# Influence of major factors on indicators of work of the pump

During realisation and processing of results of experiments the equations of regress G_{y} (τ_{r}) = f (_{Rizb} are received; h_{rt}; h_{a}) which show change of time of a dump of a portion of a material (cement) of 50 kg and second productivity depending on major factors.

The equation of regress of time of discharge τ_{r}порции in the coded sort looks like a material

Analyzing the equations of regress (4.7), and also using formulas (4), we will define the importance of factors (drawing 4.2):

- Superpressure _{Rizb} = 42 %;

- Height of an arrangement of an unloading pipe from the chamber bottom h_{rt} = 47 %;

- Arrangement height aeratsionnogo devices from the chamber bottom h_{a} =11 %.

The greatest influence on size of time of discharge renders the factor (height of an arrangement of an unloading pipe from the chamber bottom h_{rt} = 47 %), and the least value the factor x_{3} (arrangement height aeratsionnogo devices from the chamber bottom h_{a} =10 %) which almost in 5 times is less. Factor influence x_{1} (superpressure _{Rizb} = 42 %) is approximately equal to factor influence x_{2}, and approximately in 4 times there is more than factor influence x_{3}. The negative sign at the factor x_{1}показывает, that with its increase value of time of discharge decreases. A positive sign at factors of factors x_{2}и x_{3}показывает that at their increase discharge time increases. Value of factor at a member of the equation of joint influence x_{1}x_{2}указывает that the factorial space of the given members has been completely captured.

Drawing 4.2. The importance of major factors at discharge time

The regress equation in the decoded sort looks like

Using analytical package Maple 13, the three-dimensional figures showing dependence of time of discharge from change of major factors (table 4.1) have been constructed at the fixed values of time τ_{r} = 6, 12, 18 with (for presentation) (drawing 4.3). If necessary it is possible to construct the specified figures for any value not only time, but also other functions of the response (in the presence of the corresponding equation

Regresses). Thus, it is possible

To define geometrical and

Technological parametres of the pump, i.e. at what values of major factors we will receive this or that value of time of discharge, productivity, air expense (in our case).

3

Drawing 4.3. The graphic structures displaying fixed sizes of time of discharge depending on major factors:

1 - τ_{r} = 6 with; 2 - τ_{r} = 12 with; 3 - τ_{r} = 18 with

In drawing 4.4 the surface on which any point shows is displayed, at what values of factors it is possible to receive minimum time of discharge τr = 6 with, namely at a combination of values of a superpressure, heights of an arrangement of an unloading pipe from the bottom of the chamber and aeratsionnogo devices in spacings 1,2-1,5 atm., 34-59 mm and 40-59 mm accordingly.

Geometrical parametres are regulated structurally,Since it is put in pawn at designing and manufacturing of laboratory installation, and the superpressure influences air expense, and consequently on power inputs of process of transportation it is possible to assume, that it is expedient to use values of factors in a point And (drawing 4.4), selecting the minimum value of pressure:

_{Rizb}= 1,2 atm., h

_{rt}≈ 55 mm, h

_{a}≈ 55 mm, but not the fact, that at the named parametres we will receive a maximum capacity. Analyzing results of experiments (table 4.1,

Line 10) at _{Rizb} = 1,5 atm., h_{rt} ≈ 55 mm, h_{a} ≈ 55 mm discharge time τ_{r} = 6 about productivity it is equal G_{y} = 8,3 kg/with, but it is not clear what

Productivity at pressure _{Rizb} = 1,2 atm. Therefore it is necessary to consider influence of major factors on second productivity, as one of the basic technical and economic indicators of work of any device.

Drawing 4.4. The graphic structures displaying the minimum fixed size of time of discharge τ_{r} = 6 with from major factors:

3х the measured image, a projection to an axis x_{1}, a projection to an axis х_{2}, a projection to an axis х_{3}

The equation of regress of second productivity G_{y} in

The coded sort looks like

Analyzing the equations of regress (4.9), and also using formulas (4) we will define the importance of factors (drawing 4.5). The greatest influence on productivity size renders the factor x_{1} (superpressure _{Rizb} = 54 %), and the sign «+» shows that at its increase response function increases. A negative sign at factors of factors x_{2}и x_{3}показывает that at their increase productivity will decrease. The importance of factors x_{2}и x_{3}равны 31 % and 15 % that is less than factor influence x_{1}в 1,7 and 3,6 times accordingly.

