EQUIVALENT TEST METHOD OF PISTON VIBRATING MACHINE AND ROCKER-ARM VIBRATING MACHINE APPLIED IN HALF BREAKDOWN TIME TEST

Abstract

An equivalent test method of a piston vibrating machine and a rocker-arm vibrating machine applied in half breakdown time test, including: selecting three grades of samples in the same size specification; separately selecting frequencies of the piston vibrating machine and the rocker-arm vibrating machine; estimating impact times of the two vibrating machines for three grades of samples; setting up the impact times and separately impacting the samples with the two vibrating machines; sieving and weighing the impacted samples and obtaining the unbroken ratios; calculating impact cycles with an unbroken ratio of 50%; calculating the ratios of the impact cycles of the two vibrating machines for the samples; calculating an average of the ratios; calculating the relative percentages of impact cycle ratios for the three grades and assessing the linearity of the samples; and calculating equivalent impact cycles of the vibrating machines.

Claims

1. An equivalent test method of a piston vibrating machine and a rocker-arm vibrating machine applied in half breakdown time test, comprising: (S1) selecting high-grade samples, medium-grade samples and low-grade samples of a size specification S.sub.i; wherein i represents superabrasive size designation; and at least four batches of the same samples are prepared for each grade; (S2) separately setting a vibration frequency f.sub.r of the rocker-arm vibrating machine and a vibration frequency f.sub.p of the piston vibrating machine; (S3) separately estimating impact times t.sub.rH1, t.sub.rM1, and t.sub.rL1 of the rocker-arm vibrating machine for the high-grade samples, the medium-grade samples and the low-grade samples, with which times unbroken ratios of the three grade samples after being impacted can reach 45%-50%; and separately estimating impact times t.sub.pH1, t.sub.pM1, and t.sub.pL1 of the piston vibrating machine for the high-grade samples, the medium-grade samples and the low-grade samples, with which unbroken ratios of the samples after being tested can reach 45%-50%; (S4) setting up an impact time T.sub.rH1 of the rocker-arm vibrating machine for the high-grade samples according to the estimated impact time t.sub.rH1; loading one of the high-grade samples into a capsule of the rocker-arm vibrating machine; installing the capsule in the rocker-arm vibrating machine; and starting the rocker-arm vibrating machine for impact test; and setting up an impact time T.sub.pH1 of the piston vibrating machine for the high-grade samples according to the estimated impact time t.sub.pH1; loading another of the high-grade samples into a capsule of the piston vibrating machine; installing the capsule in the piston vibrating machine; and starting the piston vibrating machine for the impact test; (S5) sieving and weighing an impacted high-grade sample from the rocker-arm vibrating machine with the impact time T.sub.rH1 to obtain an unbroken ratio P.sub.rH1; and sieving and weighing an impacted high-grade sample from the piston vibrating machine with the impact time T.sub.pH1 to obtain an unbroken ratio P.sub.pH1, wherein P.sub.rH1 and P.sub.pH1 are 45%-50%; (S6) if the unbroken ratio P.sub.rH1 or P.sub.pH1 is less than 45%, appropriately shortening the impact time of the rocker-arm vibrating machine or the piston vibrating machine, repeating steps (S4)-(S5) until the unbroken ratios P.sub.rH1 and P.sub.pH1 are within 45%-50%, and at this time, recording the impact time T.sub.rH1 of the rocker-arm vibrating machine and its corresponding unbroken ratio P.sub.rH1, and the impact time T.sub.pH1 of the piston vibrating machine and its corresponding unbroken ratio P.sub.pH1; (S7) according to steps (S4)-(S6), respectively impacting the medium-grade sample and the low-grade sample with the rocker-arm vibrating machine or the piston vibrating machine with their corresponding estimated impact time t.sub.rM1 and t.sub.rL1 or t.sub.pM1 and t.sub.pL1 and then sieving and weighing the impacted samples to obtain the unbroken ratio P.sub.rM1 and P.sub.rL1 of the rocker-arm