Interactive Friction Modelling and Digitally Enhanced Evaluation of Lubricant Performance During Aluminium Hot Stamping

Abstract

Conventional lubricant testing methods focus on lab-scale constant contact conditions, which cannot represent the scenarios in actual hot-stamping processes. In recent studies, the concept of the ‘digital characteristics (DC)’ of metal forming has been proposed by unveiling the intrinsic nature of the specific forming, which presents a timely solution to address this challenge. In this work, the transient behaviours of three dedicated lubricants during the hot stamping of AA6111 material were investigated considering the effects of various contact conditions using an advanced friction testing system, and the interactive friction modelling was established accordingly. The lubricant limit diagram (LLD) of each lubricant was then generated to quantitatively evaluate the lubricant performance following the complex tool–workpiece interactions based on the tribological DCs, and a detailed investigation on the lubricant failure regions was conducted based on the interactive friction modelling. Finally, the industrial application index (IAI) was proposed and defined as a comprehensive evaluation of lubricant applications in the industry, and the most suitable lubricant was identified among the three candidates for mass production.

1. Introduction

In hot-forming processes, particularly when working with aluminium alloys, the application of lubricant at the tool–workpiece interfaces plays a critical role in optimising performance. Lubricants are primarily used to reduce friction between the tool and the workpiece, which not only minimises wear on the forming tools but also helps prevent surface defects on the formed components [1]. Due to the adhesive nature of aluminium alloy, galling wear on the tooling surface is inclined to occur, especially during the mass production of hot-formed components [2,3,4]. From this perspective, the lubricant acts as a medium to facilitate smoother material flow during the deformation process, ensuring better formability and minimising the risk of aluminium galling [5,6].

The importance of lubricant selection becomes even more pronounced in hot forming due to the elevated temperatures involved. Identifying suitable lubricant candidates for the hot forming of aluminium alloys is a complex task. The lubricant must meet specific criteria, such as providing sufficient lubricity across a wide temperature range, exhibiting low thermal degradation, and ensuring compatibility with the material being formed. Additionally, it must offer long-term durability during multiple forming operations and be easy to apply and remove without causing contamination or affecting the surface finish of the final product [7,8].

A wide range of lubricant evaluation techniques have been proposed and investigated in the literature for different application scenarios. To evaluate the lubricant efficiency in mechanical systems such as bearings or transmissions, ball-on-disc tests have been widely used to simulate these contact conditions, where a long sliding distance over the same wear track was tested with a continuous feed of lubricant [9,10]. Alternatively, various types of specifically designed lubricant testing methods were proposed to emulate a range of forming processes. For example, ring compression tests and T-shape compression tests are usually utilised to investigate the lubricant behaviour and interfacial conditions during forging processes [11,12,13,14]. Strip drawing tests, bending-over-tension tests, and strip reduction tests are typical simulative tests for the sheet metal stamping process to represent tribological conditions in different localised regions (e.g., blank holder area, die shoulder, and side wall) featured by distinct contact pressure, sliding distance, and surface expansion [5,15,16].

However, these conventional testing methods focus on lab-scale constant contact conditions, which is not the case in actual hot-forming processes. In actual forming scenarios, the interfacial contact conditions experience a highly dynamic and complex evolution history [17,18] due to tooling movement, material flow, and complicated geometries of the formed component [19,20,21]. The lubricant performance is highly dependent on the instantaneous contact conditions, which necessitates a comprehensive understanding of the complex contact conditions at the tool–workpiece interface [22,23,24].

The recent advancements in data science and digital technologies within the metal-forming industry present a timely and valuable opportunity to address these challenges [25,26,27]. Techniques such as machine learning, big data analytics, and artificial intelligence (AI) have made it possible to gather, analyse, and model vast amounts of real-time and proactive data from forming operations [28,29,30,31]. In recent studies, the concept of the ‘digital characteristics (DC)’ of metal-forming processes has been proposed, which unveils the intrinsic nature of the specific forming by visualising the manufacturing metadata captured across the design, manufacturing, and application phases of the formed components [19,20].

