METHOD FOR SETTING AGING CONDITIONS AND METHOD FOR PRODUCING TURBINE VANES

Abstract

This method for setting aging conditions is provided with: a step for acquiring a master curve (20) indicating the relationship between an aging condition parameter and a material strength parameter by executing an aging process on a standard material; a step for acquiring a fitting point (A) indicating the value of the material strength parameter of a subject material of which the chemical component parameters and/or metal structure parameters differ from those of the standard material; a step for acquiring a corrected aging curve (30) by correcting the master curve (20) in a manner so that a portion of the master curve (20) corresponds to the fitting point (A); and a step for setting aging conditions for the subject material on the basis of the corrected aging curve (30).

Description

TECHNICAL FIELD

The present invention relates to a method for setting aging conditions of a subject material and a method for producing turbine blades using the method for setting aging conditions. This application claims priority based on Japanese Patent Application No. 2012-183103 filed in Japan on Aug. 22, 2012, of which the contents are incorporated herein by reference.

BACKGROUND ART

Greatly lengthening the low pressure final stage blades of steam turbines is effective for improving thermal efficiency. Since loaded centrifugal stress increases as a turbine blade gets longer, materials having high specific strength have been used in turbine blades. As the specific materials of turbine blades, the precipitation hardening stainless steel SUS 630 (17-4PH steel) and the like have been used. This precipitation hardening stainless steel can be increased in strength by an aging process.

For example, Patent Document 1 discloses a precipitation hardening stainless steel in which the components C, Cr, Ni, Mo, Si, Mn, Nb, V, Ti and Al have been adjusted.

Patent Document 2 discloses a precipitation hardening stainless steel in which the components C, Cr, Ni, Mo, Si, Mn, P, S, N and Al have been adjusted.

PRIOR ART DOCUMENTS

Patent Documents

• Patent Document 1: Japanese Unexamined Patent Application Publication No. 2011-225913A
• Patent Document 2: Japanese Unexamined Patent Application Publication No. 2005-194626A

SUMMARY OF THE INVENTION

Technical Problem

The strength of precipitation hardening stainless steel varies greatly depending on a difference in chemical composition and a difference in aging process temperature and time. In turbine blades, because chemical composition differs among production lots, the same strength may not be obtained even if the aging process is executed under the same heat treatment conditions. For this reason, it may not be possible to satisfy the required strength characteristics. Therefore, as described in Patent Document 1 and Patent Document 2, it is difficult to stably obtain desired strength characteristics for each of the turbine blades by performing an aging process alone.

Furthermore, metal structure such as grain size may differ among turbine blades of different production lots. Irregularity in strength after the aging process occurs depending on the metal structure as well.

Turbine blades that have not attained the desired strength characteristics through an aging process as described above require further heat treatment or become discarded, which adversely affects a production yield. For this reason, a method for setting aging conditions by which desired characteristics are obtained even when chemical composition and metal structure differ.

The present invention has been devised in consideration of the circumstances described above, and an object thereof is to provide a method for setting aging conditions that make it possible to obtain desired strength characteristics even when chemical composition and metal structure vary, and a method for producing turbine blades using the method for setting aging conditions.

Solution to Problem

According to a first aspect of the present invention, the method for setting aging conditions is provided with: a step for acquiring a master curve indicating the relationship between an aging condition parameter and a material strength parameter by executing an aging process on a standard material; a step for acquiring a fitting point indicating the value of the material strength parameter of a subject material of which the chemical component parameter and/or metal structure parameter differ from those of the standard material; a step for acquiring a corrected aging curve by correcting the master curve in a manner so that a portion of the master curve corresponds to the fitting point; and a step for setting aging conditions for the subject material on the basis of the corrected aging curve.

In the first aspect of the present invention, a master curve of a standard material and a fitting point of a subject material are acquired, and additionally, since a portion of the master curve has been made to correspond to the fitting point, a highly precise corrected aging curve (age hardening curve) of the subject material is acquired. Since it is configured so that the aging conditions of the subject material are set based on this corrected aging curve, the desired strength characteristics can be obtained by an aging process even if the chemical composition or metal structure differs between the standard material and the subject material.

A standard material is a material having a specified chemical composition and metal structure used for acquiring a master curve. A standard material has a chemical composition and metal structure that serve as standards for a subject material.

