly identified after grinding, with methods such as Barkhausen noise measurements being widely applied [2]. To maintain optimal functional properties and minimize thermomechanical damage during grinding, the application of metal working fluids (MWF) is essential due to their combined cooling and lubricating effects. Previous studies have shown that the efficiency of MWF delivery to the grinding contact zone depends on parameters such as flow rate, jet velocity, jet coherence determined by nozzle geometry, and nozzle positioning [10]. These parameters govern the MWF’s ability to penetrate the air barrier surrounding the rotating grinding wheel, enabling effective jet entrainment and heat dissipation, thereby influencing thermomechanical stresses and the risk of grinding burn [11,12,13,14,15]. Beyond these fluid-dynamic considerations, the grinding wheel’s topography and porosity significantly affect MWF transport. Coarser and more porous wheels (e.g., F60 and F80) provide larger pore volumes and more open surface structures, facilitating MWF penetration into the contact zone and increasing local flow rates [16,17,18,19]. Their pronounced macro- and microstructure may also strengthen air-barrier formation, requiring higher jet velocities for effective MWF delivery [11,12]. In contrast, fine-grained wheels such as F120 present smoother surfaces and lower pore volumes, resulting in fewer pathways for MWF entrainment and a weaker air barrier [15]. From a sustainability perspective, a demand-oriented MWF supply is advantageous, as it allows reductions in system size, pump power, disposal costs, and overall energy consumption. CO₂ emissions can be estimated from the total energy demand of the grinding process E_total and the corresponding CO₂ equivalent, see Equation (1).

$${CO}_{2 \mathrm{e}\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}=E_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\cdot {CO}_{2 equivalent}$$

(1)

The total energy demand E_total is derived from the total specific grinding energy e_total and the material volume removed V_W, see Equation (2):

$$E_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=e_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\cdot V_{\mathrm{W}}$$

(2)

This relationship highlights the importance of understanding the total process energy E_total, as CO₂ emissions are directly proportional to it and its individual components, such as e_total. Accordingly, examining E_total provides a valuable perspective on process efficiency and environmental impact. The total specific energy e_total is composed of the spindle-specific energy e_s, pump-specific energy e_p, and base load energy e_bl, each calculated from the corresponding electrical power per machined volume element, see Equation (3):

$$e_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=e_{\mathrm{s}}+e_{\mathrm{p}}+e_{\mathrm{b}\mathrm{l}}={\displaystyle \frac{P_{\mathrm{s}}}{Q_{\mathrm{W}}}}+{\displaystyle \frac{P_{\mathrm{p}}}{Q_{\mathrm{W}}}}+{\displaystyle \frac{P_{\mathrm{b}\mathrm{l}}}{Q_{\mathrm{W}}}}[{\displaystyle \frac{W\cdot s}{{\mathrm{mm}}^3}}]$$

(3)

Besides the base load P_bl (fundamental energy demand for hydraulics, etc.) of the grinding machine, the electrical energy which is converted into kinetic energy (rotational motion of the spindle with partial power P_S) and the energy required for the actual grinding process (process energy—position of spindle power P_S), the supply of the MWF to the contact zone accounts for a large proportion of the total energy needed, as a result of high required hydraulic power (pump power P_P), see Figure 1 (blue segment) [20].

A promising approach to reducing CO₂ emissions in the grinding process is to lower the jet velocity of the metalworking fluid (MWF). The pump power P_P, which represents the energy delivered to the fluid per unit time, can be determined for an incompressible fluid in steady flow, see Equation (4):

$$P_{\mathrm{P}}=Q_{\mathrm{M}\mathrm{W}\mathrm{F}}\cdot {\rho }_{\mathrm{M}\mathrm{W}\mathrm{F}}\cdot g\cdot h_{\mathrm{N}\mathrm{o}\mathrm{z}\mathrm{z}\mathrm{l}\mathrm{e}}$$

(4)

