Calculation method of windage power loss of spiral bevel gear pair under oil injection lubrication

Abstract

The present invention provides a method for calculating the windage power loss of a spiral bevel gear pair under oil-spray lubrication, which belongs to the field of aero-engine power transmission systems. The method comprises the following steps: constructing a gear tooth surface equation of a spiral bevel gear pair based on a Cartesian coordinate system; establishing a parameter model of a spiral bevel gear pair equipped with an oil-spray lubrication system; calculating the tooth surface windage power loss, large and small end surface windage power loss, front and rear cone surface windage power loss, tooth top circumferential surface windage power loss, tooth groove root windage power loss, and pump flow windage power loss of the spiral bevel gear pair; and adding up the windage power losses to obtain the total windage power loss of the spiral bevel gear pair under oil-spray lubrication. The method of the present invention establishes a dedicated analytical model for each region. The use of regional modeling can be more consistent with the actual flow field and can accurately calculate the windage power loss of the spiral bevel gear pair.

Description

Technical Field

[0001] The invention belongs to the field of aero-engine power transmission systems, and in particular relates to a method for calculating windage power loss of a spiral bevel gear pair under oil injection lubrication. Background Art

[0002] Spiral bevel gears offer advantages such as high load capacity, light weight, smooth transmission, and excellent lubricity, making them irreplaceable in the high-speed transmission system of helicopter main reducers. When spiral bevel gears rotate at high speed and are lubricated by oil spray, the lubricating oil and air mix around the gears, forming an oil-air two-phase flow. The rotation of the gears drives this two-phase flow, generating strong eddies, high-velocity fields, and centrifugal fields. This generates pressure differentials and viscous forces on the gear surfaces, which produce torques opposite to the direction of gear rotation, resulting in windage losses. Furthermore, the high-speed rotation of the gears stirs the surrounding fluid, creating intense turbulence. The kinetic energy of the fluid is dissipated through turbulence, converting it into heat energy, leading to power loss and also contributing to windage losses. Windage loss is a load-independent power loss, which inevitably aggravates the power loss of the gear transmission system. Windage is also the main source of heat generation, which leads to a decrease in lubricating oil viscosity, thereby increasing wear on mechanical and bearing components and shortening service life. The gear windage effect will also deflect the motion trajectory of the lubricating oil jet, making it difficult for the lubricating oil to enter the gear meshing area, resulting in dry friction of the gear and aggravating micro-fractures and fatigue cracks on the gear surface. At the same time, windage can also cause gear vibration, noise, and increase tooth surface wear.

[0003] Based on the above analysis, if the windage power loss of the spiral bevel gear pair can be accurately calculated, it will be helpful to analyze the loss mechanism, improve transmission efficiency and reduce energy loss. Summary of the Invention

[0004] Technical issues to be solved:

[0005] In order to avoid the shortcomings of the existing technology, the present invention provides a method for calculating the windage power loss of a spiral bevel gear pair under oil injection lubrication. The windage loss of the spiral bevel gear pair is subdivided into 6 independent areas (tooth surface, large and small end faces, front and rear conical surfaces, tooth top circular surface, tooth groove root, and pump flow meshing point), and a dedicated analytical model is established for each area. The use of regional modeling can be more in line with the actual flow field and can accurately calculate the windage power loss of the spiral bevel gear pair.

[0006] The technical solution of the present invention is: a method for calculating the windage power loss of a spiral bevel gear pair under oil injection lubrication, the specific steps are as follows:

[0007] Construct the gear tooth surface equation of the spiral bevel gear pair based on the Cartesian coordinate system;

[0008] Determining preset parameters of the spiral bevel gear pair according to the gear tooth surface equation of the spiral bevel gear pair, and then establishing a parameter model of the spiral bevel gear pair equipped with an oil injection lubrication system;

[0009] Based on the gear tooth surface equation of the spiral bevel gear pair and the parameter model of the spiral bevel gear pair equipped with an oil injection lubrication system, the impact depth of the oil-gas two-phase flow on the unit tooth surface of the spiral bevel gear pair is calculated, and then a calculation model for the tooth surface windage power loss of the spiral bevel gear pair is established to calculate the tooth surface windage power loss of the spiral bevel gear pair;

[0010] According to the flow state of the oil-gas two-phase flow on the large and small end faces of the spiral bevel gear pair, a calculation model for the large and small end face windage power loss of the spiral bevel gear pair is established to calculate the large and small end face windage power loss of the spiral bevel gear pair;

[0011] Based on the flow characteristics of the oil-gas two-phase flow on the front and rear conical surfaces of the spiral bevel gear pair, a calculation model for the windage power loss of the front and rear conical surfaces of the spiral bevel gear pair is established to calculate the windage power loss of the front and rear conical surfaces of the spiral bevel gear pair;

