Academic Journal of Science and Technology ISSN: 2771-3032 | Vol. 10, No. 1, 2024 221 Grinding Force Model and Experimental Study on Ultrasonic Assisted Spiral Grinding of Silicon Carbide Ceramic Materials Chongyang Zhao1, *, Chenyu Liang1, Xiaobo Wang1, Yi Wang1, Jishan Han1 1 Henan Polytechnic University, Jiaozuo, China * Corresponding author: Chongyang Zhao (Email: zhaocy@hpu.edu.cn) Abstract: In order to reveal the mechanical properties of silicon carbide ceramic materials during the drilling process, based on the indentation fracture mechanics theory, a grinding force model of ultrasonic assisted spiral grinding for hole making was established, and the experimental results of ultrasonic assisted spiral grinding for hole making verified the mechanical model. The results showed that the experimental results had the same change trend as the predicted results of the established mechanical model, and the values were close to each other, indicating the accuracy of the established prediction model. The influence of different process parameters on the size accuracy of the hole inlet and outlet aperture after machining is analyzed. It is found that it should be selected as large rotation speed, moderate axial feed speed and small feed pitch to ensure the accuracy of the aperture and effectively suppress the aperture defects during ultrasonic assisted spiral grinding. Keywords: Ultrasonic assisted spiral grinding, Silicon carbide ceramics, Grinding force model, Size accuracy of aperture. 1. Introduction Silicon carbide ceramic materials have high hardness, high strength, high modulus physical properties, corrosion resistance ,high temperature resistance, and wear resistance chemical properties [1-2], these advantages make it have a very unique advantage in aerospace, nuclear industry ,brake system and other industries, but due to the mechanical properties of silicon carbide ceramic materials anisoanisoy, poor thermal conductivity. It is a typical material that could result in extremely harsh processing conditions combined with low strength characteristics. At present, the common processing methods of silicon carbide ceramic materials mainly fall into two categories: traditional processing and special processing. In the traditional grinding process, the grinding force is large and the tool wear is serious. In the processing process, a new type of tool needs to develop to improve the tool life [3]. Common special machining includes rapid prototyping, laser machining, abrasive water jet machining, electric discharge machining and ultrasonic assisted machining. This paper mainly studies the grinding force of ultrasonic assisted spiral grinding of silicon carbide ceramic materials. Taking silicon carbide ceramic materials as the research object, the grinding force model of longitudinal-torsional combined ultrasonic vibration assisted spiral grinding is established, the experimental platform is set up, the model is verified through experiments, and the dimensional accuracy of the aperture is analyzed, and the influence of main process parameters on the dimensional accuracy of the aperture is analyzed. The experimental results show that ultrasonic assisted spiral grinding can effectively improve the aperture quality of silicon carbide ceramic materials. Ultrasonic assisted spiral grinding plays a significant role in improving tool processing conditions, increasing tool service life and improving machining efficiency. 2. Dynamic Analysis of Ultrasonic Assisted Spiral Grinding 2.1. Principle of hole making Diamond wheel Feed direction Screw feed direction workpiece x y z (a) Three-dimensional diagram Y X workpiece hole Grinding wheel Grinding wheel revolution Wheel autobiography (b) Z direction schematic diagram Figure 1. Principle of Ultrasonic Assisted Spiral Grinding Hole Making The machining mode of ultrasonic assisted helical grinding for hole making is shown in Figure 1. The tool moves along the helix at a certain feed speed under the combined action of the workpiece feed movement along the O-XY plane and the tool feed movement along the Zaxis. Applying longitudinal vibration to the tool in the axial direction and torsional vibration in the normal direction, the tool rotates with the spindle and there is a certain distance between the central axis of the tool and the central axis of the workpiece, so that the tool is subjected to longitudinal torsional ultrasonic vibration at the same time of screw feed, and the spiral grinding hole of 222 the tool is realized. 