Using the MWF flowrate Q_MWF, the density of the MWF ρ_MWF, the gravitional acceleration g, and the height of the MWF-nozzle h_Nozzle. The flow rate itself can be approximated using the continuity equation, see Equation (5):

$$Q_{\mathrm{M}\mathrm{W}\mathrm{F}}=A_{\mathrm{N}\mathrm{o}\mathrm{z}\mathrm{z}\mathrm{l}\mathrm{e}}\cdot v_{\mathrm{j}\mathrm{e}\mathrm{t}}$$

(5)

with A_Nozzle being the nozzle outlet cross-section and v_jet the MWF jet velocity. From these relationships, it is evident that the pump power is directly proportional to the jet velocity, such that reducing v_jet results in a corresponding decrease in P_P. In the current state of the art, the speed ratio of q_s = 0.6–1.0 between MWF velocity v_jet and conventional cutting speed v_c of the grinding wheel, which is calculated according to Equation (6), is considered the optimal setting parameter for the MWF supply [12,14,16,21].

$$q_{\mathrm{s}}={\displaystyle \frac{v_{\mathrm{j}\mathrm{e}\mathrm{t}}}{v_{\mathrm{c}}}}$$

(6)

However, the topography and the pore structure of different grinding wheel specifications are not considered in these recommendations (e.g., open-pored ceramic corundum wheels with grit sizes F60, F80, or F120 grit sizes). Since wheel porosity, surface roughness, and air-barrier formation directly influence MWF entrainment, the interaction between the MWF jet and the wheel surface is expected to differ between wheel specifications. Furthermore, insufficient research has been conducted on determining the most efficient speed ratio at higher cutting speeds (e.g., 60 m/s), under constant conditions of the jet shape and nozzle positioning.

To address the identified gaps in understanding the influence of metalworking fluid supply on grinding efficiency and CO₂ emissions, this study systematically investigates the effect of the fluid jet to wheel speed ratio q_s in combination with different grinding wheel specifications (F120, F80, F60) and at two technologically relevant cutting speeds. A conventional speed of 35 m/s was selected as a representative baseline for standard grinding operations, while 60 m/s reflects a higher performance level that is increasingly used in modern grinding and is fully compatible with the thermal and mechanical limits of the open-pored ceramic corundum wheels employed in this work. This choice enables assessing whether established optimal MWF to wheel speed ratios remain valid at elevated cutting speeds, where air-barrier formation, MWF entrainment, and wheel topography may interact differently. Critical material removal rates were determined experimentally, and the corresponding specific process energies were calculated to quantify the relationship between q_s, wheel topography, cutting speed, and overall process efficiency. This approach allows evaluating the potential for optimizing MWF supply not only to improve grinding performance but also to reduce pump power demand and, consequently, CO₂ emissions associated with the grinding process.

2. Materials and Methods

To systematically investigate the influence of the fluid jet to wheel speed ratio q_s on specific grinding energy with respect to grinding wheel specification, two sets of experiments were conducted. The first series examined different grit sizes (F120, F80, F60) at a conventional cutting speed of v_c = 35 m/s. In a second series, the effect of an increased cutting speed of v_c = 60 m/s was analyzed. Figure 2 summarizes the varied parameters, illustrates the speed ratio, and shows the surface topographies of the grinding wheels used.

The rouse-nozzles used in the experiments were originally developed by Rouse et al. [22] and Webster et al. [14] to produce coherent fluid jets with minimal effort. This is achieved through an optimized internal contour that promotes favorable fluid-dynamic behavior. For this study, the nozzles with a rectangular outlet cross-section were 3D-printed from resin using stereolithography, as shown in Figure 3.

The outlet cross-section of the nozzles is rectangular, with a width B_Nozzle of 35 mm adapted to the grinding wheel to ensure uniform wetting over its 30 mm width, and a height H_Nozzle. The area of the nozzle outlet is thus given by A_Nozzle = B_Nozzle·H_Nozzle. By adjusting the height for a specific flow rate Q_MWF of 70 L/min, the corresponding jet velocity v_jet can be set. This enabled the realization of speed ratios q_s = v_jet/v_c of 1.0, 0.8, and 0.6 at cutting speeds of v_c of 35 m/s and 60 m/s. By substituting Equation (6) into Equation (5) and considering the rectangular nozzle cross-section, the required nozzle heights can be calculated using Equation (7):

$$H_{\mathrm{N}\mathrm{o}\mathrm{z}\mathrm{z}\mathrm{l}\mathrm{e},\mathrm{i}}={\displaystyle \frac{Q_{\mathrm{M}\mathrm{W}\mathrm{F}}}{B_{\mathrm{N}\mathrm{o}\mathrm{z}\mathrm{z}\mathrm{l}\mathrm{e}}\cdot v_{\mathrm{c},\mathrm{i}}\cdot q_{\mathrm{s},\mathrm{i}}}}$$

