ROTARY MECHANICAL SYSTEM USING A PROFILE WITH A FIXED CORD FEATURE

Abstract

This invention presents a structure in rotary mechanical systems containing rotor-stator-moving elements, particularly rotary vane type systems, where contact can be achieved directly through the profile geometry without the need for external springs or similar force elements. The profile used in this invention is defined to satisfy specific geometric relationships, and thanks to this structure, the movement of the moving element is geometrically directed, making the system behavior controllable. This approach enables control of the working chambers formed within the system and the resulting volumetric behavior, providing design flexibility suitable for different applications. As a result, more efficient and adaptable mechanical solutions can be obtained compared to classical systems.

Description

1 TARIFF ROTARY MECHANISM USING A PROFILE WITH A FIXED CORD FEATURE SYSTEM TECHNICAL FIELD This invention relates to the technical field of rotary displacement mechanical systems; rotor, the stator and the movable elements located between these elements (valve, vane, It is aimed at the design of profile geometries used in systems containing pistons, etc. 10 The invention applies particularly to rotary vane pumps, vacuum pumps, and gas and liquid compressors. in rotary machines that provide volumetric flow based on rotor-stator interaction This includes the stator or similar external profile geometries used. More specifically, the invention relates to closed curve profiles of stator or similar surfaces 15 its use as geometry and these profiles as rotor and moving elements the contact behavior between them, the formation of workspaces, and volumetric changes. It is aimed at determining this. The profile geometries used in this context are fixed at opposite angular positions. The invention is based on parametric closed curve structures that provide a distance relationship. This relates to the application of these geometries in mechanical systems. PREVIOUS TECHNIQUE In rotary displacement pumps, compressors and similar mechanical systems, the rotor The geometry of the volumetric chambers formed between the stator and the power supply improves system performance. This directly determines the profiles. In these systems, stator profiles are generally circular or elliptical. or limited by specific lobed curves. Especially in rotary vane type systems, the rotor They are eccentrically positioned, and the valves or vanes on the rotor have a spring force of 30. or is held in contact with the stator's inner surface by centrifugal force. 2 This design allows for the creation of variable-volume chambers between the rotor and stator. and the fluid is absorbed, transported and compressed. However, the current Stator profiles used in the techniques:  Limiting the geometric control of volumetric chambers 5  makes it difficult to optimize contact continuity,  This restricts the variety of profiles suitable for different working conditions,  It offers limited possibilities for improvement in the continuity and balance of the flow. In addition, existing solutions are generally limited to certain geometric shapes, 10 a profile that can be defined parametrically and systematically extended It does not offer a family of products. Furthermore, there is a fixed geometric relationship between opposite angular positions. The use of profile structures that provide connections in mechanical systems in current techniques It is not defined in a clear and systematic way. In addition, with profile geometry There is also a clear direct and general geometric limiting relationship between rotor dimensions. 15 It has not been presented in this way. In conclusion, all the problems mentioned above require an innovation in the relevant technical field. This has made it necessary to do it. A BRIEF DESCRIPTION OF THE INVENTION The present invention aims to overcome the disadvantages listed above and to introduce new technologies to the relevant technical field. In order to gain advantages, a closed curve with a fixed cord feature. This relates to the use of profiles in rotary mechanical systems. 25 The primary objective of the invention is to directly profile the rotor-stator-moving element interaction. The goal is to develop a rotary mechanical system defined by its geometry. Another objective of the invention is to directly profile the rotor-stator-moving element interaction. determined by its geometry and the need for external force elements The goal is to create a rotary mechanical system in which the rotational motion is reduced or eliminated. 3 Another objective of the invention is to reduce the relationship between the rotor radius and the usable working area. a systematic way in which the relationship can be directly determined through profile parameters The goal is to create a geometric design framework. Another objective of the invention is to reduce the volumetric size of the workspaces formed within the system to 5 its behavior can be controlled parametrically via its profile geometry. The aim is to offer a family of profiles that can be defined and adapted. All the purposes mentioned above and those that will emerge from the detailed explanation below. The present invention aims to realize a rotor, a stator, and a 10-degree connection between these two elements. a rotary displacement mechanical system that includes at least one movable element in a specific position It is a system. Accordingly, the matter in question  At least one of the stator and rotor surfaces must be relative to a single reference center. a closed system defined by its radial distance r(θ) which depends on its angular position having a curved profile and 15  points located at the angular positions θ and θ+π of the profile in question the linear distance between them is constant r(θ) + r(θ+π) = K, provided that K > 0  the local stator profile of the moving element during the rotational movement of the rotor a radial displacement motion that is forced depending on the radial distance This is achieved by creating a connection between the moving element and the stator profile. by the contact being continuously maintained by the profile geometry It is characterized by being 25 Thus, thanks to this system, pumps, compressors, vacuum