[0012] Based on the flow characteristics of the oil-gas two-phase flow on the tooth top circumferential surface of the spiral bevel gear pair, a calculation model for the windage power loss on the tooth top circumferential surface of the spiral bevel gear pair is established to calculate the windage power loss on the tooth top circumferential surface of the spiral bevel gear pair;

[0013] Based on the flow characteristics of the oil-gas two-phase flow at the tooth root of the spiral bevel gear pair, a tooth root windage power loss calculation model of the spiral bevel gear pair is established to calculate the tooth root windage power loss of the spiral bevel gear pair;

[0014] Based on the flow characteristics of the oil-gas two-phase flow at the meshing point of the spiral bevel gear pair, a pump flow windage power loss calculation model of the spiral bevel gear pair is established to calculate the pump flow windage power loss of the spiral bevel gear pair;

[0015] The total windage power loss of the spiral bevel gear pair under oil injection lubrication is obtained by adding the tooth surface windage power loss, large and small end surface windage power loss, front and rear cone surface windage power loss, tooth top circumference surface windage power loss, tooth root windage power loss, and pump flow windage power loss of the spiral bevel gear pair. The expression is as follows:

[0016]

[0017] Where, P w It represents the total windage power loss of the spiral bevel gear pair under oil injection lubrication. P t Indicates the power loss of tooth surface windage resistance, P s Indicates the windage power loss at the large and small end faces.P c Indicates the power loss of front and rear cone wind resistance, P f Indicates the windage power loss on the tooth tip circle. P r It represents the windage power loss at the tooth root. P b Indicates the pump flow windage power loss; i Pick q When is the driving gear, i Pick g : represents the driven gear.

[0018] A further technical solution of the present invention is: the gear tooth surface equation of the spiral bevel gear pair constructed based on the Cartesian coordinate system includes:

[0019] The center of the machining center is taken as the origin of the Cartesian coordinate system;

[0020] Based on the origin of the Cartesian coordinate system, the unit position vector and the unit normal vector of the generating surface are obtained, and multiple coordinate transformations are performed on the unit position vector and the unit normal vector respectively to obtain the gear tooth surface equations of the spiral bevel gear pair, including the gear tooth surface equations of the driving gear and the gear tooth surface equations of the driven gear.

[0021] A further technical solution of the present invention is that the parameter model of the spiral bevel gear pair equipped with an oil injection lubrication system includes a gear pair geometric parameter group and an oil injection lubrication system parameter group;

[0022] The gear pair geometric parameter group includes: driving gear rotation direction, driven gear rotation direction, total number of driving gear teeth, total number of driven gear teeth, gear big end module, gear width, pressure angle, helix angle, gear outer cone distance, driving gear partial cone angle, driven gear partial cone angle, driving gear hub radius, driven gear hub radius, driving gear small end spoke radius, driven gear small end spoke radius, driving gear big end spoke radius, driven gear big end spoke radius, driving gear front cone surface rim thickness, driving gear back cone surface rim thickness, driven gear front cone surface rim thickness, driven gear back cone surface rim thickness;

[0023] The oil injection lubrication system parameter group includes: the oil injection nozzle oil outlet position coordinates ( x 0, y 0, z 0), jet inclination angle, jet azimuth.

[0024] A further technical solution of the present invention is that the impact depth of the oil-gas two-phase flow on the tooth surface of the spiral bevel gear pair includes the impact depth of the tooth surface of the driving gear and the impact depth of the tooth surface of the driven gear;

[0025] The impact depth of the unit driving gear tooth surface The calculation formula is as follows:

[0026]

[0027] Where, is the tooth tip circle radius of the unit driving gear; 、 The coordinates of the point where the lubricating oil droplet collides with the tooth profile of the unit active gear are obtained by differentiating the dynamic equation of the lubricating oil droplet in the jet motion on the tooth surface of the unit spiral bevel gear to obtain the acceleration equation. The acceleration equation is then quadratically integrated based on the initial velocity and initial displacement to obtain the coordinates of the point where the lubricating oil droplet collides with the tooth profile of the unit active gear. 、 ;

[0028] The impact depth of the unit driven gear tooth surface The calculation formula is as follows:

[0029]

[0030] Where, is the tooth tip circle radius of the unit driven gear; 、 The coordinates of the point where the lubricating oil droplet collides with the unit driven gear tooth profile are obtained by differentiating the dynamic equation of the lubricating oil droplet in the jet motion on the tooth surface of the unit spiral bevel gear to obtain the acceleration equation. The acceleration equation is then quadratically integrated based on the initial velocity and initial displacement to obtain the coordinates of the point where the lubricating oil droplet collides with the unit driven gear tooth profile. 、 .

