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Table 1 Mechanical Physical Properties of Si3N4 Ceramic Materials Material Density
(g/cm3) bending strength
(MPa) Microhardness
(HV10) Fracture Toughness
(MP·m1â„2) Elastic Modulus
(GPa) Si3N4 Ceramics 3.2 750 1600 8 310 Abrasive Grinding Wheel: Resin Bonded Grinding Wheel, Model: EWAG BP 102 359T, Concentration: C100, Diameter 150mm, Width: 6mm Grinding Fluid: Water-based Mill with Strong Flushing Function Grinding grinding method: End grinding. Grinding parameters: grinding wheel speed Vs=14.06m/s, grinding depth Ap=30μm, wheel oscillation speed VW=0.96rn/min. Measuring instrument: Kistler three-phase piezoelectric dynamometer is used to measure the dynamic grinding force signal, and the grinding force measurement test device is shown in Figure 1. Test Results Figure 2 shows a plot of the dynamic grinding force as a function of time recorded in the test. As can be seen from the figure, the grinding force signal of Si3N4 ceramic exhibits a certain degree of fluctuation, but it cannot be observed from this curve whether the signal has stationarity, ergodicity, normality, and periodicity. 1 FIG grinding force measuring test apparatus 2 the dynamic grinding force curve diagram of time-domain test 3 test stationary grinding force signal if a discrete-time signal x (n) time mean and independent of n. The autocorrelation function rx(n1,n2) has nothing to do with the selection of n1,n2, but only with the difference of n2,n1, then the signal x(n) is called a wide stationary random signal. Because the analysis methods of stationary data and non-stationary data are very different, the stability test of the signal is the prerequisite for data analysis. The stationarity test can be performed before or after the digital/analog (A/D) conversion. Commonly used methods include visual inspection, root mean square test, and round inspection. As can be seen from the waveform characteristics shown in Figure 2, the mean value of grinding force vibration data collected during the test fluctuates little, and the peak-to-valley variation of the vibration waveform is more uniform and the frequency structure is more consistent. Therefore, the signal can be assumed to be a stationary signal. This article uses the round test method to conduct a rigorous test. The round test method is a non-parametric test method. It divides the collected data into N intervals and checks whether the measured signal is a stationary signal by judging whether the round number is within the round interval (R1, R2). In the measurement data shown in Fig. 2, the number of segments N is set to 20, and at the significance level a=0.05, the round distribution table 2 is checked, and the available round range is (6, 15). The number of rounds calculated by the round inspection program R=8 is within this round range, so this assumption is accepted. Similar conclusions can also be drawn by performing the same tests on other groups of data, which indicates that there is no obvious potential trend in the Si3N4 ceramic grinding force signal, which is a steady signal.
Table 2 Round distribution table n=N/2 0.975 0.95 0.05 0.025 ... ... ... ... ... 9 5 6 13 14 10 6 6 15 15 11 7 7 16 16 ... ... ... ... ... The ergonomic test determines theoretically whether the population of a random vibration process satisfies the ergodic assumptions, depending on whether the ensemble mean is equal to the time average, which is difficult both for analog and digital analysis of the data. . Therefore, the current test of ergodicity is mainly based on physical judgment. That is, if each sample of the random process itself is stationary, and the basic physical factors of each sample are generally the same, the random process represented by these samples is considered. The overall situation is ergodic. From the results of the above-mentioned stationarity test, it can be seen that the dynamic grinding force signal of hard and brittle materials meets the assumptions of each state. Therefore, the history of a single sample function over time may include the value experience of all sample functions of the signal. The above-mentioned stationarity and ergodicity tests are for an approximate hypothesis test in engineering applications. In fact, only by long-term observation of the objective vibration process and a large number of data analysis can we finally determine whether the random process meets the mathematical model assumptions of stationarity or ergodicity. However, in engineering practice, it is not necessary to be so demanding. Therefore, the method described above can be used to determine the smoothness and ergodicity of the grinding force signal. Normality Test Although the random data in a practical project has a normal probability distribution density