**2. Abrasive cutting as a subject of thermal investigation, modeling, and optimization**

The manufacture of workpieces by cutting is implemented on various machines and installations (automatic lathes, band cutting machines, mechanical hacksaws, band saws circular saws, abrasive cut-off machines, presses, electric spark, and electrochemical installations) depending on the dimensions, profile, type and physico-mechanical properties of the input material and the admissible deviation from nominal dimensions. When comparing cutting methods by technological criteria, the most important criteria are cutting intensity (production rate), tool life, and material loss in the form of chips related to the cut width. Choosing an optimal variant for workpiece cutting is a technical and economic task, which has a considerable impact on the cost of the machine-building production.

Abrasive cutting is a universal method that is applied to manufacturing workpieces of metal and non-metal materials of different hardness by means of highspeed reinforced abrasive (cut-off) wheels of a diameter *ds* ranging from 115 to 400 mm and a width ranging from 2 to 3.5 mm. Abrasive cut-off wheels are highly effective self-sharpening tools that perform cutting by means of thousands of miniature "cutting tools"—abrasive grains of aluminum oxide or silicon carbide.

Reinforced cut-off wheels whose grain size is in compliance with ISO 8486 grain numbers from 24 (coarse) to 60 (fine); medium-hard (*P*), hard (*R* or *S*), and very hard (*T*), with a BF bond—fiber-reinforced resinoid bond or an AGE bond—glass-fiber-reinforced resinoid bond providing higher safety against breakage, are used [13, 14].

Abrasive cutting is a complex and varied process performed under different kinematic schema (**Figure 1**) where the cut-off wheel performs the main rotary motion (at a rotational frequency *nc*) and a radial feed (at a speed *Vfr*) (**Figure 1a**). *Remote Nondestructive Thermal Control of Elastic Abrasive Cutting DOI: http://dx.doi.org/10.5772/intechopen.103115*

**Figure 1.** *Schemas of abrasive cutting.*

To facilitate the cutting process, an oscillatory motion (at a speed *Vft*) of the cut-off wheel in a direction perpendicular to the basic feed (**Figure 1b**) or a rotary motion of the workpiece (at a rotational frequency *nw*) (**Figure 1c**) is introduced [1, 2, 4, 15–17].

The oscillatory motion facilitates the cutting process and helps to reduce the cost of the abrasive wheels. However, some shocks occur at both ends of the oscillatory motion, which leads to overloading the cut-off wheel, occurrence of vibrations, and an increase in wear. The implementation of such a motion makes the machine complex and costly. Those disadvantages are avoided when using the schema including a rotary motion of the workpiece (**Figure 1c**). If we compare abrasive cutting schemas, it can be seen that when performing a cut-off cycle (cutting one workpiece), the cut-off wheel working stroke upon cutting a rotating workpiece (**Figure 1c**) is approximately twice as short as that for the schemas in **Figure 1a** and **b**. It results in reducing the cut-off time and the friction forces between the lateral surfaces of the cut-off wheel and workpiece thus, on one hand, decreasing the temperature in the cutting zone and cut-off wheel wear and, on the other hand, increasing process production rate. When cutting a rotating workpiece, the lower cut-off wheel wear and the higher production rate is also due to the shorter length *L* of the contact arc between the cut-off wheel and the workpiece in comparison to the one used when cutting a fixed workpiece. In cutting a fixed workpiece, the chips produced in the process of cutting do not fit in the cut-off wheel pores, which results from the higher values of the contact arc *L* regardless of the thinner layer being cut. Therefore, the process production rate decreases, and tool wear increases.

The cut-off wheel can be fed into the workpiece at a constant speed of radial feed (*Vfr* ¼ const) provided in a kinematic way by the cutting machine (rigid abrasive cutting) or can be pressed onto the workpiece with a constant force *F* (*Vfr* 6¼ const)—elastic abrasive cutting [3].

The kinematic schemas of rigid abrasive cutting are similar to those in external cylindrical grinding, where dependencies for defining the tool-workpiece contact area, contact arc length, and thickness of layer being cut, pointed in [14, 18–20], are required. The principal disadvantage of this method is the change in the power and heat loads of the cut-off wheel within one cut-off cycle, which is related to the change in the instantaneous cross-sectional area of the layer is cut. This results from the fact that with the cut-off wheel feed from the periphery to the center of the workpiece being cut the contact arc length between the cut-off wheel and the piece changes as the instantaneous thickness of the layer being cut *h* remains constant (with a fixed workpiece) or changes according to a particular law (with a rotating workpiece).