According to a second aspect of the present invention, the fitting point may also be acquired by executing an aging process on the subject material under prescribed conditions and collecting the material strength parameter.

By such a configuration, a highly precise fitting point can be reliably acquired. As a result, it is possible to set aging conditions that are optimal for the subject material.

According to a third aspect of the present invention, the fitting point may be acquired by determining the relationship between the chemical component parameter and metal structure parameter and the material strength parameter, and predicting the material strength parameter from differences in the chemical component parameter and the metal structure parameter between the standard material and the subject material.

By such a configuration, the master curve can be corrected based on the differences in the chemical component parameter and the metal structure parameter between the standard material and the subject material. For this reason, a highly precise corrected aging curve (age hardening curve) of the subject material can be acquired. Also, the aging conditions of the subject material can be set based on this corrected aging curve, and the desired strength characteristics can be obtained.

According to a fourth aspect of the present invention, the material strength parameter may be selected from hardness, tensile strength, and yield strength.

By such a configuration, desired strength characteristics can be obtained by an aging process because a more precise corrected aging curve can be easily acquired.

According to a fifth aspect of the present invention, the aging process may also be performed after the standard material and the subject material are forged.

By such a configuration, it is possible to form the metal structure and the shape a forged product has and to determine the strength characteristics of the forged product; thus precision of the method for setting aging conditions can be improved.

According to a sixth aspect of the present invention, the method for producing turbine blades applies the above method for setting aging conditions to turbine blades.

Because turbine blades are used in harsh environments in which large centrifugal stress is loaded, high strength and stable quality are required. In these turbine blades, the chemical composition and metal structure may differ among production lots. For this reason, irregularity in strength characteristics occurs among lots even if the aging process is performed under the same conditions. In such cases, it is possible to stably obtain desired strength characteristics by producing turbine blades using the above method for setting aging conditions. Therefore, production yield can be improved and production cost can be decreased.

According to a seventh aspect of the present invention, the turbine blade may be constructed of precipitation hardening stainless steel.

Precipitation hardening stainless steel is stainless steel having high strength and high corrosion resistance. By constructing the turbine blade of such precipitation hardening stainless steel, a turbine blade that can withstand even harsh environments can be obtained. Also, because precipitation hardening stainless steel varies greatly in strength due to differences in chemical component and metal structure even if the aging process is performed under the same heat treatment conditions, the desired strength characteristics can be obtained by applying the method for setting aging conditions of the above aspect. Specific examples of precipitation hardening stainless steel include SUS 630 containing Cu, Nb and Ta, and the like.

According to an eighth aspect of the present invention, the above chemical component parameter may be the total content of copper (Cu), niobium (Nb) and tantalum (Ta).

SUS 630 is an alloy strengthened by precipitation of Cu-rich precipitates and carbides by an aging process. By varying the total content of Cu, Nb and Ta in SUS 630, the amount of precipitation of precipitates and carbides varies, and the age hardening curve varies greatly. For this reason, a more precise corrected aging curve can be obtained by determining the total content of Cu, Nb and Ta as the chemical component parameter. The aging conditions can be set based on this corrected aging curve, and the desired strength characteristics can be obtained.

According to a ninth aspect of the present invention, the metal structure parameter may be grain size and/or residual austenite quantity.

In turbine blades constructed of precipitation hardening stainless steel such as SUS 630, the grain size and residual austenite quantity may vary among production lots. By setting the metal structure parameter in this manner, a highly precise corrected aging curve can be obtained.

Advantageous Effects of Invention

According to the aspects of the present invention described above, a method for setting aging conditions that makes it possible to obtain desired strength characteristics even when chemical composition and metal structure vary, and a method for producing turbine blades using the method for setting aging conditions can be provided.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic explanatory diagram of a turbine blade pertaining to a first embodiment of the present invention.

FIG. 2 is an age hardening curve obtained when SUS 630 is aged for various times at 550° C.

FIG. 3 is an age hardening curve obtained when SUS 630 is aged for 4 hours at various temperatures.

FIG. 4 is a flowchart for explaining the method for setting aging conditions and the method for producing turbine blades pertaining to the first embodiment.

FIG. 5 is a schematic explanatory diagram of the method for setting aging conditions pertaining to the first embodiment.

