Gas turbine engine airfoil frequency design

1. A turbomachine airfoil element comprising:

an airfoil having pressure and suction sides spaced apart from one another in a thickness direction and joined to one another at leading and trailing edges, the airfoil extending in a radial direction of a span that is in a range of 0.46-0.58 inch (11.6-14.7 mm);

a chord length extending in a chordwise direction from the leading edge to the trailing edge at 50% of the span is in a range of 0.66-0.79 inch (16.7-20.0 mm);

a first mode has a frequency of 35681 up to ±15% Hz; and

a second mode has a frequency of 39218 up to ±15% Hz;

wherein the frequencies are at a zero speed and ambient conditions, and the frequency of any given mode does not exceed the frequency of a higher order mode;

wherein the first mode is an ND51-1EB mode and the second mode is an ND51-1T mode, the ND51 corresponds to an aliased nodal diameter in which there are fifty-one peaks/troughs vibrating in the radial direction at each of inner and outer diameters of a stator stage of an array of airfoils, wherein the ND51-1EB mode corresponds to deflections substantially parallel to thickness direction, and the ND51-1T mode corresponds to twisting about the radial direction;

wherein the airfoil element is part of a stator; and

wherein the airfoil is a nickel-based superalloy, wherein the nickel-based superalloy has a density of about 0.28-0.32 lb/in 3 (7.7-8.9 g/cm 3 ), the nickel-based superalloy has a modulus of elasticity of about 27-36 Mpsi (186-248 GPa) at room temperature.

2. The element of claim 1 , comprising a third mode that has a frequency that is 21025 up to ±10% Hz, and the third mode is a ND0-1EBLE mode that corresponds to a vibration in unison axially forward and aft in a zero nodal diameter.

3. The element of claim 1 , wherein at a minimum cruise speed of 19800-22700 rpm at Mach 0.8 at 35,000 feet:

the first mode has a frequency of 33139 up to ±15% Hz; and

the second mode has a frequency of 36424 up to ±15% Hz.

4. The element of claim 1 , wherein the frequencies are up to ±10% Hz.

5. A method of repairing an airfoil comprising the steps of:

providing an airfoil having pressure and suction sides spaced apart from one another in a thickness direction and joined to one another at leading and trailing edges, the airfoil extending in a radial direction of a span that is in a range of 0.46-0.58 inch (11.6-14.7 mm), and a chord length extending in a chordwise direction from the leading edge to the trailing edge at 50% of the span is in a range of 0.66-0.79 inch (16.7-20.0 mm), wherein the provided airfoil has at least one unrestored mode frequency that is attributable to damage to the airfoil; and

repairing the airfoil to provide:

a first mode has a frequency of 35681±15% Hz; and

a second mode has a frequency of 39218±15% Hz;

wherein at least one of the first mode frequency and the second mode frequency corresponds to a restored mode frequency that supersedes the unrestored mode frequency;

wherein the frequencies are at a zero speed and ambient conditions, and the frequency of any given mode does not exceed the frequency of a higher order mode;

wherein the first mode is an ND51-1EB mode and the second mode is an ND51-1T mode, the ND51 corresponds to an aliased nodal diameter in which there are fifty-one peaks/troughs vibrating in the radial direction at each of inner and outer diameters of a stator stage of an array of airfoils, wherein the ND51-1EB mode corresponds to deflections substantially parallel to thickness direction, and the ND51-1T mode corresponds to twisting about the radial direction;

wherein the airfoil element is part of a stator; and

wherein the airfoil is a nickel-based superalloy, wherein the nickel-based superalloy has a density of about 0.28-0.32 lb/in 3 (7.7-8.9 g/cm 3 ), the nickel-based superalloy has a modulus of elasticity of about 27-36 Mpsi (186-248 GPa) at room temperature.

6. A turbofan engine comprising:

a fan section;

a compressor section arranged fluidly downstream from the fan section;

a turbine section arranged fluidly downstream from the compressor section;

a combustor arranged fluidly between the compressor and turbine sections; and

an airfoil in at least one of the fan, compressor and turbine sections, the airfoil having:

pressure and suction sides spaced apart from one another in a thickness direction and joined to one another at leading and trailing edges, the airfoil extending in a radial direction of a span that is in a range of 0.46-0.58 inch (11.6-14.7 mm);

a chord length extending in a chordwise direction from the leading edge to the trailing edge at 50% of the span is in a range of 0.66-0.79 inch (16.7-20.0 mm); and

a first mode has a frequency of 35681 up to ±15% Hz; and

a second mode has a frequency of 39218 up to ±15% Hz;

wherein the frequencies are at a zero speed and ambient conditions, and the frequency of any given mode does not exceed the frequency of a higher order mode;

wherein the first mode is an ND51-1EB mode and the second mode is an ND51-1T mode, the ND51 corresponds to an aliased nodal diameter in which there are fifty-one peaks/troughs vibrating in the radial direction at each of inner and outer diameters of a stator stage of an array of airfoils, wherein the ND51-1EB mode corresponds to deflections substantially parallel to thickness direction, and the ND51-1T mode corresponds to twisting about the radial direction;

wherein the airfoil is provided in the compressor section, the compressor section includes a high pressure compressor fluidly downstream from a low pressure compressor, and the airfoil is in the high pressure compressor which includes eight stages, the airfoil element is part of a stator; and

wherein the airfoil is a nickel-based superalloy, wherein the nickel-based superalloy has a density of about 0.28-0.32 lb/in 3 (7.7-8.9 g/cm 3 ), the nickel-based superalloy has a modulus of elasticity of about 27-36 Mpsi (186-248 GPa) at room temperature.