vibrating machine and the unbroken ratio P.sub.rM1 and P.sub.rL1 of the piston vibrating machine, and recording their respective impact times T.sub.rM1 and T.sub.rL1 and T.sub.pM1 and T.sub.pL1, wherein P.sub.rM1, P.sub.rL1, P.sub.pM1 and P.sub.pL1 are within 45%-50%; (S8) according to steps (S1)-(S7), performing impact tests of the high-grade samples, the medium-grade samples and the low-grade samples separately with the rocker-arm vibrating machine and the piston vibrating machine, wherein unbroken ratios of the high-grade samples, the medium-grade samples and the low-grade samples are within 50%-55%; if an unbroken ratio of a sample is more than 55%, increasing corresponding impact time and performing the same impact test until the unbroken ratio is within 50%-55%, and at this moment, recording the impact time T.sub.rH2 and its unbroken ratio P.sub.rH2 of the rocker-arm vibrating machine for the high-grade samples, the impact time T.sub.rM2 and its unbroken ratio P.sub.rM2 of the rocker-arm vibrating machine for the medium-grade samples, the impact time T.sub.rL2 and its unbroken ratio P.sub.rL2 of the rocker-arm vibrating machine for the low-grade samples, the impact time T.sub.pH2 and its unbroken ratio P.sub.pH2 of the piston vibrating machine for the high-grade samples, the impact time T.sub.pM2 and its unbroken ratio P.sub.pM2 of the piston vibrating machine for the medium-grade samples, and the impact time T.sub.pL2 and its unbroken ratio P.sub.pL2 of the piston vibrating machine for the low-grade samples; (S9) separately calculating, according to Equations (1)-(3), impact times T.sub.rH50, T.sub.rM50, and T.sub.rL50 of the rocker-arm vibrating machine for the high-grade samples, the medium-grade samples and the low-grade samples with an unbroken ratio of 50%; and separately converting the impact times T.sub.rH50, T.sub.rM50, and T.sub.rL50 into their appropriate impact cycles C.sub.rH50, C.sub.rM50, and C.sub.rL50: $\begin{array}{cc}{C}_{\mathrm{rH}50}=\left[T_{\mathrm{rH}1}+\frac{\left(T_{\mathrm{rH}1}-T_{\mathrm{rH}2}\right)\times \left(50-P_{\mathrm{rH}1}\right)}{\left(P_{\mathrm{rH}1}-P_{\mathrm{rH}2}\right)}\right]\times f_r=T_{\mathrm{rH}50}\times f_r;& \left(1\right)\end{array}$ $\begin{array}{cc}{C}_{\mathrm{rM}50}=\left[T_{\mathrm{rM}1}+\frac{\left(T_{\mathrm{rM}1}-T_{\mathrm{rM}2}\right)\times \left(50-P_{\mathrm{rM}1}\right)}{\left(P_{\mathrm{rM}1}-P_{\mathrm{rM}2}\right)}\right]\times f_r=T_{\mathrm{rM}50}\times f_r;\mathrm{and}& \left(2\right)\end{array}$ $\begin{array}{cc}{C}_{\mathrm{rL}50}=\left[T_{\mathrm{rL}1}+\frac{\left(T_{\mathrm{rL}1}-T_{\mathrm{rL}2}\right)\times \left(50-P_{\mathrm{rL}1}\right)}{\left(P_{\mathrm{rL}1}-P_{\mathrm{rL}2}\right)}\right]\times f_r=T_{\mathrm{rL}50}\times f_r;& \left(3\right)\end{array}$ (S10) separately calculating, according to Equations (4)-(6), impact times T.sub.pH50, T.sub.pM50, and T.sub.pL50 of the piston vibrating machine for the high-grade samples, the medium-grade samples and the low-grade samples with an unbroken ratio of 50%; and separately converting the impact times T.sub.pH50, T.sub.pM50, and T.sub.pL50 into their appropriate impact cycles C.sub.pH50, C.sub.pM50, and C.sub.pL50: $\begin{array}{cc}{C}_{\mathrm{pH}50}=\left[T_{\mathrm{pH}1}+\frac{\left(T_{pH1}-T_{pH2}\right)\times \left(50-P_{pH1}\right)}{\left(P_{pH1}-P_{pH2}\right)}\right]\times f_p=T_{pH50}\times f_p;& \left(4\right)\end{array}$ $\begin{array}{cc}{C}_{\mathrm{pM}50}=\left[T_{\mathrm{pM}1}+\frac{\left(T_{\mathrm{pM}1}-T_{\mathrm{pM}2}\right)\times \left(50-P_{\mathrm{pM}1}\right)}{\left(P_{\mathrm{pM}1}-P_{\mathrm{pM}2}\right)}\right]\times f_p=T_{\mathrm{pM}50}\times f_p;\mathrm{and}& \left(5\right)\end{array}$ $\begin{array}{cc}{C}_{\mathrm{pH}50}=\left[T_{\mathrm{pM}1}+\frac{\left(T_{\mathrm{pM}1}-T_{\mathrm{pM}2}\right)\times \left(50-P_{\mathrm{pM}1}\right)}{\left(P_{\mathrm{pM}1}-P_{\mathrm{pM}2}\right)}\right]\times f_p=T_{pH50}\times f_p;& \left(6\right)\end{array}$ (S11) separately calculating, according to Equations (7)-(9), impact cycle ratios R.sub.H50, R.sub.M50, and R.sub.L50 of the impact cycles C.sub.pH50, C.sub.pM50, and C.sub.pL50 to the impact cycles