2.2. Kinematics analysis of a single abrasive particle In order to analyze the cutting behavior of abrasive particles in ultrasonic vibration assisted spiral grinding, a coordinate system was established with the center of machining hole on the upper surface of the workpiece as the origin. Assuming that the workpiece is relatively stationary, the motion path of the tool can be broken down into four kinds: one is the ultrasonic vibration along the axis, the second is the feed movement along the axis, the third is the rotation of the tool, and the last is the revolution of the tool around the center axis of the hole on the xoy plane. The motion mode of the tool is shown in Figure 2. Therefore, in the ultrasonic spiral grinding process, the motion trajectory of the abrasive particles on the grinding needle is expressed in the coordinate system as follows: 1 2 1 2 ( ) cos cos 2 30 2 30 ( ) sin sin ( 2 30 2 30 ( ) sin(2 )f n t n tD d d x t n t n tD d d y t z t v t A ft                       (1) z x o x y o d D work piece Grinding head n1 n2 Vf Screw feed Figure 2. Schematic diagram of ultrasonic spiral grinding 2.3. Single abrasive cutting thickness model Motion path of abrasive particles is shown in figure 3 and figure 4. In the process of ultrasonic assisted spiral grinding, the motion of abrasive particles without ultrasonic vibration in the horizontal direction includes the rotating motion of the grinding wheel around the hole axis and the rotating motion of the grain around the sand wheel axis, and in the vertical direction, the motion of abrasive particles is accompanied by the axial feed of the grinding wheel. In general, most of the particles are irregular polyhedrons. In order to facilitate analysis and calculation, a large number of scholars simplified the particles into cones in the modeling process [3,4,5], as shown in Figure 5, where the diameter of a single abrasive particle is Dg, Dg =100μm,hg = √3𝐷g/3 , / 6m rad  . As shown in Figure 5, the grain distribution on the end face of the grinding wheel is uniform. On an arc of radiusRi, As shown in Figure 5, the grain distribution is uniform on the end face of the grinding wheel. On an arc of radius Ri, the center Angle between the n particle Mn and the n+1 particle Mn+1 is ΦMn. The cutting thickness of abrasive particles is shown in figure. 6, and the arc length between two adjacent abrasive particles can be expressed as: M i M nl R  (2) In the XOZ plane, the Angle between the horizontal feed velocity of the abrasive particles and the resultant velocity can be expressed as: 2 2 2 2 2 1 tan M M M M D E h V Vfa A D l V Vc Vft       (3) Because the spindle speed is much higher than the screw feed speed, the screw feed speed can be ignored and only the influence of the spindle speed can be considered. Equation (3) can be simplified as: tan 2 fa faM M c i V Vh l V R n      (4) Different numbers of particles are distributed on arcs of different radii，Suppose that the number of Rki particles on the arc isNk. when ( , )0 / 2k i jR d  , The number of particles on the arc of kiR can be expressed as kN : ki k M R N l  (5) The average central Angle between adjacent particles can be expressed as Ma : 2 Ma Na    (6) From formula (3) ~ (6), it can be deduced that the theoretical wear particle thickness can be expressed as Mh : 1 ( ) fa M k k kk v h n N n     (7) It is assumed that the grinding cross-sectional areas of adjacent grains are the same, as shown in Figure 7. The cross- sectional area is MS : 2tan M M ABCD ADEF BCJK M M M M d S S S S hg h h d               (8) End face abrasive particle Hole bottom U ltrason ic vibration Sic phase crack Figure 3 Transverse abrasive motion path Side abrasive particle Pore wall Trajectory overlap U ltrasonic vibration Figure 4 Side abrasive motion path 223 e d D 2 1 1O 0O nM ,i nM , 1i nM  1M 1X 0X 0Y Grinding wheel work piece hole Abrasive particle Figure 5 Geometric characteristics of grain movement on end face of grinding wheel Figure 6 Grinding thickness chart gh Mh A B CD E F K J Md z x y 砂轮 