Monday, September 9, 2013

DIY Mechanical angle of attack windvanes part 3

This post is the continuation of Angle of attack windvanes posts miniserie

DIY air data boom with angle of attack and angle of sideslip mechanical vanes

An example numeric design will be here presented. Refer to the following scilab file, it's a simple script file to evaluate the windvane parameters. For the sake of simplicity, when possible, the nomenclature is those of the main, freely available, reference “Wieringa (1967),Evaluation and Design of Wind Vanes, Royal Netherlands Meteorological Institute, De Bilt” By the end of the post a compact set of equations and a basic procedure for windvane sizing will be exposed.

Design process is recursive and require to go forth and back through the specification, 3D design and performance evaluation phases; formally to find the best windvane design can be seen as a multivariable, multiobjective optimization problem. To avoid a complexity explosion only a basic approach to design evaluation is presented in figure F9,3. Note that our fast preliminary design is possible thanks to the availability of a closed form math model for the vane, results and performance evaluation can be eventually refined further during a successive simulation phase.

Executing the Scilab file will return the following output, that summarize the supplied example windvane design parameters

Vane parameters

Windvane weight grams 8.00

rv lenght 25.00 mm

rw lenght 6.25 mm

Vane calculated parameters

Fin surface 380.95 mm^2

Vane inertia 0.000006 kgm^2

Natural frequency 72.63 rad/s

Damped frequency 72.60 rad/S

Damping ratio zeta 0.030

Decay distance 92.3 [m]

Shaft at test condition with no friction

Relative wind speed 30.00 m/s

Alfa value 0.10 degrees

Aerodynamic Torque 5.75e-05 Nm

Shaft at test condition with viscous friction

Viscous friction term Dm 2.000e-05 Nms/rad

Damping ratio increase due to viscous friction 0.022

Total damping ratio 0.052

Table T9.1 Scilab script output

Consider the possible model for the main shaft bearing friction in figure P9.1, let's pretend that the curve is approximate by excess so the torque values are conservative, to be more general consider also that torque values are the sum of the torque generated by all the frictions on the shaft including those derived by the position sensor.
Figure F9.1 General bearing friction model including stiction, to carry out a general analysis consider this curve comprehensive of all the friction caused by bearing and sensors.

In table 9.1 is reported the approximate torque generated by the lift of the fin at the shaft, 5.75e-05 Nm for a wind blowing at 30 m/s;. The aerodynamic torque that our vane generate for an alfa of 0,1° at 30 m/s is greater than the torque of 0,02e-3 necessary to the shaft to begin to rotate. At 30 m/s the vane will hopefully correctly rotate to 0,1° alfa. differently if the speed is reduced to the lower bound of required speed range, in our case10 m/s, the aerodynamic torque is 0,006e-3Nm so the windvane will not rotate to 0,1°; at the former speed the static error cannot be smaller than 0,02/0,006*0.1=3,3e-1.

Given storque as the static torque required to move the shaft ,statico as the max static error and N as the vane torque coefficient the following constrain should be satisfied by a healthy vane

Nstatico>>storque, where N is speed dependent
With our example numeric values 0.0036633*0,1/360*6,28>>storque, storque <<0.0064e-3
In those cases when it's non possible to reduce anymore the friction it will be necessary to increase the windvane fin area.

Table 9.1 shown a low damping ratio, quite different from our initial requirement of a value greater than 0,15. Recalling that our current model neglects the bearing damping some considerations should be added for a correct result interpretation.

Note that when wind speed is very high, as friction torque contribution is little compared to the torque generated by the fin, the behavior of the vane will be essentially those predicted by the model, so a very low damped response should be expected. At lower speeds the contribution of friction are not negligible and lead to an increase in the response damping.

Wieringa Eq.30 add a viscous term proportional to rotation speed to the ideal case model, no static friction is considered. Other authors for example 1974, JAMIES T.KARAM, JR. TECNICAL REPORT AFIT TR 74-8” page 6 have considered stiction.

Again according to Wieringa the damping ratio variation against relative wind speed is plotted on the following figure valid for the example vane.
Figure F9.2 Damping ratio against relative wind speed, Dm assumed to be 20e-6 Nms/rad
To add damping at higher speeds some mechanism, aerodynamic or mechanical based, can be employed, the example probe do not use any mean to compensate for relative wind speed.

Commonly the choice of the sensor for vane angle is oriented to the use of low friction devices, hall type sensors have been successfully employed, see a commercial available typical rotary sensor at this link.

The whole design process is somewhat recursive, the following figure pictures at glance a possible design development path.

Figure F9.3 Possible design process development path

Inspecting the figure quickly jump to attention the fact that post design simulation and testing should be carried out on the vane, although not treated here the design validation is to be considered as a primary design task.

Nice designs,

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