C.sub.rH50, C.sub.rM50 and C.sub.rL50: $\begin{array}{cc}{R}_{H50}=\frac{C_{\mathrm{pH}50}}{C_{\mathrm{rH}50}};& \left(7\right)\end{array}$ $\begin{array}{cc}{R}_{M50}=\frac{C_{\mathrm{pM}50}}{C_{\mathrm{rM}50}};\mathrm{and}& \left(8\right)\end{array}$ $\begin{array}{cc}{R}_{L50}=\frac{C_{\mathrm{pL}50}}{C_{\mathrm{rL}50}};& \left(9\right)\end{array}$ (S12) calculating, according to Equation (10), an average r.sub.A50 of the ratios R.sub.H50, R.sub.M50, and R.sub.L50: $\begin{array}{cc}{r}_{A50}=\frac{R_{H50}+R_{M50}+R_{L50}}{3};& \left(10\right)\end{array}$ (S13) repeating steps (S1)-(S12) to obtain another average r.sub.A50′; and averaging r.sub.A50 and r.sub.A50′ to obtain R.sub.A50; (S14) separately calculating the relative percentages of the high-grade sample, the medium-grade sample, and the low-grade sample according to |R.sub.A50−R.sub.x50|/R.sub.A50, wherein x is H, M or L, MAX|R.sub.A50−R.sub.x50|/R.sub.A50−R.sub.D50max/R.sub.A50; if any one of three relative percentages is not larger than 1.5% that is a given threshold, namely R.sub.D50max/R.sub.A50≤1.5%, proceeding to step (S15); if at least one of the three relative percentages is larger than 1.5%, namely R.sub.D50max/R.sub.A50>1.5%, proceeding to step (S16); and if all the three relative percentages greatly exceed 1.5%, namely R.sub.D50max/R.sub.A50>>1.5%, or exceed 3.0%, or greatly exceed the given threshold, or an expected precision value of the equivalent test result is significantly less than the given threshold, proceeding to step (S17); (S15) obtaining an impact cycle C.sub.Nrx50 or C.sub.Npx50 of its same new sample of any grade in the size specification S.sub.i by impacting the sample with the rocker-arm vibrating machine or the piston vibrating machine; and calculating its appropriate equivalent impact cycle C.sub.Exp50 of the piston vibrating machine or its appropriate equivalent impact cycle C.sub.Erx50 of the rocker-arm vibrating machine for the same samples according to Equation (11) or (12) without considering a grade relationship of the three relative percentages: $\begin{array}{cc}{C}_{\mathrm{Epx}50}=R_{A50}.Math.C_{\mathrm{Nrx}50};\mathrm{and}& \left(11\right)\end{array}$ $\begin{array}{cc}{C}_{\mathrm{Erx}50}=\frac{C_{\mathrm{Npx}50}}{R_{A50}}.& \left(12\right)\end{array}$ (S16) obtaining an impact cycle C.sub.NrH50 or C.sub.NpH50 of the same new high-grade sample, an impact cycle C.sub.NrM50 or C.sub.NpM50 of the same new medium-grade sample, and C.sub.NrL50 or C.sub.NpL50 of the same new low-grade sample in the size specification S.sub.i by impacting these samples with the rocker-arm vibrating machine or the piston vibrating machine; and calculating its appropriate equivalent impact cycle C.sub.EpH50 or C.sub.ErH50 for the same new high-grade sample, its appropriate equivalent impact cycle C.sub.EpM50 or C.sub.ErM50 for the same new medium-grade sample and its appropriate equivalent impact cycle C.sub.EpL50 or C.sub.ErL50 for the same new low-grade sample for the piston vibrating machine and the rocker-arm vibrating machine according to Equations (13)-(18) in the case of considering the grade relationship of the three relative percentages: $\begin{array}{cc}{C}_{\mathrm{EpH}50}=R_{H50}.Math.C_{\mathrm{NrH}50};& \left(13\right)\end{array}$ $\begin{array}{cc}{C}_{\mathrm{ErH}50}=\frac{C_{\mathrm{NpH}50}}{R_{H50}};& \left(14\right)\end{array}$ $\begin{array}{cc}{C}_{\mathrm{EpM}50}=R_{M50}.Math.C_{\mathrm{NrM}50};& \left(15\right)\end{array}$ $\begin{array}{cc}{C}_{\mathrm{ErM}50}=\frac{C_{\mathrm{NpM}50}}{R_{M50}};& \left(16\right)\end{array}$ $\begin{array}{cc}{C}_{\mathrm{EpL}50}=R_{L50}.Math.C_{\mathrm{NrL}50};\mathrm{and}& \left(17\right)\end{array}$ $\begin{array}{cc}{C}_{\mathrm{ErL}50}=\frac{C_{\mathrm{NpL}50}}{R_{L50}};\mathrm{and}& \left(18\right)\end{array}$ (S17) increasing the number of sample grades to 5 or 7; establishing equivalent calculation equations for 5 sample grades or 7 sample grades in the same size with reference to steps (S1)-(S16); and calculating equivalent test results between the rocker-arm vibrating machine and the piston vibrating machine according to the equivalent calculation equations newly established.