pumps, etc. can be used in structures. Fluid transfer can be applied and the profile can be extended in planar or axial direction. It can be used in three-dimensional structures or multi-level systems. A preferred configuration of the invention is that the profile in question is of the form r(θ) = R + f(θ) 30 It is defined in canonical form and satisfies the condition f(θ) + f(θ+π) = C, C > 0. This is the case. Thus, the work rooms that are created during the operation of the system. a decisive role in its formation, continuity and volumetric change behavior 4 its movement and the amplitude, angular distribution, or functional structure of this component The usable volume of the system can be controlled through this method. A preferred configuration of the invention is one in which the stator profile is equal to or equal to the rotor radius. will have a larger radial distance value and the condition r(θ) ≥ Rr, ∀θ will be 5 It is characterized by being selected in a way that will provide mobility. the element's contact with the stator profile must be uninterrupted throughout the entire operation. It rotates as it is maintained. Another preferred configuration of the invention is one where the upper limit of the rotor radius is the stator 10 It is characterized by being defined by its minimum profile value. Another preferred configuration of the invention is where the stator profile is only visible on the stator. No, it can be identified on the rotor or between the rotor and stator components. can be divided, and the moving element can be a wing, blade, piston, piston ring or similar 15 It is characterized by its ability to be implemented in different geometric and kinematic structures. It is the fact that. Another preferred configuration of the invention is defined by the antipodal component. Thanks to its geometric structure, the contact between the moving element and the stator profile is minimized. Without the need for external springs, pressure or similar force elements, the system's 20 It is characterized by being geometrically sustainable throughout the rotational motion. The fact that it is being done. All the purposes mentioned above and those that will emerge from the detailed explanation below. The present invention aims to achieve this in a rotary displacement mechanical system. It is a closed curve profile structured for use. Accordingly, the 25 in question The profile's characteristic is that it is defined relative to a single reference center. The radial distance, which depends on the angular position, is expressed as r(θ), and between points located at opposite angular positions θ and θ+π on the profile linear distance is constant r(θ) + r(θ+π) = K It is a profile structure characterized by fulfilling the condition. A preferred configuration of the invention is a polar profile relative to a reference center. in canonical form in coordinates r(θ) can be expressed as R + f(θ), where R > 0 and C > 0. The function f(θ) f(0) = 0, f(θ) + f(θ + π) = C and f(θ) ≥ 0, ∀θ satisfying the conditions, and under this structure the profile has 10 opposing angular positions. r(θ) + r(θ + π) = K by establishing a constant cord length, and When the profile in question is used with a rotor and at least one moving element, 15 by allowing the radial displacement of the moving element to be forced along the profile It is characterized by its suitability for the creation of workspaces of varying sizes. The fact that it is being done. Another preferred configuration of the invention is a stator with a specific profile, with a fixed 20 If mathematical transformations are performed while preserving the cord condition, The transformations mentioned include angular rearrangement, angular shift, angular at least one of the following: duplication, reflection, radial scaling, or change of reference point It is characterized by the fact that it involves processing and the profile maintains its fixed cord feature. that is. 25 Another preferred configuration of the invention is one in which the stator profile has a closed curve. If defined, this curve's mathematical representation would be polar, Cartesian, It must be at least one of the parametric or latent methods. Another preferred configuration of the invention is that the angular variable of the stator profile is singular. in the form of multi-layered reparameterization transformed and consequently the profile in question 6 as redefined, fixed cord under the said transformation by maintaining the condition and changing the number of lobes formed on the profile It is characterized by the ability to adjust the number of study rooms. Thus, the working chambers formed during one complete rotation cycle of the system are uninterrupted. It is formed in a certain way and there is continuity between successive volumetric regions. 5 is provided. All the purposes mentioned above and those that will emerge from the detailed explanation below. The present invention aims to achieve this in a rotary displacement mechanical system. A closed curved profile configured for use in a rotary mechanical system 10 It is a method for making it usable. Accordingly, the aforementioned The characteristic of the invention is; i. minimum radial value of a closed curve defined in polar coordinates determination, ii. referencing the angular position corresponding to the minimum value and the profile 15 by applying phase shift This involves re-expressing it in the canonical form r(θ) = R + f(θ) and iii. with the preservation of the profile's fixed cord feature under this transformation. ensuring the profile is compatible with the mechanical system components. It is characterized by 20 BRIEF DESCRIPTION OF THE FIGURE Figure 1: Representative illustration of a rotary system with a classic circular stator profile. It is shown. Figure 2a shows the circular stator profile used in classic rotary vane systems. It is shown. Figure 2b shows an example configuration of a stator profile that satisfies the fixed cord condition. It is shown. 30 7 In Figure 3, with a constant cord length of K=2.8, parameters R=0.9 and C=1 are used. the profile obtained and defined by its expression It is shown. Figure 4 shows an example configuration of a stator profile that satisfies the fixed cord condition. It is shown. In Figure 5, parameters R=1 and C=0.8 are used with a fixed cord length K=2.8. obtained with and 10 with the expression The defined profile is displayed. In Figure 6a, with its expression given in general form. The defined profile is shown. 