1. Introduction
Titanium alloys, cemented carbides, and engineering ceramics exhibit exceptional physical and mechanical properties, making them highly sought after in industries like aerospace, new energy, automotive, and general machinery manufacturing [
1,
2,
3]. Titanium alloys, for example, are frequently utilized in critical aerospace engine components like engine casings and turbine blades for the sake of their low density, superior specific strength, and remarkable temperature and corrosion resistance [
4,
5]. These materials, with their distinctive structural characteristics and superior physical attributes, fall into the category of hard-to-machine materials, leading to poor machinability. Currently, precision machining of such materials primarily relies on grinding techniques utilizing superabrasive tools like diamond and CBN grinding wheels. In traditional diamond grinding processes, the geometric structures of the abrasive grains, typically octahedral or dodecahedral, lead to a majority of grains having an NRA because the apex angle of the grains exceeds 90°. This exacerbates friction between the workpiece and abrasive grains, leading to increased plastic deformation of the workpiece. Consequently, the grinding force and temperature experienced with hard-to-machine materials like titanium alloys are significantly higher compared to the cutting forces in comparable cutting processes [
6,
7], leading to enhanced risks of plastic deformation, micro cracks, phase transformations, residual stresses, and other surface/subsurface damages in the machined workpiece. Consequently, they result in compromised surface integrity, severely impacting the performance and functionality of the machined components [
8].
Considering these challenges, this study introduces an innovative approach called PRA grinding, employing femtosecond laser technology to ablate material from the top edge region of grains and, thereby, modify the apex angle to less than 90°, ensuring that the diamond grains have a PRA at the cut-in point. This technique combines the advantages of cutting processes that include no sliding and ploughing processes and have a low friction force with the precision machining benefits of grinding with minimal material removal. By converting the traditional NRA grinding into PRA grinding, this approach aims to reduce grinding forces and temperatures, improve the grinding conditions for titanium alloys and other hard-to-machine materials, and enhance the surface quality of machined components.
Because of the stochasticity in shape, dimension, location, cone angle, and protrusion height of the numerous abrasive grains involved in grinding, the interaction between the workpiece and the grinding wheel is extremely intricate. This complexity brings great inconvenience to the observation and analysis of grinding experiments and the understanding of grinding mechanisms [
9,
10]. Therefore, this paper investigates the mechanism of PRA grinding from the perspective of single abrasive grain machining to avoid the mutual influence among multiple grains, and simplify the simulation and experimental processes.
Researchers have performed a sequence of theoretical simulations and experiments on grinding mechanisms through single abrasive grain grinding. Anderson et al. [
11,
12] combined experimental observations and finite element simulations to conduct in-depth studies on single diamond abrasive grain grinding of AISI 4340 alloy steel. The results revealed that due to the workpiece’s strain rate hardening, the normal grinding force escalates with the grinding speed, whereas the tangential grinding force diminishes with the grinding speed elevation attributed to a reduced friction coefficient between the abrasive grain and the workpiece and the change in the cutting mechanism. Liu [
13] conducted simulation and experimental studies on the machining of silicon nitride ceramic materials with single diamond abrasive grains, revealing the impact of grinding process parameters on both grinding force and surface morphology, and further integrated these findings into a model of grinding wheel surface morphology for predicting the processing quality of silicon nitride ceramic spherical surfaces. Dai et al. [
14] executed single diamond grain grinding experiments on nickel-based superalloys, investigated the influence of abrasive wear status on material removal during the grinding process, and summarized four types of abrasive wear. Fu et al. [
15] developed an FEM model for single abrasive grain grinding of Ti6Al4V by considering the variation in cutting depth along the grinding trajectory. Yin et al. [
16] developed a comprehensive model for SiCp/Al composites’ grinding with a single diamond grain, providing essential insights into grinding forces and material removal rates. Li et al. [
17] conducted a comparative analysis of mechanical behavior and the modeling of grinding forces, enhancing the accuracy of predictions in single grain grinding. Li et al. [
18] explored the material removal mechanism and grinding force modeling in ultrasonic vibration-assisted grinding of SiC ceramics via single grain scratch. Meng et al. [
19] provided a detailed review of the modeling of grinding mechanics and assessed the strengths and limitations of various models. The study analyzed the impacts of parameters, including grinding speed and grinding depth, on both grinding force and stress distribution.