(7)

Table 1. H_Nozzles of the MWF-nozzles.

MWF-nozzle i	vc, i [m/s]	qs, i	HNozzle, i [mm]
MWF-nozzle 1	35	1	0.952
MWF-nozzle 2	35	0.8	1.19
MWF-nozzle 3	35	0.6	1.587
MWF-nozzle 4	60	1	0.55
MWF-nozzle 5	60	0.8	0.694
MWF-nozzle 6	60	0.6	0.926

summarizes the six MWF-nozzles and their corresponding H_Nozzle values, calculated for a constant flow rate of 70 L/min and a fixed nozzle width of 35 mm.

After production, the outlet cross-sections of all six 3D-printed MWF-nozzles were examined under a Zeiss light microscope (Zeiss, Oberkochen, Germany), see Figure 4.

The nozzles were not post-processed. Deviations from the nominal B_Nozzle and H_Nozzle dimensions were minimal, with maximum differences of 1.46 mm and 0.066 mm, respectively. These minor variations correspond to a maximum change in jet velocity of only 0.05 m/s, which is negligible for this study. All grinding tests were carried out on the surface grinding machine Blohm Profimat 412 HSG (Blohm Jung GmbH, Hamburg, Germany), as shown in Figure 5a. The taper grinding experiments were performed according to [23] and are schematically illustrated in Figure 5b. In Figure 5b, the depth of cut a_e is indicated in green, the cutting speed v_c in red, and the tangential feed speed in blue. During the experiments, the depth of cut a_e was continuously increased from 10 µm to 200 µm, while the tangential feed speed v_ft was kept constant within a single grinding pass at 3000, 4000, or 6000 mm/min. This approach enabled achieving specific material removal rates Q’_w of up to 10, 13.33, and 20 mm³/mm·s, thereby generating different thermomechanical loads within a single grinding operation. An oil-based metalworking fluid (MWF) was supplied through tangential MWF-nozzles at a constant flow rate Q_MWF = 70 l/min. The nozzle position and angle were kept constant for all experiments, in accordance with [24]. For each test condition, the corresponding MWF-nozzle, adapted to the MWF supply adapter produced in-house by 3D printing from resin (stereolithography), was mounted in the machining area. The flow rate Q_MWF was adjusted based on the nozzle outlet cross-section using a manual control dial on the grinding machine, allowing continuous regulation of the pump output of the hydraulic MWF system. The actual flow rate was continuously monitored using an inline flow meter with a digital display. To ensure a constant MWF supply during the grinding experiments, the MWF pressure p_MWF at the adapter located directly upstream of the nozzle was recorded continuously. Case-hardened workpieces, width × length × height = 20 mm × 80 mm × 30 mm, made of AISI 5120 (20MnCr5) supplied by ABRAMS Premium Stahl (Abrams Industries GmbH & Co. KG, Osnabrück, Germany), with a case-hardening depth of 1.2 mm and a hardness of 710 HV at a depth of 200 µm, were used for the experiments. Each grinding test was performed three times to ensure statistical validity. Prior to each test, the workpieces were pre-ground (a_e = 2 × 50 µm, v_ft = 500 mm/min) to ensure uniform initial conditions and consistent material removal. Ceramic-bonded corundum grinding wheels with a diameter of 400 mm (Tyrolit, Schwaz, Austria: SU33A120II10PVB1, SU33A80II10PVB1, SU33A60II10PVB1) were employed and dressed using a single-point diamond dresser (Riegger, Stuttgart, Germany; a_ed = 3 × 30 µm, U_d = 3). During the grinding experiments, tangential F_t and normal F_n forces were recorded using a Kistler dynamometer (type 9255B, Kistler, Winterthur, Switzerland). Base load power P_bl, which remained constant at 4 kW, and pump power P_P were measured using a Yokogawa WT500 power analyzer (Yokogawa, Tokyo, Japan). After grinding, the thermal effects associated with grinding burn were evaluated. Barkhausen noise measurements were applied to enable a quantitative and non-destructive assessment of thermally induced surface and near-surface alterations.