Within one cycle of elastic abrasive cutting, the length of the contact arc *L* and the thickness *h* of the layer being cut change, while the instantaneous crosssectional area of this layer remains constant [8, 15, 21–23]. This ensures stabilization of the dynamic and thermal phenomena accompanying cutting and appears a precondition for more effective use of the cut-off wheel, as well as for enhancing the quality of the machined surface. Simultaneously, the contact arc length *L*, the thickness *h* of the layer being cut and the cutting depth *a* depend on the process operating conditions, which determines the effect of the compression force *F*, workpiece rotational frequency *nw* and cut-off wheel diameter *ds* on the process parameters—tool wear, tool life, production rate, cutting forces and power, temperatures of the cut-off wheel, workpiece, and cut piece.


The analysis has been carried out shows that elastic abrasive cutting is a sophisticated multi-parameter and multi-factor subject of study, modeling, and optimization [24]. It is characterized by a number of target parameters—economic (productivity and cost), dynamic (cutting forces and power) and technological (cut-off wheel wear and tool life, cutting temperature, noise, roughness and precision of machined surfaces, physico-mechanical properties of the surface layer structure, microhardness, surface residual stresses, flaws, etc.). Each of the above parameters has a specific meaning in relation to abrasive cutting yet is insufficient for its optimum control.

*Remote Nondestructive Thermal Control of Elastic Abrasive Cutting DOI: http://dx.doi.org/10.5772/intechopen.103115*

The parameters of elastic abrasive cutting are determined by numerous control factors—physico-mechanical properties of the materials being machined, methods and components of the cutting mode, cut-off wheel type and characteristics, type and way of supplying cooling fluids, etc.

In the course of abrasive cutting, a number of interrelated, yet of a different type, nature, and intensity, phenomena occur and various materials, cut-off wheels, and cutting modes are used. Each abrasive cutting process is unique and could be studied from different perspectives: technological, energetic, informational, organizational, etc. When it is investigated, new experimental data and models are obtained, which differ from those of the preceding processes. Therefore, its investigation, modeling, analyzing, control, and optimization are always specific.

#### **3. Thermal phenomena in abrasive cutting**

#### **3.1 Heat generation and heat removal in abrasive cutting**

The mechanical work done in cutting involves deformation (elastic and plastic) of the material being machined, action of friction forces on the face and flank of cutting abrasive grains, and formation of new surfaces (dispersion). The amount of heat generated in cutting per unit of time, expressed by the work done in cutting and the mechanical equivalent of heat (*I* ¼ 427 kgm/kcal), is as follows:

$$Q = \frac{F\_c V\_c}{I} = \Re \mathcal{S} F\_c V\_c \tag{1}$$

where: *Fc*—main cutting force;*Vc*—cutting velocity; *Vc* ¼ *Vs* (*Vs*—velocity of the main rotary motion of the cut-off wheel).

Intensive thermal fluxes flow through the tool, chip, and material being machined in high-speed abrasive cutting. The large amount of heat generated in the course of abrasive cutting is transferred to the workpiece (*Qw*), cut-off wheel (*Qs*), and chip (*Qch*) and it is released into the environment (*Qp*) [4, 7, 8, 21, 22, 25]. The transfer of heat in those directions is implemented by heat conduction, convection, and radiation.

A wide range of changes in the thermal flux components depending on the selected schema for process implementation (rigid or elastic abrasive cutting), the characteristic of the cut-off wheel, the physico-mechanical properties of the material being machined and the cutting mode has been established.

*Qw* ¼ ð Þ 10% ÷ 85% *Q*; *Qw* ¼ ð Þ 10% ÷ 85% *Q*; *Qch* ¼ ð Þ 30% ÷ 75% *Q*; *Qp* ≈10%*Q* [4, 7, 8, 22, 25, 26]. This implies different temperatures of the working and lateral surfaces of the cut-off wheel, as well as different temperatures of the workpiece and chip.

Actually, the whole action of the friction forces in the contact zone below the neutral line *АF* (**Figure 2**) is transformed into heat (*Qf* ) and enters the workpiece.