15 Figure 6b shows the profile given in Figure 6a converted to its canonical form. It is shown. REFERENCE NUMBERS GIVEN IN THE FIGURE 20 1: expressed in polar coordinates defined stator profile, 2: rotor, 3: rotor radius, and the minimum radius that satisfies the relationship is 25. 4: the contact point between the rotor and stator profiles, 5: Represents the radial distance between the rotor and stator profiles at angular position θ. f(θ) 6: Reference center point, 7: (θ+π) represents the radial distance between the rotor and stator profiles at the angular position. 30 f(θ+π) is shown. 8: fixed length in the direction of movement necessitated by the stator geometry. the channel in which the moving element moves freely in the radial direction within the rotor 8 DEFINITIONS The fundamental concepts used in this invention are defined below: - r(φ): The general form of the stator profile defined relative to the reference center. radial distance function. - d(φ): Used in the general definition of the profile and represents the deviation of the curve from the constant component. function that expresses. - (φ): Angular variable used in the overall profile description. - : The angular position where the profile reaches its minimum radial value. 10 - : The fixed radial component located within the overall form of the profile. - r(θ): The stator profile defined relative to the reference center in the canonical representation. radial distance function. - f(θ): The deviation function of the profile expressed in canonical form. - (θ): Angular 15 redefined for expressing the profile in canonical form. variable. - K: Cord length that remains constant between opposing angular positions on the profile. - C: The constant parameter that determines the amplitude of the profile's deviation function, f(θ). - : Rotor radius used in mechanical systems. - : Parameter indicating rotor diameter. 20 - : These are the weighting coefficients of the harmonic components that make up the deviation function. They satisfy the condition and are selected such that their sum will be... - : every, in the sense of. - Canonical form: A coordinate system that references the minimum value of the profile. as expressed according to the system and the profile, with a minimum radial distance of 25 from this value It is a form of expression in which the sum of the deviations is represented. These definitions include general and canonical representations of the profile and mechanical system components. It ensures that the relationship between them is clearly established. 9 DETAILED DESCRIPTION OF THE INVENTION This detailed explanation describes the invention as a rotary mechanical system and the system within it. The profile structure used is solely for the purpose of facilitating a better understanding of the subject. This is explained with non-limiting examples. 5 The profile used in the invention is defined using polar coordinates. It is a closed curve. The fundamental characteristic of this curve is that the angular positions of the objects on it are oppositely positioned. The term refers to the situation where the linear distance between two points always remains constant. This feature is referred to as the "fixed cord" feature in technical literature. 10 This invention enables the use of curve families that satisfy the constant cord condition in mechanical systems. Using this, the direct profile geometry of the rotor-stator-moving element interaction. that the volumetric and kinematic behavior of the system is determined by this geometric It relates to a mechanical structure that can be controlled via the structure itself. 15 The profile is defined based on a single reference center. Measurements are taken from this center. Radial distance varies depending on angular position. Such a profile... for use as a stator and / or rotor surface in a rotary mechanical system In this case, the contact between the rotor and the profile is only due to a natural 20 of the geometric structure. As a result, it occurs spontaneously. In the preferred design, the rotor profile is created in a circular shape, while the stator profile... It is derived from a curve that exhibits a constant cord characteristic. However, this profile... It can be applied only on the rotor or simultaneously on both elements. 25 It is possible. The fixed cord feature ensures uninterrupted contact between the rotor and the profile. This ensures that contact is continuously maintained while the system is operating. This allows the system to... Furthermore, the need to add springs, compression elements, or elastic components is eliminated. It can be eliminated or minimized. The present invention is described in document number 2026 / 003031 and is opposed to a closed curve profile that provides a constant geometric relationship between angular positions It is based on its family. The production of this profile family is described in the document in question. Methods for verification and parametric acquisition are described. The purpose of this invention is to enable the direct application of these profile structures in mechanical systems. It is the definition of an integrated structure that enables its use. For this purpose, profiles from the profile family can be used directly in mechanical systems. To ensure the structures are obtained, the profile function has 5 angular positions. in such a way that it does not take a negative value, that is, in a way that satisfies the condition. This selection is preferred. Thanks to this selection, the minimum radial value of the profile is achieved. This value is directly defined and is used as a reference for the rotor radius to be used in the system. by creating a direct boundary between geometric structure and mechanical parameters. It enables the establishment of a relationship. 