Intelligent calculation method for transmission characteristics of high-speed helical gear of ship

Abstract

This invention discloses an intelligent calculation method for the transmission characteristics of high-speed helical gears in ships. The specific steps are as follows: (1) Construct a single tooth model of a helical gear and establish the tooth surface of the cantilever beam of the gear slice in a plane coordinate system; (2) Construct a cantilever beam tooth surface model of a cracked gear; (3) Establish a tooth surface meshing model; (4) Investigate the influence characteristics of the crack initiation position, crack length and the angle between the crack and the center line on the meshing stiffness of the helical gear. The beneficial effect is that by analyzing each point on the tooth surface, the crack initiation point and the crack tip position can be accurately located, which fits the crack model of high-speed helical gears in actual engineering, and provides an important theoretical basis for the dynamic characteristic analysis and fault diagnosis of high-speed gear transmission systems in ships.

Description

Technical Field

[0001] This invention relates to the field of gear transmission technology, and in particular to an intelligent calculation method for the characteristics of high-speed helical gear transmission in ships. Background Technology

[0002] High-speed helical gear transmissions in naval vessels are crucial for power transmission, speed regulation, and torque output in ship propulsion systems. Helical gears are characterized by high overlap ratio, smooth meshing, strong load-bearing capacity, and low noise, and are widely used in high-speed gearboxes and main propulsion systems. However, due to prolonged operation under high speed, heavy load, and continuous conditions, gears are prone to developing root cracks under alternating loads, impact loads, and complex vibrations. Root cracks alter the time-varying meshing stiffness and the internal excitation characteristics of the system, thus affecting the vibration response of the transmission system and, in severe cases, leading to decreased transmission performance or even failure. Traditional methods for calculating meshing stiffness suffer from problems such as simplified tooth profile models, insufficient description of crack effects, and difficulty in accurately determining crack locations, making it difficult to reflect the changes in meshing stiffness under crack faults. Therefore, establishing a time-varying meshing stiffness calculation model for crack faults in high-speed helical gears in naval vessels is of great significance for the dynamic characteristic analysis and fault diagnosis of transmission systems.

[0003] To address the aforementioned issues, this invention proposes an intelligent calculation method for the characteristics of high-speed helical gear transmissions in ships. This method comprehensively considers the actual tooth profile geometry, crack initiation location, and crack fault characteristics of the high-speed helical gears in ships. Combining the potential energy method, it establishes analytical calculation models for the time-varying meshing stiffness of a single tooth of the helical gear under healthy and crack fault conditions, providing a theoretical basis for the dynamic characteristic analysis and fault diagnosis of high-speed gear transmission systems in ships. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies and fill related technological gaps, this invention provides an intelligent calculation method for the transmission characteristics of high-speed helical gears in ships. This method is based on the geometric design principles, processing methods, and meshing mechanisms of high-speed helical gears in ships. Considering the actual tooth profile, a planar coordinate system is established, and the equation of the cantilever beam tooth surface curve is derived. Simultaneously, considering the crack initiation point, crack tip position, and the altered cantilever beam model under the influence of cracks, a crack fault model is established, laying a theoretical foundation for the accurate analysis of the meshing transmission process of high-speed helical gears in ships. Based on this, key points on the tooth surface are analyzed, and the potential energy method is used to establish analytical models of the time-varying meshing stiffness of helical gears under healthy and crack fault states, respectively. The traditional slicing method is improved by directly assigning values ​​to the meshing points within the meshing surface, increasing the computational freedom and efficiency of the model. Furthermore, the influence of different crack lengths on meshing stiffness is explored, accurately and effectively studying the time-varying meshing stiffness variation law of high-speed helical gears in healthy and cracked states. This method improves upon the traditional method for calculating the stiffness of cracked helical gears, enhancing both calculation accuracy and efficiency. It provides a theoretical basis for the dynamic characteristic analysis, fault diagnosis, and safe operation assessment of ship gear transmission systems, and has significant academic and engineering application value.