During the initial contact between the abrasive grain and the workpiece, taking into account the comma-shaped cross-section of the layer being cut when *h*<*hk* (*hk*-thickness of the layer being cut, where micro-cutting starts, and which depends on the radius of curvature of the edge of the abrasive grain), chipless plastic ejection of the material being machined occurs before the abrasive grain. There is also some heat dissipation [14, 17, 19]. Heat transfer is implemented by heat conduction and radiation.

When the values of the layer being cut are *h*>*hk*, a cutting process where chips are formed starts. The heat *Qd* generated as a result of deformation and used for

**Figure 2.** *Schema of chip formation in abrasive cutting.*

shear along the shear surface within chip formation depends on the thickness of the material being cut *h*<sup>z</sup> and the cross-section *A*<sup>z</sup> of the material being cut by one abrasive grain. It is distributed as the heat transferred to the chip and heat transferred to the workpiece. It is assumed that the part of heat *Qd* transferred to the workpiece is *Qw* ¼ 0*:*7*Qd* [14, 17, 19]. In fact, the heat resulting from chip formation and transferred to the chip is less due to convection losses.

The part of heat transferred to the workpiece is reduced when increasing the cutting speed because of the change in the ratio between the cutting speed and the heat dissipation rate in the deformation zone [14, 17, 19]. The dissipation rate of generated heat depends on the gradient of the temperatures along the shear surface and the heat conductivity of the material being machined. When the cutting speed, i.e. the speed at which the abrasive grain crosses the thermal flux, is low, the heat from the shear surface is transferred unobstructed to the workpiece. As the cutting speed increases, the cutting abrasive grain crosses the thermal flux faster and faster. As a result, a smaller amount of heat is transferred to the workpiece and a larger amount of heat remains in the chip:

$$\mathbf{Q}\_w = \mathbf{0}.\mathbf{7}\chi\mathbf{Q}\_d\tag{2}$$

where *χ* is a coefficient of a decrease of the heat transferred to the workpiece caused by the change in the ratio between the cutting speed and heat dissipation rate [19, 27] *<sup>χ</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>3</sup> <sup>þ</sup> ð Þ <sup>80</sup>*:*<sup>1</sup> � *Vc* <sup>10</sup>�3.

Since a large part of heat (almost all the heat generated by plastic deformation and part of the heat generated by friction) is generated in the chip, the largest part of process heat remains there. Heat in the abrasive grain occurs externally as a result of friction and heat transfer from the hot chip to the colder abrasive grain, from plastic deformation, from the shear of the material under the neutral line, as well as from friction along the grain flank. As a consequence of conduction, the heat generated on the surface AB (**Figure 2**) is transferred to the abrasive grain and workpiece. The better the heat transfer from the surfaces being heated, the lower the temperature of those surfaces, i.e. the properties of heat conductivity and heat resistance influence the performance of cut-off wheels and the quality of machined surfaces.

The temperature of the cut-off wheel work surfaces (above 100°C) depends on the thermal flux density *ϕ* ¼ *dQ=dA* (*A*—contact surface area of the abrasive cutoff wheel and workpiece) and tool thermal characteristics. In the course of cutting heat enters the material being machined through the contact area between the cutoff wheel and workpiece. The size of that area and, respectively, the dimensions and power of the heat source depend on the parameters of the cutting mode. The shape and dimensions of the heat source are mainly determined by the cut-off wheel thickness *b*s, the wheel characteristics, and the length of the contact arc *L* between the tool and workpiece. In the course of cutting the workpiece appears a coolant of

#### *Remote Nondestructive Thermal Control of Elastic Abrasive Cutting DOI: http://dx.doi.org/10.5772/intechopen.103115*

the tool, absorbing part of the released heat, which is consequently transferred to the chip. In this respect, it would be better to expand the contact zone (*b*s*L*), which would result in an increase of the workpiece temperature and a decrease in the cutoff wheel temperature. Simultaneously, the temperature in the cutting zone is also affected by load of abrasive grains and the volume of the machined material removed by one abrasive grain, which are directly dependent on the wheel characteristics.