10 The profile geometry allows for the creation of multiple workspaces within the system. It recognizes. As the rotor rotates, the volume of these chambers changes depending on the angular position; this This change also directly enables the transport or compression of the fluid. This volumetric variation is entirely due to the profile geometry and 15 It plays a crucial role in determining system performance. The profile structures used are defined in the document with application number 2026 / 003031. It is based on a closed curve family that satisfies the constant cord condition. The curves are defined in polar coordinates and for opposite angular positions, the following 20 The relationship is expressed using functions that establish the connection: Here, K > 0 represents a constant length and 25 The condition is met. This relationship is between points located mutually on the profile. It defines a specific geometric structure by ensuring that the distance between them remains constant. These types of curves, according to a suitable reference system, take the following general canonical form: It can be expressed in this way: Here, the function exhibits complementary behavior for opposite angular positions. It displays. 11 - R is a geometric parameter that represents the minimum radial distance of the profile, It defines the minimum radial limit of the profile. - The function f(θ) represents the deviation of the profile from this minimum value, and It describes the change in the profile depending on its angular position. This representation allows for the parametric definition of profile geometry and the use of different profiles. This invention makes it possible to systematically obtain their structures. within this scope, for use in mechanical systems from the aforementioned profile family Suitable subclasses are selected and the impact of these profiles on physical systems is assessed. is being examined. 10 Within this structure defined in canonical form, the deviation function f(θ) is as follows: It is defined in a way that will satisfy the structural conditions: 15 And , From these given conditions, the result can be derived, and the expression in question... a 20 that can be used for fast elimination purposes in the production algorithm It is considered an auxiliary control condition. Here, and its parameters are the basic geometric dimensions of the profile. These parameters also determine the profile's fixed cord length. It is directly related. In this context, the fixed cord length is 25. This is expressed as follows: Suitable R and C parameters for a given K value. A profile can be created by selecting, or the K value can be set to 30 from the selected R and C values. This can be achieved. This form allows the profile geometry to be directly integrated into the mechanical system. This makes it possible to associate it with its parameters. 12 The parameter R, defined in canonical form, is the rotor to be used in the mechanical system. This establishes an upper limit for the radius. In this context, the rotor radius Rr is defined as follows: satisfies the condition: If the rotor radius is selected as [specific value], the rotor and stator profiles will be different. Tangential contact occurs between them at least at one angular position. Rotor radius. In this case, the contact between the rotor and stator is made by a moving part located between them. This is achieved through the element. Therefore, the parameter R is rotor 10 It functions as a fundamental limiting value in determining its geometry. The profile, expressed in canonical form, describes the kinematic behavior of the moving element. It directly determines this. In this context, the moving element rotates together with the rotor. a 15 that is simultaneously challenged by the profile geometry while performing the movement. It performs radial displacement motion. Therefore, the movable element... motion profile consisting of a combination of rotational and radial displacement components. It exhibits a forced kinematic structure depending on its geometry. This kinematic structure is the radial variation component of the profile defined in the canonical form, 20. It is guided by the function f(θ). The function f(θ) minimizes the profile. It represents the deviation from its value, within the profile geometry. It constitutes the fundamental component of the defined radial change. In this context: - The value of the function f(θ) is 25 at a given angular position, the minimum value of the profile. It refers to the radial deflection as defined by, - this deviation is directly related to the change in radial distance occurring within the mechanical system. related, - When the rotor radius is chosen as , the function f(θ) is the moving part. It directly expresses the amount of radial displacement of the element, 30 - C, the maximum value of the function f(θ), represents the maximum radial current generated in the system. It determines the range of variation. 13 Therefore, f(θ) represents the volumetric change of the working chambers formed within the system. It functions as one of the fundamental quantities determining the deviation function. f(θ) is a constant that allows for parametric variation of the profile geometry. It can be expressed with a structure that satisfies the cord condition. In this context, f(θ) is the boundary. a core component that directly satisfies the conditions and an additional component that does not disrupt this structure. It can be defined as a combination of functional terms. The basic component is as follows: It can be selected as follows: This basic structure, , and , , conditions It provides. Building upon this basic structure, additional elements are defined in a way that preserves those conditions. The profile geometry can be extended with functional terms and adapted to different applications. Suitable variations can be obtained. In this context, the deviation function is a special function that satisfies the specified conditions. Within the class, it can be expressed as follows: In this expression, each term takes the value zero at θ = 0 and becomes negative. It exhibits a non-existent structure. Furthermore, the function f(θ) defined in this way is... The relevant conditions are met. 25 Controlled modification of the lobe structure and angular distribution of the profile geometry. For this purpose, single-stage reparameterization of the angular variable can be applied. This angular variable within the scope 14 It is redefined as follows and the deviation function It is expressed in this form. Under this