[0005] The technical solution adopted by this method to solve its technical problem is as follows: A smart calculation method for the characteristics of high-speed helical gear transmission in ships, characterized by including the following steps:

[0006] Step (1): Construct a single tooth model of the helical gear, and establish the tooth surface of the cantilever beam slice of the gear in a plane coordinate system. The tooth profile equation is divided into the tooth root transition curve and the involute curve, and the calculation formula is as follows:

[0007] ;

[0008] in, , Let x and y be the coordinates of any point on the involute tooth profile. , Let x and y be the coordinates of any point on the tooth root transition curve. The radius of the base circle, The starting point of the involute tooth profile on the base circle The angle between the line connecting the center of the circle and the centerline of the gear. This represents the pressure angle corresponding to the current tooth profile point. The radius of the pitch circle, For the transition curve parameter angle, , The radius of the transition curve. The distance from the center of the fillet at the tip of the blade to the centerline is calculated as follows:

[0009] ;

[0010] The bending stiffness under healthy operating conditions is solved based on the tooth surface model. shear stiffness axial compressive stiffness Hertzian contact stiffness and matrix potential energy stiffness The expression is as follows:

[0011] ;

[0012] in, , The x and y coordinates are at the meshing point. This represents the pressure angle at the engagement point. This is the pressure angle corresponding to the intersection of the tooth root transition curve and the involute. For cross-sectional area, Let the moment of inertia of the cross section be... The values ​​represent the tooth width of a gear slice. The subscripts 1 and 2 indicate the transition curve regions between the involute tooth profile and the tooth root, respectively. Shear modulus For the elastic modulus, use subscripts. and The formula for distinguishing between pinions and gears is as follows:

[0013] ;

[0014] ;

[0015] in, Indicates the tooth width of a helical gear. Indicates the number of gear slices. Indicates the gear rotation angle. Indicates Poisson's ratio;

[0016] The stiffness of a single tooth of a slice gear is obtained by connecting the stiffnesses in parallel. The calculation formula is as follows:

[0017] ;

[0018] Subscript , Indicates the driving wheel and the driven wheel;

[0019] Step (2): Construct a model of the tooth surface of a cracked gear cantilever beam;

[0020] Crack initiation location , The calculation formula is as follows:

[0021] ;

[0022] in, , The coordinates of the center of the transition curve are... This is the distance from the crack initiation point to the origin of the coordinate system.

[0023] When the crack endpoint does not exceed the gear centerline, the crack endpoint location is... , for:

[0024] ;

[0025] When the crack endpoint extends beyond the gear centerline, the crack endpoint location is... , for:

[0026] ;

[0027] in, The length of the crack when it does not extend beyond the centerline of the gear. The angle between the crack propagation path and the centerline of the gear. This indicates the maximum length of the crack as it extends to the centerline of the gear. This indicates the length of the crack that propagates in the opposite direction along the centerline.

[0028] Crack limit line With the corrected cantilever bearing line The calculation formula is as follows:

[0029] ,

[0030] ;

[0031] in, , Indicates the intersection point of the transition curve and the tooth root circle. The x and y coordinates, , Indicates the intersection of the tooth tip and the cantilever beam tooth profile. The x and y coordinates, This represents the x-coordinate when the integration point lies within the corrected cantilever beam's load-bearing line. This represents the different integral intervals of the tooth profile, the tooth root transition curve, and the bearing line.

[0032] For bending stiffness, shear stiffness, and Hertzian contact stiffness, the expressions considering the variation of the load line of the cantilever beam are as follows:

[0033] ;

[0034] The corrected formulas for calculating the effective tooth thickness, cross-sectional area, and moment of inertia are as follows:

[0035] ;

[0036] The crack causes the central axis to shift, changing the lever arm of the radial component of the meshing force, and the shifted central axis... The formulas for calculating the lever arm in different integration intervals are as follows:

[0037] ;

[0038] in, , The point where the line of action of the meshing force intersects the centerline of the gear. , This is the midpoint of the offset bearing line.

[0039] For the matrix potential energy stiffness under crack conditions, such as Figure 4 As shown, after offset equal to line segment Length, equal to line segment Length, after offset The calculation formula is as follows:

[0040] ;

[0041] The stiffnesses of the single-tooth slice under crack conditions are obtained by connecting the various stiffnesses in parallel. The calculation formula is as follows:

[0042] ;

[0043] Step (3): Establish the tooth surface meshing model. When the ordinate of the meshing point is the same, the cantilever beam tooth profile is the same, and the stiffness at the meshing point is equal. The expression for the meshing line at the initial position is as follows:

[0044] ;

[0045] in, Indicates the helix angle of the gear base circle;

[0046] As the gear rotates, the equation of the line of engagement, which changes over time, is expressed as follows:

[0047] ;

[0048] in, For a single-tooth meshing cycle, the slice position is used instead of the horizontal axis position. ,get Time of the first The expression for the ordinate of the meshing point of the gear on the meshing surface is as follows:

[0049] ;

[0050] For gear slices The expression for the ordinate of the meshing point on the meshing surface at any given moment is as follows:

[0051] ;

[0052] when Stiffness at the meshing point Equal to gear slices Time stiffness Based on this, the stiffness of all meshing points on the meshing surface is obtained, and the helical gear in The single-tooth meshing stiffness at a given moment is the sum of the stiffnesses of all meshing points on the meshing line, expressed as follows:

[0053] ;

[0054] Step (4): Investigate the influence of crack initiation location, crack length, and the angle between the crack and the centerline on the meshing stiffness of the helical gear; select the distance from the crack initiation point to the center of the tooth surface. Crack length Angle between the crack and the center line of the tooth surface As influencing parameters, the variation state of helical gear meshing stiffness under different parameters is solved.

