A Study of Dynamic Characteristics of the Meteorological Tower of the Pole Shape in Case of with and Without Guys

Transcription

1 International Journal of Applied Engineering Research ISSN Volume 11, Number 7 (016) pp A Study of Dynamic Characteristics of the Meteorological Tower of the Pole Shape in Case of with and Without Guys Dongchan Shin Department of Mechatronics Engineering, Jungwon University, South Korea. Kibong Han Department of Mechatronics Engineering, Jungwon University, South Korea. Corresponding author Abstract This paper compared and analyzed the dynamic characteristics of the meteorological tower with and without guys with using simplified analysis model. First, the natural frequency. ω n, equivalent stiffness. K eq, equivalent mass. M, and equivalent damping coefficient. C eq, of the meteorological tower without guys were obtained from the vibration analysis and deflection analysis using finite element method. Next, the equivalent stiffness. K eqs, and equivalent damping. coefficient. C eqs, of the tower with guys were calculated by adding the stiffness of the guy wire to the stiffness of the tower without guys. The results of the compared and analyzed dynamic characteristics of the tower by using the equivalent parameters show the importance of the guys for vibration isolations. Key words: dynamic characteristics; vibration analysis; deflection analysis; finite element method; vibration isolation. Introduction Due to rapid changes in climate environment, the meteorological tower has been very important to observe weather conditions in order to obtain temperature, humidity, the wind speed and direction data in the past few years[1]. In the wind power industry, the meteorological tower plays an important role to predict the power generation efficiency of the wind turbine by collecting the wind speed and direction data[]. Because the height of the wind meteorological tower is approximately 50~100m and it is installed in strong windy areas, robust designs are required for the tower not to be shaken by the wind. There are two types of meteorological tower, a pole shape and a form of the truss structure. In general, the truss structure type is mainly suitable for high-rise because it is robust and lightweight but it also has disadvantages of expensive construction costs due to the complex structure. The pole type has advantages of simple structure and low construction costs but it also has disadvantages of height limit of a skyscraper because it is heavy and less robust compared to the truss structure type. So recently, a method using guy wires for the pole type structure has been applied in order to support the pole structure and improve the problems of the pole type for the wind farm composition[3][4]. The engineering and construction process for the guy wire installation has been conducted relying on manual experiences and operations mainly because they did not know the simple dynamic analysis methods. So this article present simple theoretical analysis methods for the dynamic characteristics of the meteorological tower complementing existing empirical and manual methods at the construction field. A pole type meteorological tower model for the dynamic characteristic analyses A meteorological tower pole was designed as Figure1 in order to analyze the dynamic characteristics. Figure1(a) is a shape of the meteorological tower pole without guy wires. The meteorological tower pole is consisted of 3 different diameter stages. The length of the first, second, and third stage of the pole is each of 5(m), 5(m), and 0(m) long and the inner diameter of each is 1(inches), 10(inches), and 8(inches). And the thickness of every stage of the pole is 10(mm). Figure 1(b) is a shape of the meteorological tower pole with guy wires. The height of the pole is 70m as same as the pole without guys. One ends of the wires are fixed tightly on the ground each 18m and 30m apart from the center of the tower in four directions north, south, east and west, respectively. And the other ends of the wires are tied tightly to the pole in each of the 6 height positions. Figure 1: Shape of the meteorological tower with and without guys 5169