3. Results

3.1. Influence of the Speed Ratio q_s on the Critical Specific Material Removal Rate Q’_{w, crit}

For each of the 54 grinding tests, the critical specific material removal rate Q’_{w, crit} up to the occurrence of grinding burn was determined by Barkhausen noise measurements. Therefore, each characteristic trend of the Barkhausen noise amplitude along the grinding path of the taper grinding workpieces was recorded by a Stresstech Rollscan R350 (Stresstech, Vaajakoski, Finland; sensor: S8508; voltage: 5 V; frequency: 125 Hz; filter range: 70 Hz–200 Hz; air signal: 5.4 mp) and analyzed graphically. To calibrate the amplitude profiles, taper grinding processes were carried out, and metallographic cross-sections were prepared. For the case-hardened steel AISI 5120 (20MnCr5), it was found that the first slight tempering zones consistently appear at the inflection point of the Barkhausen noise amplitude curve and intensify progressively with increasing depth of cut along the taper grinding path. In Figure 6, the green area indicates undamaged material, the red area shows the affected (tempered) zone, and the dotted line marks the inflection point of the amplitude curve.

The fast and non-destructive analysis using Barkhausen noise measurement is therefore employed to reliably detect grinding burn. The critical specific material removal rate Q’_{w, crit} for each grinding test was calculated based on the critical depth of cut a_{e, crit}, which was determined from the geometry of the grinded ramp and the distance traveled along the measured path before grinding burn occurred. The corresponding tangential feed speed v_ft was also considered, see Equation (8):

$$Q_{\mathrm{w},\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}^{\prime }=a_{\mathrm{e},\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}\cdot v_{\mathrm{f}\mathrm{t}}$$

(8)

Depending on the quality of the MWF supply into the contact zone, the inflection point and thus the onset of grinding burn occurred at varying distances along the grinding path. Improved MWF supply enhances better cooling and lubrication effects [24], allowing higher specific material removal rates to be achieved before grinding burn occurs. Consequently, the influence of the fluid jet to wheel speed ratio q_s on the MWF supply, under varying cutting speeds and grinding wheel topographies, can be effectively demonstrated. The calculated critical specific material removal rate of each grinding test and its two repeats was averaged. At a cutting speed of 35 m/s, the F120 grinding wheel shows no clear dependency between the speed ratio q_s and the critical specific material removal rate, see Figure 7. The dashed arrows highlight the changes in the critical specific material removal rate across the investigated speed ratios and grinding wheel specifications. Across the three speed ratios 1.0, 0.8, and 0.6, the measured values fluctuate without a consistent direction. Although the standard deviations are not particularly high, their magnitude relative to the small changes in the mean values prevents the identification of a reliable trend. In contrast, the F80 and F60 wheels exhibit a distinct influence of the speed ratio. For the fine grit size F120, absolute variations in Q’_{w, crit} across the investigated speed ratios remained small and non-systematic at both cutting speeds. Therefore, no percentage change is reported for this wheel specification. For both F80 and F60 specifications, the critical specific material removal rate increases steadily as the speed ratio decreases from 1.0 to 0.6. For grit size F60, the mean critical specific material removal rate increased from Q’_{w, crit} ≈ 2.42 mm³/mm·s at q_s = 1.0 to ≈ 2.74 mm³/mm·s at q_s = 0.6, corresponding to an increase of approximately 13%. For grit size F80, Q’_{w, crit} increased from ≈ 2.25 mm³/mm·s to ≈ 2.86 mm³/mm·s, which corresponds to an increase of approximately 27%. The variation is sufficiently low to confirm this trend, and the more porous wheels achieve higher critical specific material removal rates than the finer F120 wheel.

