The Effect of Cable Span Length on the Maximum Amplitude of Dragon Fruit Basket Oscillation

3.7.4. Influence of cable span lengthto the maximum amplitude of the dragon fruit basket oscillation

When the length value changes and because the hanging distance between the baskets is s, the number of baskets changes, so the number of equations in the differential equation system (2.95) representing the horizontal oscillation of the basket will change. This will affect the solution value, that is, the parameters of the received oscillation will change, including the parameter of the maximum oscillation amplitude of the basket.

Use Matlab to solve the system of differential equations for oscillations with changes in length in the range of 20 - 28 m. The results table of maximum oscillation amplitudes at positions on the cable span is in table 3.12 and graph in figure 3.13.

Table 3.12. Maximum oscillation amplitude (m) of the basket corresponding to the valueswhen H=3500N, S=0.80m, r=0.30m

Length (m)	Basket position 10	Basket position 8	Basket position 6	Basket position 2
1	20	0.143	0.153	0.168	0.191
2	22	0.164	0.176	0.194	0.220
3	24	0.173	0.196	0.214	0.244
4	26	0.202	0.214	0.248	0.279
5	28	0.210	0.240	0.273	0.304

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Figure 3.13. Graph of maximum oscillation amplitude of the basket corresponding tochange

Comment: With the same constant horizontal tension, at all hanging positions of the basket, the maximum oscillation amplitude increases as the cable span length increases. This proves that the cable span length also significantly affects the oscillation amplitude of the basket.

3.7.5. The influence of the length of the dragon fruit basket hanging wire r on the maximum amplitude of the dragon fruit basket oscillation

With fixed parameters as in the first part of section 3.7, for varying values of the basket hanging wire length r, we get the results in table 3.13 and graph in figure 3.14.

Table 3.13. Maximum oscillation amplitude (m) of the basket corresponding to r values

Basket wire length r (m)	Cart number 6	Cart number 8	Cart number 10	Cart number 15
1	0.2	0.073	0.084	0.092	0.104
2	0.25	0.079	0.092	0.101	0.114
3	0.3	0.087	0.099	0.107	0.122
4	0.35	0.094	0.106	0.117	0.134
5	0.4	0.105	0.117	0.128	0.143

Figure 3.14. Graph of maximum oscillation amplitude of the hanging basket corresponding to the length of the basket wire r

different, when horizontal tension H = 3500N, = 2400 cm

Comment :

+ From the calculation results, we can see that when the length of the wire hanging the basket increases, the maximum oscillation amplitude of the basket increases.

+ With the length of the hanging wire r varying from 20 - 40 cm, the maximum amplitude of the hanging basket in the middle of the span is less than 15 cm.

3.7.6. Survey of formula for calculating system capacity

Notice the two quantities H and

f ( i ) are inversely dependent on each other. Therefore,

When Q, v and the q i are constant, there will be a value of H for which W is a minimum.

The closed cable line has 23 spans, with a total distance between supports of 50000 cm. Calculate the power consumption corresponding to cable lengths varying from 50010 cm – 50080 cm and the number of pulleys changing direction in the cycle varying from 4 – 8.

The results are given in Table 3.14. Note that if the cable length is reduced, the loops at the spans will be reduced, which leads to an increase in the horizontal tension.

Table 3.14. Power consumption of the cable system corresponding to the total cable length and total number of turns in the system

L(cm)

H(N)	Power (W) (corresponding to total number of turns)
H(N)	4	5	6	7	8
50040	5009	236 *	262	285	318	331
50045	4842	240	261	283	314	326
50050	4610	240	261 *	281	311	342
50055	4478	241	261	280	310	319
50060	4272	242	261	280 *	298	317
50065	4078	244	262	280	298	316
50070	3895	246	263	280	297	315
50075	3620	247	264	281	297 *	314
50080	3452	249	265	281	298	315 *

The graph for the dependence between power consumption and cable length (related to horizontal tension) is given in the graph in Figure 3.15.

