Preliminary Design Forces

2.2. Calculus Relations

Figure 7 presents the calculus diagram for the reactions in the seasonal rotational axis and in the linear actuator (a) and in the bearings of the vertical axis (b). The reaction in the linear actuator is calculated with relation

М + Ge, cosa)cosae

Fc =- — -, (1)

Подпись: where a e = arctan- Подпись: a Подпись: . Positive values mean compression of the actuator’s screw and

a sin ф

negative values mean tension on the actuator’s screw. The reactions in the A axis are:

Подпись:F-a = G cos a — Fc cos^-a e); Fz1A = W + G sin a — Fc cos^- a e)

and the reactions in the bearings of the A axis are:

Подпись: (3)

Подпись: 1st International Congress on Heating, Cooling, and Buildings " ' 7th to 10th October, Lisbon - Portugal * a Fig. 6. Calculus diagrams Подпись: b

RA’= Ra»= ^ ^ ; FaA = 0.

image055

The reactions in the vertical axis are:

Подпись:FaD = W sin a + G.

The optimal design of a linkage mechanism like the one involving the linear actuator is looking for symmetrical extreme positions C and C2 of the C link, relative to the less loaded position with ф = 90°, in order to obtain proper ф pressure angles.

Figure 7 presents the extreme positions of the linear actuator mechanism. Based on fig. 7, the following relations have been established:

Подпись:rn = 90° + -(amx—• ф . = 90° —

max min

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(5)

 

image059

ф

 

5.2. Results

Based on relations (1).. .(5), the loads on the elements of the azimuthal tracking system with linear actuator have been calculated for the two loading cases and for the six wind cases. The dimensions of the tracking system, involved in calculus are: l = 670 mm; e1 = 40 mm; e2 = 140 mm; a = 80 mm; l1 = 270 mm; l2 = 340 mm.

Figure 8 presents the main reactions on the bearings of the mechanism and on the linear actuator for the two loading case (a and b). There have been considered the possible wind cases, numbered from 1 to 6, presented in table 1.

A comparison between the values presented in fig. 8 allows drawing few conclusions on some aspects that must be considered during the embodiment design of an azimuthal tracking system with linear actuators.

 

image060

image061

Fig. 8. Main reactions on bearings and linear actuator

5. Conclusion

Based on the results presented above, the following conclusions can be drawn:

• The radial loads on the bearings of the vertical axis (RD and RE) are clearly depending on the wind case considered; biggest values are obtained for wind case 1 (for front wind), respectively wind case 4 (for back wind) and the smallest values are obtained for wind case 2 9for front wind), respectively wind case 5(for back wind); Same observations are valid for the axial force on the vertical axis (FaD) more clear for the loading case 2 (fig. 8, b);

• The force on the A bearings (RA) is bigger for wind case 2 (for front wind), respectively wind case 5 (for back wind) and smaller for wind case 1 (for front wind), respectively wind case 4 (for back wind);

• The axial force in the actuator’s screw is always negative meaning tension on the actuator and is is bigger for wind case 2 (for front wind), respectively wind case 5 (for back wind) and smaller for wind case 1 (for front wind), respectively wind case 4 (for back wind);

• Loading case 1 (summer solstice — noon) gives the biggest radial load RD;

• Loading case 2 (winter solstice — noon) gives the biggest axial load FaD and biggest force on the A bearings (Ra);

• Radial load RD is slightly different between the two loading cases;

• Load on the screw’s actuator is maximum for the two extreme loading cases;

• The permissible axial load on the actuator is few times bigger than the maximum load for the extreme loading case, even if the actuator is the smallest of its class. Anyway, normal solar tracker systems have bigger dimensions than the tracker presented in this paper, using actuators at their permissible load [9]. Considering the geometry of the linkage mechanism with actuator, the axial load on the actuator’s screw is increasing with the decrease of actuator stroke.

References

[1] R. N. Clark, B. D. Vick, Performance Comparison of Tracking and Non-Tracking Solar Photovoltaic Water Pumping Systems, Presentation at the 1997 ASAE Annual International Meeting Minneapolis, Minnesota (1997). http://www. cprl. ars. usda. gov/REMM Publishers. htm.

[2] I. Visa, D. Diaconescu, V. Dinicu, B. Burduhos, The Incidence Angles of the Trackers Used for the PV Panels’ Orientation. Part I: Part II: Azimuthally Trackers (2007), International Conference on Economic Engineering and Manufacturing Systems RECENT, Vol. X, Brasov.

[3] NP-082-04. Eurocode 1. Design Code. Bases of Design and Actions on Buildings. Action of Wind. Monitorul oficial al Romaniei.

[4] A. Roger, J, Messenger, Photovoltaic Systems Engineering (2004), CRC Press, Boca Raton.

[5] C. I. Co§oiu, A. Damian, R. M. Damian, M. Degeratu, Numerical and experimental investigation of wind induced pressures on a photovoltaic solar panel (2008) International Conference on Energy, Environment, Ecosystems and Sustainable Development, Algarve, Portugal.

[6] B. Sorensen, Renewable Energy (2004), Elsevier Academic Press.

[7] S. Blackman, R. Popoli, Design and Analysis of Modern Tracking Systems (2000), Artech House Publishers, Boston.

[8] G. Pahl, W. Beitz, Engineering Design (1995), Springer, London.

[9] R. Velicu, G. Moldovean, C. C. Gavrila, Constructive Aspects on the Altitudinal System of a Solar Tracking PV Platform (2008). International Conference on Sustainable Energy, Bra§ov, Romania.