A method for prediction of active grits count in surface grinding
Introduction
In a metal cutting process, the knowledge about the mechanism of material removal and surface generation is essential for the optimizing the process. In the case of machining, known geometry and position of the cutting tool over the workpiece surface define the material removal mechanism. Advanced simulation [1] and experimental techniques [2] are available to give an insight into the chip formation mechanism in machining operations. However, in the case of grinding, the study of material removal mechanism is complicated due to several factors associated with the grits such as grits stochastic distribution on a grinding wheel, undefined geometry, and unknown number of cutting edges. In spite of the complexities, some physical analogous studies like indentation and scratch tests have been adopted to understand the abrasive grit and work material behavior, and material removal mechanism during the grinding [3], [4].
In grinding, the sequential motion of individual grits associated with micron level depth of cut leads to a macroscopic material removal. As a result, the grinding performance can only be described by individual grits behavior. In this aspect, the most important parameter which describes the grinding performance is the active cutting edges count on wheel surface. However, due to the abrasive grits stochastic distribution on a grinding wheel, an exact determination of this number is not possible. Therefore, individual grits position with wheel surface, number, and shape of the abrasive grits are analyzed stochastically and related to the process kinematics. In order to compare a variety of grinding processes (surface or cylindrical), researchers defined general and comparable process parameters such as geometric contact length, chip length, and the chip thickness.
Fig. 1 demonstrates the path of cutting edge over a work surface. The path the center travels between the two engagements of the wheel depends on the feed movement and the time required. The cutting edge engagement and the resulting uncut chip parameters such as uncut chip thickness (hcu) and uncut chip length (hch) depend on the cutting edge density (C) on the grinding wheel and other parameters as given in Eq. (1).where ‘vw’ is the speed of the workpiece, ‘vc’ is the speed of the wheel, ‘ae’ is the depth of cut, and ‘deq’ is equivalent wheel diameter. On the basis of uncut chip parameters values, a theoretical assessment has been made on the grinding process.
A thorough literature search shows that several researchers revealed the significance of uncut chip thickness and depth of cut in relating the process responses. Several equations had been proposed for analytical prediction of process responses in terms of uncut chip thickness. A basic relation between the uncut chip thickness and process responses such as grinding force, specific energy, surface roughness and the temperature is given below [6]:
Force per grit
Temperature
Specific energy
Surface roughness
From the above relations, it can be observed that the uncut chip thickness and hence cutting edges count on a grinding wheel is an important parameter in estimating the process output. All the abrasive grits protruding from the bond and passing through the grinding zone can be called as static grits, and the static grits may have one or more than one cutting edge depend on the wheel micro-topography, which can be decided by the dressing operation. The nomenclature Sstat, Nstat, and Cstat represent the number of static grits per unit length, per unit surface area, and per unit volume respectively. However, active grits (grits which are participating in the cutting process) count is different from the static grits count, which mainly depends on the grinding conditions such as process type, parameters, and the nature of work material. Hence, the number and density of the active grits is smaller than the static grits.
There are several methods available to measure the cutting edges count (Static and active) experimentally. Based on the method of measurement technique, they can be classified into three types such as pre-processing method, in-process method, and post-process method (Table 1).
The method in which information about only static grits can be obtained is called as a static method. In static methods all abrasive grits on the surface of the grinding tool are considered, there is no distinction, whether a cutting edge of the grinding process is actively involved or not in the cutting process. Static methods are independent of the grinding conditions. Whereas in dynamic methods, the number of actual abrasive grits (active grits) engaged with workpiece are considered. The active cutting edge number is the totality of cutting edges involved in the cutting process [6].
A complete review on the importance of the number of active grits [7], analytical models [8], [9], [10] for its calculation and experimental techniques [7], [10], [11] to measure the active grits are available in the literature. Some of the commonly used analytical models for predicting the cutting edges density have been given below [12], [13], [14].where ‘Vg’ is the volume fraction of grits on the wheel, ‘dg’ is the diameter of abrasive grit, ‘f’ is the fraction of abrasive particles that actively cut in grinding, and ‘β’ is a constant related to the holding strength of the abrasive grits in the wheel and has a value from 0 to 1 [9].