Figure 3.15. Graph showing the dependence of power consumption on the horizontal tension of the cable and the number of pulleys.

Comment:

- Power consumption increases as the number of turns in the system increases, i.e. the more winding the closed cable is, the more power is consumed.

- In each cable system, there will be a suitable horizontal cable tension force to minimize power consumption.

- As shown in table 3.14: With a cable line with a total span length of 500m, and a total number of turns from 4 to 8, the total cable length is only in the range of 500.4m - 500.8m, then the horizontal tension of the cable is in the range of 5009

– 3452 N and minimum power consumption between 236 – 315 W.

Chapter 3 Conclusion

From the survey results obtained in chapter 3, the thesis draws the following conclusions:

1. When the span length is 24 m with the largest allowable curves

f max

about 30  46 cm and evenly distributed load with intensity q in the range of 0.08  0.2 ( N / cm) , the elongation of the cable is quite small (less than 1.5 cm - Table 3.4). From there, it can be applied to the non-stretchable cable model for calculation, which will simplify the calculation process.

2. With the largest loops f max in the range of 15 – 40 cm and the distance between the two pulleys in the span in the range of 20 – 30 m, the length L of the cable on the span is a maximum of 2.1 cm (table 3.1). This allows the assumption of uniformly distributed loads instead of uniformly distributed loads on L to be acceptable. With this assumption, the model building and calculation are greatly simplified.

3. In addition to the value of the load q , the distance between the supports greatly affects the maximum curvature of the cable span. When the horizontal tension H increases, the curvature f decreases.

4. The increase in horizontal cable tension will cause the force acting on the directional pulley to increase, leading to increased rolling friction and thus increased power consumption.

5. With the design parameters of the cable line: Span distance = 24m, horizontal tension H = 3500N, basket hanging wire length r = 0.3m , baskets are 0.8m apart, uniform load q = 20N/m, then the resonance frequency region of the baskets oscillates horizontally, at positions on the cable span in the range (5.3 6.5) (Table 3.9), in the direction change area in the range (5.5 - 8). Under the influence of wind, if resonance occurs (vibration with large amplitude), we can adjust the horizontal tension to increase or decrease to change the vibration resonance area of the dragon fruit basket.

6. The maximum oscillation amplitude of the dragon fruit baskets increases gradually from the beginning of the span to the middle point. The hanging basket at the middle position has the largest maximum oscillation amplitude. When the horizontal tension increases, the maximum oscillation amplitude of the basket decreases. When the length of the hanging wire increases, the maximum oscillation amplitude of the basket increases.

7. Power consumption increases as the number of turns in the system increases, that is, if the closed cable line has many turns, it consumes power. In each cable system, there will be a suitable horizontal tension force on the cable line to minimize power consumption. With a cable line with a span length of 500m, and a total number of turns from 4 to 8, the horizontal tension force on the cable is in the range of 5009 - 3452 N and the smallest power consumption is in the range of 236 - 315 W (Table 3.13).

Chapter 4

EXPERIMENTAL RESEARCH

4.1. Objectives and tasks of experimental research

The thesis conducts experimental research for the following reasons:

Firstly: To investigate the theoretical problem, it is necessary to determine some dynamic parameters of the cable line. These parameters are not included in the technical documents, so it is necessary to conduct experiments to determine them.

Second: From the experimental research results to compare the calculation results according to the theoretical model, from there we will evaluate the reliability of the theoretical calculation model that has been built.

Third: Determining the reasonable dynamic parameters of the dragon fruit transport cable line by theory is very difficult, so it is necessary to conduct experimental research to determine the reasonable parameters of the research cable line.

Based on the above reasons, the thesis conducts experimental research with the following research objectives and tasks:

4.1.1. Objectives of experimental research

- Determine the numerical values of some quantities and coefficients in the formulas for calculating the mechanical parameters of the cable line to serve the survey of the dynamic parameters of the cable line.