Although the single grain grinding method has been widely applied in the study of grinding mechanisms for various materials and has made significant progress, research concerning the mechanism of PRA grinding using this approach has not yet been reported. This paper employs the single grain grinding method and conducts finite element simulations and experimental comparisons of positive and negative rake angle grinding on Ti6Al4V titanium alloy material. It explores the variation patterns in grinding force, grinding temperature, surface morphology, and surface roughness under different process parameters. The study hypothesizes that PRA grinding will provide lower grinding forces and superior grinding quality compared to traditional NRA grinding, and it is expected to be validated by both simulation and experimental data. By quantifying the performance differences between PRA and NRA grinding, this research not only demonstrates the feasibility and advantages of PRA grinding but also provides empirical evidence for engineering applications.
2. Finite Element Model
2.1. Material Constitutive Modeling
The grinding of metallic materials is a thermo-mechanical coupling process involving high strain, a high strain rate, and elevated temperatures, during which phenomena like material strain hardening and material strain rate strengthening typically occur. Before simulating, it is essential to determine the material’s constitutive features under deformation at elevated temperatures. Many researchers have proposed various material constitutive models, including the Johnson–Cook model, Bodner–Partom model, Khan–Huang model, and Zerilli–Armstrong model [
20,
21]. The Johnson–Cook constitutive model posits that materials experience strain rate strengthening, strain hardening, and thermal softening at elevated strain rates. Therefore, this model can effectively describe the deformation behavior of titanium alloys in single grain grinding. The expression for the Johnson–Cook model is provided below [
22]:
where
σ is the equivalent flow stress,
A is the initial yield strength of the material,
B denotes the hardening strength,
C is the strain rate strengthening coefficient,
ε represents the equivalent plastic strain,
n is the strain hardening exponent,
and
are the equivalent and referential strain rates, respectively,
Tr is the ambient temperature,
Tm is the melting temperature of the workpiece material,
T is the current grinding temperature, and
m is the thermal softening coefficient. The constitutive model parameters of Ti6Al4V titanium alloy material are shown in
Table 1.
The simulation employs a single crystal diamond as the single abrasive. Single crystal diamonds are characterized by ultra-high hardness, good strength, and excellent thermal conductivity, and it is commonly used in grinding and cutting processes for its superior performance [
24,
25]. Its physical and thermal properties are presented in
Table 2.
2.2. Material Failure Criterion
From a microscopic perspective, the failure of titanium alloy materials is primarily due to plastic fracture caused by the formation and propagation of cracks. This paper adopts the Johnson–Cook failure criterion based on the strain analysis to control the material failure process. Whether the magnitude of the equivalent plastic strain surpasses the material’s failure strain value is the basis for determining the occurrence of failure, according to the strain failure criterion. The failure parameter
ω of the Johnson–Cook fracture model is defined as follows [
22]:
When
ω > 1, the material is considered to have failed, and the element mesh at the failed material location is removed, signifying the separation of chips from the workpiece.
represents the increment of equivalent plastic strain, and
represents the critical equivalent plastic strain, which is expressed as follows [
22]:
where
D1–
D5 are material failure parameters,
represents the dimensionless force,
p represents the hydrostatic pressure;
represents the dimensionless strain rate,
is the dimensionless temperature. The values of
D1–
D5 are shown in
Table 3.
2.3. Geometric Model and Simulation Parameters
In conventional wheel grinding, the motion of an individual grain is a rotational movement associated with a changing grinding thickness. However, since the grinding arc length is generally on the millimeter scale, while the grinding thickness is on the micrometer scale, the motion of abrasive grains can be considered as a linear movement with a constant grinding thickness over a short grinding wheel path. Finite element simulations using ABAQUS were conducted separately for the grinding of Ti6Al4V titanium alloy with single diamond abrasive grains having a PRA and an NRA. The grinding schemes for single diamond grains with an NRA and a PRA are shown in
Figure 1a and
Figure 1b, respectively.