The tribological DC enables a deeper understanding of how lubricants behave under different conditions, facilitating the identification of patterns and correlations that would be difficult to discern through traditional trial-and-error methods. Additionally, the integration of sensor technologies and real-time monitoring systems allows for continuous feedback and adaptive control of the forming process [32,33,34,35], ensuring that lubricants are performing as expected and adjustments can be made instantly to maintain optimal conditions. By applying these data-driven approaches, manufacturers and researchers can develop predictive models to simulate complex tool–workpiece interactions and optimise lubricant performance.

Advanced interactive friction modelling has been established to enable accurate descriptions and predictions of the transient lubricant behaviour under complex loading conditions [16,22]. Additionally, robust evaluation of the lubricant performance via the reproduction of actual forming loading history can be accomplished by a combination of the advanced friction modelling and digital characteristics. This makes it possible to bridge the gap between lab-scale lubricant testing and actual application in the real forming of industrial-scale components [19].

In this work, the transient lubricant behaviour of each of the three lubricants during hot stamping will be investigated under various contact conditions, such as interfacial temperature, contact load, and relative sliding speed, by using a dedicated friction testing system. The interactive friction model will be established for each lubricant accordingly and lubricant limit diagrams (LLDs) will be generated to quantitatively evaluate the lubricant performance following the complex tool–workpiece interactions and identify the best lubricity. Furthermore, a detailed evaluation and comparisons among these lubricants will be conducted in terms of the key feature regions during the hot stamping. Finally, the industrial application index is proposed, and the optimal lubricant product will be identified for the application of the hot stamping of aluminium alloys.

2. Methodology

Friction tests were conducted between the AA6111 blank under the T4 condition as the workpiece material and P20 tool steel under the pre-hardened condition as the die material. The workpiece and die materials were provided by Novelis and West Yorkshire Steel, respectively. Three dedicated lubricant candidates developed for the novel hot-stamping process were studied and evaluated in this work. The detailed information and lubricant properties are listed in

Table 1. Lubricant properties of three candidates studied in this work.

	Specific Gravity @ 15 °C	Kinematic Viscosity (cSt) @ 40 °C	Dry Matter (%)
Lubricant #1	0.92	123	0.15
Lubricant #2	1.05	463	0.24
Lubricant #3	0.89	372	0.59

.

The advanced friction testing system, TriboMate [22,24] (as shown in Figure 1), was utilised via a pin-on-strip setup to study the transient lubricant behaviour of each lubricant under complex loading conditions. This testing system was composed of a flexible robotic arm and a precision thermal box, which enables precise motion, load, and temperature implementation during testing. The pin specimen had a spherical tip shape with a diameter of 6 mm. The workpiece strip had a thickness of 2 mm. During each test, the lubricant was applied on the cold pin tip by using a dedicatedly designed lubricant reservoir for accurate application volume control. Subsequently, the sliding test was initiated when the hot specimen reached the target testing temperature. A flowchart of the testing procedure is shown in Figure 2. The coefficient of friction (COF) evolution was recorded as the function of the sliding distance and each testing condition was repeated at least three times.

3. Experimental Studies and Interactive Friction Modelling of the Transient Lubricant Behaviour

3.1. Experimental Results and Discussion of the Transient Lubricant Behaviour

During the relative sliding process, the lubricant entrapped at the tool–workpiece interfaces was consumed due to various reasons, such as physical transfer or squeeze-out and high-temperature degradation. This leads to the reduction in lubricant thickness at the contact interfaces until a critical value is reached and the breakdown phenomenon occurs. As a consequence of the lubricant breakdown, the COF value increased as the sliding distance increases, demonstrating a transient lubricant behaviour. The transient lubricant behaviour was highly dependent on the interfacial contact conditions, such as interfacial temperature, contact pressure, and relative sliding speed. Therefore, to investigate the transient behaviour of the three lubricant candidates, friction tests were conducted under various contact conditions, as shown in Figure 3, Figure 4 and Figure 5. The testing matrix of each lubricant candidate is shown in

Table 2. A test matrix for studying the transient behaviours of lubricant #1.

Test Condition No.	Temperature (°C)	Load (N)	Speed (mm/s)
1	300	5	30
2	300	5	50
3	300	10	50
4	250	5	30
5	250	5	50
6	250	10	50

,

Table 3. A test matrix for studying the transient behaviours of lubricant #2.