2. The equivalent test method of claim 1, further comprising: (S18) respectively converting equivalent impact cycles C.sub.Epx50 and C.sub.Erx50 into equivalent impact times T.sub.Epx50 and T.sub.Erx50 according to Equations (19)-(20) to obtain equivalent test results between the piston vibrating machine and the rocker-arm vibrating machine for individual grades of samples with the same size:
T.sub.Epx50=C.sub.Epx50×f.sub.p  (19); and
T.sub.Erx50=C.sub.Erx50×f.sub.r  (20).

3. The equivalent test method of claim 2, further comprising: (S19) acquiring equivalent test results between the piston vibrating machine and the rocker-arm vibrating machine for all sample size specifications in each grade.

4. The equivalent test method of claim 1, wherein i is selected from D851 to D46 for diamonds, or from B301 to B46 for cubic boron nitrides.

5. The equivalent test method of claim 1, wherein in step (S2), f.sub.r is set to 2400 r/min.

6. The equivalent test method of claim 1, wherein in step (S2), f.sub.p is set to 1420 r/min.

7. The equivalent test method of claim 1, wherein in step (S14), the expected precision value of the equivalent test result is 1.0%.

8. A system for implementing the equivalent test method of claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0037] FIG. 1 is schematic diagram of a piston vibrating machine in the prior art;

[0038] FIG. 2 is schematic diagram of a rocker-arm vibrating machine in the prior art;

[0039] FIG. 3 graphically shows a relationship that the relative percentages related to a high-grade sample, a medium-grade sample and a low-grade sample are not larger than 1.5% according to an embodiment of the present disclosure;

[0040] FIG. 4 graphically shows a relationship that the relative percentages related to a high-grade sample, a medium-grade sample and a low-grade sample are larger than 1.5% according to an embodiment of the present disclosure; and

[0041] FIG. 5 graphically shows a relationship that the relative percentages related to a high-grade sample, a medium-grade sample, a middle-high-grade sample, a middle-low-grade sample, and a low-grade sample are greatly larger than 1.5% according to an embodiment of the present disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS

[0042] The technical solutions of the present invention will be further described below with reference to the accompanying specific embodiments.

[0043] For three grades of samples (the high-grade sample, the medium-grade sample and the low-grade sample) with the same particle size, their half-breakdown impact cycles are measured by using a piston vibrating machine and a rocker-arm vibrating machine through the half-breakdown time test method to respectively calculate the half-breakdown impact cycle ratios of the three grades of samples impacted with the piston vibrating machines and the rocker-arm vibrating machine. Then, the average impact cycle ratio of the half-breakdown impact cycle ratios for the three grades is calculated. The relative percentages of the half-breakdown impact ratios for the three grades are calculated. A deviation limit for the relative percentages of the half-breakdown impact cycle ratios for the three grades is set (e.g., 1.5% or 2.0%). The relative percentages of the half-breakdown impact cycle ratios for the three grades of the samples are separately compared with the deviation limit to assess the linearity of the impulse ratios of the piston vibrating machine and the rocker-arm vibrating machine on the three grades of samples. The types of equations used for the equivalent calculation are further chosen or determined by the linearity of the impulse ratio. For the samples with a good linearity of the impulse ratios, the average of the half-breakdown impact cycle ratio of the three grade samples impacted with the two vibrating machines is used to calculate the equivalent test values. For the samples with a poor linearity of the impulse ratios, the half-breakdown impact cycle ratios of the three grades of samples impacted with the two vibrating machines are used to calculate the equivalence test values. In this way, the equivalent test values for each grade sample of the same size superabrasive tested by the piston vibrating machine and the rocker-arm vibrating machine can be obtained.

[0044] As described above, this application provides an equivalent test method for half breakdown time of a piston vibrating machine and a rocker-arm vibrating machine, which includes the following steps.

[0045] (S1) High-grade samples, medium-grade samples and low-grade samples of a size specification S.sub.i are selected, where i represents superabrasive size designation, and at least four batches of the same samples are prepared for each grade.

[0046] (S2) A vibration frequency f.sub.r and f.sub.p of the rocker-arm vibrating machine and the piston vibrating machine are respectively set as 2400 r/min and 1420 r/min.

[0047] (S3) The impact times t.sub.rH1, t.sub.rM1, and t.sub.rL1 of the rocker-arm vibrating machine for the high-grade samples, the medium-grade samples and the low-grade samples are separately estimated, with which times the unbroken ratios of the three grade samples after being impacted can reach 45%-50%. The impact times t.sub.pH1, t.sub.pM1, and t.sub.pL1 of the piston vibrating machine for the high-grade samples, the medium-grade samples and the low-grade samples are separately estimated, with which the unbroken ratios of the three grade samples after being impacted can reach 45%-50%.

[0048] (S4) An impact time T.sub.rH1 of the rocker-arm vibrating machine for the high-grade samples is set up according to the estimated impact time t.sub.rH1. One of the high-grade samples is loaded into a capsule of the rocker-arm vibrating machine. The capsule is installed in the rocker-arm vibrating machine, and the rocker-arm vibrating machine is started for impact test.