磨粒Grinding wheel Abrasive particle Figure 7 Grinding area diagram 2.4. Average cutting force model of a single abrasive particle Under the action of ultrasonic vibration, wear particles continuously impact the workpiece material and produce a certain indentation depth. According to the theory of indentation fracture mechanics, the relationship between the impact force Fnof a single wear particle on the workpiece and the cutting depth within one ultrasonic vibration cycle is expressed [6] : 21 (tan ) 2 Fn Hv  (9) Where,  is the geometric factor of abrasive pressure head, =1.8544. In one cycle, the effective time of the interaction between the abrasive particle and the material is t : 1 [ arcsin (1 )] 2 t f A       (10) Replacing the trajectory wave line of the action of abrasive particles on the material with a triangular wave, it can be simplified as: / 2t Af (11) According to the impulse theorem, the average cutting force of a single abrasive particle in an ultrasonic cycle is Fc : Fc Fn f t    (12) Where, is the impact waveform coefficient, and the triangular wave value is 0.5. The theoretical material removal volume of a single abrasive particle in one ultrasonic cycle is 0V : 0 1 3 L hV C C L (13) Among them, the distance of a single abrasive particle scratched on the workpiece surface in one ultrasonic cycle is L : 2 1 [ 2 cos(2 )] 30 t t rn L fB ft dt       (14) Simplify to: 2 sin 60 rn B L Af A      (15) Marshall et al. [7] studied the lateral crack and obtained the expression of the lateral crack length LC and depth hC : 3 55 14 812 2 2 1 2 2 1 ( ) [ ] tan (1 ) L IC E C C Fn HvK v    (16) 1 1 12 3 2 2 1 ( ) tanh E C C Fn Hv  (17) Where, ICK is the fracture toughness of the material, E is the elastic modulus of the material, Hvis the hardness of the material, v is the Poisson ratio of the material, nF is the force of the abrasive particle on the work, 2C is a dimensionless constant with the value 2C =0.226,  is the half top cone Angle of a single abrasive particle. According to the definition of abrasive concentration, the effective number of abrasive particles on the end face of the tool can be obtained as Na [8] : 224 2 3 2 2 0 02 ( ) 4 a i c Na C D D sa   (18) According to formula (12) and (18), the grinding force of the tool can be obtained as mF : m n aF F t f N     (19) In summary, the expression of the cutting depth of a single abrasive particle can be expressed as: 4 3 1 13 28 4 9 7 28 8 2 1 180 (1 ) tan 2 ( ) ( 120 sin ) 2 v lcMRRH K v A k c Na E rn Bf                  (20) The grinding force experienced by the tool can be expressed as mF : 12 1 1 13 2 20 2 4 51 1 62 35 1 1 12 12 26 26 13 26 13 13 13 13 7 2 8 2 90( ) (1 ) 12 ( ) (tan ) 2 ( 120 sin ) lc m p f D e K v F Hv A Na a v kec E rn Bf                   (21) 3. Experimental Research on Cutting Force of Ultrasonic Assisted Spiral Grinding of Silicon Carbide Ceramic Materials 3.1. Experimental scheme In order to verify the correctness of the established cutting force model and analyze the degree of influence of different process parameters on the cutting force of ultrasonic assisted spiral grinding, ultrasonic assisted spiral grinding hole experiments were carried out. The experimental devices mainly included CNC machine tools, ultrasonic vibration devices, force measuring systems, tools and workpieces, and the experimental system devices were shown in Figure 9. In this experimental system, the ultrasonic signal generated by the ultrasonic power supply is transmitted to the transducer through the wireless transmission disk, and the amplitude is amplified and transmitted to the tool through the amplitude transformer. The experiment was carried out on VMC850 machine tool. In the experiment, Kistle triaxial tester, 5057 multi-channel charge amplifier and computer were used to measure the grinding force dynamically. The grinding force data output by the force measuring system is analyzed by computer software. The validity of the grinding force model is verified by a set of single factor tests, and the influence of different process parameters on grinding force can be analyzed by the experimental results. The test parameters are shown in Table 1, the silicon carbide ceramic material used in the experiment is shown in Figure 10, the size is 20cm×20cm×5cm, and