OPTIMIZATION METHOD FOR SCREEN SURFACE DYNAMIC LOAD OF VIBRATING SCREEN

Abstract

The present invention discloses an optimization method for a screen surface dynamic load of a vibrating screen. The method includes the following steps: step 1. selecting design variables, and establishing an experimental matrix; step 2. performing a response curved surface experiment; step 3. establishing two double-objective optimization models and solving the same to obtain two groups of Pareto solution sets, wherein the solution sets respectively represent screening efficiency optimization paths of the vibrating screen under the conditions of a high screen surface dynamic load and a low screen surface dynamic load; and step 4. calculating an optimization space for a screen surface dynamic load under a high screening efficiency. According to the method of the present invention, the screen surface dynamic load can be directly reduced, and the service life of the screen surface and the whole vibrating screen is prolonged.

Claims

1. An optimization method for a screen surface dynamic load of a vibrating screen, comprising following steps: step 1. selecting design variables, and establishing an experimental matrix; step 2. performing a response curved surface experiment; step 3. establishing two double-objective optimization models and solving the two double-objective optimization models to obtain two groups of Pareto solution sets, wherein the two groups of Pareto solution sets respectively represent screening efficiency optimization paths of the vibrating screen under conditions of a high screen surface dynamic load and a low screen surface dynamic load; and step 4. calculating an optimization space for the screen surface dynamic load under a high screening efficiency, wherein: in the step 3, the method of establishing the two double-objective optimization models and solving the two double-objective optimization models comprises: establishing mathematical models of screening efficiency and the screen surface dynamic load through multiple linear regression; establishing the two double-objective optimization models; and solving two double-objective optimization problems by applying a non-dominated sorting genetic algorithm-IL NSGA-II, to obtain the two groups of Pareto solution sets; in the method of establishing mathematical models of the screening efficiency and the screen surface dynamic load, evaluation indexes for the screening efficiency are shown in following formulas:
M.sub.c=100γ.sub.cQ.sub.f,
M.sub.f=100γ.sub.fQ.sub.c,
P.sub.c=γ.sub.c−M.sub.c+M.sub.f,
F.sub.f=γ.sub.f−M.sub.f+M.sub.c, $E_c=\frac{{\gamma }_c-M_f}{F_c},$ $E_f=\begin{array}{ccc}{\gamma }_f& & M_f\\ & F_f& \end{array},$
η=E.sub.c+E.sub.f−100; wherein M.sub.c is content of misplaced materials in screen overflow, that is, a percentage of fine particles in the screen overflow to a feed, %; M.sub.f is the content of the misplaced materials in screen underflow, that is, a percentage of coarse particles in the screen underflow to the feed, %; γ.sub.c is an actual yield of the screen overflow, %; γ.sub.f is an actual yield of the screen underflow, %; Q.sub.f is content of the fine particles in the screen overflow, %; Q.sub.c is content of the coarse particles in the screen underflow, %; F.sub.c is the content of the coarse particles in the feed, that is, a theoretical yield of the screen overflow, %; F.sub.f is the content of the fine particles in the feed, that is, a theoretical yield of the screen underflow, %; E.sub.c is a positive matching efficiency of the coarse particles, %; E.sub.f is a positive matching efficiency of the fine particles, %; η is the screening efficiency, %; a screen surface dynamic load index takes a mean value of differences between peak values of a stress signal at a connection between a screen surface structure and a side plate under unloaded and loaded conditions of the vibrating screen as a quantitative index, denoted as F, and is calculated according to the following formulas: $F=\underset{i=1}{\overset{n}{.Math.