The cutting process in abrasive cutting is accompanied by melting of chips and plenty of sparking, which result from a large amount of heat generated in the cutting zone by friction forces, deformation of the material being machined, and reaction during burning. During burning every material has a specific point at which it ignites. When reaching the ignition temperature under the influence of oxygen, the physically and chemically clean surfaces of the steel workpieces being machined are oxidized to form iron oxide and slag. During oxidation, a considerable amount of heat is released, which provides additional heating of the very small volumes of metal of the chips removed by the abrasive grains up to the melting temperature. The presence of carbon in the material being machined increases burning and the temperature in the cutting zone, which is the reason for the different colors of the formed sparks in abrasive machining. Under the influence of the high speed of the abrasive cut-off wheel grains, the slag and iron oxide been formed are removed as glowing sparks [17]. The oxidation of the chip and the material being machined is useful since the oxide crust is fragile and facilitates chip removal. In accordance with the foregoing, the melting of the chip can be viewed as a positive factor because after melting the chip decreases its dimensions, which contributes to its easier removal by the cut-off wheel and to avoiding the filling of the tool pores with chips.

The burning of materials in abrasive cutting does not allow us to directly measure the temperature of the removed chip since it ignites when it forms or immediately after that. The brightness and type of sparks formed during abrasive machining (a product of burning) are defined solely by the content of the chemical elements in the material being machined. The density and length of the spark flow depend on the components of the cutting mode.

The increase of the heat entering the cut-off wheel intensifies tool wear and decreases tool reliability and cutting intensity as a result of a decrease in the relative pressure of the abrasive grains on the surface being machined (because of the softening of the cut-off wheel bond). Heating up the workpiece in the cutting zone leads to changes in the microstructure of the surface material and the occurrence of thermal flaws. Structural changes in the cross-section of the cut, which require further machining, also occur as a result of smearing and chipping parts of the cutoff wheel, as well as of friction between its lateral surfaces and workpiece face [6, 7]. All the above mentioned demonstrates the decisive role of temperature in abrasive cutting regarding cut-off wheel performance and quality of machined surfaces. It also shows that the heat released in the course of abrasive cutting is an important informative factor for optimizing the operating conditions in abrasive cutting and enhancing the effectiveness of the process and the quality of machined surfaces. Therefore, it needs to be studied, modeled, and optimized. The investigation and measurement of temperature distribution in abrasive cutting play a key role in machine building.

A great number of studies [4, 7, 15, 21, 22, 28] show that by controlling the thermal fluxes in the cutting zone, possibilities for improving the cut-off thermal mode are provided thus ensuring longer tool life, higher intensity of the cutting process and higher quality of machined surfaces. This could be achieved not only by changing abrasive cutting conditions (cutting schema and parameters of cutting

mode), which directly determine the thickness of the layer being cut, and respectively the temperatures of the tool, chip, workpiece, and cut piece, but also by choosing the cut-off wheel characteristic.

#### **3.2 Methods and tools for investigating temperature in abrasive cutting**

Depending on the specific nature of cutting processes, various methods for investigating temperature are applied [27]:

1.Analytical and numerical methods (heat source method; finite difference method; finite element method)—They are based on the heat balance equation and the differential equation of heat conduction [27]:

$$
\lambda \left( \frac{\partial \theta^2}{\partial^2 \mathbf{x}} + \frac{\partial \theta^2}{\partial^2 \mathbf{y}} \right) - \rho \, \mathbf{C}\_p \left( \mathbf{V}\_c \frac{\partial \theta}{\partial \mathbf{x}} + \mathbf{V}\_f \frac{\partial \theta}{\partial \mathbf{y}} \right) + \dot{\mathbf{Q}} = \mathbf{0} \tag{3}
$$

where: *λ*—thermal conductivity coefficient; *Cp*—specific heat capacity of the chip material; *ρ*—material density; *θ*—temperature of a point with coordinates *<sup>x</sup>*, *<sup>y</sup>*; *<sup>Q</sup>*\_ <sup>¼</sup> *<sup>τ</sup>sε*\_—heat exchange rate per unit of volume (*τs*—stress of cutting; *ε*\_—speed of plastic deformation).

	- Contact methods—Indirect (calorimetric technique, microstructural analysis technique, method of chip coloring, thermal pain technique, and electrical modeling) and direct—thermocouple technique (artificial, semi-artificial, natural, and running). With those methods, the energy exchange between the environment and thermometric substance is based on heat conduction [29].
	- Wireless measurement methods—They are based on the laws of thermal radiation of bodies. The wireless temperature measurement devices used in practice are as follows: optical pyrometers, spectral ratio pyrometers, radiation pyrometers, infrared thermometers, thermal imaging cameras [29, 30]. Choosing a proper device depends on a number of factors—temperature range, material, object dimensions, distance, ambient temperature. It should also be taken into account that the devices record the total energy in their range of vision. When measuring, they also include additional energy sources, including reflected energy, if they are in the range of vision.