2 International Journal of Applied Engineering Research ISSN Volume 11, Number 7 (016) pp The dynamic analysis model of the meteorological tower without guys This study used FEM(Finite Element Method) to get the deflection at the end of the pole and vibration modes of the pole in case of without guys. Figure (a) is the first vibration mode shape of the meteorological tower without guys. The natural frequency of the first vibration modeω n is as follows. [5] ω n = K eq M eq ⑴ K eq andm eq isequivalent stiffness and equivalent mass of the meteorological tower respectively in the equation⑴. M eq isas follows from the equation⑴. M eq = K eq ω n () Equivalent damping coefficient C eq is as follows. C eq = M eq ζω n (3) ζ isthe damping ratio of the meteorological tower in the equation ⑶. Figure (b) is the shape of the deflection and displacementx when a force P is applied to the end of the pole. The equation between the force and deflection can be obtained by Hooke s law. P = K eq x (4) The equivalent stiffness K eq isas follows from the equation⑶. K eq = P x (5) Therefore the kinetic equation can be expressed with system parameters of the meteorological tower from equation⑶, ⑶, and ⑶, M eq, C eq, and K eq as follows. M eq x (t) C eq x (t) K eq x(t) = F(t) (6) F(t)isthe force applied to the end of the meteorological tower andx(t)isthe displacement of the top end of the tower by the forcef(t)in the equation⑶. Figure 3 is the equivalent vibration system model of the meteorological tower pole without guys. The transfer function G eq (s) by Laplace transform in order for the frequency response analysis for the meteorological tower pole is as follows. 1 G eq (s) = M eq s C eq s K eq (7) Figure 3: The equivalent vibration system model of the meteorological tower pole without guys The dynamic analysis model of the meteorological tower with guys. The dynamic analysis model of the meteorological tower with guys is obtained by follow procedures in this study. 1 The vibration mode and the deflection at the end point of the meteorological tower without guys is obtained by using FEM. Calculate the equivalent stiffness and equivalent mass with the vibration mode and deflection. 3 Experiment or calculate the stiffness coefficient of the guy wires. 4 Calculate the equivalent stiffness of the meteorological tower with guys with the equivalent stiffness of the meteorological tower without guys from and the stiffness of the guy wires from 3. 5 Model the kinetic equation and dynamic analysis of the meteorological tower with guys. In the previous section, the equivalent stiffness K eq and equivalent massm eq of the meteorological tower without guys was obtained. Next, we calculate the stiffness of the guy wires supporting the tower. Figure 4 shows each length of the guy wires which support the tower. Figure : The first vibration mode shape of the meteorological tower without guys 5170

3 International Journal of Applied Engineering Research ISSN Volume 11, Number 7 (016) pp F, l, Δl, Ain the Figure 5 is tensile force applied to the wire, the length of the wire, extended length of the wire, and the section area of the wire respectively. The equation by Hooke s law with these variables is as follows. Δl = Fl AE (9) E is Young s modulus of the wire in the equation⑶. So, the tensile force F is as follows. F = AE Δl l (10) In the equation⑶, AE is the stiffness of the guy wire. Therefore l each stiffness, K a1, K a, K a3, K b1, K b, K b3 of the wires supporting the meteorological tower is as follows. K a1 = AE l a1, K a = AE l a K a3 = AE, K l b1 = AE a3 l b1 K b = AE, K l b3 = AE b l b3 (11) Figure 6 is the free body diagram of the meteorological tower when a force P applies to the top end of the tower. Figure 4: The length of the guy wires The length of the wires can be calculated as follows. l a1 = a l 1, l a = a l l a3 = a l 3, l b1 = b l 4 l b = b l 5, l b3 = b l 6 ⑻ l a1, l a, l a3, l b1, l b, l b3 is the length of the guy wires respectively and l 1, l, l 3, l 4, l 5, l 6 is the height of the fixed point on which one end of the wires are tied to the pole from the ground level. a, b is the distance from the center of the tower to the ground points on which the other end of the wires are tied to the ground. Figure 5 is the free body diagram of the guy wire applied by a tensile force. Figure 5: The Free Body Diagram of the guy wire applied by a tensile force Figure 6: The Free Body Diagram of the meteorological tower when a force P applies to the top end of the tower 5171

4 International Journal of Applied Engineering Research ISSN Volume 11, Number 7 (016) pp Each x 1, x, x 3, x 4, x 5, x 6 is displacement amount at the guy wire fixing point of l 1, l, l 3, l 4, l 5, l 6 height when a force P applies to the top end of the towerin the Figure 6 and each displacement can be equated as follows. x 1 = l 1 l 6 x 6, x = l l 6 x 6 x 3 = l 3 x l 6, x 4 = l 4 x 6 l 6 6 x 5 = l 5 x l 6, x 6 = x 6 6 (1) Summation of moment ΣM O at the coordinate point Ois as follows. ΣM O = F 1 l 1 F l F 3 l 3 F 4 l 4 F 5 l 5 F 6 l 6 F eq l 6 P l 6 = 0 (13) The external force P is as follows. l 1 l l 3 l 4 l 5 P = F 1 F l F 6 l 3 F 6 l 4 F 6 l 5 F 6 l 6 F eq 6 (14) In the equation⑶, F 1 through F 6 are elastic forces acted by the guy wires and F eq is the equivalent force acted by the elasticity of the meteorological tower, and they are expressed as follows. F 1 = K a1 x 1, F = K a x F 3 = K a3 x 3, F 4 = K b1 x 4 F 5 = K b x 5, F 6 = K b3 x 6, F eq = K eq x 6 (15) Equation(14) is expressed with using equation(8), (11), (1), (15) as follows. Therefore, the equivalent mass and equivalent stiffness of the meteorological tower with guys is M eq and K eqs and the natural frequency ω ns is as follows. ω ns = K eqs M eq (19) And the damping coefficient C eqs is as follows. C eqs = M eq ζ s ω ns (0) ζ s isthe damping ratio of the meteorological towerwith guys in the equation (0). Figure 7is the equivalent vibration system model of the meteorological tower pole with guys. The dynamic equation of the model can be expressed as follows. M eq x (t) C eqs x (t) K eqs x(t) = F(t) (1) F(t)isthe force applied to the meteorological tower by wind andx(t)isthe displacement of the top end of the tower by the forcef(t)in the equation (1). P = AEl 1 AEl AEl 3 { l 6 a l 1 l 6 a l l 6 a l 3 AEl 4 l 6 b l 4 AEl 5 l 6 b l 5 AE b l 6 K eq } x 6 (16) The equation (16) can be expressed as follows substituting the expression in the { }into K eqs. P = K eqs x 6 (17) In other words, K eqs is as follows. Figure 7: The equivalent vibration system model of the meteorological tower pole with guys The transfer function G eqs (s) by Laplace transform in order for the frequency response analysis for the meteorological tower pole is as follows. 1 G eqs (s) = M eq s C eqs s K eqs () K eqs = AEl 1 AEl AEl 3 { l 6 a l 1 l 6 a l l 6 a l 3 AEl 4 l 6 b l 4 AEl 5 l 6 b l 5 AE K eq b l 6 } (18) Simulation Results and Consideration Computer simulations have been conducted in order to compare and analyze the dynamic characteristics of the meteorological tower with and without guys in this study. Table 1 shows the specification of the meteorological tower for computer simulations. 517