In the FEM geometric model of single diamond grain grinding, the dimension of the Ti6Al4V workpiece is 0.2 mm × 0.06 mm. The main physical properties of Ti6Al4V are listed in
Table 4, and the thermal physical properties are listed in
Table 5 [
27]. To reduce computational costs while maximizing the accuracy of the simulation calculations, the meshing of the undeformed chip layer, the grinding area on the workpiece substrate, and the vicinity surrounding the diamond grinding edge were refined. The simplified FEM geometric model of single diamond grain grinding is shown in
Figure 2. Both the tool and the workpiece use four-node thermo-mechanical coupled elements in the model. During the simulation, the bottom of the workpiece substrate remained completely fixed, and the left and right boundaries were only constrained in terms of movement and rotation in the X direction. The diamond grain was considered as a rigid body, the upper right corner of the grain is set as a reference point, and it was bound with constraints to the grain, with the grinding direction being horizontally to the left. At the onset of the simulation, both the abrasive grain and the workpiece were initialized to a temperature of 20 °C, consistent with the ambient temperature.
In the simulation of single grain grinding, the clearance angle of the grain was kept at 0°. The process parameters that are subject to change include the grinding speed, depth, and the rake angle of the diamond abrasive grain. Four levels were selected for each of these parameters:
Grinding Speeds: 6 m/s, 8 m/s, 10 m/s, and 12 m/s. These values were selected to represent a range from the low to moderately high speeds typically used in single grain grinding operations.
Grinding Depths: 5 μm, 10 μm, 15 μm, and 20 μm. The selected depths cover a range of shallow to moderately deep cuts.
Abrasive Grain Rake Angles: −10°, −5°, 0°, 5°, 10°, and 30°. These angles were chosen to explore the impact of both negative and positive rake angles on grinding performance.
A single-factor experimental method was utilized to investigate the variation patterns of grinding force and grinding temperature with different process parameters. To ensure consistent and comparable results, the grinding time for each simulation test and each grinding experiment was set to 1 min. This time duration was chosen based on preliminary tests to ensure adequate material removal while preventing excessive tool wear.
4. Experimental Setup and Scheme
Based on the preliminary research, femtosecond pulse laser ablation was determined to be a feasible technique to remove the material from the top edge region of the grains [
28]. After laser fabrication, the apex angle became acute, and thereby transformed the traditional NRA grinding into PRA cutting, as shown in
Figure 9. We mounted the brazed insert of a single diamond abrasive grain, which had been processed to have a PRA structure using a femtosecond laser, onto the grinding wheel. For comparison, a similarly sized original negative rake angle diamond abrasive brazed insert was also used in the experiment. The chosen single crystal diamond abrasive grain has a diameter of approximately 2 mm and is shaped as a truncated octahedron. The assembled single grain grinding tool, as shown in
Figure 10, consists of a wheel, an abrasive grain insert, a balancing block, and fixed press plates. Screws on both sides of the groove on the grinding wheel facilitate quick replacement between PRA and NRA abrasive inserts.
Comparative grinding experiments were conducted on an SL800A/1-HZ-type precision surface grinding machine using a dry grinding method to prevent interference from the grinding fluid on force measurement. To enhance the resemblance between the grinding method of single diamond abrasive grain and the operations observed with actual grinding wheels, and ensure that the processing path aligned with the real grinding, the experiment adjusted the movement speed of the worktable of the grinding machine to produce continuous grinding traces. During the process, the grinding forces were measured using a Kistler 9119AA2 dynamometer with a measurement range of −400 kN to 400 kN and a sensitivity of 26 pC/N. The experiment utilized a Ti6Al4V titanium alloy with dimensions of 60 mm × 25 mm × 12 mm, and the workpiece surface was polished in advance. The grinding wheels equipped with diamond abrasive inserts with a PRA and an NRA were mounted onto the grinding machine, respectively. The worktable of the grinding machine was equipped with an electromagnetic chuck, on which the dynamometer was securely mounted. To carry out single grain grinding experiments for comparison, the Ti6Al4V alloy was clamped on the dynamometer with a specially designed fixture. The experimental equipment for single grain grinding is shown in
Figure 11. Following the grinding process, observation of the titanium alloy’s surface morphology was made through a Zeiss inverted metallographic microscope, Axio Vert.A1, which is capable of up to 1000× magnification, equipped with digital imaging and analysis software. And the surface roughness of the workpiece was assessed using a TIME3200 handheld surface roughness gauge with a measurement range from 0.05 µm to 10 µm, and an accuracy of ±5%.