FIG. 6 is a flowchart for explaining the method for setting aging conditions and the method for producing turbine blades pertaining to a second embodiment.

FIG. 7 is a schematic explanatory diagram of the method for setting aging conditions pertaining to the second embodiment.

DESCRIPTION OF EMBODIMENTS

First Embodiment

Below, embodiments of the present invention will be described while referring to the appended drawings.

The turbine blade 1 pertaining to this embodiment, as illustrated in FIG. 1, is provided with a long blade 11, a shroud 12 provided on the distal end of the long blade 11, a stub 13 provided in the center portion of the long blade 11, and a blade root 14 provided on the proximal end of the long blade 11. This turbine blade 1 is a rotating blade of a steam turbine. The turbine blade 1 is configured such that a plurality of turbine blades 1 are provided on a turbine rotor (not illustrated) by the blade roots 14 being implanted around the axis of rotation of the turbine rotor. The shrouds 12 and stubs 13 provided on the turbine blades 1 are formed in a ring shape in which adjacent ones combine to form concentric circles. For example, 50 or more turbine blades 1 are disposed on one turbine rotor.

The turbine blade 1 is loaded with large centrifugal stress because it is used at a rotation speed of 3000 rpm or above when the steam turbine operates. For this reason, SUS 410, which is a high-strength 12 Cr stainless steel, SUS 630 (17-4PH steel), which is a precipitation hardening stainless steel, the steel described in Patent Document 2, or Ti-6Al-4V alloy or the like may be used, for example. In this embodiment, the turbine blade 1 is constructed of the precipitation hardening stainless steel SUS 630 (17-4PH steel).

SUS 630 is stainless steel containing C, Si, Mn, P, S, Cu, Ni, Cr, Nb and Ta, and the remainder Fe. This SUS 630 is an age hardening alloy. SUS 630 is strengthened by precipitation of Cu-rich precipitates and carbides by an aging process performed after solution heat treatment.

FIG. 2 is an age hardening curve obtained when a hardness test was performed after SUS 630 underwent an aging process at 550° C. for from 1 to 10 hours. In FIG. 2, the solid line indicates the age hardening curve of SUS 630 standard material (total content of Cu, Nb and Ta 3.77% by mass). The dashed line indicates the age hardening curve of SUS 630 having a different chemical composition from the standard material (total content of Cu, Nb and Ta 3.52% by mass).

A standard material is something that has the chemical composition and metal structure typical of alloys thereof. In this embodiment, SUS 630 in which the total content of Cu, Nb and Ta is 3.77% by mass, grain size is #6, and residual austenite quantity is 5% is used as the standard material.

Grain size indicates the size of crystal grains determined in accordance with, for example, JIS G 0551. Residual austenite quantity indicates the value measured by quantification of SUS 630 by X-ray diffraction.

FIG. 3 is an age hardening curve obtained when a hardness test was performed after SUS 630 underwent an aging process at from 520° C. to 600° C. for 4 hours. In FIG. 3, the solid line indicates the age hardening curve of SUS 630 standard material (total content of Cu, Nb and Ta 3.77% by mass). The dashed line indicates the age hardening curve of SUS 630 having a different chemical composition from the standard material (total content of Cu, Nb and Ta 3.52% by mass).

The age hardening curve of the standard material is called a master curve (the same hereinafter).

In FIGS. 2 and 3, Vickers hardness testing was performed as a hardness test. In FIGS. 2 and 3, the ratio of the measured value of Vickers hardness to the target value of Vickers hardness (required hardness) is shown on the vertical axis. Therefore, the range in which the ratio of hardness (measured value) to hardness (target value) is close to 1 is the range of required hardness after the aging process. An example of this range is indicated by the dots in FIGS. 2 and 3.

As shown in FIG. 2, when SUS 630 has undergone an aging process at 550° C., it reaches its maximum strength when the aging time is around 1 hour, and strength decreases thereafter. Normally, aging of SUS 630 is performed on the over-aging side. For SUS 630 standard material, the range indicated by Z is the range of aging conditions that satisfy the desired required characteristics. Also, the overall strength of SUS 630 having a lower total content of Cu, Nb and Ta than the standard material is lower than that of the SUS 630 of the standard composition, as indicated by the dashed line. From this fact it is understood that when the chemical composition differs, the same strength is not obtained even when the aging process is performed under the same heat treatment conditions.