}}\stackrel{\_}{\Delta F_i},$ $\stackrel{\_}{\Delta F_i}=\stackrel{\_}{F_{i\mathrm{load}}}-\stackrel{\_}{F_{i\mathrm{unload}}};$ wherein $\stackrel{\_}{F_{i\mathrm{load}}}$ and $\stackrel{\_}{F_{i\mathrm{unload}}}$ are mean values of maximum stress values at an i.sup.th measuring point in unit time under stable loaded and unloaded states of a screening machine, respectively; in the method of establishing the two double-objective optimization models, the double-objective optimization models are as follows: $\{\begin{array}{c}\mathrm{Max}\left(M_{\mathrm{Efficiency}}\right)\\ \mathrm{Max}\left(M_{\mathrm{load}}\right)\\ \frac{{\mathrm{Aw}}^2\sin \beta }{ℊ\cos \alpha }>a_1\\ \frac{{A\left(2\pi f\right)}^2}{ℊ\cos \alpha }>a_2\\ x_{\mathrm{imin}}<x_i<x_{\mathrm{imax}}\end{array},$ $\{\begin{array}{c}\mathrm{Min}\left(M_{\mathrm{Efficiency}}\right)\\ \mathrm{Min}\left(M_{\mathrm{load}}\right)\\ \frac{{\mathrm{Aw}}^2\sin \beta }{ℊ\cos \alpha }>a_1\\ \frac{{A\left(2\pi f\right)}^2}{ℊ\cos \alpha }>a_2\\ x_{\mathrm{imin}}<x_i<x_{\mathrm{imax}}\end{array};$ wherein M.sub.efficiency represents a function expression of the screening efficiency; M.sub.load represents a function expression of the screen surface dynamic load; a.sub.1 represents a minimum value of a throwing index of the screen surface in an experimental point; a.sub.2 represents a minimum value of a vibration intensity in the experimental point; A represents a vibration amplitude; g represents an acceleration of gravity; β represents a vibration direction angle; a represents a screen surface inclination angle; w represents an angular frequency; f represents a vibration frequency; X.sub.i represents a variable in an objective function; X.sub.imin represents a lower limit of the variable X.sub.i; and X.sub.imax represents an upper limit of the variable X.sub.i; in the method of solving the two double-objective optimization problems by applying the NSGA-II, a solution set obtained according to $\{\begin{array}{c}\mathrm{Max}\left(M_{\mathrm{Efficiency}}\right)\\ \mathrm{Max}\left(M_{\mathrm{load}}\right)\\ \begin{array}{c}{\mathrm{Aw}}^2\sin \beta \\ ℊ\cos \alpha \end{array}>a_1\\ \frac{{A\left(2\pi f\right)}^2}{ℊ\cos \alpha }>a_2\\ x_{\mathrm{imin}}<x_i<x_{\mathrm{imax}}\end{array}$ is taken as a first solution set, and a solution set obtained according to $\{\begin{array}{c}\mathrm{Min}\left(M_{\mathrm{Efficiency}}\right)\\ \mathrm{Min}\left(M_{\mathrm{load}}\right)\\ \frac{{\mathrm{Aw}}^2\sin \beta }{ℊ\cos \alpha }>a_1\\ \frac{{A\left(2\pi f\right)}^2}{ℊ\cos \alpha }>a_2\\ x_{\mathrm{imin}}<x_i<x_{\mathrm{imax}}\end{array}$ is taken as a second solution set; and in the step 4, a calculation formula is as follows: ${\left(\mathrm{Optimization}\mathrm{space}\right)}_i=\frac{{\left(\mathrm{screen}\mathrm{surface}\mathrm{dynamic}\mathrm{load}\right)}_{i1}-{\left(\mathrm{screen}\mathrm{surface}\mathrm{dynamic}\mathrm{load}\right)}_{i2}}{{\left(\mathrm{screen}\mathrm{surface}\mathrm{dynamic}\mathrm{load}\right)}_{i2}};$ wherein, the (optimization space).sub.i represents the optimization space for the screen surface dynamic load under a certain screening efficiency level; the (screen surface dynamic load).sub.i1 represents a screen surface dynamic load value in the first solution set corresponding to the screening efficiency; and the (screen surface dynamic load).sub.i2 represents a screen surface dynamic load value in the second solution set corresponding to the screening efficiency.

2. The optimization method for the screen surface dynamic load of the vibrating screen according to claim 1, wherein in the step 1, the method of establishing the experimental matrix comprises: selecting factors that have a greater impact on the screening efficiency and the screen surface dynamic load as the design variables; determining factor levels, and determining the experimental matrix by using a center-circumscribed compound method; and performing a pre-experimental test on the experimental matrix.

3. The optimization method for the screen surface dynamic load of the vibrating screen according to claim 2, wherein in the method of selecting factors, a number of the design variables is either 3 or 4; and the design variables include an excitation parameter, a screen mesh shape, and Jhe_screen surface inclination angle.