[0031] A further technical solution of the present invention is that in the tooth surface windage power loss calculation model of the spiral bevel gear pair, the tooth surface windage power loss of the active gear is P tq The expression is as follows:

[0032]

[0033] Where, B is the gear width; is the cone angle of the driving gear; is the rotational angular velocity of the driving gear; ξ Correction factor , which indicates the number of active gear teeth directly affected by the lubricating oil jet line at a certain moment Total number of teeth on the driving gear proportion; is the impact depth on the tooth surface of the unit driving gear that is not directly affected by the jet line; is the density of the lubricating oil; ρ is the equivalent density of the oil-gas two-phase fluid in the box around the gear; The axial coordinate is equal to z The helix angle at The impact depth in the local reference coordinate system is H The pressure angle at

[0034] Power loss from windage on the driven gear tooth surface P tg The expression is as follows:

[0035]

[0036] Where, is the cone angle of the driven gear; is the rotational angular velocity of the driven gear; Correction factor , which indicates the number of driven gear teeth directly affected by the lubricating oil jet line at a certain moment Total number of driven gear teeth proportion; It is the impact depth on the tooth surface of the unit driven gear that is not directly affected by the jet line.

[0037] A further technical solution of the present invention is: in the calculation model of windage power loss of large and small end faces of the spiral bevel gear pair, in laminar flow state:

[0038] The expression for windage power loss of the large and small end faces of the driving gear is as follows:

[0039]

[0040] Where, ν is the kinematic viscosity of the fluid; r shq is the spoke radius of the big end of the driving gear; r stq is the spoke radius of the small end of the driving gear; r hgq is the radius of the driving gear hub;

[0041] The power loss expression of windage resistance on the large and small end faces of the driven gear is as follows:

[0042]

[0043] Where, r shg is the spoke radius of the big end of the driven gear; r stg is the spoke radius of the small end of the driven gear; r hgg is the driven gear hub radius;

[0044] In turbulent flow:

[0045] The expression for windage power loss of the large and small end faces of the driving gear is as follows:

[0046]

[0047] Where, r cq The transition radius of the fluid state from laminar flow to turbulent flow on the end face of the driving gear;

[0048] The power loss expression of windage resistance on the large and small end faces of the driven gear is as follows:

[0049]

[0050] Where, r cg The transition radius of the fluid state from laminar flow to turbulent flow on the end face of the driven gear.

[0051] A further technical solution of the present invention is that the calculation model expression of the windage power loss of the front and rear cone surfaces of the spiral bevel gear pair is as follows:

[0052] The expression for wind resistance power loss of the front and rear cone surfaces of the driving gear is as follows:

[0053]

[0054] Where, μ is the fluid dynamic viscosity; l hq The rim thickness of the back cone surface of the driving gear; l tq The rim thickness of the front cone surface of the driving gear; δ B is the back cone angle of the spiral bevel gear;

[0055] The expression for windage power loss on the front and rear cone surfaces of the driven gear is as follows:

[0056]

[0057] Where, l hg The rim thickness of the back cone surface of the driven gear; l tg It is the rim thickness of the front cone surface of the driven gear.

[0058] A further technical solution of the present invention is that the calculation model expression of the windage power loss on the tooth tip circumference of the spiral bevel gear pair is as follows:

[0059] The expression of wind resistance power loss on the tooth top circle of the driving gear is as follows:

[0060]

[0061] Where, r taq is the radius of the tooth tip circle at the small end face of the driving gear;

[0062] The expression for the windage power loss on the tooth tip circle of the driven gear is as follows:

[0063]

[0064] Where, r tag is the radius of the tooth top circle at the small end face of the driven gear.

[0065] A further technical solution of the present invention is that the calculation model expression of the windage power loss of the tooth root of the spiral bevel gear pair is as follows:

[0066] The power loss expression of the tooth root windage of the active gear is as follows:

[0067]

[0068] Where, is the coefficient of the biharmonic equation of the driving gear; is the radius of the tooth tip circle of the driving gear; is the root circle radius of the driving gear;

[0069] The power loss expression of the windage resistance at the tooth root of the driven gear is as follows:

[0070]

[0071] Where, is the coefficient of the biharmonic equation of the driven gear; is the addendum radius of the driven gear; is the root circle radius of the driven gear.