5 International Journal of Applied Engineering Research ISSN Volume 11, Number 7 (016) pp Table 1: The specification of the meteorological tower Parts Value Bottom stage pipe(diameter, height) 1(inches), 5(m) Middle stage pipe(diameter, height) 10(inches), 5(m) Top stage pipe(diameter, height) 8(inches), 0(m) Fixed height point of the guy wires l 1 =1. 5(m) l =5. 0(m) l 3 =37. 5(m) l 4 =50. 0(m) l 5 =60. 0(m) l 6 =70. 0(m) Young's modulus of the pole pipes 50(GPa) Young's modulus of the guy wires 190(GPa) Wire diameter 0. 03(m) Figure 8 shows the FEM deflection analysis result for the meteorological tower without guys. The displacement amount of the top end of the tower is (m) when 100(N) of external force is applied to the top end of the tower according to the analysis result. In this case, the equivalent stiffness coefficient of the meteorological tower pole without guys, K eq is 91. 6(N/m). Figure 9: FEM modal analysis result for the meteorological tower without guys For the case of the meteorological tower with guys, the equivalent stiffness of the tower K eqs is (N/m) by the equation (18) and the equivalent damping coefficient of the tower C eqs is (N sec/m). From the above described, the transfer function G eq (s)for the dynamic behavior of the top end of the meteorological tower without guys is 1 G eq (s) = s 3. s And the transfer function G eqs (s)for the dynamic behavior of the top end of the meteorological tower with guys is 1 G eqs (s) = s s 6761 Figure 10 shows the frequency response function for the dynamic behavior of the top end of the meteorological tower with and without guys. Figure 8: FEM deflection analysis result for the meteorological tower without guys Figure 9 shows the FEM modal analysis result for the meteorological tower without guys. It shows the natural frequency of the first, second, and third mode is each 0. (Hz), 1. 08(Hz), and. 48(Hz). In order to find out the motion of the top end point of the tower, the first mode is most governed. Therefore the equivalent mass M eq is (kg) and the equivalent damping coefficient C eq is 3. (N sec/m) respectively calculating with using equation (), (3) and (5). Figure 10: Frequency response function for the dynamic behavior of the top end of the meteorological tower with and without guys 5173