transformation, the constant cord condition is preserved because 5 The equality applies. In this way, the number of lobes formed on the profile can be increased, and the number of working rooms can be expanded. It can be regulated in a controlled manner. Thus, the volumetric behavior and flow of the system are controlled. continuity and pulsation characteristics according to different application requirements. arrangeable This invention covers the fluid or gaseous material that lies between the stator profile and the rotor. the usable interior space serving the transfer, the total area surrounded by the stator It is defined as the difference between the area occupied by the rotor and the area occupied by the rotor. In this context, the available space generally This is expressed as follows: The rotor radius is selected as the upper limit value. In this case, the available space is expressed directly in terms of the deviation function as follows: It can be expressed as follows: 25 This statement implies that the usable area is determined not only by the constant radial component R, but also directly. This shows that it is determined by the deviation function. In canonical form 30 , And , Since the conditions are met, the parameter C determines the amplitude of the deviation function. As a fundamental magnitude, it has a direct impact on the usable area. Therefore, the selection of parameters R and C determines the internal geometry of the profile parametrically. 5 It can be adjusted accordingly and, based on this, serves the transfer of fluids or gases. The usable area can be determined in a controlled manner. A closed curve that satisfies the constant cord condition is, in general, including; It is defined by its relationship. However, profiles that meet this condition are initially 15 It may not be directly expressed in canonical form. Therefore, the mechanical aspect of the profile... It needs to be converted to a canonical form so that it can be associated with systems. In this context, the profile, in its general form, For R > 0, 20 It is expressed as follows: The minimum value of the profile. This is determined as the angular position reference where this minimum value occurs. taken Variable transformation is applied. If the minimum value is in more than one angular position. 16 If this is possible, the transformation can be achieved by selecting any of these locations as a reference. The process can be carried out. Under this transformation, the profile, It is brought into canonical form in this way. Here, its function depends on the following structural conditions: provides: , And , where R > 0 and C > 0; K = 2R + C This structure is defined as follows: This structure also exists under the canonical form of the fixed cord condition. that it is protected and can be re-expressed around the minimum value of the profile 15 This shows that, consequently, it provides the fixed cord condition and as described above. Each profile that meets the requirements of the specified general form will be subject to a suitable reference selection. It can be transformed into a canonical form. This transformation alters the geometric structure of the profile. not changing it, it only becomes directly related to the mechanical system. It ensures that it is brought in. 20 In this context, the canonical form is the rotor-stator-moving element system of the profile. It is the fundamental form of representation that defines the geometric and kinematic relationships within it. Furthermore, in this context, the detection algorithm uses a profile converted to a canonical form. The assessment made based on this shows that the curve in question is 25 in terms of the mechanical system. determining suitability and, if suitability is achieved, rotor-stator similar It offers an analytical framework that makes it possible to establish a geometric relationship. The profile geometry, rotor, stator and these elements are defined within the scope of this invention. 30 that will work together with the moving element (valve, vane, piston, etc.) located between them. It is designed in this way. The rotor rotates within the stator profile. during this process, the movable element profile surface located between the rotor and the stator They are in contact. This contact is achieved by selecting appropriate geometric parameters. In this case, an external spring, elastic element, or similar force mechanism is needed. 17 This can be achieved without being noticed. The profile is expressed according to an appropriate reference system. as can be done and in canonical form In cases where the moving element can be represented in this way, the distance between the rotor and the stator is between the moving element. It directly describes the displacement behavior. The moving element, rotation. In addition to its movement, there is a radial displacement movement determined by the profile. It also accomplishes this; the combination of these two components creates a forced kinematic structure. It consists of 10. In particular, the displacement range determined by its function, the working rooms It directly affects the maximum and minimum volumes. Thanks to this structure: - Continuous contact can be ensured between the moving element and the stator profile, 15 - continuity of contact independent of external force elements is sustainable, - and the system behavior is guided by the geometric structure. Furthermore, thanks to the ability to parametrically define the profile geometry, the system has 20 The operating characteristics can be adapted to different application requirements. In this context, the invention relates to the relationship between profile geometry and mechanical motion. a geometrically oriented mechanical study by establishing a direct relationship It presents the principle. The profile family described in this invention has specific geometric and physical characteristics. It is characterized in terms of magnitudes. The profile is in polar coordinates. It is a closed curve defined by the function, and the area it covers is given by the following integral: It is expressed as: 18 The geometric structure of the profile can be parametrically controlled, and this structure can be varied. It can be re-expressed under angular parameterizations. In this context, angular Redefining