the basic parameters of the material are shown in Table 2. dynamometer Computer Ultrasonic power supply Data collector workpiece cutter Figure 9. Experimental system diagram Figure 10. Experiment material diagram Table 1. Experiment parameters for model verification Group number Ultrasonic amplitude A/μm Screw feed speed Vf/（mm/min） Spindle speed n/（r/min） Screw pitch ap/mm 1 2.5 500 6000 1 1 3 500 6000 1 1 3.5 500 6000 1 1 4 500 6000 1 1 4.5 500 6000 1 2 3.5 450 6000 1 2 3.5 500 6000 1 2 3.5 550 6000 1 2 3.5 600 6000 1 2 3.5 650 6000 1 3 3.5 500 5000 1 3 3.5 500 5500 1 3 3.5 500 6000 1 3 3.5 500 6500 1 3 3.5 500 7000 1 4 3.5 500 6000 0.5 4 3.5 500 6000 1 4 3.5 500 6000 1.5 4 3.5 500 6000 2 4 3.5 500 6000 2.5 225 Table 2. Basic parameters of materials Density g/cm3 Bending strength Mpa Compressive strength Mpa Tensile Strength Mpa Fracture Toughness Mpaꞏm1/2 2.26 443.8 454 271.4 24.1 2 3 4 5 6 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 experimental value theoretical value gr in di ng f or ce /N ultrasonic amplitude/μm (a) 450 500 550 600 650 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 gr in di ng f or ce (N ) screw feed speed（mm/min） experimental value theoretical value (b) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 G ri nd in g fo rc e( N ) Screw pitch(mm) Experimental value Theoretical value (c) 5000 5500 6000 6500 7000 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 G ri nd in g fo rc e( N ) Spindle speed(r/min) Experimental value Theoretical value (d) Figure. 11 Influence of different process parameters on grinding force 3.2. Analysis of experimental results Figure. 11 respectively shows the comparison between ultrasonic amplitude, spiral feed speed, pitch and spindle speed theoretical values and experimental results. It can be seen from the figure that there is little difference between experimental values and theoretical values, which verifies the accuracy of the grinding force model. It can be seen from the figure that the influence law of different process parameters on the experimental results. It can be seen in Figure 11(a) that the grinding force decreases with the increase of ultrasonic amplitude. This is because with the increase of ultrasonic amplitude, the contact area between the particle and the workpiece becomes larger, the cutting volume per unit time increases, and the effective cutting time decreases, resulting in a decrease in grinding force. When the amplitude is before 2-4.5μm, the experimental value is less than the theoretical value, mainly because the ultrasonic amplitude is small and the influence on the grinding force is small. With the increase of the amplitude, the influence degree of the amplitude on the grinding force is increasing, resulting in the phenomenon that the experimental value is greater than the theoretical value. It can be seen from Figure. 11 (b) that the grinding force increases with the increase of the screw feed speed. This is because the increase of the screw feed speed increases the material removal rate, thus increasing the grinding force. It can be seen from Figure 11 (c) that the grinding force gradually increases with the increase of the pitch, because the increase of the pitch essentially increases the cutting depth of the abrasive particle, and the amount of material removal per unit time also increases correspondingly, thus increasing the grinding force. It can be seen from Figure. 11 (d) that the grinding force decreases with the increase of the spindle speed. This is because the increase of the spindle speed increases the number of abrasive particles involved in grinding per unit time, resulting in a decrease in the cutting amount of materials by a single abrasive particle. At the same time, it is also conducive to the formation of smaller chips in time to discharge the processing area, reduce tool wear, etc., so as to effectively reduce the cutting force. 3.3. Dimensional accuracy analysis of holes in ultrasonic assisted spiral grinding of Silicon carbide ceramic matrix composites 3.3.1. The influence of speed on the dimensional accuracy of aperture Figure. 12 shows the change curve of measured inlet and outlet diameters of holes with different eccentricities along with spindle speed. It can be seen from Figure. 