Furthermore, the aging conditions at peak strength where aged strength is a maximum do not change even if the composition varies approximately within the composition specification range.

As shown in FIG. 3, for SUS 630, strength decreases as aging temperature increases when the aging temperature is in the range of 540° C. to 600° C. For SUS 630, it is understood that if the total content of Cu, Nb and Ta is lower, strength is lower.

As shown in FIGS. 2 and 3, when heat treatment is performed for 4 hours at 550° C., the strength of the standard material is in the required range. However, the strength of SUS 630 having a total content of Cu, Nb and Ta of 3.52% is below the required range.

This difference in strength is not due to the chemical composition alone, but also due to the grain size and the quantity of residual austenite.

Therefore, if the chemical composition or metal structure differs from that of SUS 630 of the standard composition, the same strength may not be obtained and the desired strength characteristics may not be obtained even when heat treatment in the same manner as SUS 630 of the standard composition is performed. For this reason, the optimal aging conditions must be set in accordance with chemical composition and metal structure. When turbine blades 1 are produced, there are variations in chemical composition and metal structure among lots of turbine blades 1. It takes time and increases production cost to produce turbine blades according to aging conditions determined after collecting an age hardening curve by performing the aging process under different time and temperature conditions and measuring hardness for each lot.

Below, the method for setting aging conditions by which an age hardening curve of a subject material having a different chemical composition from the standard material is acquired from a master curve of SUS 630 standard material and then desired strength characteristics are obtained, and the method for producing turbine blades, will be described using FIGS. 4 and 5.

A method for producing turbine blades pertaining to a first embodiment is performed by steps S11 to S15 as illustrated in FIG. 4. The details thereof will be described below.

(S11)

An aging process is executed on SUS 630 standard material at 550° C. for from 1 to 10 hours (aging condition parameters), and the hardness test is performed. A master curve 20 (age hardening curve) of the standard material is acquired, as indicated by the solid line in FIG. 5.

(S12)

An aging process is executed on at 550° C. for 4 hours, for example, and Vickers hardness testing is performed on SUS 630 (subject material) of which the chemical composition (chemical component parameter) and/or metal structure (metal structure parameter) differ from those of the standard material. A fitting point (point A in FIG. 5) that indicates the relationship between hardness (material strength parameter) and aging conditions is acquired.

The chemical component parameter is a factor that affects material strength. Examples thereof are Cu content, Nb content, Ta content, total content of Cu, Nb and Ta, and the like. The metal structure parameter is also a factor that affects material strength. Examples thereof are grain size and residual austenite quantity.

(S13)

By sliding the master curve 20 so that a portion thereof corresponds to the fitting point A, a corrected aging curve 30 (age hardening curve) of the subject material is acquired, as indicated by the dashed line in FIG. 5.

(S14)

Next, the optimal aging conditions for obtaining the desired strength characteristics are determined based on the corrected aging curve 30. In FIG. 5, the time indicated by X is the optimal aging condition. The two-way arrow in FIG. 5 indicates an example of the range of hardness required in the turbine blade 1. The range of required hardness may be set to the optimal range in accordance with the size and type of the turbine blade.

(S15)

Finally, an aging process is performed on the turbine blade 1 under the heat treatment conditions set in S14.

In this manner, a turbine blade 1 having the desired strength characteristics (hardness) can be obtained.

The case where a master curve is acquired at an aging temperature of 550° C. has been described in S1, but the aging conditions are not limited thereto, and the temperature may be set as appropriate. Additionally, a master curve may be acquired under a plurality of temperature conditions, or a master curve may be acquired by fixing the time and varying the temperature. Furthermore, in such cases, the aging conditions performed in S2 may be selected in accordance with the conditions of the master curve acquired in S1.

According to the method for setting aging conditions and the method for producing turbine blades pertaining to the first embodiment of the present invention, a master curve 20 of a standard material is acquired, and a fitting point A is acquired by executing an aging process on a subject material and measuring hardness (material strength parameter), and the master curve 20 is made to correspond to the fitting point A. As a result, a highly precise corrected aging curve 30 (age hardening curve) of the subject material can be acquired. Since it is configured so as to set the aging conditions of the subject material based on this corrected aging curve 30, the desired strength characteristics can be obtained by an aging process even if the chemical composition or metal structure differs between the standard material and the subject material. Therefore, turbine blades 1 that satisfy the required strength characteristics can be reliably obtained and production cost can be decreased.