Test Condition No.	Temperature (°C)	Load (N)	Speed (mm/s)
1	250	5	50
2	300	5	50
3	350	5	50
4	400	5	50
5	300	10	50
6	300	5	30

and

Table 4. A test matrix for studying the transient behaviours of lubricant #3.

Test Condition No.	Temperature (°C)	Load (N)	Speed (mm/s)
1	250	5	30
2	300	5	30
3	350	5	30
4	400	5	30
5	300	10	50
6	300	5	50

. Different testing conditions were selected to clearly demonstrate the effects of temperature, load, and speed on the transient lubricant behaviours of each candidate within the typical sliding distance of the hot-stamping process, i.e., 75 mm.

As shown in Figure 3a, for lubricant #1, when the interfacial temperature increased from 250 °C to 300 °C while keeping the contact load of 5 N and sliding speed of 50 mm/s unchanged, the friction value at the initial low stage increased from approximately 0.11 to 0.24 and an earlier lubricant breakdown was observed with a decrease in the breakdown distance from 15 mm to less than 1 mm. This was probably due to the decrease in the lubricant viscosity and increase in the lubricant evaporation and degradation at elevated temperatures, leading to more lubricant being consumed during the sliding process. When the interfacial temperature remained at 250 °C and the contact load increased from 5 N to 10 N, the lubricant breakdown distance decreased from approximately 33 mm to 13 mm, as shown in Figure 3b. This could be caused by the fact that as the contact load, namely contact pressure, increased, more lubricant was transferred onto or squeezed out of the wear track, leading to quicker entrapped lubricant consumption and thus an earlier lubricant breakdown. As the relative sliding speed decreased from 50 mm/s to 30 mm/s under the interfacial temperature of 250 °C and contact load of 5 N, there was no significant difference in the initial friction value, although the lubricant breakdown was postponed with the increase in sliding distance from 33 mm to 49 mm. This was due to the decrease in the lubricant viscosity caused by the frictional heat generated at elevated sliding speeds [36].

In terms of lubricant #2, the effects of contact conditions on the transient lubricant behaviour were investigated, and the results are shown in Figure 4. As the interfacial temperature increased from 250 °C to 400 °C, there was a trend where COF values increased and lubricant breakdown distances decreased. For example, when the temperature increased from 300 °C to 400 °C, the friction value at the initial low-friction stage increased from approximately 0.21 to 0.33 with the lubricant breakdown distances decreasing from 33 mm to less than 2 mm. While the temperature remained unchanged at 300 °C and relative sliding speed at 50 mm/s, the increase in contact load from 5 N to 10 N would lead to an earlier lubricant breakdown from a distance of 33 mm to 20 mm. It was interesting to observe that when the sliding speed decreased from 50 mm/s to 30 mm/s at a temperature of 300 °C, there was little difference introduced on the breakdown distance. This phenomenon was probably due to the competing effects of two factors. On the one hand, the entrapped lubricant thickness would increase as the inletting sliding speed increased [37,38]; on the other, the decrease in the lubricant viscosity caused by the generation of frictional heat led to a reduction in the entrapped thickness.

Figure 5 demonstrates the COF evolutions of lubricant #3 as a function of the sliding distance under various contact conditions including temperature, load, and speed. As shown in Figure 5a, the effect of interfacial temperature on the transient lubricant behaviours was investigated. Unlike lubricant #2, which presented a monotonic trend of lubricity deterioration as the temperature increased, the behaviour of lubricant #3 was influenced by temperature in a more complex manner. When the temperature increased from 300 °C to 350 °C while keeping the contact load of 5 N and sliding speed of 30 mm/s unchanged, the lubricant breakdown phenomenon was postponed from approximately 51 mm to over 75 mm, indicating an enhancement in the performance as the temperature increased. However, as the temperature increased from 350 °C to 400 °C and other conditions remained unchanged, the breakdown distance decreased to approximately 52 mm. This contrasting trend of temperature effect was probably caused by the contact pressure decrease accompanied by the temperature increase. Although the contact load was unchanged as 5 N, the aluminium material became soft as the temperature increased, thus leading to a larger contact area and lower pressure at the interface. The effect of the contact load and sliding speed on the transient behaviour of lubricant #3 shared a similar trend as lubricant #1, namely the increase in contact load and sliding speed accelerated the lubricant breakdown phenomenon.

