Preliminary Design Forces

4.1. Calculus Relations

Three coordinate systems can be defined (fig. 7), resulting by consequent rotations with angles у and p. According to the three coordinate systems, the components of weight and wind loads are:

Gz =-G; Gxl = Gz sin у; Gyl = 0; Gzl = Gz cos у;

Подпись: Fig. 7. Specific coordinate systems.

Gx2 = Gxi = Gzsin y ; Gy2 = Gzisin P = Gzcos y sin P; Gz2 = Gzicos P = Gzcos y cos P; (1)

i1

image025

Fig. 8. Calculus diagram for daily axis forces.

Table 3. Loads on the A axis.

Point

Forces

Moments

x2

У^

Z2

x2

Ук.

Z2

A

Gx2

Gy2 + FC cos^-Pe )

Gz2 + Wz2 + FC sin^-Pe )

0

M y 2 — Gx 2 ei

0

Fx2

Fy2

Fz2

A’

Gx2

Gy2 + FC cos^-P e )

Gz2 + W + Fc sin(ф-Pe) ,

/

/

/

2

+ My 2 — G x2 Є1

+ ll

2

A’’

0

Gy2 + FC COs(ф-P e )

Gz2 + W + Fc sin^-Pe)

/

/

/

2

My 2 — Gx 2 ei

ll

2

image026

Figure 9 presents the calculus diagram for the reactions in the daily rotational axis and in the linear actuator. The reaction in the linear actuator is calculated with relation

Table 4 presents the loads on the D axis and the forces on the bearings.

Table 3. Loads on the D axis.

Point

Forces

Moments

Xl

Уі

Zl

MDx1

MDv1

MDz1

D

Gx1 + FE cos(y-Ye )

Wyi

Wz1 + Gz1 + FE sin(y — Ye )

— Wy1 (Єз + e1 cos P) — (Gz1 + Wz1)e1 sin p

0

Mz1 + Gx1e1 sin P

Fxi

Fyi

Fzi

D’

Gx1 + FE C°s(y-Y e ) + 2

+mda

12

Wyi

Wz1 + Gz1 + FE sin(y-Ye ) + 2

+ MDx1

І2

/

/

/

D’’

Gx1 + Fe cos(y-Ye)

0

Wz1 + Gz1 + Fe sin(y-Ye)

/

/

/

2

мол

2

2

MDx1

І2

The reactions on the bearings of t

ie D axis are:

Подпись: (P max P min ) (P max P min ) Tmax = 90 + —- — ; Ф min = 90 - —' — ; Ф ~ Фшт +P-P min ;
image028 Подпись: (8) (9)

Figures 8, b and 9, b present the extreme positions of each linear actuator mechanism. The optimal design of a linkage mechanism with linear actuator is looking for symmetrical extreme positions C1 (E1) and C2 (E2) of the C (E) link, relative to the less loaded position with ф (у) = 90°, in order to obtain proper ф (у) pressure angles. The following relations have been established:

4.2. Results

Loads on the elements of the equatorial tracking system with linear actuator have been calculated for the six loading cases and for the six wind cases. The dimensions of the tracking system, involved in calculus are: l = 1480 mm; e1 = 40 mm; e2 = 85 mm; a = 160 mm; l1 = 600 mm; e3 = 80 mm; e4 = 140 mm; d = 125 mm; l2 = 50 mm.

Figure 8 presents the reactions on the bearings and on the linear actuators for two loading cases (a — loading case 1 and b-loading case 6 — see table 2), for which the biggest reactions result. There have been considered the possible wind cases, numbered from 1 to 6, presented in table 1.

Figure 11 presents the reactions on the bearings and on the linear actuators for all six loading cases (see table 2). There have been considered the wind cases 2 (a) and (4), presented in table 1, for which the biggest reactions result.

3. Conclusion

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

• Wind cases 2 (for front wind) and 5 (for back wind) give bigger radial loads for D axis and axial force in the seasonal actuator E; The effect of wind cases on the other loads is irrelevant (fig. 10), even if the maximum load on the A axis is given by wind case 4;

• Loading case 6 and wind case 4 (fig. 11, b) give the bigger radial load on the A axis; The bigger axial load on the A axis is given by loading case 3 and wind case 2 (fig. 11, a); The bigger radial load on the D axis is given by loading case 1 and wind case 2 (fig. 11, a) and the bigger axial load on the D axis is given by loading cases 4 and 6 and wind case 4 (fig. 11, b);

• The bigger axial load on the screw’s actuator C is maximum for loading cases 4 (tension) and 2 (compression) and wind case 2 (fig. 11, a); The bigger axial load on the screw’s actuator E is maximum (tension) for loading cases 1 and 2 and wind case 2 (fig. 11, a).

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

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

[4] 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.

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