Second Embodiment

The method for setting aging conditions and the method for producing turbine blades pertaining to a second embodiment of the present invention will be described.

The configuration of the turbine blade and the material that constitutes the turbine blade pertaining to the second embodiment are the same as those of the first embodiment. The same constituents are given the same reference numerals, and the detailed descriptions thereof are omitted.

In the method for setting aging conditions and the method for producing turbine blades pertaining to the second embodiment, a master curve 120 is acquired, and the relationship between the master curve 120 and the chemical component parameter and metal structure parameter is determined in advance. For example, a corrected aging curve 130 (age hardening curve) of the subject material is acquired by correcting the master curve 120 from the chemical composition and metal structure of the subject material. The details thereof will be described below with reference to FIGS. 6 and 7.

(S21)

An aging process is executed on SUS 630 standard material at 550° C. for from 1 to 10 hours (aging condition parameters), and the hardness test is performed. The master curve 120 (age hardening curve) of the standard material is acquired, as indicated by the solid line in FIG. 7.

(S22)

The relationships between the chemical component parameter and metal structure parameter and the material strength parameter are determined for SUS 630 of which the chemical component parameter and/or metal structure parameter differ from those of the standard material.

To explain more specifically, for example, an aging process is executed on for 4 hours at 550° C. and Vickers hardness testing is performed on SUS 630 of which the total content of Cu, Nb, and Ta (chemical component parameter) differs from that of the standard material but the metal structure parameter is the same. Then, using the hardness value measured in this manner and the hardness value of the master curve obtained when the aging process is executed for 4 hours at 550° C. and the measured hardness value acquired in S22, the relationship with chemical composition is determined by, for example, linear approximation. For example, the following relational expression is obtained:

Δhardness=−28×(3.77−(Cu+Nb+Ta)),

• • where Δhardness means the difference between the hardness after aging of the subject material under the prescribed aging conditions and the hardness of the master curve. Also, (Cu+Nb+Ta) means the total content of Cu, Nb and Ta in percent by mass.

(S23)

Using the relationship between the content of Cu+Nb+Ta (chemical component parameter) and hardness (material strength parameter), the chemical component parameter and metal structure parameter of the subject material are made to correspond to each other, and a fitting point B that indicates the material strength parameter of the subject material is acquired. For example, when (Cu+Nb+Ta)=3.52%, Δhardness=−7; thus the fitting point is a point B, which is 7 less than the hardness of the master curve at an aging temperature of 550° C.

(S24)

By sliding the master curve 120 so that a portion thereof corresponds to the fitting point B, the corrected aging curve 130 (age hardening curve) of the subject material is acquired, as indicated by the dashed line in FIG. 7.

(S25)

Next, the optimal aging conditions for obtaining the desired strength characteristics are determined based on the corrected aging curve 130. In FIG. 7, the time indicated by Y is the optimal aging condition. The two-way arrow in FIG. 7 indicates an example of the range of hardness required in the turbine blade 1.

(S26)

Finally, an aging process is performed on the turbine blade 1 under the aging conditions set in S25.

In this manner, a turbine blade 1 having the desired characteristics can be obtained. The case where a master curve 120 is acquired at an aging temperature of 550° C. has been described in S21, but the aging conditions are not limited thereto, and the temperature may be set as appropriate. Additionally, a master curve may be acquired under a plurality of temperature conditions, or a master curve may be acquired by fixing the time and varying the temperature. Furthermore, in such cases, the aging conditions performed in S22 may be selected in accordance with the conditions of the master curve acquired in S21.

According to the method for setting aging conditions and the method for producing turbine blades pertaining to the second embodiment of the present invention, a master curve 120 of a standard material is acquired, and from the differences in chemical component parameter and metal structure parameter between the standard material and subject material, the material strength parameter is predicted and the master curve 120 is corrected. As a result, a highly precise corrected aging curve 130 (age hardening curve) of the subject material can be obtained. Since it is configured so as to set the aging conditions of the subject material based on this corrected aging curve 130, the desired strength characteristics can be obtained by an aging process even if the chemical composition or metal structure differs between the standard material and the subject material. Therefore, turbine blades 1 that satisfy the required strength characteristics can be reliably obtained, and production cost can be decreased.