[0072] A further technical solution of the present invention is that the pump flow windage power loss calculation model expression of the spiral bevel gear pair is as follows:

[0073]

[0074] Where, For the discrete positions of the gear pair meshing on the active gear control body The extrusion power loss, represents the discrete position number of the gear pair, and ,in, represents the total number of discrete positions within a base segment; Indicates in discrete position of the driving gear j A fluid control body, which is the cavity formed during the meshing process of the gear pair, and is composed of the involute surface and tooth root profile of the two meshing teeth; , For the The total number of active gear control bodies at discrete positions depends on the overlap of the gear pairs; For the discrete positions of the gear pair meshing with the driven gear control body Extrusion power loss; Indicates in discrete position of the driven gear k A fluid control body, , For the The total number of driven gear control bodies at discrete positions depends on the degree of overlap of the gear pair.

[0075] Beneficial effects

[0076] The beneficial effects of the present invention are as follows: in the calculation process of the windage power loss of the high-speed spiral bevel gear pair under oil injection lubrication, the present invention takes into account the influence of the interaction between the lubricating oil and the flow field around the gear on the windage power loss of the spiral bevel gear, and takes into account the influence of the meshing effect and pump flow effect of the gear pair on the windage power loss, so that the total windage power loss of the spiral bevel gear pair finally calculated is closer to the actual value and the calculation accuracy is higher (such as Figure 8 The specific effect analysis is as follows:

[0077] 1. This invention replaces traditional CFD full-flow field simulation by constructing a regional physical analytical model (tooth surface, large and small end faces, front and rear conical surfaces, tooth tip circumference, tooth root, and pump flow meshing area). This improves computational speed while maintaining accuracy. For example, a traditional CFD full-flow field simulation using two nodes running at full cores would take approximately 50 hours to complete a single calculation; using the analytical model proposed in this invention, a single calculation can be completed in approximately three minutes.

[0078] 2. A special model is proposed based on the complex geometric characteristics of spiral bevel gear pairs. Among them, the tooth surface impact depth model combines jet dynamics to quantify the distribution of lubricating oil and accurately quantify the influence of jet lubrication on wind resistance, solving the problem that traditional models ignore the distribution of oil film; the large and small end face wind resistance power loss calculation model simplifies the gear into a rotating disk, determines the fluid motion state on the rotating disk according to the gear speed and gear geometric dimensions, and distinguishes between laminar flow and turbulent flow to reduce the calculation error; the front and rear cone wind resistance power loss calculation model divides the front and rear cones of the arc bevel gear pair into several small cones. When the division width is small enough, the micro-element cone is regarded as a unit cylinder to solve the problem of non-uniform distribution of the flow field caused by the conical surface curvature; the tooth top circle surface wind resistance power loss calculation model uses the tooth top circle radius as the characteristic dimension, establishes an equivalent rotating cylinder model, and simplifies the complex conical surface flow into an equivalent two-dimensional problem; the tooth root creep flow model is based on the annular cavity theory to solve the problem of small-scale flow field prediction; the pump flow loss model simulates the leakage in the meshing area through discrete control bodies, which is more in line with the transient effects under high-speed working conditions.

[0079] 3. This invention reveals the influence mechanism of jet parameters on windage loss by introducing the oil-gas two-phase flow equivalent density and dynamic impact depth, and supports nozzle layout optimization.

[0080] 4. The present invention can predict the temperature rise hotspot area of ​​the gear system by accurately calculating the windage power loss, thereby avoiding problems such as lubricant failure and tooth surface bonding caused by windage overheating. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 Schematic diagram of a flow chart of a method for calculating windage power loss of an aviation high-speed spiral bevel gear pair under oil injection lubrication in an embodiment of the present invention;

[0082] Figure 2 A schematic diagram of a spiral bevel gear pair model equipped with an oil injection lubrication system according to an embodiment of the present invention;

[0083] Figure 3 Schematic diagram of the principle of calculating the windage power loss on the tooth surface of a spiral bevel gear pair in an embodiment of the present invention;

[0084] Figure 4 Schematic diagram of the principle of calculating windage power loss of large and small end faces of a spiral bevel gear pair in an embodiment of the present invention;

[0085] Figure 5 Schematic diagram of the principle of calculating the windage power loss on the front and rear cone surfaces of a spiral bevel gear pair in an embodiment of the present invention;

[0086] Figure 6 Schematic diagram of the principle of calculating windage power loss at the tooth root of a spiral bevel gear pair according to an embodiment of the present invention;

[0087] Figure 7 Schematic diagram of the principle of calculating the windage power loss of the spiral bevel gear pair pump in an embodiment of the present invention;

[0088] Figure 8 This is a comparison chart between the calculated and experimental windage power loss values ​​of the spiral bevel gear pair in an embodiment of the present invention. DETAILED DESCRIPTION

[0089] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0090] In aviation high-speed transmission systems, spiral bevel gear pairs are widely used in main reducers due to their high load-bearing capacity and low noise. When the gears rotate at high speeds under oil-spray lubrication, the interaction between the gears and the surrounding oil-air mixture produces significant windage power loss, severely reducing transmission efficiency. The resulting temperature rise also causes the lubricant's viscosity to fail, exacerbating the risk of tooth surface bonding, micropitting, and other failures. Current windage loss prediction technologies have the following drawbacks:

[0091] 1. CFD simulation methods (such as CN114547789B): They rely on three-dimensional fluid domain meshing, and single-condition calculations take hours, which cannot meet the rapid design iteration requirements of aviation gears. Furthermore, the resolution of microscale flow fields such as tooth grooves and meshing areas is insufficient, with errors exceeding 15%.