Drawing 4.5. The importance of major factors for second productivity:

As the importance of the factor х_{3} is rather small, for simplification of the analysis of influence of factors on productivity we accept value

Arrangement heights aeratsionnogo devices from the chamber bottom equal h_{a} =55 mm to value of the basic (zero) level of a variation.

The regress equation in the decoded sort looks like

Using analytical package Maple 13, the three-dimensional figures showing dependence of productivity from change of major factors (table 4.1) at fixed values have been constructed

In drawing 4.7 the surface on which any point shows is displayed, at what values of factors it is possible to receive maximum second productivity G_{y} = 8,3 kg/with, namely at a combination of values of a superpressure, heights of an arrangement of an unloading pipe from the bottom of the chamber and aeratsionnogo devices in spacings 1,36-1,5 atm., 28-55 mm and 40-58 mm accordingly. Geometrical parametres are regulated

Structurally, since it is put in pawn at designing and manufacturing of laboratory installation, and the superpressure influences air expense, and consequently on power inputs of process of transportation it would be possible to assume, expediently to use value of factors in a point (drawing 4.7), selecting the minimum value of pressure: _{Rizb} = 1,36 atm., h_{rt} ≈ 45 mm, h_{a} ≈ 50 mm.

The surface reflecting a peak value of productivity has vozrastajushche-decreasing character. Function decrease occurs because of influence of effect of interaction of pair members x_{1}x_{2}и x_{1}x_{3} (drawing 4.8), factors which are negative also a share of influence of size of factor х_{1} (58 %) (as the most significant) on 32 % more than total influence of shares х_{2} (18 %) and х_{3} (8 %), and factor joint influence of effect of interaction of a pair member x_{2}x_{3}положителен and renders 16 % of influence.

Drawing 4.7. The graphic structures displaying the maximum fixed size of productivity G_{y} = of 8,3 kg/with from major factors:

3х the measured image, a projection to an axis x_{1}, a projection to an axis х_{2}, a projection to an axis х_{3}

х3

Drawing 4.8. The importance of influence of effects of interaction of each of pair members for second productivity:

Let's consider dependence of productivity on change of a superpressure and height of an arrangement of an unloading pipe from the chamber bottom on all range of their variation at the fixed values of height of an arrangement aeratsionnogo devices h_{a}=40, 46, 55, 64, 70 mm (drawing 4.9). The analysis of schedules has shown, that they carry vozrastajushche - decreasing character.

The greatest productivity for everyone h_{a}получим:

- At h_{a} = 40 mm and pressure Р_{изб}=1,25-1,5 atm., G_{y}=5,8-8 kg/with at h_{rt} = 34 mm; G_{y}=6-7,5 kg/with at h_{rt} = 55 mm (drawing 4.9,);

- At h_{a} = 46 mm and pressure Р_{изб}=1,25-1,5 atm., G_{y}=6,5-8,6 kg/with at h_{rt} = 34 mm; G_{y}=7-8,3 kg/with at h_{rt} = 55 mm (drawing 4.9,);

- At h_{a} = 55 mm and pressure Р_{изб}=1,25-1,5 atm., G_{y}=6,6-8,1 kg/with at h_{rt} = 34 mm; G_{y}=7,2-8 kg/with at h_{rt} = 55 mm (drawing 4.9,);

- At h_{a} = 64 mm and pressure Р_{изб}=1,25-1,5 atm., G_{y}=5-6,1 kg/with at h_{rt} = 34 mm; G_{y}=5,8-6,1 kg/with at h_{rt} = 55 mm (drawing 4.9,);

- At h_{a} = 70 mm and pressure Р_{изб}=1,25-1,5 atm., G_{y}=3,1-3,7 kg/with at h_{rt} = 34 mm; G_{y}=3,9 kg/with at h_{rt} = 55 mm (drawing 4.9,); at pressure Р=1,36 atm. ^^ D kg/with.