In single diamond grain grinding, the grain mounted on the circumference of the grinding wheel rotates at a grinding speed of
vs, while the worktable of the grinding machine drives the workpiece to move horizontally at feed speed
vw. The motion trajectory of the single grain during the grinding operation is an extended cycloidal path, and the expression for its processing path is [
13]
where
rs represents the diameter of the grinding wheel, and ± is used to distinguish between down grinding and up grinding.
Figure 12 depicts the grinding path for a single abrasive grain. In the figure,
agmax represents the maximum undeformed chip thickness, and it is used to assess the maximum cutting thickness of a single grain. This parameter is influenced by various factors, including grinding speed, grinding depth, and feed rate, and it significantly impacts the grinding force, the maximum temperature of grinding area, wear on the abrasive grain, and the surface finish of the machined components.
Figure 12 also illustrates the two grinding traces that a diamond abrasive grain leaves on the surface of the workpiece after two continuous rotations of the wheel, while the workpiece moves at a feed speed of
vw. The spacing between these two traces is denoted as
s, which can be expressed as
To make the single grain grinding process more closely resemble the actual wheel grinding, it is necessary to ensure that the single grain grinding has a similar processing method and cutting path to the actual wheel grinding, which means it can form continuous scratches on the workpiece surface. For this purpose, the maximum undeformed chip thickness produced by the single grain should be less than the depth of grinding, and geometrically it should satisfy
s <
l/2, where
l represents the length of the scratch, which can be approximately expressed as
Therefore, to achieve the condition for generating continuous grinding traces, the feed speed should satisfy the following criteria:
To ensure continuous grinding, the feed speed
vw = 2 mm/s was maintained constantly during the experiment. In the experiments with single diamond grains with a PRA and an NRA, the influence of the PRA, which was fabricated by a femtosecond laser, on the edge strength and grinding force was considered, and a rake angle of 5° was selected for the PRA diamond grain. The rake angle range for the original single diamond grain, which had not been processed by laser, generally lay between −20° and −40. Hence, a rake angle of −30° was selected in the NRA grinding experiment. Comparative experiments were conducted by varying the grinding speed and grinding depth, with specific machining process parameters, as presented in
Table 6.
6. Conclusions
In this study, finite element simulation combined with grinding experiments have been conducted to comparatively and comprehensively analyze the variations in grinding force, temperature, and surface integrity during the single diamond grain grinding of Ti6Al4V alloy, featuring both a PRA and an NRA. It offers new insights into the distinct effects of rake angles on grinding performance, validating the superior benefits of employing a positive rake angle. The key findings are outlined below:
In single diamond grain grinding, both tangential and normal grinding forces slightly decline as the grinding speed is increased, regardless of PRA or NRA. With the increment in grinding depth, the grinding forces gradually rise. When the rake angle is varied from −30° to 5°, the tangential grinding forces decrease by 25–41% and the normal forces decrease by 81–89%.
In the grinding with both PRA and NRA single diamond abrasive grains, there is a gradual increase in the maximum temperature within the grinding zone correlating with increases in both grinding speed and depth. When the rake angle of the diamond grain transitions from negative to positive, the maximum grinding temperature significantly decreases.
After the single grain grinding process, the roughness of the workpiece surface exhibits a decrease as the grinding speed rises and shows an increase in response to a greater grinding depth. Compared to NRA single grain grinding, PRA single diamond grain grinding skips the friction and ploughing stages, directly cutting into the material without inducing severe compressive sliding deformation, resulting in shallower grinding traces and fewer processing defects. The surface roughness in single grain grinding with a PRA were reduced by 58% to 66%, indicating that a diamond abrasive grain with a PRA can effectively improve the surface integrity after grinding for hard-to-machine materials.
Using diamond abrasive grains with a PRA significantly reduces grinding forces and improves the surface integrity of hard-to-machine materials. These benefits have substantial practical implications, especially in industries like aerospace, new energy, and automotive, where precision is critical. However, this study is limited by its simplified model assumptions, specific grinding conditions, and the absence of interaction analyses between process parameters. Future research will focus on the fabrication methodologies and grinding processes for cylindrical grinding wheels equipped with PRA diamond abrasives. This will aim to further expand the application scope of PRA grinding techniques in the field of hard-to-machine materials grinding.