4. The optimization method for the screen surface dynamic load of the vibrating screen according to claim 2, wherein, the method of performing the pre-experimental test on the experimental matrix comprises the following steps: calculating the throwing index τ or the vibration intensity K.sub.v of the screen surface in all experimental points in an experimental table; $\tau -\frac{{A\left(2\pi f\right)}^2}{ℊ\cos \alpha },$ $K_v-\frac{{\mathrm{Aw}}^2\sin \beta }{ℊ\cos \alpha };$ wherein A represents the vibration amplitude; f represents the vibration frequency; g represents the acceleration of gravity; β represents the vibration direction angle; α represents the screen surface inclination angle; w represents the angular frequency; selecting three experimental points with the lowest throwing index or lowest vibration intensity of the screen surface in the experimental matrix for pre-experiment; and determining whether material screening systems corresponding to three pre-experiment points can reach a steady state, and completing the pre-experiment test if all material screening systems reach the steady state, otherwise returning to re-adjust the factor levels.

5. The optimization method for the screen surface dynamic load of the vibrating screen according to claim 4, wherein, the method of determining whether the material screening systems corresponding to the three pre-experiment points can reach the steady state, comprising the following steps: acquiring an acceleration signal on the side plate of the vibrating screen through an accelerometer, and determining that the material screening system reaches the steady state if the acceleration signal reaches a steady state.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0042] FIG. 1 is a flowchart of an optimization method for a screen surface dynamic load of a vibrating screen as provided by an embodiment of the present invention.

[0043] FIG. 2 is a schematic diagram of positional layout of stress sensors for a side plate on a screen surface in the embodiment of the present invention.

[0044] FIG. 3 is a schematic diagram of positional layout of acceleration sensors for the side plate on the screen surface in the embodiment of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0045] The present invention discloses an optimization method for a screen surface dynamic load of a vibrating screen, which solves the problems in the prior art that a vibrating screen is seriously affected by particle impact, resulting in low structural performances of a screening machine and short service life of the screening machine.

[0046] The above objective of the present invention is achieved by the following technical solutions.

[0047] An optimization method for a screen surface dynamic load of a vibrating screen includes the following steps:

[0048] S1. selecting design variables, and establishing an experimental matrix;

[0049] S2. performing a response curved surface experiment;

[0050] S3. establishing two double-objective optimization models and solving the same to obtain two groups of Pareto solution sets, wherein the solution sets respectively represent screening efficiency optimization paths of the vibrating screen under the conditions of a high screen surface dynamic load and a low screen surface dynamic load; and

[0051] S4, calculating an optimization space for the screen surface dynamic load under a high screening efficiency, wherein a specific calculation method is shown in Formula 1:

[00009]$\begin{array}{cc}{\left(\mathrm{Optimization}\mathrm{space}\right)}_i=\frac{{\left(\mathrm{screen}\mathrm{surface}\mathrm{load}\right)}_{i1}-{\left(\mathrm{screen}\mathrm{surface}\mathrm{load}\right)}_{i2}}{{\left(\mathrm{screen}\mathrm{surface}\mathrm{load}\right)}_{i2}}& \left(1\right)\end{array}$

[0052] wherein an (optimization space).sub.i represents an optimization space for a screen surface dynamic load under a certain screening efficiency level; a (screen surface dynamic load).sub.i1 represents a screen surface dynamic load value in the first solution set corresponding to this screening efficiency; and the (screen surface dynamic load).sub.i2 represents a screen surface dynamic load value in the second solution set corresponding to this screening efficiency.

[0053] In the step S1, the method of selecting the design variables and establishing the experimental matrix includes:

[0054] S11. selecting factors that have a greater impact on the screening efficiency and the screen surface dynamic load as design variables, such as an excitation parameter, a screen mesh shape, and a screen surface inclination angle, wherein the number of the design variables is preferably 3-4;

[0055] S12. determining factor levels, and determining the experimental matrix by using a center-circumscribed compound (CCC) method; and

[0056] S13. performing a pre-experimental test on the experimental matrix.