in many cases, there are exceptions and normality tests are required. The normality test methods of random vibration process include physical judgment method, probability density function measurement method and c2 goodness-of-fit test method. In this paper, the Pearson c2 test method is used to test the normality of the grinding force vibration signal of Si3N4 ceramics. This method is a non-parametric hypothesis test, that is, a general inference of the population without knowing the mathematical form of the population distribution. The normality test is performed on the data shown in Figure 2 (take one segment and the sample size is 374). Assume that the random process generally obeys the normal distribution. The results calculated using the c2 test program are shown in Table 3. At a significant level of a=0.05, c20.05(8)=15.51
(i) Group limits
(Xi) Group limits
(ui) probability
(Pi) Expected frequency
(nPi) Actual frequency
(fi) (fi-nPi)2/nPi 1 -0.005 -2.079 0.0189 7.054 2 5.0879 2 -0.003 -1.68 0.0277 10.36 6 3 -5×10-4 -1.281 0.0574 21.475 23 0.1083 4 0.0015 -0.882 0.0849 31.764 60 25.1004 ... ... ... ... ... ... ... 11 0.0155 1.909 0.0374 13.98 11 0.6353 12 0.175 2.3077 0.0176 6.597 3 1.9501 13 ∞ ∞ 0.0105 3.935 3 1 373.87 374 64.009 Periodically check whether the random vibration signal has periodicity, can be estimated based on whether its physical factor has the possibility of generating a periodic signal, or data analysis methods (such as autocorrelation function analysis, probability density function curve judgment method, and The power spectral density function graph judgment method etc.) is judged. This paper uses autocorrelation function analysis method to determine whether the dynamic grinding force signal of Si3N4 ceramic has periodicity. Assume that the acquired signal x(n) is composed of grinding force signal s(n) and white noise signal u(n), ie, x(n)=s(n)+u(n). Suppose s(n) is a periodic signal whose period is M and the length of x(n) is 
1 INTRODUCTION Grinding force is one of the basic physical phenomena in the grinding process. It relates to the wear of the grinding wheel, the grinding intensity of the grinding zone, the deformation of the grinding process system, the dynamic contact state of the grinding wheel/workpiece and finally the formation of Grinding the surface roughness has a great influence. When studying the grinding mechanism of materials, it is necessary to analyze the instantaneous change of the grinding force, and when making the grinding process, it is also necessary to refer to the grinding force data. In addition, grinding force is also an important parameter for diagnosing grinding conditions and adaptively controlling the grinding process. Due to the limitations of research methods, the past researches on grinding forces were mostly limited to the static components of grinding forces, and there were few studies on the dynamic components of grinding forces. With the continuous improvement of scientific research on the accuracy requirements of grinding force analysis, the measurement and analysis of dynamic grinding force has been gradually put on the agenda. In grinding most metal materials, the dynamic grinding force signal is a stationary signal with a normal distribution. However, in the grinding of hard and brittle materials such as engineering ceramics, because these materials have the characteristics of non-uniform distribution of microstructures, the grinding force clearly exhibits randomness, nonlinearity, and other characteristics. Therefore, in the grinding of hard and brittle materials such as engineering ceramics, the dynamic grinding force signal as a random vibration signal is uncertain in the time domain. Through the smoothness, ergodicity, normality and periodicity of the grinding force signal, it is helpful to analyze the distribution characteristics of the grinding force signal, and to study the hard and brittle material grinding using appropriate digital signal processing methods. The theoretical basis is laid on the time domain and frequency domain characteristics of the cutting force signal and further analysis of its influence on the grinding process. In this paper, through the grinding experiment of Si3N4 ceramics, digital signal processing (DSP) method was used to strictly test the grinding force signal. The distribution characteristics of grinding force signals of engineering ceramics and other hard and brittle materials were analyzed and summarized. 2 Si3N4 ceramic grinding tests Test conditions Test machine: mountains FC-200D type PCD & PCBN tool grinder. Grinding material: Si3N4 based ceramics, specimen size: 24.Omm × 8.5mm × 59.4mm, the mechanical physical properties of the material are shown in Table 1. Table 3 Pearson c2 test calculation table grouping