At a cutting speed of 60 m/s, the behavior of the F120 wheel again shows no identifiable dependency between the speed ratio q_s and the critical specific material removal rate, see Figure 8. The dashed arrows mark the corresponding changes in the critical specific material removal rate. The values at the three speed ratios 1.0, 0.8, and 0.6 fluctuate in both directions, and the standard deviations remain at a level that does not allow a consistent trend to be derived. For the more porous F80 and F60 wheels, the standard deviations are somewhat higher than at 35 m/s, yet still sufficiently small to clearly reveal the underlying trend. In contrast to the observations at lower cutting speeds, the critical specific material removal rate now decreases systematically as the speed ratio is reduced from 1.0 to 0.6. For grit size F60, Q’_{w, crit} decreased from ≈ 3.34 mm³/mm·s at q_s = 1.0 to ≈ 2.24 mm³/mm·s at q_s = 0.6, corresponding to a reduction of approximately 33%. For grit size F80, a decrease from ≈ 2.8 mm³/mm·s to ≈ 1.83 mm³/mm·s was observed, representing a reduction of approximately 35%. Despite this reversal of the trend direction, the F80 and F60 wheels again reach higher critical specific material removal rates than the F120 wheel.

Overall, the results show that the influence of the speed ratio q_s on the critical specific material removal rate strongly depends on both the cutting speed and the porosity of the grinding wheel. For the fine grit size F120, no consistent trend can be identified at either cutting speed. The mean values at the three speed ratios 1.0, 0.8, and 0.6 show slight upward and downward fluctuations, but these changes remain small in magnitude and do not follow a systematic direction. The standard deviations, although moderate, are sufficiently large relative to these small variations to prevent the identification of a clear dependency. This behavior can be explained by the low pore volume and smooth surface topography of the F120 wheel. Due to its fine grain structure, the wheel provides fewer pathways for MWF entrainment and forms only a weak air barrier. As a result, variations in the jet to wheel speed ratio have only a minor effect on the actual MWF penetration into the contact zone, which explains why the small shifts in the mean values are still too small to indicate a systematic trend. In contrast, the more porous F80 and F60 wheels exhibit clear and reproducible trends. At 35 m/s, the critical specific material removal rate increases continuously as the speed ratio decreases, whereas at 60 m/s, the trend reverses and the critical specific material removal rate decreases with lower speed ratios. Across both cutting speeds, the F80 and F60 wheels consistently achieve higher critical specific material removal rates than the finer F120 wheel. These observations can be explained by the interaction between MWF jet entrainment and air-barrier formation. At lower cutting speeds, reduced jet reflection and improved entrainment enhance MWF penetration into the contact zone, enabling higher material removal rates at lower speed ratios. At higher cutting speeds, however, the intensified air barrier increasingly deflects slower jets, limiting MWF access to the contact zone and thereby reducing the achievable critical specific material removal rates when the speed ratio is decreased.

3.2. Calculation of the Specific Process Energy

The critical specific material removal rates Q’_{w, crit} solely give information about the productivity of the grinding processes. In order to value their efficiency, the specific process energies are taken into account. The total specific process energy e_total of a grinding process consists of the spindle energy e_s, the pump energy e_p, and the base load energy of the machine e_bl [20]. Due to the experimental setup used, the grinding power P_g replaces the spindle power P_s in the calculation of the total energy. Each summand is calculated from the applied power and the critical material removal rate of each process, see Equation (9):

$$e_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=e_{\mathrm{g}}+e_{\mathrm{p}}+e_{\mathrm{b}\mathrm{l}}={\displaystyle \frac{P_{\mathrm{g}}}{Q_{\mathrm{w},\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}}}+{\displaystyle \frac{P_{\mathrm{p}}}{Q_{\mathrm{w},\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}}}+{\displaystyle \frac{P_{\mathrm{b}\mathrm{l}}}{Q_{\mathrm{w},\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}}}[{\displaystyle \frac{J}{{\mathrm{mm}}^3}}={\displaystyle \frac{Ws}{{\mathrm{mm}}^3}}]$$