[0049] An impact time T.sub.pH1 of the piston vibrating machine for the high-grade samples is set up according to the estimated impact time t.sub.pH1. One of the high-grade samples is loaded into a capsule of the piston vibrating machine. The capsule is installed in the piston vibrating machine, and the piston vibrating machine is started for impact test.

[0050] (S5) The high-grade sample impacted by the rocker-arm vibrating machine with the impact time T.sub.rH1 is sieved and weighed to obtain an unbroken ratio P.sub.rH1. The high-grade sample impacted by the piston vibrating machine with the impact time T.sub.pH1 is sieved and weighed to obtain an unbroken ratio P.sub.pH1, where P.sub.rH1 and P.sub.pH1 are 45%-50%.

[0051] (S6) If the unbroken ratio P.sub.rH1 or P.sub.pH1 is less than 45%, the impact time of the rocker-arm vibrating machine or the piston vibrating machine is appropriately shortened, and steps (S4)-(S5) are repeated until the unbroken ratios P.sub.rH1 and P.sub.pH1 are within 45%-50%, and at this time, the impact time T.sub.rH1 of the rocker-arm vibrating machine and its corresponding unbroken ratio P.sub.rH1, and the impact time T.sub.pH1 and its corresponding unbroken ratio P.sub.pH1 of the piston vibrating machine on the high-grade sample are recorded.

[0052] (S7) According to steps (S4)-(S6), the medium-grade sample and the low-grade sample are respectively impacted by the rocker-arm vibrating machine or the piston vibrating machine with their corresponding estimated impact time t.sub.rM1 and t.sub.rL1 or t.sub.pM1 and t.sub.pL1, and then the impacted samples are sieved and weighed to obtain the unbroken ratio P.sub.rM1 and P.sub.rL1 of the rocker-arm vibrating machine and the unbroken ratio P.sub.rM1 and P.sub.rL1 of the piston vibrating machine, and their respective impact times T.sub.rM1 and T.sub.rL1 and T.sub.pM1 and T.sub.pL1 are recorded, where P.sub.rM1, P.sub.rL1, P.sub.pM1 and P.sub.pL1 are 45%-50%.

[0053] (S8) According to steps (S1)-(S7), the high-grade samples, the medium-grade samples and the low-grade samples are separately impacted by the rocker-arm vibrating machine and the piston vibrating machine, where the unbroken ratios of the high-grade samples, the medium-grade samples and the low-grade samples are 50%-55%. If an unbroken ratio of a sample is more than 55%, the corresponding impact time is increased and the same impact test is performed until the unbroken ratio is 50%-55%, and at this time, the impact time T.sub.rH2, and its unbroken ratio P.sub.rH2 of the rocker-arm vibrating machine for the high-grade samples, the impact time T.sub.rM2 and its unbroken ratio P.sub.rM2 of the rocker-arm vibrating machine for the medium-grade samples, the impact time T.sub.rL2 and its unbroken ratio P.sub.rL2 of the rocker-arm vibrating machine for the low-grade samples, the impact time T.sub.pH2 and its unbroken ratio P.sub.pH2 of the piston vibrating machine for the high-grade samples, the impact time T.sub.pM2 and its unbroken ratio P.sub.pM2 of the piston vibrating machine for the medium-grade samples, and the impact time T.sub.pL2 and its unbroken ratio P.sub.pL2 of the piston vibrating machine for the low-grade samples are recorded.

[0054] (S9) According to Equations (1)-(3), the impact times T.sub.rH50, T.sub.rM50, and T.sub.rL50 of the rocker-arm vibrating machine for the high-grade samples, the medium-grade samples and the low-grade samples with an unbroken ratio of 50% are separately calculated and the impact times T.sub.rH50, T.sub.rM50, and T.sub.rL50 are separately converted into their appropriate impact cycles C.sub.rH50, C.sub.rM50, and C.sub.rL50:

[00007]$\begin{array}{cc}{C}_{\mathrm{rH}50}=\left[T_{\mathrm{rH}1}+\frac{\left(T_{\mathrm{rH}1}-T_{\mathrm{rH}2}\right)\times \left(50-P_{\mathrm{rH}1}\right)}{\left(P_{\mathrm{rH}1}-P_{\mathrm{rH}2}\right)}\right]\times f_r=T_{\mathrm{rH}50}\times f_r;& \left(1\right)\end{array}$$\begin{array}{cc}{C}_{\mathrm{rM}50}=\left[T_{\mathrm{rM}1}+\frac{\left(T_{\mathrm{rM}1}-T_{\mathrm{rM}2}\right)\times \left(50-P_{\mathrm{rM}1}\right)}{\left(P_{\mathrm{rM}1}-P_{\mathrm{rM}2}\right)}\right]\times f_r=T_{\mathrm{rM}50}\times f_r;\mathrm{and}& \left(2\right)\end{array}$$\begin{array}{cc}{C}_{\mathrm{rL}50}=\left[T_{\mathrm{rL}1}+\frac{\left(T_{\mathrm{rL}1}-T_{\mathrm{rL}2}\right)\times \left(50-P_{\mathrm{rL}1}\right)}{\left(P_{\mathrm{rL}1}-P_{\mathrm{rL}2}\right)}\right]\times f_r=T_{\mathrm{rL}50}\times f_r.& \left(3\right)\end{array}$