[0055] Compared with existing technologies, the beneficial effects of this invention are as follows: Based on consideration of the machining shape, an accurate cantilever beam tooth surface is established. Furthermore, by measuring the distance between the crack initiation point and the gear center, the position of the crack initiation point on the tooth root transition curve is accurately located. The tooth surface is divided into three parts by the crack tip: the cantilever beam bearing line, the tooth root transition curve, and the involute tooth profile. Considering the parabolic crack constraint line, an accurate time-varying meshing stiffness analytical calculation model is established, and the stiffness calculation is improved to increase computational efficiency. Through this model, the influence of different crack lengths and the angle between the crack and the centerline on meshing stiffness is explored in depth. This invention not only improves the accuracy of crack helical gear stiffness calculation, but also makes the model more closely aligned with industrial realities, providing a reference for structural optimization design and fault detection of helical gear transmissions. Attached Figure Description

[0056] Figure 1 This is a flowchart of an intelligent calculation method for the characteristics of high-speed helical gear transmission in ships.

[0057] Figure 2 It is a single-tooth healthy cantilever beam model;

[0058] Figure 3 It is a cantilever beam model with crack failure;

[0059] Figure 4 These are the gear base parameters under crack fault conditions;

[0060] Figure 5 It is a plan view of the meshing surface;

[0061] Figure 6 This is a graph showing the time-varying meshing stiffness of a gear pair as a function of crack length. Detailed Implementation

[0062] Embodiments of the present invention will be described with reference to the accompanying drawings, which will be further described below. Figure 1 — Figure 6 The specific embodiments of the present invention will be described in detail below.

[0063] Figure 1 This is a flowchart of an intelligent calculation method for the characteristics of high-speed helical gear transmission in ships, including the following steps:

[0064] Step (1): Construct a single tooth model of the helical gear, and establish the cantilever beam tooth surface of the gear slice in a planar coordinate system, such as... Figure 2 As shown, the tooth profile equation is divided into the root transition curve and the involute curve, and the calculation formula is as follows:

[0065] ;

[0066] in, , Let x and y be the coordinates of any point on the involute tooth profile. , Let x and y be the coordinates of any point on the tooth root transition curve. The radius of the base circle, The starting point of the involute tooth profile on the base circle The angle between the line connecting the center of the circle and the centerline of the gear. This represents the pressure angle corresponding to the current tooth profile point. The radius of the pitch circle, For the transition curve parameter angle, , The radius of the transition curve. The distance from the center of the fillet at the tip of the blade to the centerline is calculated as follows:

[0067] ;

[0068] The bending stiffness under healthy operating conditions is solved based on the tooth surface model. shear stiffness axial compressive stiffness Hertzian contact stiffness and matrix potential energy stiffness The expression is as follows:

[0069] ;

[0070] in, , The x and y coordinates are at the meshing point. This represents the pressure angle at the engagement point. This is the pressure angle corresponding to the intersection of the tooth root transition curve and the involute. For cross-sectional area, Let the moment of inertia of the cross section be... The values ​​represent the tooth width of a gear slice. The subscripts 1 and 2 indicate the transition curve regions between the involute tooth profile and the tooth root, respectively. Shear modulus For the elastic modulus, use subscripts. and The formula for distinguishing between pinions and gears is as follows:

[0071] ;

[0072] ;

[0073] in, Indicates the tooth width of a helical gear. Indicates the number of gear slices. Indicates the gear rotation angle. Indicates Poisson's ratio;

[0074] The stiffness of a single tooth of a slice gear is obtained by connecting the stiffnesses in parallel. The calculation formula is as follows:

[0075] ;

[0076] Subscript , Indicates the driving wheel and the driven wheel;

[0077] Step (2): Construct a cantilever beam tooth surface model of the cracked gear, such as Figure 3 As shown;

[0078] Crack initiation location , The calculation formula is as follows:

[0079] ;

[0080] in, , The coordinates of the center of the transition curve are... This is the distance from the crack initiation point to the origin of the coordinate system.