the variable using positive integer multiples: In this case, the area occupied by the profile remains unchanged. That is to say: This situation results in the invariant area occupied by the profile under angular reparametrization. This indicates that it remains. Accordingly, the mechanical systems in which the profile in question is used The volumetric behavior of the workspaces formed in the systems is similar. This feature can be preserved. This property ensures that the system is similar under different parametric expressions. This allows it to exhibit volumetric characteristics. As a result, the word 15 The subject profile family not only offers a geometric definition, but also controllable and predictable physical behavior in mechanical systems over time It creates a suitable structure for this. Another important feature of the profile defined within the scope of the invention is a suitable mass 20 It is the equilibrium behavior under the distribution. Radial distance of mass distribution along the profile. If chosen inversely proportional to, theoretically the reference center point It can behave in a way that coincides with the center of mass of the system. This The situation is such that the profile is balanced not only geometrically but also dynamically. This feature enables it to offer a structure that reduces vibration, especially in rotary systems. a structural basis that is favorable in terms of behavior, equilibrium conditions and system stability It can offer. The profile family with a fixed cord invariant, as defined within the scope of the invention, various 30 corresponding to its parametric or geometric re-expression It is also preserved under transformations. In this context, the angular structure that preserves the antipodal structure. reparameterization 19 Transformations that satisfy the condition can be applied. Also angular shift, angular multiplication, reflection, radial scaling or Parametric and geometric aspects such as amplitude scaling of the deformation function 5 Transformations can also be applied to the profile. In addition, the reference center where the profile is defined is located on the plane. Changing it does not affect the fixed cord feature. These conversions are part of the profile. The fundamental fixed cord invariant is not altered. Therefore, under these transformations, 10 is obtained. The profiles obtained are equivalent geometric profiles of the profile family defined within the scope of the invention. They are considered to have accomplished this. The profile structure described in this invention is expressed by its ideal mathematical definition. However, considering practical production, assembly and usage conditions, 15 It may include certain deviations and local geometric adaptations. In this context, production minor deviations resulting from tolerances, surface roughness, rounding (Filling), chamfering and similar local geometric modifications, keep the profile constant. The invention covers the following as long as it does not functionally impair the cord's character. It is evaluated. 20 In addition, local studies were conducted to enable the profile to be integrated into the mechanical system. sectioning, material removal or addition, creating connection areas, and Structural arrangements, such as leaving mounting gaps, also determine the basic geometric shape of the profile. It is considered within the scope as long as it does not change its principle. Consequently, the ideal 25 Deviations from the mathematical definition, local geometric interventions, and different applications. equivalent applications as long as the forms do not alter the fundamental principle of the invention. It is considered as such. The profile with a fixed cord feature, as defined in this invention, has a specific 30 It is not limited to mechanical devices, but different mechanical devices that use the same geometric principle. It can be implemented within various structures and configurations. In this context, the profile's stator In addition to systems where it is used as such, the profile is defined on the rotor or Arrangements where the rotor and stator components are shared are also included. The moving part is evaluated. This includes the vane, paddle, piston, piston ring, or similar different components. Implementation in geometric and kinematic structures, single or multiple elements. Variants such as maintaining continuous or intermittent contact through its use are also the same. They are considered inventions as long as they preserve the basic geometric relationship. Additionally, the system may include a pump, compressor, vacuum pump, fluid transfer system, or The application in the form of similar volumetric machines does not limit the scope of the profile. In addition to its planar application, it can also be applied to three-dimensional structures through axial extension. transformation, positioning on different axes, or multi-stage Its use in systems is also evaluated within the framework of the same geometric principle. 10 Consequently, within the scope of the invention, the profile that provides the fixed cord connection is used. and the mechanisms by which this relationship is functionally effective within the mechanical system, as equivalent applications regardless of specific mechanical configuration It is evaluated. 15 In Figure 1; 1: expressed in polar coordinates defined stator profile, 2: rotor, 20 3: rotor radius, which is the minimum radius that satisfies the relationship. 4: the contact point between the rotor and stator profiles, 5: Represents the radial distance between the rotor and stator profiles at angular position θ. f(θ) 6: reference center point, 25 7: (θ+π) represents the radial distance between the rotor and stator profiles at the angular position. f(θ+π) is shown. 8: fixed length in the direction of movement necessitated by the stator geometry. the channel in which the moving element moves freely in the radial direction within the rotor When the magnitudes (3), (5) and (7) shown in the figure are evaluated together, they are constant The cord length is expressed as K = 2R + (f(θ) + f(θ+π)), where f(θ) + Under the condition f(θ+π) = C, the relation K = 2R + C is obtained. 