[0092] 2. Empirical formula method (such as CN116108652A): Based on the simplified model of spur gear / face gear, it ignores the spatial surface geometry of spiral bevel gear (such as spherical involute and back cone angle), resulting in distortion of cone surface flow field prediction;

[0093] 3. Windage-oil churning coexistence model (e.g., CN116187081B): This model is only applicable to oil-immersed lubrication scenarios and does not consider the dynamic impact effect of the oil jet. The error can be as high as 40% in aviation oil-spray lubrication environments.

[0094] Based on the existing defects, the present invention proposes a regional physical analytical model for the windage loss of aviation spiral bevel gear pairs under oil injection lubrication for the first time, solving the problems of low CFD simulation efficiency and inapplicability of coexistence models.

[0095] The present invention provides a method for calculating windage power loss of a spiral bevel gear pair under oil injection lubrication, and the specific steps are as follows:

[0096] Construct the gear tooth surface equation of the spiral bevel gear pair based on the Cartesian coordinate system;

[0097] Determining preset parameters of the spiral bevel gear pair according to the gear tooth surface equation of the spiral bevel gear pair, and then establishing a parameter model of the spiral bevel gear pair equipped with an oil injection lubrication system;

[0098] Based on the gear tooth surface equation of the spiral bevel gear pair and the parameter model of the spiral bevel gear pair equipped with an oil injection lubrication system, the impact depth of the oil-gas two-phase flow on the unit tooth surface of the spiral bevel gear pair is calculated, and then a calculation model for the tooth surface windage power loss of the spiral bevel gear pair is established to calculate the tooth surface windage power loss of the spiral bevel gear pair;

[0099] According to the flow state of the oil-gas two-phase flow on the large and small end faces of the spiral bevel gear pair, a calculation model for the large and small end face windage power loss of the spiral bevel gear pair is established to calculate the large and small end face windage power loss of the spiral bevel gear pair;

[0100] Based on the flow characteristics of the oil-gas two-phase flow on the front and rear conical surfaces of the spiral bevel gear pair, a calculation model for the windage power loss of the front and rear conical surfaces of the spiral bevel gear pair is established to calculate the windage power loss of the front and rear conical surfaces of the spiral bevel gear pair;

[0101] Based on the flow characteristics of the oil-gas two-phase flow on the tooth top circumferential surface of the spiral bevel gear pair, a calculation model for the windage power loss on the tooth top circumferential surface of the spiral bevel gear pair is established to calculate the windage power loss on the tooth top circumferential surface of the spiral bevel gear pair;

[0102] Based on the flow characteristics of the oil-gas two-phase flow at the tooth root of the spiral bevel gear pair, a tooth root windage power loss calculation model of the spiral bevel gear pair is established to calculate the tooth root windage power loss of the spiral bevel gear pair;

[0103] Based on the flow characteristics of the oil-gas two-phase flow at the meshing point of the spiral bevel gear pair, a pump flow windage power loss calculation model of the spiral bevel gear pair is established to calculate the pump flow windage power loss of the spiral bevel gear pair;

[0104] The total windage power loss of the spiral bevel gear pair under oil injection lubrication is obtained by adding the tooth surface windage power loss, large and small end surface windage power loss, front and rear cone surface windage power loss, tooth top circumference surface windage power loss, tooth root windage power loss, and pump flow windage power loss of the spiral bevel gear pair. The expression is as follows:

[0105]

[0106] Where, P w It represents the total windage power loss of the spiral bevel gear pair under oil injection lubrication. P t Indicates the power loss of tooth surface windage resistance, P s Indicates the windage power loss at the large and small end faces. P c Indicates the power loss of front and rear cone wind resistance, P fIndicates the windage power loss on the tooth tip circle. P r It represents the windage power loss at the tooth root. P b Indicates the pump flow windage power loss, i Pick q When is the driving gear, i Pick g : represents the driven gear.