[0081] When the crack endpoint does not exceed the gear centerline, the crack endpoint location is... , for:

[0082] ;

[0083] When the crack endpoint extends beyond the gear centerline, the crack endpoint location is... , for:

[0084] ;

[0085] in, The length of the crack when it does not extend beyond the centerline of the gear. The angle between the crack propagation path and the centerline of the gear. This indicates the maximum length of the crack as it extends to the centerline of the gear. This indicates the length of the crack that propagates in the opposite direction along the centerline.

[0086] Crack limit line With the corrected cantilever bearing line The calculation formula is as follows:

[0087] ,

[0088] ;

[0089] in, , Indicates the intersection point of the transition curve and the tooth root circle. The x and y coordinates, , Indicates the intersection of the tooth tip and the cantilever beam tooth profile. The x and y coordinates, This represents the x-coordinate when the integration point lies within the corrected cantilever beam's load-bearing line. This represents the different integral intervals of the tooth profile, the tooth root transition curve, and the bearing line.

[0090] For bending stiffness, shear stiffness, and Hertzian contact stiffness, the expressions considering the variation of the load line of the cantilever beam are as follows:

[0091] ;

[0092] The corrected formulas for calculating the effective tooth thickness, cross-sectional area, and moment of inertia are as follows:

[0093] ;

[0094] The crack causes the central axis to shift, changing the lever arm of the radial component of the meshing force, and the shifted central axis... The formulas for calculating the lever arm in different integration intervals are as follows:

[0095] ;

[0096] in, , The point where the line of action of the meshing force intersects the centerline of the gear. , This is the midpoint of the offset bearing line.

[0097] For the matrix potential energy stiffness under crack conditions, such as Figure 4 As shown, after offset equal to line segment Length, equal to line segment Length, after offset The calculation formula is as follows:

[0098] ;

[0099] The stiffnesses of the single-tooth slice under crack conditions are obtained by connecting the various stiffnesses in parallel. The calculation formula is as follows:

[0100] ;

[0101] Step (3): As Figure 5 As shown, a tooth surface meshing model is established. When the ordinate of the meshing point is the same, the cantilever beam tooth profile is the same, and the stiffness at the meshing point is equal. The expression for the meshing line at the initial position is as follows:

[0102] ;

[0103] in, Indicates the helix angle of the gear base circle;

[0104] As the gear rotates, the equation of the line of engagement, which changes over time, is expressed as follows:

[0105] ;

[0106] in, For a single-tooth meshing cycle, the slice position is used instead of the horizontal axis position. ,get Time of the first The expression for the ordinate of the meshing point of the gear on the meshing surface is as follows:

[0107] ;

[0108] For gear slices The expression for the ordinate of the meshing point on the meshing surface at any given moment is as follows:

[0109] ;

[0110] when Stiffness at the meshing point Equal to gear slices Time stiffness Based on this, the stiffness of all meshing points on the meshing surface is obtained, and the helical gear in The single-tooth meshing stiffness at a given moment is the sum of the stiffnesses of all meshing points on the meshing line, expressed as follows:

[0111] ;

[0112] Step (4): Investigate the influence of crack initiation location, crack length, and the angle between the crack and the centerline on the meshing stiffness of the helical gear; select the distance from the crack initiation point to the center of the tooth surface. Crack length Angle between the crack and the center line of the tooth surface As influencing parameters, the variation state of helical gear meshing stiffness under different parameters is solved.

[0113] In the example, the distance from the crack initiation point to the center of the tooth surface. The overlap ratio is 1.4 cm. Using the above method, the overlap ratio of the helical gear is between 2 and 3, at which point the gear pair has three-tooth and two-tooth alternating meshing. The comprehensive meshing stiffness of the helical gear is defined as the sum of the stiffness of all gears involved in the meshing process. For a cracked helical gear, the comprehensive stiffness expression is as follows:

[0114] ;

[0115] The time-varying meshing stiffness of the gear pair under healthy and fault conditions as a function of crack length was calculated, and the results are as follows: Figure 6 As shown.

[0116] Figure 6 This indicates that the decrease in meshing stiffness increases with the increase in crack length. During the complete meshing process, the decrease in meshing stiffness increases as the meshing point moves from the root to the tip of the driving gear, and the decrease in meshing stiffness is greater in the double-tooth meshing region than in the triple-tooth meshing region.