3.2. Interactive Friction Modelling

The transient behaviour and lubricant breakdown phenomenon are determined by the transformation process of interfacial friction mechanisms from the boundary lubrication condition to the final metal-to-metal contact, namely the dry sliding condition. Accordingly, the friction value remains at a low level and rapidly increases to a high plateau due to the friction mechanism transition. To accurately describe and predict the transient lubricant behaviour considering the effects of contact conditions and process parameters, such as interfacial temperature, contact pressure, relative sliding speed, and surface roughness, a novel interactive modelling framework has been established based on this mechanism transition. The model equations are listed as Equations (1)–(5).

$$\mu \left(t\right)=\left(1-\beta \right){\mu }_l\left(t\right)+\beta {\mu }_d\left(t\right)$$

(1)

$$\beta =\mathrm{e}\mathrm{x}\mathrm{p}\{-{\left[{\displaystyle \frac{h_t\left(t\right)}{{\lambda }_1}}\right]}^{{\lambda }_2}\}$$

(2)

$$h_t\left(t\right)=h_l\left(t\right)+h_s\left(t\right)$$

(3)

$$\dot{h_l}\left(t\right)=c\left[h_l\left(t\right)·{\displaystyle \frac{P^{k_1}{v}^{k_2}}{{\eta }^{k_{\eta }}}}\right]+D_l(T){\left[h_l\left(t\right)\right]}^{k_{\alpha }}$$

(4)

$$\dot{h_s}\left(t\right)=m{D}_l\left(T\right){\left[h_l\left(t\right)\right]}^{k_{\alpha }}-K(T){\displaystyle \frac{P^{n_P}{v}^{n_v}}{H_c}}$$

(5)

Detailed derivation procedures of the interactive modelling equations and definitions of the model parameters have been thoroughly investigated and depicted in references [16,22].

The calibration and optimisation of interactive friction model parameters was performed by minimising the overall deviations between experimental results and model predictions under various contact conditions, as expressed in Equation (6).

$$f\left(x\right)=\sum _{i=1}^r{({\mu }_i^e-{\mu }_i^p)}^2$$

(6)

where $f\left(x\right)$ is the sum of deviations for the friction values between experimental results, ${\mu }_i^e$, and model predictions, ${\mu }_i^p$, under all testing conditions and $x$ is a vector representing the model parameters to be determined. In addition, $r$ is the total number of testing points during the calibration.

The calibrated model parameters for the three lubricant candidates #1–#3 are demonstrated in

Table 5. Model parameters of the interactive friction modelling for lubricant #1.

Parameter	${\lambda }_1 \left(\mathsf{\mu }\mathrm{m}\right)$	${\lambda }_2 (-)$	$k_1 (-)$	$k_2 (-)$	$k_{\alpha } (-)$	$k_s (-)$
Value	1.25	2.45	1.85	1.48	0.44	1.20
Parameter	$D_0 \left({\mathrm{s}}^{-1}\right)$	$Q_D (\mathrm{k}\mathrm{J}·{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1})$	$c \left[\mathrm{m}\mathrm{m}{\left(\mathrm{G}\mathrm{P}\mathrm{a}·\mathrm{s}\right)}^{-1}\right]$		${\eta }_0 \left({\mathrm{m}\mathrm{m}}^2{\mathrm{s}}^{-1}\right)$	$Q_{\eta } (\mathrm{k}\mathrm{J}·{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1})$
Value	1.52 × 109	12.29 × 101	7.04 × 104		0.090	18.81
Parameter	$K_0 \left({\mathrm{s}}^{-1}\right)$	$Q_K (\mathrm{k}\mathrm{J}·{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1})$	$n_P (-)$	$n_v (-)$	$k_{\eta } (-)$	$m (-)$
Value	5.43 × 104	77.26	1.55	1.89	7.45	0.15

,

Table 6. Model parameters of the interactive friction modelling for lubricant #2.

