Turbomachine blade

1. A turbomachine airfoil element being a blade, the blade formed of a nickel based superalloy and comprising:

a platform having an outboard surface and an underside;

an inboard attachment root extending from the platform underside; and

an airfoil having: an inboard end; an outboard end; a leading edge; a trailing edge; a pressure side; and a suction side, the inboard end at the platform outboard surface and the outboard end being a free tip, a cooling passageway system in the airfoil having one or more inlets and one or more outlets,

wherein:

at 70° F. the nickel-based superalloy is a single crystal alloy having a density of 0.315-0.330 pounds per cubic inch and a modulus of elasticity of 17.5-18.5E06 psi;

a span between the inboard end and the outboard end is 1.35-1.65 inches;

a chord length at 50% span is 1.20-1.60 inches; and

in a zero speed free condition and measured by suspended ping test or laser vibrometry:

a first mode resonance frequency is 4678±5% Hz;

a second mode resonance frequency is 7672±5% Hz; and

a third mode resonance frequency is 11383±5% Hz;

a fourth mode resonance frequency is 14112±10% Hz;

a fifth mode resonance frequency is 16734±10% Hz; and

a six mode resonance frequency is 18419±10% Hz.

2. The element of claim 1 wherein at said zero speed free condition and measured by said suspended ping test or laser vibrometry:

a fourth mode resonance frequency is 14112±10% Hz;

a fifth mode resonance frequency is 16734±10% Hz; and

a six mode resonance frequency is 18419±10% Hz.

3. The element of claim 2 wherein at said zero speed free condition and measured by said suspended ping test or laser vibrometry:

the fourth mode resonance frequency is 14112±5% Hz;

the fifth mode resonance frequency is 16734±5% Hz; and

the six mode resonance frequency is 18419±5% Hz.

4. A method for remanufacturing a turbomachine airfoil element to form the turbomachine airfoil element of claim 1 , the method comprising addition or removal of superalloy to provide at least one of the first mode resonance frequency, second mode resonance frequency, and third mode resonance frequency wherein:

a provided turbomachine airfoil element has at least one unrestored mode frequency that is attributable to damage to the provided turbomachine airfoil element; and

the at least one of the first mode resonance frequency, second mode resonance frequency, and third mode resonance frequency corresponds to a restored mode frequency that supersedes the at least one unrestored mode frequency.

5. The method of claim 4 wherein the providing comprises addition of the nickel-based superalloy.

6. The method of claim 5 wherein the providing comprises removal of material after the addition.

7. The method of claim 5 wherein the providing comprises measuring a frequency response after the addition and thereafter further modifying the turbomachine airfoil element via removing or adding the nickel-based superalloy.

8. The method of claim 5 further comprising:

applying a thermal barrier coating over the added nickel-based superalloy.

9. A combination of a turbomachine blade and a turbine disk or fixture in which the blade is mounted, the blade formed of a nickel based superalloy and comprising:

a platform having an outboard surface and an underside;

an inboard attachment root extending from the platform underside and mounted in the turbine disk or fixture; and

an airfoil having: an inboard end; an outboard end; a leading edge; a trailing edge; a pressure side; and a suction side, the inboard end at the platform outboard surface and the outboard end being a free tip, a cooling passageway system in the airfoil having one or more inlets and one or more outlets,

wherein:

at 70° F. the nickel-based superalloy is a single crystal alloy having a density of 0.315-0.330 pounds per cubic inch and a modulus of elasticity of 17.5-18.5E06 psi;

a span between the inboard end and the outboard end is 1.35-1.65 inches;

a chord length at 50% span is 1.20-1.60 inches; and

at zero speed and ambient conditions:

a first mode resonance frequency is 2858±5% Hz;

a second mode resonance frequency is 4916±5% Hz;

a third mode resonance frequency is 7160±5% Hz;

a fourth mode resonance frequency is 10268±10% Hz;

a fifth mode resonance frequency is 14235±10% Hz; and

a sixth mode resonance frequency is 15088±10% Hz.

10. The combination of claim 9 wherein at zero speed and ambient conditions at least one of:

all the fourth mode resonance frequency is 10268±5% Hz;

all the fifth mode resonance frequency is 14235±5% Hz; and

all the sixth mode resonance frequency is 15088±5% Hz.

11. The combination of claim 9 wherein, the element is mounted in said turbine disk in a turbine engine and at a running speed/condition:

the first mode resonance frequency is 2826±10% Hz;

the second mode resonance frequency is 4808±10% Hz;

the third mode resonance frequency is 6891±10% Hz;

the fourth mode resonance frequency is 9984±10% Hz;

the fifth mode resonance frequency is 13772±10% Hz; and

the sixth mode resonance frequency is 14619±10% Hz.

12. The combination of claim 9 wherein, the element is mounted in said turbine disk in a turbine engine and at a running speed/condition:

the first mode resonance frequency is 2826±5% Hz;

the second mode resonance frequency is 4808±5% Hz;

the third mode resonance frequency is 6891±5% Hz;

the fourth mode resonance frequency is 9984±5% Hz;

the fifth mode resonance frequency is 13772±5% Hz; and

the sixth mode resonance frequency is 14619±5% Hz.

13. The combination of claim 9 wherein the element is a casting.

14. A combination of a turbomachine blade and a turbine disk of a gas turbine engine in which the blade is mounted, the blade formed of a nickel based superalloy and comprising:

a platform having an outboard surface and an underside;

an inboard attachment root extending from the platform underside and mounted in the turbine disk;

an airfoil having: an inboard end at the platform; an outboard end; a leading edge; a trailing edge; a pressure side; and a suction side, a cooling passageway system in the airfoil having one or more inlets and one or more outlets,

wherein:

at 70° F. the nickel-based superalloy is a single crystal alloy having a density of 0.315-0.330 pounds per cubic inch and a modulus of elasticity of 17.5-18.5E06 psi;

a span between the inboard end and the outboard end is 1.35-1.65 inches;

a chord length at 50% span is 1.20-1.60 inches; and

at a running speed/condition:

a first mode resonance frequency is 2826±5% Hz;

a second mode resonance frequency is 4808±5% Hz;

a third mode resonance frequency is 6891±5% Hz;

a fourth mode resonance frequency is 9984±5% Hz;

a fifth mode resonance frequency is 13772±5% Hz; and

a sixth mode resonance frequency is 14619±5% Hz.