It can be observed in Eqs. (2), (3), (4) that the researchers had made an attempt to predict the cutting edges count as static grits count only. Unfortunately, none of the available models consider the abrasive grit size, grits concentration, depth of cut and work material nature characteristics simultaneously which has an influence on active grits count as shown in Fig. 2. Hence, in this work, an attempt has been made to develop a method for determining the static grits and active grits count stochastically by considering the effect of wheel nature (grit size and concentration), depth of cut given during the grinding process and work material nature. Moreover, the effect dressing condition has also considered on cutting edges count.
Section snippets
Stochastic approach for determining grit count
The method developed in the present investigation should be treated as an early attempt by considering the grinding wheel grit size, wheel structure, and depth of cut and work material nature to determine the active grits count. Hence, keeping in the view of the complex nature of the grinding process, several assumptions have been made in this analysis:
- i.
The analysis is based on the statistical distribution (normal) of the abrasive grits height on the grinding wheel surface; the same distribution
Conclusions
A new method for predicting active grits was presented in this study, and the influence of process parameters, including depth of cut, and particularly the abrasives grit size, abrasives concentration and the hardness of work material was considered simultaneously. Moreover, incorporation of dressing effect also taken care in predicting the cutting edges count. This has considerably improved the model predictability and making it more realistic. Predicted results corresponded with the available
References (22)
- et al.
Very high speed cutting of Ti–6Al–4V titanium alloy – change in morphology and mechanism of chip formation
Int. J. Mach. Tools Manuf.
(2013) - et al.
Grinding mechanisms for ceramics
CIRP Ann. - Manuf. Technol.
(1996) - et al.
On the mechanics of the grinding process – Part I. Stochastic nature of the grinding process
Int. J. Mach. Tools Manuf.
(2003) - et al.
Modelling of ceramic grinding processes Part I. Number of cutting points and grinding forces per grit
J. Mater. Process. Technol.
(1997) - et al.
A model for the topography of diamond grinding wheels
Wear
(1993) - et al.
An investigation of grinding with electroplated CBN wheels
CIRP Ann. - Manuf. Technol.
(2003) Wear by hard particles
Tribol. Int.
(1998)- et al.
The relation between the traverse dressing of vitrified grinding wheels and their performance
Int. J. Mach. Tools Manuf.
(2000) - et al.
Investigations on the chip formation mechanism and shear localization sensitivity of high-speed machining Ti6Al4V
Int. J. Adv. Manuf. Technol.
(2014) - et al.
Study on surface cracking of alumina scratched by single-point diamonds
J. Mater. Sci.
(1988)
Cited by (31)
Position-dependent rough surface formation in face gear worm grinding
2024, International Journal of Mechanical SciencesForce modeling of vertical surface grinding considering wheel-workpiece contact geometry
2024, International Journal of Mechanical SciencesUnderstanding of the effect of wear particles removal from the surface on grinding silicon carbide by molecular dynamics simulations
2023, Diamond and Related MaterialsInvestigations on the micro-interactions of grit-workpiece and forces prediction in ultrasonic vibration side grinding of optical glass
2022, Journal of Materials Processing TechnologyCitation Excerpt :The previous studies about measurement (Darafon et al., 2013) and simulation (Ding et al., 2017) of the wheel surface topography show that the stochastic nature of wheel surface would affect the penetration depth of these grits with varied shapes and positions and the undeformed cutting chip thickness. Thus, it is apparent that the grits-workpiece micro-interaction would be affected by the grit stochastic property, which exerts a significant influence on the grinding output responses in UVSG, e.g., cutting force, specific energy, surface quality (Setti et al., 2017). Many investigations about the mechanisms of grits-workpiece interaction in the grinding process have been carried out.
Modelling and analysis of micro-grinding surface generation of hard brittle material machined by micro abrasive tools with helical chip pocket
2021, Journal of Materials Processing Technology