Method to Calculate Cutting Force when Longitudinal Feed Centerless Grinding

DOI: http://dx.doi.org/10.24018/ejers.2019.4.10.1567 9  Abstract—The paper presents the results of analyzing the relationship between cutting force components and the force components exerting on the workrest blade, the ratio of slip acceleration of the rotation motion between the part and control wheel, translational motion acceleration of the part along the axial axis when longitudinal feed centerless grinding. From that, the method of calculating cutting force components is calculated by measuring the force components exerting on the workrest blade, the ratio of slip, acceleration of the rotation motion between the part with control wheel, translational motion acceleration of the part along the axial axis. On that basis, this research also provides orientation for the construction of a system to measure the force, acceleration, velocity components, ... Then the development direction for the next research is also mentioned in the article.


I. INTRODUCTION
Centerless grinding cutting force is an important parameter in controlling the grinding process [1], [2].However, the measurement of cutting force components in general and longitudinal feed centerless grinding in particular is often difficult because the workpiece is not centered, but is placed between the grinding wheel, control wheel, and the workrest blade (for plunge centerless grinding, there is an additional stopper along the axial axis the workpiece).With the plunge centerless grinding method: there have been a number of studies on constructing the method of measuring cutting force, such as: by determining hydrostatic pressure on the bearing of the control wheelbearing shaft [3]; by determining power on the grinding wheel-shaft [4].However, according to Yongbo Wu et al. [5], both of these methods have many limitations: in the first, the measurement system is quite complicated and in the second, the reliability of measurement results is not high.From this they developed a method of measuring the cutting force by measuring the force components exerting on the workrest blade and the stopper along the axial axis the workpiece [5].For the longitudinal feed centerless grinding method, to date, no published research on cutting force measurement methods has been published.Therefore, in this study, we analyze the relationship between cutting force components and the force components acting on the workrest blade, the ratio of slip -acceleration of the rotation motion between the part and control wheel, translational motion acceleration of the part along the axial axis when longitudinal feed centerless grinding.From that, the method of calculating cutting force components is calculated by measuring the force components exerted on the the workrest blade, the ratio of slip -acceleration of the rotation motion between the part and control wheel, translational motion acceleration of the part along the axial axis.This study was carried out with the following assumptions: (1) absolutely rigid machining system; (2) the longitudinal movement speed is a constant value during the grinding process when processing small length workpieces (roller bearings, ball bearings, etc.); Later, the development direction for further research is also mentioned in this paper.

II. GRINDING FORCE ANALYSIS MODEL
A model for analyzing the force components when longitudinal feed centerless grinding is presented in Figure 1.During machining, the workpiece is placed between the grinding wheel, control wheel and the workrest blade.
The machining system is located in the XYZ coordinate system, where the X axis is perpendicular to the platform, the Y axis parallel to the platform and the Z axis is the center line of the workpiece.
When centerless grinding along the longitudinal feed: the control wheel is rotated at an angle in the vertical plane to create a component of the axial force that pushes the part move linear in the z axis.At the same time, the control wheel must be repaired in hyperboloic shape to ensure that the workpiece and control wheel are always in contact with each other by a straight line [2].
The force components and the velocity on the contact points between the workpiecegrinding wheel, workpiececontrol wheel and workpieceworkrest blade are shown in Figure 2.
In order to facilitate the formulation of expressions for determining cutting force components, a number of major parameters of a technological system in a grinding scheme are denoted as follows: O -Center of the grinding wheel, workpiece and center of the control wheel at position Z = 0 (coordinate origin).
 -Slope angle of the workrest blade surface. -The inclination angle of the control wheel in the vertical plane.q -The relative sliding velocity between the workpiece and the control wheel in the XY plane.Figure 2b shows the velocity of the control wheel, the velocity of the workpiece and the force components on the general tangent plane of the workpiece -the control wheel, which is perpendicular to the straight line connecting the center of workpiece and center of control wheel (line In which, the velocity of a workpiece and the velocity of the control wheel are brought together at an angle  equal to the angle of the control wheel in the vertical plane.The friction force component n CC F  appears between the contact area of the workpiece and the control wheel, which forces the opposite direction with the relative velocity between the workpiece and the control wheel WC V .Figure 2c shows the velocity of the component and the force components on the workrest blade surface plane.The tangent force component t B F is the friction force between the workpiece and the workrest blade and is determined accordingly