[0117] The above description is merely a preferred embodiment of the invention and does not constitute any limitation on the invention. Any modifications, alterations, or equivalent changes made to the above embodiments based on the essence of the invention shall still fall within the protection scope of the invention.

Claims

1. A method for intelligently calculating the characteristics of high-speed helical gear transmission in ships, characterized in that, Includes the following steps: Step (1): Construct a single tooth model of the helical gear, and establish the tooth surface of the cantilever beam slice of the gear in a plane coordinate system. The tooth profile equation is divided into the tooth root transition curve and the involute curve, and the calculation formula is as follows: ； in, , Let x and y be the coordinates of any point on the involute tooth profile. , Let x and y be the coordinates of any point on the tooth root transition curve. The radius of the base circle, The starting point of the involute tooth profile on the base circle The angle between the line connecting the center of the circle and the centerline of the gear. This represents the pressure angle corresponding to the current tooth profile point. The radius of the pitch circle, For the transition curve parameter angle, , The radius of the transition curve. This is the distance from the center of the fillet at the tip of the blade to the centerline. The bending stiffness under healthy operating conditions is solved based on the tooth surface model. shear stiffness axial compressive stiffness Hertzian contact stiffness and matrix potential energy stiffness ; The stiffness of a single tooth of a slice gear is obtained by connecting the stiffnesses in parallel. The calculation formula is as follows: ； Among them, subscript , Indicates the driving wheel and the driven wheel; Step (2): Construct a model of the tooth surface of a cracked gear cantilever beam; Crack initiation location , The calculation formula is as follows: ； in, , The coordinates of the center of the transition curve are... This is the distance from the crack initiation point to the origin of the coordinate system. When the crack endpoint does not exceed the gear centerline, the crack endpoint location is... , for: ； When the crack endpoint extends beyond the gear centerline, the crack endpoint location is... , for: ； in, The length of the crack when it does not extend beyond the centerline of the gear. The angle between the crack propagation path and the centerline of the gear. This indicates the maximum length of the crack as it extends to the centerline of the gear. Indicates the length of the crack propagating in the opposite direction along the centerline; Crack limit line With the corrected cantilever bearing line The calculation formula is as follows: ， ； in, , Indicates the intersection point of the transition curve and the tooth root circle. The x and y coordinates, , Indicates the intersection of the tooth tip and the cantilever beam tooth profile. The x and y coordinates, This represents the x-coordinate when the integration point lies within the corrected cantilever beam's load-bearing line. This represents the different integral intervals of the tooth profile, the tooth root transition curve, and the bearing line. For bending stiffness, shear stiffness, and Hertzian contact stiffness, the expressions considering the variation of the load line of the cantilever beam are as follows: ； The corrected formulas for calculating the effective tooth thickness, cross-sectional area, and moment of inertia are as follows: ； The crack causes the central axis to shift, changing the lever arm of the radial component of the meshing force, and the shifted central axis... The formulas for calculating the lever arm in different integration intervals are as follows: ； in, , The point where the line of action of the meshing force intersects the centerline of the gear. , The midpoint of the offset bearing line; For the matrix potential energy stiffness under crack conditions, as shown in Figure 4, the offset... equal to line segment Length, equal to line segment Length, after offset The calculation formula is as follows: ； The stiffnesses of the single-tooth slice under crack conditions are obtained by connecting the various stiffnesses in parallel. The calculation formula is as follows: ； Step (3): Establish the tooth surface meshing model. When the ordinate of the meshing point is the same, the cantilever beam tooth profile is the same, and the stiffness at the meshing point is equal. The expression for the meshing line at the initial position is as follows: ； As the gear rotates, the equation of the line of engagement, which changes over time, is expressed as follows: ； in, For a single-tooth meshing cycle, the slice position is used instead of the horizontal axis position. ,get Time of the first The expression for the ordinate of the meshing point of the gear on the meshing surface is as follows: ； For gear slices The expression for the ordinate of the meshing point on the meshing surface at any given moment is as follows: ； when Stiffness at the meshing point Equal to gear slices Time stiffness Based on this, the stiffness of all meshing points on the meshing surface is obtained, and the helical gear in The single-tooth meshing stiffness at a given moment is the sum of the stiffnesses of all meshing points on the meshing line, expressed as follows: ； Step (4): Investigate the influence of crack initiation location, crack length, and the angle between the crack and the centerline on the meshing stiffness of the helical gear; select the distance from the crack initiation point to the center of the tooth surface. Crack length Angle between the crack and the center line of the tooth surface As influencing parameters, the variation state of helical gear meshing stiffness under different parameters is solved.

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