Parameter	${\lambda }_1 \left(\mathsf{\mu }\mathrm{m}\right)$	${\lambda }_2 (-)$	$k_1 (-)$	$k_2 (-)$	$k_{\alpha } (-)$	$k_s (-)$
Value	1.24	2.56	1.85	1.21	0.40	1.19
Parameter	$D_0 \left({\mathrm{s}}^{-1}\right)$	$Q_D (\mathrm{k}\mathrm{J}·{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1})$	$c \left[\mathrm{m}\mathrm{m}{\left(\mathrm{G}\mathrm{P}\mathrm{a}·\mathrm{s}\right)}^{-1}\right]$		${\eta }_0 \left({\mathrm{m}\mathrm{m}}^2{\mathrm{s}}^{-1}\right)$	$Q_{\eta } (\mathrm{k}\mathrm{J}·{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1})$
Value	7.03 × 107	10.53 × 101	9.03 × 104		0.099	2.20
Parameter	$K_0 \left({\mathrm{s}}^{-1}\right)$	$Q_K (\mathrm{k}\mathrm{J}·{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1})$	$n_P (-)$	$n_v (-)$	$k_{\eta } (-)$	$m (-)$
Value	5.52 × 104	68.21	1.65	1.92	5.50	0.24

and

Table 7. Model parameters of the interactive friction modelling for lubricant #3.

Parameter	${\lambda }_1 \left(\mathsf{\mu }\mathrm{m}\right)$	${\lambda }_2 (-)$	$k_1 (-)$	$k_2 (-)$	$k_{\alpha } (-)$	$k_s (-)$
Value	0.94	3.09	1.205	2.14	1.56	1.625
Parameter	$D_0 \left({\mathrm{s}}^{-1}\right)$	$Q_D (\mathrm{k}\mathrm{J}·{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1})$	$c \left[\mathrm{m}\mathrm{m}{\left(\mathrm{G}\mathrm{P}\mathrm{a}·\mathrm{s}\right)}^{-1}\right]$		${\eta }_0 \left({\mathrm{m}\mathrm{m}}^2{\mathrm{s}}^{-1}\right)$	$Q_{\eta } (\mathrm{k}\mathrm{J}·{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1})$
Value	1.31 × 104	59.40	19.30		2.83	12.70
Parameter	$K_0 \left({\mathrm{s}}^{-1}\right)$	$Q_K (\mathrm{k}\mathrm{J}·{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1})$	$n_P (-)$	$n_v (-)$	$k_{\eta } (-)$	$m (-)$
Value	4.82 × 104	68.32	1.60	1.99	2.49	0.59

, respectively. The comparisons of the COF evolution curves between the experiments and modelling predictions are shown in Figure 3, Figure 4 and Figure 5, where the scatter represents experimental results and solid lines represent modelling predictions. Good agreements (with deviations less than 8%) have been achieved between experimental and modelling results for all three lubricants. It has been thoroughly investigated and validated that the interactive model can accurately describe and predict transient lubricant behaviours under complex loading conditions after calibration against a minimum number of tests under various constant conditions [21,22].

4. Digitally Enhanced Evaluation and Comparison of Lubricant Performance

Many lubricant testing methods have been proposed to evaluate lubricity under lab-scale testing conditions, which may introduce inaccuracy and deviations from the real forming process due to additional complexity of the real component. Therefore, a novel lubricant evaluation method has been established to evaluate lubricant performance by considering the contact condition evolution and forming history experienced during the actual industry-scale forming process [19,20]. The actual contact loading history can be fully captured by the tribological DC, which demonstrates a highly dynamic and complex loading pattern. Consequently, the developed interactive friction models are utilised to describe and predict transient lubricant behaviour following these complex loading conditions, presenting a more robust and relevant lubricant performance evaluation aiming for the real forming world.

An example of how to implement the interactive modelling in the prediction of transient lubricant behaviour following the evolution history of contact conditions experienced during the forming process is shown in the subsequent figures. Figure 6a shows the evolutions of contact conditions, such as interfacial temperature, contact pressure, and relative sliding speed, as a function of sliding distance for one randomly selected element at the tool–workpiece interface, which presents a highly dynamic feature. As the interactive model is time-dependent, the changing contact conditions can be input into the model for each time step and the corresponding COF value can be calculated, as shown in Figure 6b.