(9)

The grinding power P_g is calculated from the critical tangential grinding force F_{t, crit}, measured by the dynamometer, and the tangential feed speed v_ft, see Equation (10).

$$P_{\mathrm{g}}=F_{\mathrm{t},\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}\cdot v_{\mathrm{f}\mathrm{t}}$$

(10)

The pump power as well as the base load were measured with the power analyzer WT500 (Yokogawa, Tokyo, Japan). The base load remained constant throughout each test (P_bl = 4 kW). Q_{w, crit} is calculated as the product of the critical depth of cut obtained through Barkhausen noise analysis, the associated tangential feed speed, and the grinding wheel width. Depending on the power input and the material removed before grinding burn occurs, the partial specific process energies vary for each grinding test, see Figure 9.

The ratio between grinding power and the critical specific material removal rate remains nearly constant across all grinding tests, as both the critical tangential force F_{t, crit} and Q’_{w, crit} are governed by the ramp position and the corresponding critical depth of cut. In contrast, the specific pump energy and base load energy depend strongly on the fluid jet to wheel speed ratio q_s and cutting speed, see Figure 9. Since the volumetric flow rate Q_MWF is the product of nozzle cross-section and jet velocity, the hydraulic power demand of the MWF pump scales with fluid velocity. Consequently, lower speed ratios and lower cutting speeds (e.g., q_s = 0.6 at 35 m/s) enable higher Q’_{w, crit} and reduced pump and total specific energy, whereas higher q_s or elevated cutting speeds (60 m/s) increase the hydraulic and total energy due to higher jet velocities and limited MWF penetration. The specific base load energy e_bl follows the same trend, as the base load power remains constant while Q’_{w, crit} varies, resulting in the lowest e_bl for processes with the highest Q’_{w, crit}. Across all energy components, standard deviations increase slightly at higher cutting speeds for grit sizes F120 and F60, with a more pronounced increase for F80. By summing all partial energy contributions, the total specific process energy e_total is obtained, see Figure 10.

The grinding process using grit size F60 at 35 m/s, a tangential feed speed of 4000 mm/min, and q_s = 0.6 exhibits the lowest e_total of 152.75 J/mm³, representing the most energy-efficient configuration. In contrast, the process using grit size F120 at 60 m/s and q_s = 0.8 shows the highest e_total of 333.13 J/mm³, more than twice the energy per unit volume of material removed. These trends reflect the interplay between achievable material removal rates, MWF supply efficiency, and the associated pump and base load contributions. Coarser grit wheels (F80 and F60) generally achieve higher Q’_{w, crit} and lower total specific energy than F120. At higher cutting speeds, increased jet velocities elevate pump energy requirements, partially offsetting the benefits of higher Q’_{w, crit}. At lower speeds, reduced jet velocities allow more efficient MWF entrainment and lower pump energy. Overall, these observations illustrate the strong coupling between the fluid jet to wheel speed ratio, achievable material removal rates, and the corresponding energy components.

3.3. Consideration of the Carbon Footprint

Based on the differences in specific process energy identified in Section 3.2, the resulting impact on the carbon footprint of the grinding process is evaluated in the following. CO₂ emissions are calculated based on the total energy demand of the grinding process E_total and the CO₂ emission factor, see Equation (1). The total energy demand E_total is expressed as the product of the total specific energy e_total and the removed material volume V_W, see Equation (2). As stated in the Introduction, CO₂ emissions are directly proportional to the total process energy E_total and, consequently, to its individual energy components such as e_total. Therefore, differences in CO₂ emissions can be directly inferred from differences in energy demand. Therefore, differences in CO₂ emissions can be directly inferred from differences in energy demand. For illustrative purposes, an exemplary calculation of annual CO₂ emissions for the production of the workpieces is provided. The workpieces (width × height × depth = 20 mm × 30 mm × 80 mm) are processed in four grinding operations: two rough grinding strokes (a_{e, rough} = 0.1 mm) and two fine grinding strokes (a_{e, fine} = 0.05 mm). This results in a removed material volume of 416 mm³ per workpiece. Assuming a production of 100 workpieces per day, 5 days per week, and 52 weeks per year, the total removed material volume V_W amounts to 10,816,000 mm³.

