Natural Frequency and Resonance of a Wind Turbine Tower: 1P, 3P, Vortex Shedding

Why the check is needed

The rotor excites the tower at two main frequencies. The rotation frequency, 1P, gives a force from rotor imbalance. The blade passing frequency, 3P for a three-blade rotor, gives a periodic push each time a blade passes the tower. If the natural frequency of the tower coincides with one of them, the amplitude rises sharply, and fatigue builds up in welds and flange joints.

The natural frequency also affects the wind load: the sway period decides which table of the height coefficient to use and whether a special dynamic calculation is needed. This is covered in Wind Load on a Pole under DBN V.1.2-2.

Excitation frequencies

The 1P frequency in hertz equals the revolutions per minute divided by 60, and 3P is three times that. The speed range comes from the turbine manufacturer. Roughly it can be estimated from the tip speed ratio, the ratio of the blade tip speed to the wind speed.

For illustration, a conditional example is given below for a rotor with a speed range of 20–50 rpm; the numbers do not relate to any particular turbine.

A conditional example.

Where to place the natural frequency

There are three options for the first natural frequency of the tower. A “soft” tower has it below 1P, a “stiff” one above 3P, and an intermediate one lies between 1P and 3P. The intermediate option exists only when the highest speed is less than three times the lowest: 3P at the lowest speed must be above 1P at the highest. In the conditional example above this holds: the lowest 3P is 1.00 Hz and the highest 1P is 0.83 Hz, so there is a window between them.

When the speed range is wide and there is no window, the first frequency is placed above 1P over the whole range, and a 3P crossing is allowed at low speed under the controller’s control. The choice of strategy depends on the turbine manufacturer’s requirements and on the permitted displacements of the tower: a soft tower more often fails on displacements.

Speed exclusion zone

When the natural frequency of the tower falls within the excitation range, the turbine controller does not allow long running in the speed band around the coincidence. The limits of the zone and the speed of passing through it are set by the turbine manufacturer, and the tower cannot decide this by itself, so the control requirements are passed to the manufacturer as a separate item.

For each pair of natural frequency and excitation harmonic the frequency ratio is also checked: the turbine manufacturer’s requirements state the permitted margins to 1P and 3P, and to higher harmonics.

Effect of the base and a check after erection

Natural frequencies are usually calculated with a fixed base, and the compliance of the foundation and the soil lowers the first frequency. So a minimum rotational stiffness of the base is specified for the foundation design, and the ground data come from the geotechnical survey.

After erection the first frequency is measured, for example by impulse excitation with accelerometers, and compared with the calculation. The permitted downward deviation is set by the design or by the turbine manufacturer.

Vortex shedding

Wind flowing round a pole sheds vortices at a frequency proportional to its speed. If this frequency coincides with the natural one, the pole sways across the flow. DBN V.1.2-2 requires a vortex shedding check for tall structures with h/d above 7 (clause 9.17), where h is the height and d the minimum section size at 2/3 of the height. The calculation method is usually taken from Annex E of EN 1991-1-4.

The critical speed is vcrit = f1 · b / St, where f1 is the first natural frequency, b the characteristic section size and St the Strouhal number (about 0.2 for a circular section). The sway amplitude is smaller the larger the Scruton number Sc = 2 · δs · me / (ρ · b²), where δs is the logarithmic decrement, me the equivalent mass per unit length and ρ the air density.

If the vortex shedding amplitude is unacceptable, helical strakes or dampers are used, or the stiffness of the tower is changed. The fatigue check including vortex shedding and rotor cycles is done from the manufacturer’s load spectrum.

What to pass to the manufacturer and the customer

• the speed range, the possibility of an exclusion zone and the speed of passing it;
• the manufacturer’s requirements for tower stiffness: the lowest first frequency, head tilt, top displacement;
• the loads on the top flange and the fatigue load spectrum;
• the position of the head’s centre of mass and its moment of inertia;
• the requirement for the rotational stiffness of the base, for the foundation design.

The overall calculation sequence is described in Calculation of a Wind Turbine Pole, and anchor bolts in Anchor Bolts for Poles and Masts.

Standards and validity

• DBN V.1.2-2:2006 “Loads and actions. Design standards”: clause 9.13 (special dynamic calculation), clause 9.17 (vortex shedding).
• EN 1991-1-4 “Wind actions”: Annexes B and E, methods for gust response and vortex shedding.
• Requirements for wind turbines (IEC 61400-1, IEC 61400-2) concern the turbine and are met by its manufacturer.

The validity of the documents is checked before the work starts.