The friction value at the initial low stage, i.e., before the breakdown occurs, is influenced by the lubricant types and additives contained, which can hardly be used as a standard benchmark for the determination of lubricant failure in terms of different lubricant products. Therefore, the lubricant performance grade for lubricity, $PG$, is introduced and transformed from the corresponding COF value by considering the underlying mechanism of lubricant failure, as expressed in Equation (7).

$$PG (\%)=\left\{\begin{array}{c}100, \mu \left(t\right)={\mu }_l\left(t\right)\\ 100·\left({\displaystyle \frac{{\mu }_d-\mu }{{\mu }_d-{\mu }_1}}\right), {\mu }_l\left(t\right)<\mu \left(t\right)<{\mu }_d\left(t\right)\end{array}\right.$$

(7)

where $\mu \left(t\right)$ is the instantaneous COF value; ${\mu }_l\left(t\right)$ and ${\mu }_d\left(t\right)$ are friction values under the boundary lubrication condition and dry sliding condition, respectively. The grade is 100% before the lubricant breakdown occurs. It starts to decrease as the COF increases due to the transition from boundary lubrication to dry sliding. By applying Equation (7) into the example COF evolution, the performance grade evolution as a function of the sliding distance can be obtained and demonstrated, as shown in Figure 6b.

The same evaluation procedure can be applied for each individual element at the tool–workpiece interface and the COF and performance grade evolutions can be obtained accordingly based on the developed interactive friction models and tribological DCs of the target-forming process. This generates a data package which incorporates all the tribological-related information ranging from interfacial conditions and process parameters to the corresponding instantaneous lubricant behaviours and performance grades, which can be visualised using the dedicated lubricant limit diagram (LLD).

The LLD has been developed to intuitively demonstrate and quantitatively evaluate the lubricant performances following a DC-guided approach [19,20]. The overall lubricity performance grade (OPG) is calculated by averaging the performance grade of the individual element for each forming step. Figure 7 shows the LLDs of the three lubricant candidates when applied to the hot-stamping process. The colour bar indicates the distinct lubricant performance under various contact conditions, e.g., contact pressure and sliding distance, with the blue denoting good lubricity and red for lubricant failure. The OPG value provides a quantitative and comparable criterion for identifying the suitable lubricant candidate for the target forming process. In this case of hot stamping, lubricant #1 only demonstrates an OPG of 69.4%, while lubricant #3 shows a much higher value of 98.5%, indicating only 1.5% of elements fail during the hot-stamping process. This comparison can also be intuitively observed by the colour maps, with Figure 7a showing more red regions and Figure 7c mostly covered by blue.

In addition to the comparison of overall performance, the LLD can also achieve the specific evaluation of lubricant performance in terms of the individual geometric regions following the DC-guided approach. During the hot-stamping process, there are five key feature regions, specifically the blank holder region, die corner region, flat bottom region, die shoulder region, and side wall region, as shown in Figure 8.

Figure 9 demonstrates the specific performance evaluation results for these five regions. It can be observed that lubricant #1 presents relatively lower performance grades in the die shoulder and blank holder regions, with only around 63%, while in the flat bottom region, the highest grade of approximately 82% is achieved. This can be due to the fact that in the die shoulder region, approximately 50% of the elements experienced a greater contact pressure of over 8 MPa and higher interfacial temperature of over 450 °C. In the blank holder region, the elements experienced both a high contact pressure and long relative sliding distance, leading to premature lubricant failure. Compared to lubricant #1, lubricant #2 achieves a similar performance grade (64%) in the die shoulder region, while a much higher grade (89%) in the blank holder region. This may be caused by the higher viscosity of lubricant #2 to withstand long sliding wear under high-contact-pressure conditions. Lubricant #3 has the most remarkable performance, presenting full grades, i.e., 100%, in four of the five key feature regions except the die shoulder region, thus leading to an ideal OPG of 98.5%.