Thus, the greatest productivity it is received at a spacing of a variation of pressure Р_{изб}=1,25-1,5 atm. And following design data: at height aeratsionnogo devices from the chamber bottom h_{a} = 46 mm and h_{a} = 55 mm, at height of an arrangement of an unloading pipe from the chamber bottom h_{rt} = 34 mm - G_{y}=6,5-8,6 kg/with and G_{y}=6,6-8,1 kg/with; at h_{rt} = 55 mm - G_{y}=7-8,3 kg/with and G_{y}=7,2-8 kg/with (drawing 4.9,), accordingly. That is in bolshej to a measure depends on height of an arrangement of an unloading pipe h_{rt}, but thus aeratsionnoe ustrojsvo it is located above an unloading pipe on 12 mm and 15 mm, accordingly.

The analysis of schedules (drawing 4.10) dependences of productivity on change of a superpressure and arrangement height aeratsionnogo devices at a variation of height of an unloading pipe from the chamber bottom h_{rt}=20, has shown 34, 55, 76, 90 mm, that they are not linear and have increasing character. The greatest productivity for everyone h_{rt}получим (table 4.3):

- At h_{rt} = 20 mm and pressure Р_{изб}=0,8-1,5 atm., G_{y}=5,3-6,7 kg/with at h_{a} = 46 mm; G_{y}=5,1-6,2 kg/with at h_{a} = 55 mm; G_{y}=4,6-6,2 kg/with at h_{a} = 40 mm (drawing 4.9,);

- At h_{rt} = 34 mm and pressure Р_{изб}=0,8-1,5 atm., G_{y}=7,2-8,4 kg/with at h_{a} = 46 mm; G_{y}=7,2-8,0 kg/with at h_{a} = 55 mm; G_{y}=5,4-6,0 kg/with at h_{a} = 40 mm (drawing 4.9,);

- At h_{rt} = 55 mm and pressure Р_{изб}=0,8-1,5 atm., G_{y}=7,4-8,1 kg/with at h_{a} = 46 mm; G_{y}=7,5-7,9 kg/with at h_{a} = 55 mm; G_{y}=6,5-7,4 kg/with at h_{a} = 40 mm (drawing 4.9,);

- At h_{rt} = 76 mm and pressure Р_{изб}=0,8-1,5 atm., G_{y}=4,4-4,7 kg/with at h_{a} = 46 mm; G_{y}=4,7 kg/with at h_{a} = 55 mm; G_{y}=3,3-38 kg/with at h_{a} = 40 mm (drawing 4.9,);

- At h_{rt} = 90 mm and pressure Р_{изб}=0,8-1,5 atm., G_{y}=0,5 kg/with at; G_{y}=0,9 - 0,7 kg/with at h_{a} = 55 mm (drawing 4.9,).

116

Table 4.3.

The greatest productivity from superpressure change (_{Rizb} =0,8-1,5 atm.), arrangement heights aeratsionnogo devices (h_{a} = 40-55 mm) and heights of an unloading pipe (h_{rt} = 20-55 mm)

^{h}rt | ^{h}a | ^{G}y^{для Rizb} min^{0,8} ^{atm}. | ^{G}y^{для Rizb} max ^{1,5 atm}. |

34 | 40 | 5,4 | 6,0 |

46 | 7,2 | 8,4 | |

55 | 7,2 | 8,0 | |

55 | 40 | 6,5 | 7,4 |

46 | 7,4 | 8,1 | |

55 | 7,5 | 7,9 |

The analysis of the results tabulated, has shown, that at height of an unloading pipe from the chamber bottom h_{rt} = 20-34 mm, and for values of height aeratsionnogo devices from the chamber bottom h_{a} = 40 mm and h_{a} = 46-55 mm at minimum Р_{изб}=0,8 atm. Productivity is equal G_{y}=5,4 kg/with and G_{y}=7,2 kg/with, accordingly. Also at peak value Р_{изб}=1,5 atm. Productivity is maximum G_{y}=8,4 kg/with at h_{rt}=34мм, h_{a}=46мм, and at h_{rt}=55мм, h_{a}=55мм, Р_{изб}=0,8 atm. (Table 4.3) G_{y}=7,5 kg/with. Here it is necessary to notice, that at pressure increase almost in 2 times productivity will increase approximately in 1,2 times and 1,1 times, accordingly.

4.2.2

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