[0107] In one embodiment, constructing the gear tooth surface equation of the spiral bevel gear pair based on the Cartesian coordinate system includes:

[0108] The center of the machining center is taken as the origin of the Cartesian coordinate system;

[0109] Based on the origin of the Cartesian coordinate system, the unit position vector and the unit normal vector of the generating surface are obtained, and multiple coordinate transformations are performed on the unit position vector and the unit normal vector respectively to obtain the gear tooth surface equations of the spiral bevel gear pair, including the gear tooth surface equations of the driving gear and the gear tooth surface equations of the driven gear.

[0110] In one embodiment, in the gear tooth surface equation of the spiral bevel gear pair, the tooth surface equation of the driving gear is expressed as follows:

[0111]

[0112] Wherein, each coordinate transformation matrix is ​​as follows:

[0113] , , , , , , , ,

[0114] ,

[0115] Where, is the current rotation angle of the driven gear being processed, , is the radius of the driving gear cutter head; The coordinate system of the driving gear and the current rotation angle of the cradle; is the root cone angle of the driving gear machine; For active gear beds; It is the vertical wheel position of the driving gear; It is the axial position of the driving gear; It is the angular tool position of the driving gear; It is the radial tool position of the driving gear; and Represents the surface coordinates of the driving gear cone surface; is the tooth profile angle of the active gear cutter; is the unit position vector of the driving gear generating surface; is the unit normal vector of the active gear generating surface; is the unit position vector of the driving gear tooth surface, is the unit normal vector of the tooth surface of the driving gear;

[0116] The tooth surface equation of the driven gear is as follows:

[0117]

[0118] Wherein, each coordinate transformation matrix is ​​as follows:

[0119] , , , , , , , ,

[0120] ,

[0121] Where, is the current rotation angle of the driven gear being processed, , is the radius of the driven gear cutter head, is the coordinate system of the driven gear and the current rotation angle of the cradle; is the root cone angle of the driven gear machine; For the driven gear bed; It is the angular tool position of the driven gear; is the radial tool position of the driven gear; and is the surface coordinate of the cone surface of the driven gear; is the tooth profile angle of the driven gear cutter; is the unit position vector of the driven gear generating surface, is the unit normal vector of the driven gear generating surface; is the unit position vector of the driven gear tooth surface, is the unit normal vector of the driven gear tooth surface;

[0122] In one embodiment, the spiral bevel gear pair is started, an oil injection lubrication system is installed in the spiral bevel gear pair, preset parameters of the spiral bevel gear pair are determined according to the gear tooth surface equation of the spiral bevel gear pair, and a parameter model of the spiral bevel gear pair installed with the oil injection lubrication system is established, including the following steps:

[0123] Obtaining parameters of the oil injection lubrication system of the spiral bevel gear pair and establishing an oil injection lubrication system model;

[0124] The geometric parameters of the spiral bevel gear pair and the oil injection lubrication system model are obtained, and a parameter model of the spiral bevel gear pair equipped with the oil injection lubrication system is established.

[0125] The parameter model of the spiral bevel gear pair equipped with an oil injection lubrication system includes a gear pair geometric parameter group and an oil injection lubrication system parameter group;

[0126] The gear pair geometric parameter group includes: driving gear rotation direction, driven gear rotation direction, total number of driving gear teeth, total number of driven gear teeth, gear big end module, gear width, pressure angle, helix angle, gear outer cone distance, driving gear partial cone angle, driven gear partial cone angle, driving gear hub radius, driven gear hub radius, driving gear small end spoke radius, driven gear small end spoke radius, driving gear big end spoke radius, driven gear big end spoke radius, driving gear front cone surface rim thickness, driving gear back cone surface rim thickness, driven gear front cone surface rim thickness, driven gear back cone surface rim thickness;

[0127] The oil injection lubrication system parameter group includes: the oil injection nozzle oil outlet position coordinates ( x 0, y 0, z 0), jet inclination angle, jet azimuth.

[0128] In one embodiment, based on the parameter model of the spiral bevel gear pair equipped with the oil injection lubrication system, the impact depth of the oil-gas two-phase flow on the unit tooth surface of the spiral bevel gear pair is calculated, and then a calculation model for the tooth surface windage power loss of the spiral bevel gear pair is established. The steps for calculating the tooth surface windage power loss of the spiral bevel gear pair are as follows:

[0129] According to the spiral bevel gear pair equipped with an oil injection lubrication system, the dynamic equation of the lubricating oil droplet in the jet motion on the spiral bevel gear tooth surface is established, and the expression is as follows:

[0130]

[0131] Where, C D is the fluid resistance coefficient, which is determined according to the fluid rotation Reynolds number; d o is the diameter of the lubricating oil droplet; v rz 、 v tz Lubricating oil droplet edge The velocity component in the direction, Lubricating oil droplet edge Acceleration component in the direction;v g is the gear tangential speed; 、 Lubricating oil droplet edge Force value in the direction; ρ is the equivalent density of the oil-gas two-phase fluid in the box around the gear, and its calculation formula is as follows:

[0132]

[0133] Where, is the volume fraction of lubricating oil; is the density of the lubricating oil; is the density of air;

[0134] The dynamic equation of the lubricating oil droplet in the jet motion on the tooth surface of the unit spiral bevel gear is derived to obtain the acceleration equation. Then, the acceleration equation is quadratically integrated based on the initial velocity and initial displacement to obtain the coordinates of the collision point between the lubricating oil droplet and the unit active gear tooth profile. 、 , the coordinates of the collision point between the lubricating oil droplet and the unit driven gear tooth profile 、 ;

[0135] The calculation of the impact depth of the unit tooth surface of the spiral bevel gear pair includes the impact depth of the unit driving gear tooth surface and the impact depth of the unit driven gear tooth surface;

[0136] The impact depth of the unit driving gear tooth surface The calculation formula is as follows:

[0137]

[0138] Where, is the addendum circle radius of the unit driving gear;

[0139] The impact depth of the unit driven gear tooth surface The calculation formula is as follows:

[0140]

[0141] Where, is the tooth tip circle radius of the unit driven gear;

[0142] Construct a calculation model for the windage power loss on the tooth surface of a spiral bevel gear pair and calculate the windage power loss on the tooth surface of the active gear. P tq The expression is as follows:

[0143]

[0144] Where,B is the gear width; is the cone angle of the driving gear; is the rotational angular velocity of the driving gear; ξ Correction factor , which indicates the number of active gear teeth directly affected by the lubricating oil jet line at a certain moment Total number of teeth on the driving gear proportion; is the impact depth on the tooth surface of the unit driving gear that is not directly affected by the jet line; is the density of the lubricating oil; ρ is the equivalent density of the oil-gas two-phase fluid in the box around the gear; The axial coordinate is equal to z The helix angle at The impact depth in the local reference coordinate system is H The pressure angle at

[0145] Calculate the windage power loss on the driven gear tooth surface P tg The expression is as follows:

[0146]

[0147] Where, δ g is the cone angle of the driven gear; ω g is the rotational angular velocity of the driven gear; Correction factor , which indicates the number of driven gear teeth directly affected by the lubricating oil jet line at a certain moment Total number of driven gear teeth proportion; It is the impact depth on the tooth surface of the unit driven gear that is not directly affected by the jet line.

[0148] In one embodiment, in the calculation model of windage power loss of the large and small end faces of the spiral bevel gear pair, in laminar flow state:

[0149] The expression for windage power loss of the large and small end faces of the driving gear is as follows:

[0150]

[0151] Where, ν is the kinematic viscosity of the fluid; r shq is the spoke radius of the big end of the driving gear, r stq is the spoke radius of the small end of the driving gear, r hgq is the radius of the driving gear hub;

[0152] The power loss expression of windage resistance on the large and small end faces of the driven gear is as follows:

[0153]

[0154] Where, r shg is the spoke radius of the big end of the driven gear, r stg is the spoke radius of the small end of the driven gear, r hgg is the driven gear hub radius;

[0155] In turbulent flow:

[0156] The expression for windage power loss of the large and small end faces of the driving gear is as follows:

[0157]

[0158] Where, r cq The transition radius of the fluid state from laminar flow to turbulent flow on the end face of the driving gear;

[0159] The power loss expression of windage resistance on the large and small end faces of the driven gear is as follows:

[0160]

[0161] Where, r cg The transition radius of the fluid state from laminar flow to turbulent flow on the end face of the driven gear.

[0162] In one embodiment, the calculation model expression of the windage power loss of the front and rear cone surfaces of the spiral bevel gear pair is as follows:

[0163] The expression for wind resistance power loss of the front and rear cone surfaces of the driving gear is as follows:

[0164]

[0165] Where, μ is the fluid dynamic viscosity; l hq is the rim thickness of the back cone surface of the driving gear, l tq is the rim thickness of the front cone surface of the driving gear, δ B is the back cone angle of the spiral bevel gear;

[0166] The expression for windage power loss on the front and rear cone surfaces of the driven gear is as follows:

[0167]

[0168] Where, l hg is the rim thickness of the back cone surface of the driven gear, l tg It is the rim thickness of the front cone surface of the driven gear.

[0169] In one embodiment, the calculation model expression of the windage power loss on the tooth tip circumference of the spiral bevel gear pair is as follows:

[0170] The expression of wind resistance power loss on the tooth top circle of the driving gear is as follows:

[0171]

[0172] Where, r taq is the radius of the tooth tip circle at the small end face of the driving gear;

[0173] The expression for the windage power loss on the tooth tip circle of the driven gear is as follows:

[0174]

[0175] Where, r tag is the radius of the tooth top circle at the small end face of the driven gear.