3.3.1. Comparison of the Most and Least Efficient Grinding Tests

As shown in Figure 11, the total specific energy e_total for the most and least efficient grinding processes differs by 54%. Under the assumption of a constant CO₂ emission factor, this difference directly translates into a 54% difference in CO₂ emissions.

To machine the case study volume of V_w = 10,816,000 mm³, the least efficient process (e_total = 333.1 J/mm³) requires a total energy demand E_total of 1.001 MWh. Using a CO₂ emission factor of 0.435 t CO₂/MWh, as prescribed in [25], this corresponds to an annual CO₂ output of 0.435 t. In contrast, the most efficient process (e_total = 152.8 J/mm³) requires only 0.459 MWh, resulting in an annual CO₂ output of 0.199 t. It should be noted that different grinding wheels (with varying grit sizes), cutting speeds, and tangential feed speeds were used. Nevertheless, these calculations serve primarily to illustrate the magnitude of CO₂ savings and confirm that the relative difference in e_total directly determines the relative difference in CO₂ emissions.

3.3.2. Comparison of CO₂ Emissions by Adjusting Only q_s

To investigate the potential for reducing CO₂ emission solely by adjusting the fluid jet to wheel speed ratio, two grinding processes using the same grinding wheel (grit size F80) and cutting speed of 35 m/s are compared, with speed ratios q_s of 1 and 0.6, see Figure 12.

The process with a speed ratio q_s of 0.6 has been shown to be more efficient due to its lower specific energy consumption. Applying the respective process energies to the calculation example, the resulting annual CO₂ emissions are 0.206 t for a speed ratio of 0.6 and 0.284 t for a speed ratio of 1. The more efficient process thus achieves a reduction in CO₂ emissions of approximately 27%. These efficiency gains also result in lower power consumption costs.

4. Discussion

The results presented in Section 3.1, Section 3.2 and Section 3.3 provide a comprehensive overview of how the fluid jet to wheel speed ratio q_s influences grinding performance, energy consumption, and the associated carbon footprint. In Section 3.1, the critical specific material removal rates Q’_{w, crit} were determined for different grinding wheels and cutting speeds. At 35 m/s, decreasing speed ratios q_s increase Q’_{w, crit} for coarser wheels (F80 and F60) due to improved MWF entrainment, whereas at 60 m/s the trend reverses as slower jets are deflected by an intensified air barrier. Fine grit wheels (F120) show no systematic dependency of Q’_{w, crit} on q_s, with comparatively low achievable material removal rates. Section 3.2 shows that variations in q_s predominantly affect the thermal and hydraulic energy demand, while the ratio between grinding power and Q’_{w, crit} remains nearly constant. Lower speed ratios (e.g., q_s = 0.6) at 35 m/s achieve higher Q’_{w, crit} and lower pump and total specific energy, whereas at 60 m/s the same q_s coincides with lower Q’_{w, crit} and increased total energy due to limited MWF penetration. Base load energy follows the same dependency. Section 3.3 implicates the carbon footprint of the grinding process. CO₂ emissions scale proportionally with total energy E_total, and comparison of the most and least efficient processes shows a 54% difference in e_total, corresponding to a 54% difference in annual CO₂ emissions. For 10,816,000 mm³ of material, this translates to 0.435 t CO₂ for the least efficient and 0.199 t CO₂ for the most efficient process. Adjusting q_s alone for F80 wheels at 35 m/s reduces annual CO₂ emissions from 0.284 t to 0.206 t (~27%), illustrating that changes in e_total directly translate into equivalent changes in emissions. Building on these results, several aspects warrant further investigation. In particular, the influence of the fluid jet to wheel speed ratio q_s when using medium porous grinding wheels compared to open-pore grinding wheels needs to be clarified. Moreover, the point at which the inversion of the trend occurs, where lower jet speeds begin to negatively affect process efficiency, should be determined. Finally, the effect of the air barrier on the interaction between the MWF and the grinding wheel, depending on the fluid jet to wheel speed ratio q_s, needs to be investigated in future research. Addressing these aspects will contribute to a deeper understanding of the mechanisms of interaction and, ultimately, to the design of more energy-efficient grinding processes.