Measuring temperature in abrasive cutting is difficult because of the small dimensions of the zone being heated (only tenths of mm2 ), high temperatures (hundreds of degrees Celsius), high-temperature gradient (more than 200<sup>о</sup> С/mm<sup>2</sup> ), high mechanical load, and high heating speed. This predetermines the preferential use of analytical and numeric methods, as well as wireless methods, for investigating the thermal phenomena in that process.

The thermal phenomena in rigid abrasive cutting are well studied unlike those in elastic abrasive cutting. Numeric, analytical, and finite-element models were

#### *Remote Nondestructive Thermal Control of Elastic Abrasive Cutting DOI: http://dx.doi.org/10.5772/intechopen.103115*

developed to define and analyze temperature distribution [3, 13, 18, 20, 31]. Thermal fluxes were investigated under different cutting conditions and strategies for optimizing the parameters of rigid abrasive cutting with regard to decreasing the temperature in the cutting zone were proposed [32–41]. In addition, a highaccuracy simulation model for forecasting temperature was proposed. It can be used for forecasting and preventing thermal flaws [33].

Analytical models for determining the temperature in elastic abrasive cutting were also proposed. On the basis of the analysis of thermal phenomena, the inability to directly measure chip temperature was justified and a methodology and an analytical dependency for the theoretic definition of chip temperature, reflecting the effect of the cutting speed and the workpiece rotational frequency, were proposed [42]. A model of the chip temperature, proving the decisive influence of the thickness of the layer being cut by one abrasive grain on it, was developed. An approach to the theoretical and experimental definition of the amount of heat released for one cut-off cycle and transferred to the workpiece being machined, as well as of the cut piece temperature, was proposed [43].

By applying the calorimetric technique for measuring temperature and the methodology of the planned experiment, a theoretical and experimental model for the temperature of the cut piece made of С45 steel depending on the cut-off wheel speed and workpiece rotational frequency was built. It was established that cut piece temperature decreases as cutting speed decreases and workpiece rotational frequency increases. This effect is related to the enhanced heat removal resulting from an increase in the thickness of the layer being cut, the cross-section of the chip being cut by one abrasive grain, and time per cut.

The possibilities for wireless temperature measurement and monitoring by applying infrared thermography are studied in [4, 7, 25, 44]. It was found that the cut-off wheel compression force on the workpiece had the greatest effect on the maximum cut-off wheel temperature, respectively on the tool life [4, 7]. It was also found that temperature increased as the workpiece diameter increased. Furthermore, when cutting fixed workpieces, the combination of larger cut-off wheel diameter and a greater compression force results in generating higher temperatures and obtaining lower values of G-ratio. Studies were done with a focus on the possibilities of using infrared thermography as a tool for wireless and non-invasive thermal investigation of the process and tools of elastic abrasive cutting of rotating workpieces [25, 44]. Experimental data from thermographic measurements done by an infrared camera regarding the effect of workpiece rotational frequency, compression workforce, and cut-off wheel diameter when machining various materials on the temperature distribution on workpiece surface, cut-off wheel, and cut piece were presented.

The analysis of the methods and approaches used for investigating and monitoring temperature in abrasive cutting shows the advantages of wireless measurement methods such as infrared thermography (IRT). This method is increasingly recognized and widely used as a reliable and effective tool for thermal wireless nondestructive testing under real conditions of dynamic processes such as abrasive cutting [4, 7, 12, 25, 29, 44]. Its application allows us to enhance the effectiveness of abrasive cutting. However, the use of IRT has some disadvantages.

The availability of metal parts in equipment leads to a number of reflections that impede temperature measurements on the surfaces under study and vary depending on their orientation, temperature, and wavelength. Temperature measurements by using thermography do not provide us with absolute temperature values. To obtain such values, we should use modeling and look for a correlation with the change in surface temperature. IRT measurements are indirect with regard to temperature measurements in the cutting zone. Although the cut-off zone can be observed from

the side at a specific position of the camera, the infrared radiation from the cut-off wheel, workpiece, and produced chips affect the results from the temperature measurement of the surface being observed. Therefore, a thorough study of the possibilities for applying infrared thermography in abrasive cutting is required.