[0055] (S10) According to Equations (4)-(6), the impact times T.sub.pH50, T.sub.pM50, and T.sub.pL50 of the piston vibrating machine for the high-grade samples, the medium-grade samples and the low-grade samples with an unbroken ratio of 50% are separately calculated, and the impact times T.sub.pH50, T.sub.pM50, and T.sub.pL50 are separately converted into their appropriate impact cycles C.sub.pH50, C.sub.pM50, and C.sub.pL50:

[00008]$\begin{array}{cc}{C}_{\mathrm{pH}50}=\left[T_{\mathrm{pH}1}+\frac{\left(T_{pH1}-T_{pH2}\right)\times \left(50-P_{pH1}\right)}{\left(P_{pH1}-P_{pH2}\right)}\right]\times f_p=T_{pH50}\times f_p;& \left(4\right)\end{array}$

[00009]$\begin{array}{cc}{C}_{\mathrm{pM}50}=\left[T_{\mathrm{pM}1}+\frac{\left(T_{\mathrm{pM}1}-T_{\mathrm{pM}2}\right)\times \left(50-P_{\mathrm{pM}1}\right)}{\left(P_{\mathrm{pM}1}-P_{\mathrm{pM}2}\right)}\right]\times f_p=T_{\mathrm{pM}50}\times f_p;\mathrm{and}& \left(5\right)\end{array}$$\begin{array}{cc}{C}_{\mathrm{pH}50}=\left[T_{\mathrm{pM}1}+\frac{\left(T_{\mathrm{pM}1}-T_{\mathrm{pM}2}\right)\times \left(50-P_{\mathrm{pM}1}\right)}{\left(P_{\mathrm{pM}1}-P_{\mathrm{pM}2}\right)}\right]\times f_p=T_{pH50}\times f_p.& \left(6\right)\end{array}$

[0056] (S11) According to Equations (7)-(9), the impact cycle ratios R.sub.H50, R.sub.M50, and R.sub.L50 of the impact cycles C.sub.pH50, C.sub.pM50, and C.sub.pL50 to the impact cycles C.sub.rH50, C.sub.rM50 and C.sub.rL50 are separately calculated:

[00010]$\begin{array}{cc}{R}_{H50}=\frac{C_{\mathrm{pH}50}}{C_{\mathrm{rH}50}};& \left(7\right)\end{array}$$\begin{array}{cc}{R}_{M50}=\frac{C_{\mathrm{pM}50}}{C_{\mathrm{rM}50}};\mathrm{and}& \left(8\right)\end{array}$$\begin{array}{cc}{R}_{L50}=\frac{C_{\mathrm{pL}50}}{C_{\mathrm{rL}50}}.& \left(9\right)\end{array}$

[0057] (S12) According to Equation (10), an average r.sub.A50 of the impact cycle ratios R.sub.H50, R.sub.M50, and R.sub.L50 is calculated:

[00011]$\begin{array}{cc}{r}_{A50}=\frac{R_{H50}+R_{M50}+R_{L50}}{3}.& \left(10\right)\end{array}$

[0058] (S13) Steps (S1)-(S12) are repeated to obtain another average r.sub.A50′, and r.sub.A50 and r.sub.A50′ are averaged to obtain a result R.sub.A50.

[0059] (S14) Relative percentages of the high-grade sample, the medium-grade sample, and the low-grade sample are respectively calculated according to |R.sub.A50−R.sub.x50|/R.sub.A50, where x is H, M or L. For example, the relative percentage of the high-grade sample is represented by [(R.sub.A50−R.sub.H50)/R.sub.A50]. MAX|R.sub.A50−R.sub.x50|/R.sub.A50=R.sub.D50max/R.sub.A50. If any one of the three relative percentages is not larger than 1.5% that is a given threshold, namely R.sub.D50max/R.sub.A50≤1.5%, as shown in FIG. 3, step (S15) is performed. If at least one of the three relative percentages is larger than 1.5%, namely R.sub.D50max/R.sub.A50>1.5%, as shown in FIG. 4, step (S16) is performed. If all the three relative percentages are far larger than 1.5%, namely R.sub.D50max/R.sub.A50>>1.5%, as shown in FIG. 5, for example larger than 3.0%, or greatly exceed the given threshold, or the expected precision value of the equivalent test result is significantly less than the given threshold, step (S17) is performed.