III. RELATIONSHIP BETWEEN FORCE COMPONENTS
From the analytical model of force components presented in Figure 1 and Figure 2, we have the equilibrium force equations as follows: W sin cos sin cos sin cos 0 cos sin cos sin cos sin 0 In addition, according to Figure 2b, we have the following relationships: From the equations ( 1) to ( 5) we determine the force components on the surface of the grinding wheel by the following formula: W cos sin tan cos( ) cos sin( ) sin

IV. MOTION EQUATION OF THE WORKPIECE
Considering the motion of the part in the XYZ coordinate system, the equation of rotation of the workpiece around the Z axis is written as follows: From the equations (3), ( 4) and ( 5), we have the following relationship: Analysis of force components and vertically x T F , gives the following relationship: Substituting equations (7), (9) into equation (8) and combining with equations (10), (11), we get: V. GRINDING FORCE COMPONENTS When considering the relative slippage between the workpiece and the control wheel, the slippage rate q is determined by the following formula: According to the analysis in Figure 2b, we have the following relationship: In the process of grinding, the velocity is the relative sliding acceleration between the workpiece and the control wheel in the XY plane.
Substituting the equations ( 12), ( 14), (15) into equations ( 6), (7), we formulate the formula for calculating the normal force and tangent force as follows: Based on the expressions ( 16), (17), it is possible to orient for the construction of a force-measuring system with some basic contents as follows: -Components x B F , y B F measured by attaching a force measuring system that allows measurement of at least two directions to the workrest blade.
-The slip rate q between the workpiece and the control wheel is determined by the device's velocity measuring device (tachometer) because the velocity of the control wheel is determined under specific machining conditions.
-The values of Building a measuring system for cutting force components based on the research results presented in this paper that we will conduct in subsequent studies.

Fig. 1 .
Fig. 1.Model for analyzing the force components


on the surface of grinding wheel, control wheel and workpiece.WCV-The relative velocity (follow velocity) between the workpiece and the control wheel G R , C R , W R -Radius of grinding wheel, control wheel and workpiece.W h -Height of workpiece center compared with straight line connecting center of grinding wheel and center of control wheel.-Angle by direction of follow velocity VW-C and Z axis t G F , n G F -Tangential and normal forces on the surface of the grinding wheel.

F
-Tangential and normal forces on the surface of the workrest blade.

F
-Tangential force, normal force and axial force on the surface of control wheel.C  -Friction coefficient between workpiece and control wheel.B  -Friction coefficient between workpiece and the workrest blade.W m , W G -Mass and weight of workpiece.W I -Moment of inertia of the workpiece around the Z axis.

W
Figure2ashows the velocity of the grinding wheel, the velocity of the workpiece and the force components on the general tangent plane of the workpiecegrinding wheel, which is perpendicular to the straight line connecting the center of workpiece and the center of grinding wheel (line W G OO).Figure2bshows the velocity of the control wheel, the velocity of the workpiece and the force components on the general tangent plane of the workpiece -the control wheel, which is perpendicular to the straight line connecting the center of workpiece and center of control wheel (line the control wheel  in the vertical plane are constants, the derivative equation (13) over time we get:

a
are determined by using the accelerometer to allow measurement in either direction (rotational and translational motion) or using two separate types of accelerometer to measure in each direction.VI.CONCLUSIONS It is possible to calculate cutting force components by measuring the force components exerting on the workrest blade surface ( x B F , y B F ), slip rate, slip acceleration between workpiece and control wheel ( q , W xy a ) and acceleration translational motion of the component along the longitudinal axis ( z B a).When processing small length parts, with the assumption that the speed of the workpiece is constant, the calculation of cutting force components is based only on measurement of the components x presented in this study.