21 Figure 2a shows the circular stator profile used in classic rotary vane systems. This configuration is shown with a stator diameter of Ø2.8 (R = 1.4) and a rotor diameter of Ø2.0 (R = 1.0) It is positioned to ensure rotor-stator operating conditions. For this purpose, the stator center has been eccentrically shifted to the point (-0.4, 0). The flow To ensure continuity, the input and output ports are approximately ±(35°–40°) angularly aligned. It is positioned within this range. This geometry is typical of classic rotary vane pump systems. It is used as a reference structure. In such systems, the ratio between the stator diameter and the rotor diameter is typically 1.2–1.4 It is accepted that it was selected within the range of 10. The available space corresponding to this profile is as follows: is being calculated. Figure 2b shows an example configuration of a stator profile that satisfies the fixed cord condition. 15 This profile shows the stator geometry in polar coordinates. It is defined by the expression. The profile is shown together with a rotor with a diameter of Ø2.0, and 20 The fixed cord length between opposite angular positions θ and (θ+π) is K=2.8. is obtained. The straight line shown in the figure represents a cord of fixed length. is doing. The available space corresponding to this profile is 25. This structure is calculated in terms of static interior volume compared to the classic circular profile. an increase of approximately 8.3% was achieved, and the contact was geometric. This allows for the use of springs or similar external force elements. It has been observed that the need can be reduced. In Figure 3, with a constant cord length of K=2.8, parameters R=0.9 and C=1 are used. the profile obtained and defined by its expression is shown. The available space corresponding to this profile, 22 This value is calculated as shown in Figure 2b. It is approximately 22.5% larger compared to its value. When comparing Figure 2b and Figure 3, the fixed cord length remains the same. However, the usable area can be modified by selecting the R and C parameters. 5 It is clearly visible. Figure 4 shows an example configuration of a stator profile that satisfies the fixed cord condition. This profile shows the stator geometry in polar coordinates. It is defined by the expression. Profile, Ø2.0 10 It is shown together with a rotor of diameter, between the opposing angular positions θ and (θ+π). The fixed cord length is obtained as K=2.8. The straight line shown in the figure, It represents a fixed-length cord. The available options corresponding to this profile are: The area is calculated as follows. When comparing Figure 2b and Figure 4, only the angular parameter θ is replaced with 3θ. With the selection of this, it is observed that the profile transforms into a multi-lobed structure. despite the fixed cord feature being preserved and the usable area remaining unchanged. It is understood that he remained there. In Figure 5, parameters R=1 and C=0.8 are used with a fixed cord length K=2.8. obtained with and The profile defined by the expression is shown. The selected R and C values ​​are as follows: It is the same as in Figure 2b, where the varying element is the structure of the deviation function f(θ). Here, ε is a real parameter chosen within a range, for example ε = 0.1 It has been received. In this profile, the minimum value is maintained at θ=0, while the deviation... The angular distribution of the function is modified, and the angular variation character of the profile is altered. It is differentiated. 23 This example is a binomial special function of the special class of functions with coefficients αm given earlier. It is obtained in its current state. By adding such functional components, a constant is formed. The angular variation characteristics of the profile can be differentiated while maintaining the cord length. And consequently, control can be established over the impulse behavior of the system. In Figure 6a, with its expression given in general form. The defined profile is shown. The fixed cord length is for this profile. Therefore, K = 6 is obtained. This is the minimum value of the profile, and this minimum value is an angular 10. It takes place at this location. Figure 6b shows the profile given in Figure 6a converted to its canonical form. This is shown. In this context, it is re-expressed in the form of an angular variable. profile 15 defined This is obtained through the expression. This transformation involves a profile defined in a general form that satisfies the fixed cord condition, that it can be systematically transformed into a canonical form with a suitable selection of references 20 and thus the profile is directly connected to the rotor-stator-moving element system. This shows that it has become relatable. The invention describes the interaction between the rotor, stator, and the moving elements in between. It aims to ensure that the profile geometry is directly determined by the profile. This 25 in this context, the workspaces formed within the system and the associated volumetric areas It is possible to control the change through the geometric structure of the profile. It is being done. The invention also directly explains to the user the relationship between rotor diameter and usable area. by determining and selecting the profile geometry, the impulse characteristics of the flow and similar characteristics. It offers the possibility to adjust performance specifications. 24 To achieve the purposes stated above, the invention has a fixed cord feature. by selecting the profile structures within the rotor-stator-moving element system It is characterized by its use. Consequently, the invention is based on the profile geometry. It goes beyond being merely a definition of shape, and encompasses the kinematics of a mechanical system. a 5 that directly determines its volumetric behavior and performance characteristics an integrated mechanical structure that allows it to be used as a design element It offers. The scope of protection of the invention is set out in the claims attached hereto and is strictly limited to these. The detailed explanation cannot be limited to the examples given. Because in technique, there are 10 A specialist, without deviating from the main theme of the invention, will do what is described above. It is clear that similar structures can emerge in light of this.