[0060] (S15) An impact cycle C.sub.Nrx50 or C.sub.Npx50 of its same new sample of any grade in the size specification S.sub.i is obtained by impacting the sample with the rocker-arm vibrating machine or the piston vibrating machine. The appropriate equivalent impact cycle C.sub.Exp50 of the piston vibrating machine or the appropriate equivalent impact cycle C.sub.Erx50 of or the rocker-arm vibrating machine for the same sample is calculated according to Equation (11) or (12) without considering a grade relationship of the three relative percentages:

[00012]$\begin{array}{cc}{C}_{\mathrm{Epx}50}=R_{A50}.Math.C_{\mathrm{Nrx}50};\mathrm{and}& \left(11\right)\end{array}$$\begin{array}{cc}{C}_{\mathrm{Erx}50}=\frac{C_{\mathrm{Npx}50}}{R_{A50}}.& \left(12\right)\end{array}$

[0061] (S16) An impact cycle C.sub.NrH50 or C.sub.NpH50 of the same new high-grade sample, an impact cycle C.sub.NrM50 or C.sub.NpM50 of the same new medium-grade sample, and C.sub.NrL50 or C.sub.NpL50 of the same new low-grade sample in the size specification S.sub.i are obtained by impacting these samples with the rocker-arm vibrating machine or the piston vibrating machine. Its appropriate equivalent impact cycle C.sub.EpH50 or C.sub.ErH50 for the same new high-grade sample, its appropriate equivalent impact cycle C.sub.EpM50 or C.sub.ErM50 for the same new medium-grade sample and its appropriate equivalent impact cycle C.sub.EpL50 or C.sub.ErL50 for the same new low-grade sample for the piston vibrating machine or the rocker-arm vibrating machine are calculated according to Equations (13)-(18) in the case of considering the grade relationship of the three relative percentages:

[00013]$\begin{array}{cc}{C}_{\mathrm{EpH}50}=R_{H50}.Math.C_{\mathrm{NrH}50};& \left(13\right)\end{array}$$\begin{array}{cc}{C}_{\mathrm{ErH}50}=\frac{C_{\mathrm{NpH}50}}{R_{H50}};& \left(14\right)\end{array}$

[00014]$\begin{array}{cc}{C}_{\mathrm{EpM}50}=R_{M50}.Math.C_{\mathrm{NrM}50};& \left(15\right)\end{array}$$\begin{array}{cc}{C}_{\mathrm{ErM}50}=\frac{C_{\mathrm{NpM}50}}{R_{M50}};& \left(16\right)\end{array}$$\begin{array}{cc}{C}_{\mathrm{EpL}50}=R_{L50}.Math.C_{\mathrm{NrL}50};\mathrm{and}& \left(17\right)\end{array}$$\begin{array}{cc}{C}_{\mathrm{ErL}50}=\frac{C_{\mathrm{NpL}50}}{R_{L50}}.& \left(18\right)\end{array}$

[0062] (S17) The number of sample grades is increased to 5 or 7, as shown in FIG. 5. In this case of severe non-linearity in relative percentages, equivalent calculation equations for 5 sample grades or 7 sample grades in the same size are established with reference to steps (S1)-(S16), and equivalent test results between the rocker-arm vibrating machine and the piston vibrating machine are calculated according to the equivalent calculation equations newly established.

[0063] (S18) After the relevant parameters for equivalent testing between the piston vibrating machine and the rocker-arm vibrating machine (e.g., C.sub.rH50, C.sub.rM50, C.sub.rL50, C.sub.pH50, C.sub.pM50, C.sub.pL50, R.sub.A50, R.sub.H50, R.sub.M50, R.sub.L50, and so on) are established, an equivalent test result of a new sample for one vibrating machine can be calculated by a test result of the same size sample impacted with another vibrating machine without actual measurement. In the equivalent test method provided herein, the equivalent impact cycle can be converted into equivalent impact time, and the two parameters are interchangeable. The equivalent impact cycles C.sub.Epx50 and C.sub.Erx50 are converted into the equivalent impact times T.sub.Epx50 and T.sub.Erx50 according to Equations (19)-(20):

T.sub.Epx50=C.sub.Epx50×f.sub.p  (19); and

T.sub.Erx50=C.sub.Erx50×f.sub.r  (20).

[0064] In this way, equivalent test results between the piston vibrating machine and the arm-rocker vibrating machine for each grade of the samples with the same size can be obtained.

[0065] (S19) Equivalent test results of the piston vibrating machine and the rocker vibrating machine for each grade of superabrasive in various sizes are acquired. After the relevant parameters for equivalence testing between the piston vibrating machine and rocker-arm vibrating machine have been established for all sample size specifications S.sub.D851 to S.sub.D46 and S.sub.B301 to S.sub.B46, this equivalent test method will be universally applicable for equivalence testing of superabrasives of all sizes.