6 International Journal of Applied Engineering Research ISSN Volume 11, Number 7 (016) pp Figure 11 shows the characteristics of the wind as time domain velocity used for computer simulation. The RMS(root mean square) of the wind velocity is. 44(m/sec) and the maximum velocity(v p p ) is 10. 6(m/sec). Figure 11: The characteristics of the wind used for computer simulation (RMS. 44 m/sec) Figure 1 shows the amount of the displacement at the top end of the meteorological tower with and without guys by computer simulation when the wind velocity. 44(m/sec) of the Figure 11 is applied. The amount of the displacement of the tower with guys is RMS 4. 8(mm) and the maximum amplitude 0(mm) and the amount of the displacement of the tower without guys is RMS 10(mm) and the maximum amplitude 300(mm). Figure 13: The characteristics of the wind used for computer simulation (RMS 4. 9 m/sec) Figure 14 shows the amount of the displacement at the top end of the meteorological tower with and without guys by computer simulation when the wind velocity 4. 9(m/sec) of the Figure 13 is applied. The amount of the displacement of the tower with guys is RMS 19(mm) and the maximum amplitude 80(mm) and the amount of the displacement of the tower without guys is RMS (mm) and the maximum amplitude 100(mm). Figure 1: The displacement at the top end of the meteorological tower with and without guys by computer simulation (RMS. 44 m/sec) Figure 13 shows the characteristics of the wind as time domain velocity used for computer simulation. The RMS(Root Mean Square) of the wind velocity is 4. 9(m/sec) and the maximum velocity(v p p ) is (m/sec). Figure 14: The displacement at the top end of the meteorological tower with and without guys by computer simulation (RMS 4. 9 m/sec) Figure 15 shows the characteristics of the wind as time domain velocity used for computer simulation. The RMS(Root Mean Square) of the wind velocity is 9. 8(m/sec) and the maximum velocity(v p p ) is 46(m/sec). 5174

7 International Journal of Applied Engineering Research ISSN Volume 11, Number 7 (016) pp Figure 17: The characteristics of the windused for computer simulation (RMS m/sec) Figure 10: The characteristics of the windused for computer simulation (RMS 9. 8 m/sec) Figure 16 shows the amount of the displacement at the top end of the meteorological tower with and without guys by computer simulation when the wind velocity 9. 8(m/sec) of the Figure 15 is applied. The amount of the displacement of the tower with guys is RMS 0. 08(m) and the maximum amplitude 0. 3(m) and the amount of the displacement of the tower without guys is RMS 1. 6(m) and the maximum amplitude 4. 8(m). Figure 18 shows the amount of the displacement at the top end of the meteorological tower with and without guys by computer simulation when the wind velocity 14. 6(m/sec) of the Figure 17 is applied. The amount of the displacement of the tower with guys is RMS (m) and the maximum amplitude 0. 7(m) and the amount of the displacement of the tower without guys is RMS (m) and the maximum amplitude 11(m). Figure 18: The displacement at the top end of the meteorological tower with and without guys by computer simulation (RMS m/sec) Figure 16: The displacement at the top end of the meteorological tower with and without guys by computer simulation (RMS 9. 8 m/sec) As described above, this study conducted dynamic analyses for the meteorological tower with and without guys, and the results showed the vibration by the wind force was lessened in the case of supporting with guys, which increased the bending stiffness of the pole. Figure 17 shows the characteristics of the wind as time domain velocity used for computer simulation. The RMS(Root Mean Square) of the wind velocity is 14. 6(m/sec) and the maximum velocity(v p p ) is 66(m/sec). Conclusion In this study, first, equivalent bending stiffness(91. 6N/m) and equivalent mass(184. 7kg)of the meteorological tower without guys were obtained respectively from the vibration analysis and deflection analysis using FEM and the equivalent 5175

8 International Journal of Applied Engineering Research ISSN Volume 11, Number 7 (016) pp dynamic model of the meteorological tower without guys was established by using above parameters. Next, each stiffness of the guy wires supporting the meteorological tower were obtained and the ultimate stiffness of the meteorological tower with guys was obtained by the summation of the bending stiffness of the meteorological tower without guys and the stiffness of the guy wires to support the tower. And this paper also presented a method to obtain the natural frequency(0. 96Hz) and the dynamic model of the meteorological tower with guys. By comparing and analyzing the dynamic characteristics of the tower with and without guys, it showed that the way to support the meteorological tower with guy wires increases the bending stiffness of the tower and configures the vibration isolation. And this study is also supposed to be contributed to researches in the future for vibration isolation for the skyscrapers, high structures and long bridges by wind and earthquakes. References [1] R. E. Munn, I. M. Stewart. "The use of meteorological towers in urban air pollution programs", Journal of the Air Pollution Control Association, Vol. 17, No., pp , [] C. J. Moon, Y. H. Chang, T. S. Park, et al. "A Study on design of offshore meteorological tower", Journal of the Korean Solar Energy Society, Vol. 34. No., pp , 014. [3] M. I. R. de Oliveria et al. "Structural Analysis of Guyed Steel Telecommunication Towers for Radio Antennas", Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 9, No., pp , 007. [4] C. Gantes, et al. "Modeling, Loading, And Preliminary Design Considerations for Tall Guyed Towers", Computers & Structures, Vol. 49, No. 5, pp , [5] Thomson, M. D. Dahleh. "Theory of Vibration with Applications", Prentice-Hall, [6] Crandall, Stephen H. "LEscCps(Mit) an Introduction to the Mechanics of Solids", McGraw- Hill Science/Engineering/Math,