[0057] In S13. the method of performing the pre-experimental test on the experimental matrix includes the following specific steps:

[0058] S131. calculating a throwing index τ or a vibration intensity K.sub.v of the screen surface in all the experimental points in an experimental table;

[00010]$\begin{array}{cc}\tau =\frac{{A\left(2\pi f\right)}^2}{ℊ\cos \alpha }& \left(2\right)\end{array}$$\begin{array}{cc}{K}_v=\frac{{\mathrm{Aw}}^2\sin \beta }{ℊ\cos \alpha }& \left(3\right)\end{array}$

[0059] S132. selecting three experimental points with the lowest throwing index or lowest vibration intensity of the screen surface in the experimental matrix for pre-experiment; and

[0060] S133. determining whether material screening systems corresponding to the three pre-experiment points can reach a steady state, and completing the pre-experiment if all material screening systems reach a steady state, otherwise returning to the step S12 to re-adjust the factor levels.

[0061] In S133, the method of determining whether the material screening systems corresponding to the three pre-experiment points can reach the steady state includes: acquiring an acceleration signal on a side plate of the vibrating screen through an accelerometer, and considering that the material screening system reaches the steady state if the signal reaches a steady state.

[0062] In the step 2, the process of establishing the two double-objective optimization models and solving the same includes:

[0063] S21: establishing mathematical models of the screening efficiency and the screen surface dynamic load through multiple linear regression, wherein evaluation indexes of the screening efficiency are shown in Formulas 4-10:

M.sub.c=100γ.sub.cQ.sub.f  (4)

M.sub.f=100γ.sub.fQ.sub.c  (5)

F.sub.c=γ.sub.c−M.sub.c+M.sub.f  (6)

F.sub.f=γ.sub.f−M.sub.f+M.sub.c  (7)

[00011]$\begin{array}{cc}{E}_c=\frac{{\gamma }_c-M_f}{F_c}& \left(8\right)\end{array}$$\begin{array}{cc}{E}_f=\frac{{\gamma }_f-M_f}{F_f}& \left(9\right)\end{array}$
η=E.sub.c+E.sub.f−100  (10)

[0064] wherein M.sub.c is the content of misplaced materials in screen overflow (coarse particles), that is, a percentage of fine particles in the screen overflow to the feed, %; M.sub.f is the content of misplaced materials in screen underflow (fine particles), that is, a percentage of coarse particles in the screen underflow to the feed, %; γ.sub.c is an actual yield of the screen overflow (coarse particles), %; γ.sub.f is an actual yield of the screen underflow (fine particles), %; Q.sub.f is the content of fine particles in the screen overflow (coarse particles),%; Q.sub.c is the content of the coarse particles in the screen underflow (fine particles), %; F.sub.c is the content of coarse particles in the feed, that is, a theoretical yield of the screen overflow (coarse particles), %; F.sub.f is the content of fine particles in the feed, that is, a theoretical yield of the screen underflow (fine particles), %; E.sub.c is a positive matching efficiency of coarse particles, %; E.sub.f is a positive matching efficiency of fine particles. %; and η is the screening efficiency, %;

[0065] a screen surface dynamic load index takes a mean value of differences between peak values of a stress signal at the connection between a screen surface structure and the side plate under unloaded and loaded conditions of the vibrating screen as a quantitative index, denoted as F; the specific calculation formulas are shown in Formula 11 and Formula 12, wherein

[00012]$\stackrel{\_}{F_{i\mathrm{load}}}$

and

[00013]$\stackrel{\_}{F_{i\mathrm{unload}}}$

are mean values of maximum stress values at an i.sup.th measuring point in unit time under the stable loaded and unloaded states of the screen machine, respectively;

[00014]$\begin{array}{cc}F=\underset{i=1}{\overset{n}{.Math.}}\stackrel{\_}{\Delta F_i}& \left(11\right)\end{array}$$\begin{array}{cc}\stackrel{\_}{\Delta F_i}=\stackrel{\_}{F_{i\mathrm{load}}}-\stackrel{\_}{F_{i\mathrm{unload}}}& \left(12\right)\end{array}$

[0066] S22: establishing two double-objective optimization models, which are specifically as shown in the following formulas:

[00015]$\begin{array}{cc}\{\begin{array}{c}\mathrm{Max}\left(M_{\mathrm{Efficiency}}\right)\\ \mathrm{Max}\left(M_{\mathrm{load}}\right)\\ \frac{{\mathrm{Aw}}^2\sin \beta }{ℊ\cos \alpha }>a_1\\ \frac{{A\left(2\pi f\right)}^2}{ℊ\cos \alpha }>a_2\\ x_{\mathrm{imin}}<x_i<x_{\mathrm{imax}}\end{array}& \left(13\right)\end{array}$$\begin{array}{cc}\{\begin{array}{c}\mathrm{Min}\left(M_{\mathrm{Efficiency}}\right)\\ \mathrm{Min}\left(M_{\mathrm{load}}\right)\\ \frac{{\mathrm{Aw}}^2\sin \beta }{ℊ\cos \alpha }>a_1\\ \frac{{A\left(2\pi f\right)}^2}{ℊ\cos \alpha }>a_2\\ x_{\mathrm{imin}}<x_i<x_{\mathrm{imax}}\end{array}& \left(14\right)\end{array}$

[0067] wherein M.sub.efficiency represents a function expression of the screening efficiency; M.sub.load represents a function expression of the screen surface dynamic load; a.sub.1 represents a minimum value of a throwing index of the screen surface in an experimental point; a.sub.2 represents a minimum value of a vibration intensity in the experimental point; A represents the vibration amplitude; g represents the acceleration of gravity; β represents the vibration direction angle; α represents the screen surface inclination angle; X.sub.i represents a variable in an objective function; X.sub.imin represents a lower limit of the variable X.sub.i; and X.sub.iman represents an upper limit of the variable X.sub.i; and

[0068] S23: solving two double-objective optimization problems by applying an NSGA-II algorithm to obtain two groups of Pareto solution sets. A solution set obtained according to Formula 13 is taken as a first solution set, and a solution set obtained according to Formula (14) is taken as a second solution set.

Embodiments

[0069] As shown in FIG. 1, the present invention provides an optimization method for a screen surface dynamic load of a vibrating screen. In this embodiment, experiments are carried out with linear screens. The size of a screen surface of each linear screen is 2,000 mm*1,300 mm, and a screen surface inclination angle can be adjusted by a support structure. There are four stress sensors in total, namely a first stress sensor 1-1, a second stress sensor 1-2, a third stress sensor 1-3, and a fourth stress sensor 1-4 respectively, and their arrangement positions are shown in FIG. 2. There are two acceleration sensors in total, namely a first acceleration sensor 2-1 and a second acceleration sensor 2-2 respectively, and their arrangement positions are shown in FIG. 3.

[0070] In S1: experiments are performed by using the linear screens. Excitation parameters (amplitude, frequency, and vibration direction angle) and the screen surface inclination angle are selected as design variables, and a feed flow rate is set to 16 t/h. A set of effective experimental matrices are determined through pre-experiments, and the specific factor level settings and experimental tables are shown in Tables 1 and 2. Based on relevant theories of a stochastic process, in each group of experiments, whether a steady state is reached is determined through the acceleration sensors, particle size distribution and stress data of particles over and under the screen in the steady state are collected, and the screen surface dynamic load and the screening efficiency data in the experiments obtained by calculation are shown in Table 2. A calculation formula for the screen surface load is shown in Formula 15:

[00016]$\begin{array}{cc}F=0.1\stackrel{\_}{\Delta F_1}+0.2\stackrel{\_}{\Delta F_2}+0.3\stackrel{\_}{\Delta F_3}+0.4\stackrel{\_}{\Delta F_4}.& \left(15\right)\end{array}$

TABLE-US-00001 TABLE 1 Design variables and factor level settings Level Factor −2 −1 0 1 2 A(mm) 6.5 5.5 4.5 3.5 2.5 f(Hz) 12 14.5 17 19.5 22 α(°) 2 4.5 7 9.5 12 β(°) 40 45 50 55 60