[0066] The equivalent test method provided herein is validated by actual test certifications, the relevant data is shown in Table 1, which verifies that the equivalent test method provided herein is very effective. Diamond samples of size D426 with a weight of 0.4 g per impact are used for the tests. The samples are divided into three grades, namely, a high-grade sample, a medium-grade sample and a low-grade sample. BY using the half-breakdown time method, the tests are conducted with a piston vibrating machine and a rocker-arm vibrating machine respectively to acquire the half-breakdown time and half-breakdown cycle of the three grades of samples. Then, the impact cycle ratios R.sub.x50 of the three grades, the average ratio R.sub.A50 and the relative percentage of the impact cycle of the three grades of samples are calculated. As the relative percentages of the three grades of sample are 0.0%,-2.9%, and 1.9%, respectively, where two of the three values are greater than 1.5%, then the equations for equivalence tests of the two vibrating machines should be selected to be of a graded algorithm. The high-grade sample, the medium-grade sample and the low-grade sample are newly selected from the samples of size D426 and are tested with the rocker-arm vibrating machine and the piston vibrating machine respectively by using the half-breakdown time method. The test results of the rocker vibrating machine are used to calculate the equivalent test results of the piston vibrating machine according to the equations provided in the present disclosure, and then the equivalent test results of the piston vibrating machine are subtracted from the actual test results of the piston vibrating machine, expressed by (C.sub.Epx50−C.sub.Npx50). The differences between the calculated equivalent cycles and the actual test cycles for the three grades for a piston vibrating machine are very small, and are −62 (r), 8 (r) and 49 (r) for the three grades respectively, which are −0.9%, 0.1% and 0.9% of the measured values respectively, significantly less than the required test accuracy of 1.5% (positive and negative numbers are not counted, and the comparison is performed in absolute values).

TABLE-US-00001 TABLE 1 Certification test of the equivalence test method for a piston vibrating machine and a rocker-arm vibrating machine by using a half-breakdown time method Sample size D426(40/45) Sample weight 0.4 g PVM (1420 Hz) RVM (2400 Hz) Sample grade HBT (s) HBC (r) HBT (s) HBC (r) RoHBC ARoHBC RP High grade T.sub.pH50 = C.sub.pH50 = T.sub.rH50 = C.sub.rH50 = R.sub.H50 = 1.02% 0.0% 278 6583 161 6458 1.02 Middle grade T.sub.pM50 = C.sub.pM50 = T.sub.rM50 = C.sub.rM50 = R.sub.M50 = −2.9% 249 5891 141 5630 1.05 Low grade T.sub.pL50 = C.sub.pL50 = T.sub.rL50 = C.sub.rL50 = R.sub.L50 = 1.9% 178 4202 105 4208 1.00 Sample grades ATRR EHBCP ATRP DOERAATR PROPD High grade C.sub.NrH50 = C.sub.EpH50 = C.sub.NpH50 = −62 (r) −0.9% 6422 6550 6612 Middle grade C.sub.NrM50 = C.sub.EpM50 = C.sub.NpM50 = 8 (r) 0.1% 5630 5911 5903 Low grade C.sub.NrL50 = C.sub.EpL50 = C.sub.NpL50 = 49 (r) 0.9% 5533 5533 5484 Noted: PVM denotes a piston vibrating machine; RVM denotes a rocker-arm vibrating machine; HBT denotes half-breakdown time (T.sub.px50 or T.sub.rx50); HBC denotes a half-breakdown cycle (C.sub.px50 or C.sub.rx50); RoHBC denotes the ratio of the half-breakdown impact cycle of the piston vibrating machine to the rocker vibrating machine (R.sub.x50 = C.sub.px50/C.sub.rx50); ARoHBC denotes the average ratio of the half-breakdown impact cycle of the piston vibrating machine to the rocker vibrating machine (R.sub.A50); RP denotes the relative percentage of the impact cycle ratio [(R.sub.A50 − R.sub.x50)/R.sub.A50]; ATRR denotes the actual test result of the rocker-arm vibrating machine (C.sub.Nrx50); EHBCP denotes the equivalent test result of half-breakdown cycle of the piston vibrating machine (C.sub.Epx50 = R.sub.x50 .Math. C.sub.Nrx50); ATRP denotes the actual test result of the piston vibrating machine (C.sub.Npx50); DOERAATR denotes a cycle difference between the equivalent test result of the piston vibrating machine and the actual test result of the piston vibrating machine (C.sub.Epx50 − C.sub.Npx50); and PROPD denotes the percentage of the cycle difference to the actual test result of the piston vibrating machine [(C.sub.Epx50 − C.sub.Npx50 )/C.sub.Npx50].

[0067] Described above are merely preferred embodiments of the present invention, which are not intended to limit the present invention. Though the present invention has been described in detail above, one of ordinary skill in the art can still make various modifications and variations to the embodiments provided herein. It should be noted that those modifications and variations made without departing from the spirit and scope of the present invention shall fall within the scope of the present invention defined by the appended claims.