Unlike the first embodiment, once the chemical component parameter and metal structure parameter of the subject material are made to correspond to each other, the fitting point can be acquired thereafter without performing an aging process on each turbine blade (subject material). For this reason, production cost can be reduced, and the time required to determine aging conditions can also be reduced.

In the second embodiment, the case where only one fitting point is acquired has been described, but it is also possible to determine the relationship between the chemical component parameter and metal structure parameter and hardness for a plurality of points and to make the master curve correspond to a plurality of fitting points to acquire a corrected aging curve (age hardening curve) of the subject material.

In the above embodiments, the case where the relationship between hardness and total content of Cu, Nb and Ta is determined has been described, but it is not limited thereto, and the relationships between other chemical component parameters or metal structure parameters and hardness may be determined. Additionally, the chemical components used in the chemical component parameter may be selected according to material. For example, in the steel described in Patent Document 2, Al and Ni, which are the constituent elements of precipitates, may be selected.

A plurality of chemical component parameters and metal structure parameters may also be selected, rather than one parameter. In that case, the relationships between the chemical component parameter and metal structure parameter and hardness may be determined using multiple regression analysis.

Methods for setting aging conditions and methods for producing turbine blades that are embodiments of the present invention have been described above, but the present invention is not limited thereto, and may be modified as appropriate within a range that does not deviate from the technical concept of the invention.

In the above embodiments, the case where an aging process is executed on a standard material and a subject material and the material strength parameter is measured has been described, but it may also be configured such that a forging process that simulates the turbine blade is performed before an aging process. For example, the material strength parameter may be acquired by executing an aging process on a waste which is cut off from a forging raw material for the turbine blade and is forged (hot-forged) into a shape that simulates the blade root of the turbine blade. By so doing, a more accurate material strength parameter can be obtained, and a more precise corrected aging curve (age hardening curve) can be obtained.

In the above embodiments, the case where Vickers hardness is used as the material strength parameter has been described, but it is not limited thereto. For example, hardness measurement by another hardness test may be used, or the measured value of tensile strength or yield strength (0.2% yield strength) may be used.

INDUSTRIAL APPLICABILITY

According to this method for setting aging conditions, desired strength characteristics can be obtained even when chemical composition and metal structure differ. Furthermore, a method for producing turbine blades which employs the above method for setting aging conditions can be provided.

REFERENCE SIGNS LIST

• 1 Turbine blade
• 20, 120 Master curves
• 30, 130 Corrected aging curves
• A, B Fitting points

Claims

1. A method for setting aging conditions, comprising the steps of:

acquiring a master curve indicating a relationship between an aging condition parameter and a material strength parameter by executing an aging process on a standard material;

acquiring a fitting point indicating a value of the material strength parameter of a subject material of which a chemical component parameter and/or metal structure parameter differ from those of the standard material;

acquiring a corrected aging curve by correcting the master curve in a manner so that a portion of the master curve corresponds to the fitting point; and

setting aging conditions for the subject material on a basis of the corrected aging curve.

2. The method for setting aging conditions according to claim 1, wherein

the fitting point is acquired by executing an aging process on the subject material under prescribed conditions and collecting the material strength parameter.

3. The method for setting aging conditions according to claim 1, wherein

the fitting point is acquired by determining a relationship between the chemical component parameter and metal structure parameter and the material strength parameter, and predicting the material strength parameter from differences in the chemical component parameter and the metal structure parameter between the standard material and the subject material.

4. The method for setting aging conditions according to claim 1, wherein

the material strength parameter is selected from hardness, tensile strength, and yield strength.

5. The method for setting aging conditions according to claim 1, wherein

the aging process is performed after the standard material and the subject material are forged.

6. A method for producing turbine blades for applying the method for setting aging conditions described in claim 1 to a turbine blade.

7. The method for producing turbine blades according to claim 6, wherein

the turbine blade is constructed of precipitation hardening stainless steel.

8. The method for producing turbine blades according to claim 7, wherein

the chemical component parameter is a total content of copper, niobium and tantalum.

9. The method for producing turbine blades according to claim 7, wherein

the metal structure parameter is grain size and/or residual austenite quantity.