5. Conclusions

This study investigated the influence of the fluid jet to wheel speed ratio (q_s) on grinding performance, energy demand, and associated CO₂ emissions in surface grinding. Using taper grinding experiments, critical specific material removal rates were determined for grinding wheels with different grit sizes (F60–F120) at cutting speeds of 35 m/s and 60 m/s, with the onset of grinding burn identified by Barkhausen noise analysis. Based on these critical limits, the total specific process energy was quantified by considering grinding, pump, and machine base load contributions. The results demonstrate that the effectiveness of q_s strongly depends on both cutting speed and wheel topography, leading to substantial differences in achievable material removal rates and energy efficiency. Consequently, optimizing q_s offers significant potential to improve grinding efficiency and reduce the carbon footprint of grinding processes, particularly for coarser and more porous grinding wheels.

Key Findings

• F120 (fine grit):

  ○

  No systematic effect of q_s on critical specific material removal rate (Q’_{w, crit}) at either cutting speed. Minor fluctuations only.
• F80 and F60 (coarser grit):

  ○

  35 m/s: Decreasing q_s from 1.0 → 0.6 increases Q’_{w, crit}:

  ▪

  F60: ≈ 2.42 → 2.74 mm³/mm·s → +13%

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  F80: ≈ 2.25 → 2.86 mm³/mm·s → +27%

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  60 m/s: Same reduction decreases Q’_{w, crit}:

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  F60: ≈ 3.34 → 2.24 mm³/mm·s → −33%

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  F80: ≈ 2.8 → 1.83 mm³/mm·s → −35%

• Specific process energy (e_total):

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  Most efficient: F60, 35 m/s, q_s = 0.6 → 152.8 J/mm³

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  Least efficient: F120, 60 m/s, q_s = 0.8 → 333.1 J/mm³

• Carbon footprint (CO₂):

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  Adjusting q_s alone (F80, 35 m/s) reduces annual CO₂ emissions from 0.284 t → 0.206 t (~27% reduction). This demonstrates that relative changes in e_total directly translate into equivalent changes in CO₂ output.

The fluid jet to wheel speed ratio (q_s) significantly affects both productivity and overall grinding efficiency. For fine grit wheels (F120), only minor, non-systematic variations in Q’_{w, crit} were observed at both cutting speeds, while coarser wheels (F80 and F60) showed a strong dependency. At 35 m/s, decreasing q_s from 1.0 to 0.6 increased Q’_{w, crit} by approximately 13% for F60 and 27% for F80. Conversely, at 60 m/s the same reduction decreased Q’_{w, crit} by 33% for F60 and 35% for F80. Analysis of specific process energy e_total confirms these trends. The most efficient process (F60, 35 m/s, q_s = 0.6) required 152.8 J/mm³, whereas the least efficient (F120, 60 m/s, q_s = 0.8) required 333.1 J/mm³. The ratio between grinding power and Q’_{w, crit} remains nearly constant, indicating that variations in q_s predominantly affect thermal and hydraulic energy demand rather than mechanical cutting load. Lower speed ratios (q_s = 0.6) at 35 m/s allow high Q’_{w, crit} and reduced pump and total specific energy, whereas at 60 m/s the same low speed ratios coincide with lower Q’_{w, crit} and increased total energy due to limited MWF penetration. The specific base load energy follows a similar trend. Applying these results to a case-study production volume, adjusting q_s alone for F80 wheels at 35 m/s reduces annual CO₂ emissions from 0.284 t to 0.206 t (~27%), demonstrating that relative changes in e_total directly translate into equivalent changes in emissions. Overall, optimizing q_s enhances grinding efficiency, reduces energy consumption, and lowers the carbon footprint, particularly for coarser grit wheels, emphasizing the strong coupling between fluid jet to wheel speed, achievable material removal rates, energy components, and the resulting environmental impact.