Claims

REQUESTS 1. Rotor, stator, and at least one movable element located between these two elements. It is a rotary displacement mechanical system, the characteristic of which is  At least one of the stator and rotor surfaces must be 5 degrees relative to a single reference center. a closed system defined by its radial distance r(θ) which depends on its angular position having a curved profile and  points located at the angular positions θ and θ+π of the profile in question the linear distance between them is constant r(θ) + r(θ+π) = K, provided that K > 0  the local stator profile of the moving element during the rotational movement of the rotor a radial displacement motion that is forced depending on the radial distance this was achieved and thus the 15 between the moving element and the stator profile by the contact being continuously maintained by the profile geometry It is characterized by being 2. According to Claim 1, it is a rotary displacement mechanical system, and its characteristic is that it is the aforementioned The profile is defined in the canonical form r(θ) = R + f(θ) and f(θ) + f(θ+π) = C, 20 The condition C > 0 must be satisfied.

3. It is a rotary displacement mechanical system according to claim 1, and its characteristic feature is the stator. its profile has a radial distance value equal to or greater than the rotor radius 25 The fact that it is being done.

4. According to claim 1, it is a mechanical system with rotary displacement, and its characteristic feature is the rotor. by determining the upper limit of the radius with the minimum value of the stator profile It is characterized by... 30 26 5. It is a rotary displacement mechanical system according to claim 1, and its characteristic feature is the stator. the profile can be defined not only on the stator but also on the rotor, or the rotor and can be distributed between stator components, and the moving element is the wing, 5 in different geometric and kinematic structures such as vanes, pistons, rings or similar. It is characterized by its feasibility.

6. According to claim 1, it is a rotary displacement mechanical system, and its characteristic feature is the antipodal Thanks to the geometric structure defined by the component, the movable element and the stator profile are compatible. The contact between them requires no external spring, pressure or similar force elements. 10 without being detected, the system is geometrically sustainable throughout its rotational motion. It is characterized by being...

7. Enclosed structure designed for use in a rotary displacement mechanical system. It has a curved profile and its characteristic is 15 Defined according to a single reference center, The radial distance, which depends on the angular position, is expressed as r(θ), and Points located at opposite angular positions θ and θ+π on the profile the linear distance between them is constant r(θ) + r(θ+π) = K 20 It is a profile structure characterized by fulfilling the specified condition.

8. According to claim 7, it is a curve profile whose characteristic is that the profile is relative to a reference center. in canonical form in polar coordinates r(θ) can be expressed as R + f(θ), where R > 0 and C > 0. The function f(θ) is 25 f(0) = 0, f(θ) + f(θ + π) = C and 27 f(θ) ≥ 0, ∀θ satisfying the conditions, and under this structure the profile for opposing angular positions r(θ) + r(θ + π) = K by establishing a constant cord length through its relationship, and 5 the profile in question, together with a rotor and at least one moving element when used, the radial displacement of the moving element is stressed along the profile. by allowing for its modification, the creation of variable-volume workspaces. It is characterized by being convenient. 10 9. According to claim 7, it has a curved profile and its characteristic is that a stator with a specific profile is constant. subjecting to mathematical transformations while maintaining a cord condition In this case, the aforementioned transformations involve angular rearrangement, angular scrolling, angular multiplication, reflection, radial scaling, or 15 of the reference point It must include at least one operation, such as a change, and the profile must retain its fixed cord feature. It is characterized by...

10. According to claim 7, it is a curved profile, characterized by the stator profile being a closed curve. If defined, the mathematical representation of this curve is polar, Cartesian, 20 It must be at least one of the parametric or latent methods.

11. According to claim 7, it is a curve profile whose characteristic is the angular variability of the stator profile. in the form of single-story reparameterization. transformed and consequently the profile in question 25 as redefined, fixed cord under the said transformation by maintaining the condition and changing the number of lobes formed on the profile It is characterized by the ability to adjust the number of study rooms. 28 12. A closed system configured for use in a rotary displacement mechanical system. making a curved profile usable in a rotary mechanical system It is a method and its characteristic is; i. minimum radial value of a closed curve defined in polar coordinates determination, 5 ii. referencing the angular position corresponding to the minimum value and the profile by applying phase shift This involves re-expressing it in the canonical form r(θ) = R + f(θ) and iii. with the preservation of the profile's fixed cord feature under this transformation. 10 by ensuring the profile is compatible with the mechanical system components It is characterized by...

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