- Verify some theoretical calculation results to evaluate the reliability of the established mathematical equation.

- Determine some reasonable parameters of the cable as a basis for completing the cable line for transporting dragon fruit.

4.1.2. Experimental research tasks

To achieve the above goal, the tasks of the experimental research are as follows:

- Determine the cable span length (cm);

- Determine the cable tension H (N);

- Determine the cable loop f (cm);

- Determine the amplitude of oscillation of the basket containing dragon fruit a (cm).

4.1.3. Experimental research subjects

The experimental research object is the cable system for transporting dragon fruit designed and manufactured by the state-level project " Research on design and manufacture of some mechanization and automation equipment for some stages in harvesting some fruit trees in the Southwest region " code KHCN-TNB.DT/14-19/C30. The experimental location is at the Forestry University and at the production facility in Cho Gao district, Tien Giang province.

4.2. Choose research method

4.2.1. Select experimental method

The process of determining the dynamic parameters of the cable line is very complicated and affected by many factors. The investigation of the influence of each factor on the objective functions has been studied in the theory of calculating the dynamics of the cable line, but the study of the simultaneous influence of many factors on the objective function has not been analyzed. To determine the influence of many factors on the research index, the thesis chose the experimental planning method.

The experimental planning method is the theoretical basis of modern experimental research with many advantages, in which mathematical tools play an active role. The mathematical basis of experimental planning theory is statistical mathematics with two important fields: variance analysis and regression analysis [8]; [9]. The content of the experimental planning method is presented in documents [6]; [7]; [9]. Below, we only apply this method to specific problems.

4.2.2. Select the research objective function

To evaluate the dynamic quality of the cable transport line, people rely on many criteria, including the criterion of the largest loop of the cable line. If the loop of the cable line is too large, the basket containing the dragon fruit will touch the ground, and at the same time, when the basket containing the dragon fruit moves through the intermediate support column, it will be difficult. In this thesis, the objective function of the largest loop of the cable line is chosen for study.

The amplitude of the dragon fruit basket is also an important dynamic indicator to evaluate the stability of the cable during operation. The amplitude of the dragon fruit basket is evaluated through the amplitude in the direction of motion.

The vibration amplitude of the dragon fruit basket is chosen as the second objective function to study.

Summary : In the thesis, two objective functions are selected: the smallest roundabout function of the cable, denoted by f , unit of cm, and the oscillation amplitude function of the dragon fruit basket, denoted by a, unit of cm.

4.2.3. Choosing parameters that affect the objective function

From the analysis results in chapter 2, we see that there are many factors affecting the objective function including:

- Span length: When the span length changes, the cable line's loop length also changes. The longer the span length, the larger the loop length and vice versa. When the span length is short, the loop length is small but requires many intermediate supports, thereby increasing the construction cost. Therefore, determining a reasonable span length to satisfy the loop length and at the same time reduce the number of intermediate supports to reduce construction investment costs. From the above analysis, the thesis chooses the span length as the influencing parameter to study.

- Load hanging on the cable: When the load changes, the curvature also changes. According to the design, each dragon fruit basket contains 1-2 dragon fruits. It cannot contain more because the cable moves continuously. The cutter will put it in another basket, so the thesis does not choose this parameter.

- The specific gravity of the cable also affects the cable's loop, according to the design of the cable with a diameter of 6mm, the specific gravity has a certain value, so the thesis does not choose this parameter.

- Initial horizontal tension: The initial horizontal tension of the cable also affects the cable's curvature and the oscillation amplitude of the dragon fruit basket. The larger the tension, the smaller the curvature and oscillation of the basket. However, when the tension is large, it affects the cable tensioning technology, the durability of the support column, and the power to move the cable. Therefore, calculating and determining a reasonable initial horizontal tension is very important to meet the requirements of curvature and oscillation, but is easy to tighten the cable and reduce the power consumption of the power source. From the above analysis, the thesis chooses the initial horizontal tension parameter for research.