TABLE-US-00002 TABLE 2 Design variables and factor level settings Screen surface Vibration Screening Operating inclination direction efficiency Screen surface sequence Amplitude Frequency angle angle (%) load (N) S −1 −1 −1 −1 85.026 3.2629 2 0 0 0 0 81.649 2.9097 3 0 0 0 −2 83.633 2.7794 4 1 −1 −1 −1 89.172 3.7480 5 0 0 0 0 81.165 2.8000 6 0 −2 0 0 88.36 3.3472 7 −1 1 1 1 67.205 2.7970 8 −1 −1 −1 1 84.351 3.9317 9 0 0 0 0 81.29 2.8728 10 0 2 0 0 73.891 2.9012 11 2 0 0 0 86.144 3.1731 12 0 0 −2 0 85.913 4.2500 13 −1 −1 1 −1 79.859 2.5077 14 −1 1 −1 1 75.618 3.6539 15 0 0 0 0 81.78 2.9262 16 −2 0 0 0 74.398 2.9219 17 0 0 0 0 81.577 2.8464 18 1 −1 1 1 83.098 2.8907 19 0 0 0 0 81 2.9024 20 1 −1 −1 1 89.106 4.7786 21 0 0 0 2 80.595 3.5892 22 1 1 1 −1 79.029 2.4312 23 1 −1 1 −1 85.198 2.6472 24 −1 1 1 −1 71.963 2.4563 25 −1 1 −1 −1 76.983 3.0416 26 1 1 −1 1 82.837 3.8878 27 0 0 0 0 81.492 2.8501 28 1 1 1 1 76.053 2.7751 29 −1 −1 1 1 77.542 2.8018 30 1 1 −1 −1 84.05 3.1497 31 0 0 2 0 73.865 2.4410

[0071] In S2: functional relationships among the screen surface load, the screening efficiency and the design variables are established respectively by using a multiple linear regression method. As shown in FIG. 16 and FIG. 17, M.sub.e is the screening efficiency, and M.sub.s is the screen surface load. Therefore, the two double-objective optimization models are established and shown in Formulas 18 and 19.

M.sub.e=0.885+0.0624x1−0.00108x2+0.00506x3+0.000351x4−0.00621x1x1−0.000034x2x2−0.000728x3x3−0.002039x1x20.000742xx3+0.000044x2x3−0.000036x2x4−0.000056x3x4  (16)

M.sub.s=14.01−1.671x1−0.602x2−0.715x3+0.0651x4−0.0475x1x1+0.00734x2x2 +0.01620x3x3+0.0422x1x2+0.0498x1x3+0.01600x2x30.00050x2x4−0.00457x3x4  (17)

[00017]$\begin{array}{cc}\{s.t.\begin{array}{cc}\min M_s\left(x_1,x_2,x_3,x_4\right)& \\ \min M_e\left(x_1,x_2,x_3,x_4\right)& \\ \frac{{\mathrm{Aw}}^2\sin \beta }{ℊ\cos \alpha }>3.3& \\ \frac{{A\left(2\pi f\right)}^2}{ℊ\cos \alpha }>3.5& \\ x_{\mathrm{imin}}<x_i<x_{\mathrm{imax}}& i\in 1,2,3,4\end{array}& \left(18\right)\end{array}$$\begin{array}{cc}\{s.t.\begin{array}{cc}\max M_s\left(x_1,x_2,x_3,x_4\right)& \\ \max M_e\left(x_1,x_2,x_3,x_4\right)& \\ \frac{{\mathrm{Aw}}^2\sin \beta }{ℊ\cos \alpha }>3.3& \\ \frac{{A\left(2\pi f\right)}^2}{ℊ\cos \alpha }>3.5& \\ x_{\mathrm{imin}}<x_i<x_{\mathrm{imax}}& i\in 1,2,3,4\end{array}& \left(19\right)\end{array}$

[0072] In S3, two groups of Pareto solution sets are solved by using an NSGA-II algorithm, wherein the solution sets respectively represent screening efficiency optimization paths of the vibrating screen under the conditions of a high screen surface dynamic load and a low screen surface dynamic load.

[0073] In S4: the screen surface dynamic load under a high screening efficiency is calculated to optimize an optimization space. When the screening efficiency is 80%, a space for the screen surface load can be optimized by about 39%; when the screening efficiency is 85%, a space for the screen surface load can be optimized by about 26%; the screening efficiency is 90%, a space for the screen surface load can be optimized by about 18%.

[0074] A configuration scheme of some process parameters in the optimization path of the low screen surface load is shown in Table 3.

TABLE-US-00003 TABLE 3 Configuration scheme of process parameters of the low screen surface load during the vibration under a high screening efficiency Inclination Direction Screen surface Screening Sequence Amplitude Frequency angle angle dynamic load efficiency 1 3.72 16.98 2.03 69.98 6.210 7.089 2 365 20.38 2.09 69.98 5.752 6.097 3 4.01 21.66 2.08 69.97 5.469 5.580 4 4.86 21.87 2.1 69.98 5.282 5.356 5 5.57 21.91 2.09 69.99 5.161 5.191