3 that the inlet diameter of the holes processed in the three experiments is larger than the outlet diameter. Based on the movement law of spiral grinding holes, the main reason that the inlet diameter of the holes is larger than the outlet diameter is caused by the constant wear of the tool and the elastic deformation of the workpiece caused by the vibration of the tool during the machining process of the holes. Under the same eccentricity, the diameter of the entrance and outlet of the hole decreases first and then increases with the change of 226 the grinding head speed, mainly because the axial force and radial force decrease first and then increase with the increase of the rotating speed during the machining process. 3000 3500 4000 4500 5000 8.970 8.972 8.974 8.976 8.978 8.980 8.982 8.984 8.986 8.988 8.990 ho le d ia m et er (m m ) rotational speed(rpm) entrance exit (a) e=0.5mm 3000 3500 4000 4500 5000 10.970 10.972 10.974 10.976 10.978 10.980 10.982 10.984 10.986 10.988 10.990 ho le d ia m et er ( m m ) rotational speed(rpm) entrance exit (b) e=1mm 3000 3500 4000 4500 5000 11.970 11.972 11.974 11.976 11.978 11.980 11.982 11.984 11.986 11.988 11.990 H ol e di am et er ( m m ) rotational speed(rpm) entrance exit (c) e=1.5mm Figure.12 Influence of spindle speed on aperture under different eccentricity 3.3.2. The influence of axial feed speed on the dimensional accuracy of the aperture Figure 13 shows the change curve of hole inlet and outlet diameters measured under different eccentricities along with the axial feed speed. It can be seen from Figure.4 that under the same eccentricity, the diameter of hole inlet and outlet tends to decrease with the increase of the axial feed speed, because the cutting thickness keeps increasing with the increase of the axial feed speed, while the cutting depth remains unchanged. The axial force and radial force of ultrasonic assisted spiral grinding are increased, resulting in the difference between the actual machining aperture and the theoretical machining aperture. 500 1000 1500 2000 2500 8.955 8.960 8.965 8.970 8.975 8.980 8.985 8.990 8.995 ho le d ia m et er ( m m ) feed speed (mm/min) entrance exit (a)e=0.5mm 500 1000 1500 2000 2500 10.970 10.972 10.974 10.976 10.978 10.980 10.982 10.984 10.986 10.988 ho le d ia m et er ( m m ) feed speed (mm/min) entrance exit (b)e=1mm 500 1000 1500 2000 2500 11.968 11.970 11.972 11.974 11.976 11.978 11.980 11.982 11.984 11.986 11.988 ho le d ia m et er ( m m ) feed speed (mm/min) entrance exit (c)e=1.5mm Figure13 Effect of tool axial feed speed on aperture under different eccentricity 3.3.3. The influence of axial feed pitch on the dimensional accuracy of the aperture Figure 14 shows the change curve of inlet diameter measured by axial feed pitch with different eccentricities. It can be seen from Figure15 that under the same eccentricity, due to the constant axial feed speed, the cutting thickness and cutting depth increase with the increase of the pitch, and the axial force and radial force both increase, leading to serious tool wear, resulting in the continuous reduction of inlet aperture. The aperture deviation of the inlet and outlet decreases first and then increases with the increase of eccentricity. When the eccentricity is 1mm, the aperture deviation is small. 227 1.0 1.2 1.4 1.6 1.8 2.0 8.955 8.960 8.965 8.970 8.975 8.980 8.985 8.990 ho le d ia m et er ( m m ) pitch (mm) entrance exit (a)e=0.5mm 1.0 1.2 1.4 1.6 1.8 2.0 10.970 10.972 10.974 10.976 10.978 10.980 10.982 10.984 10.986 10.988 ho le d ia m et er ( m m ) pitch (mm) entrance exit (b)e=1mm 1.0 1.2 1.4 1.6 1.8 2.0 11.965 11.970 11.975 11.980 11.985 11.990 ho le d ia m et er ( m m ) pitch (mm) entrance exit (c)e=1.5mm Figure 14 Influence of tool pitch on aperture under different eccentricity In the process of spiral grinding of silicon carbide ceramics, the surface quality of the hole is mainly determined by the quality of the entrance, the quality of the exit and the surface quality of the hole wall. This experiment mainly observed the entrance of the hole, observed the appearance of the entrance of the hole after processing through a super-depth microscope, and analyzed the quality of the entrance of the machining hole. 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