The digitally enhanced LLD provides an effective evaluation method for the lubricant performance, which mainly focuses on the perspective of friction reduction and surface protection. In the industry-scale application of lubricant products, it is also important to consider the removal of the residual lubricant after completely forming of the component. Therefore, another lubricant evaluation parameter, the cleanness grade ($CG$), for the forming production is introduced to consider how difficult it is to remove the lubricant. The equation for calculating $CG$ is expressed as Equation (8).

$$CG \left(\%\right)={\displaystyle \raisebox{1ex}{$\left({\eta }_c-\eta \right)$}\!\left/ \!\raisebox{-1ex}{${\eta }_c$}\right.}·100\%$$

(8)

where $\eta$ is the lubricant viscosity at room temperature and ${\eta }_c$ is the critical viscosity set by the industry considering the effectiveness of removal methods and the requirement for subsequent assembly procedures. In general, the cleanness grade would decrease as the lubricant viscosity increases, except some scenarios where dedicated developed solvents were introduced to efficiently remove the lubricant. As a comprehensive evaluation of the lubricant application performance in mass production, the industrial application index (IAI) is proposed and defined as Equation (9).

$$IAI \left(\%\right)=\sum w_i·G_i$$

(9)

where $G_i$ represents each individual performance grade considering different aspects of the lubricant, e.g., lubricity, cleanness, and quenching effectiveness; $w_i$ denotes the weight ratio between different grades.

As a case study, an evaluation of the three lubricants investigated in this work was conducted by considering the lubricity and cleanness grades, both of which are key factors influencing the successful formation of aluminium hot-stamped components. The weights of lubricity and cleanness are considered equally, where the critical value was set based on the industrial requirements and all three lubricants were cleaned using a standard method in this case. The calculated results of the industrial application index (IAI) are listed in

Table 8. The performance evaluation of three lubricants, #1-3, considering the industrial application index (IAI).

	Weighted Lubricity Grade (%)	Cleanness Grade (%)	Industrial Application Index (%)
Lubricant #1	69.4	84.6	77.0
Lubricant #2	82.9	42.1	62.5
Lubricant #3	98.5	53.5	76.0

. Although lubricant #3 demonstrates a remarkable lubricity, the forming industry might prefer lubricant #1 due to its higher feasibility and flexibility in the automated production lines.

5. Conclusions

In the present research, the transient lubricant behaviour of three lubricant candidates developed for the hot stamping of aluminium alloys was investigated under a range of temperatures, contact pressure, and sliding speed. The advanced mechanism-based interactive friction models were established for each lubricant to accurately describe and predict the friction behaviours under complex loading conditions, which formed a theoretical basis for the subsequent digitally enhanced performance evaluation following a DC-guided approach. Incorporating the advanced friction modelling and the tribological DC, LLDs were generated for a more comprehensive and straightforward comparison between different lubricant products. The following conclusions can be drawn corresponding to the objectives listed in the previous section:

• The lubricant breakdown phenomenon was accelerated, leading to shorter breakdown distance as the interfacial temperature and contact pressure increased, which was due to decreased viscosity and additional consumption of the entrapped lubricant. In terms of the change in relative sliding speed, its effect on the transient behaviour was dependent on the competition between increased lubricant thickness due to inletting speed and a decreased viscosity due to frictional heat.
• An interactive friction model was established and calibrated for each lubricant candidate, leading to a quantitative evaluation of performance based on the LLD. It has been found that lubricant #3 presented the most remarkable lubricity, with an excellent performance grade of 98.5%, while lubricant #1 only demonstrates an OPG of 69.4%.
• The tool–workpiece interface during hot stamping has been divided into five key feature regions, namely blank holder, die corner, flat bottom, die shoulder, and side wall. The digitally enhanced lubricant evaluation is capable of identifying the critical regions with the most lubricant failure. For example, lubricant #1 presents the most failure in the die shoulder and blank holder regions, with a performance grade of only 63%.
• The industrial application index is proposed to evaluate the lubricant application in mass forming production by considering not only the lubricity and surface effects but residual cleaning after forming as well. By considering both the lubricity grade and cleanness grade, lubricant #1 demonstrates the best performance among the three candidates.