[0176] In one embodiment, the calculation model expression of the windage power loss of the tooth root of the spiral bevel gear pair is as follows:

[0177] The power loss expression of the tooth root windage of the active gear is as follows:

[0178]

[0179] Where, is the coefficient of the biharmonic equation of the driving gear, is the radius of the tooth tip circle of the driving gear, is the root circle radius of the driving gear;

[0180] The power loss expression of the windage resistance at the tooth root of the driven gear is as follows:

[0181]

[0182] Where, is the coefficient of the biharmonic equation of the driven gear, is the addendum circle radius of the driven gear, is the root circle radius of the driven gear;

[0183] In one embodiment, the pump flow windage power loss calculation model expression of the spiral bevel gear pair is as follows:

[0184]

[0185] Where, For the discrete positions of the gear pair meshing on the active gear control body The extrusion power loss, represents the discrete position number of the gear pair, and ,in, represents the total number of discrete positions within a base segment; Indicates in discrete position of the driving gear j A fluid control body, which is the cavity formed during the meshing process of the gear pair, and is composed of the involute surface and tooth root profile of the two meshing teeth; , For the The total number of active gear control bodies at discrete positions depends on the overlap of the gear pairs; For the discrete positions of the gear pair meshing with the driven gear control body Extrusion power loss; Indicates in discrete position of the driven gear k A fluid control body, , For the The total number of driven gear control bodies at discrete positions depends on the degree of overlap of the gear pair.

[0186] The above technical solution is further described below with reference to the accompanying drawings:

[0187] In one embodiment, referring to Figure 1 As shown in FIG, the calculation method of the windage power loss of aviation high-speed spiral bevel gear pair under oil injection lubrication specifically includes the following steps:

[0188] Step 101: Construct the gear tooth surface equation of the spiral bevel gear pair based on the Cartesian coordinate system.

[0189] Specifically, the machining parameters of the driven gear are determined, and then the local synthesis method is used to determine the machining parameters of the driving gear, thereby establishing the tooth surface equations of the driving and driven gears. Taking the left-handed driving gear of a spiral bevel gear pair as an example, with the center of the machining machine as the origin of the Cartesian coordinate system, the tool parameters and gear cutting parameters include: the surface coordinates of the cone surface, the tool tooth profile angle, the cutter head radius, the bed position, the vertical wheel position, the axial wheel position, the gear cutter head radius, the current rotation angle of the production coordinate system and the cradle, and the current rotation angle of the gear being machined.

[0190] The unit position vector of the generating surface and the unit normal vector After a series of coordinate transformations, the equation of the tool cutting surface is expressed in the gear coordinate system, and then the tooth surface equations of the driving gear and the driven gear of the spiral bevel gear pair can be obtained.

[0191] Step 102: Based on the preset parameters of the spiral bevel gear pair, a parameter model of the spiral bevel gear pair equipped with an oil injection lubrication system is established.

[0192] Specifically, refer to Figure 2 As shown in the figure, the parameter model of the spiral bevel gear pair equipped with an oil injection lubrication system includes: the rotation direction of the driving gear is left-handed, the rotation direction of the driven gear is right-handed, and the total number of teeth of the driving gear is z q The total number of teeth on the driven gear is 27. z g 81, gear big end module m 3.85mm, gear width b 38mm, pressure angle α p The helix angle is 20° β The outer cone distance of the gear is 35°. R em 164.31mm, the driving gear cone angle δ q The cone angle of the driven gear is 16.91° δ g 52.86, the driving gear hub radius r hgq 20mm, driven gear hub radius r hgg 35mm, the spoke radius at the small end of the driving gear r stq 27mm, the spoke radius of the driven gear small end r stg 106.6mm, the spoke radius of the driving gear big end r shq 35mm, the spoke radius of the driven gear big end r shg The rim thickness of the front cone of the driving gear is 148.4mm. l tq The thickness of the rim of the back cone of the driving gear is 3.6mm. l hq 10mm, the rim thickness of the front cone of the driven gear is l tg 6mm, the rim thickness of the back cone of the driven gear is l hg is 20mm, the nozzle outlet position coordinates ( x 0,y 0, z 0) is (120, 90, 50) mm, the jet inclination angle η is 100°, the jet azimuth φ is 90°.

[0193] Step 103: Combining the gear tooth surface equation and the parameter model of the spiral bevel gear pair equipped with an oil injection lubrication system, the impact depth of the oil-gas two-phase flow on the unit tooth surface of the spiral bevel gear pair is calculated, and then a tooth surface windage power loss calculation model of the spiral bevel gear pair is established to calculate the tooth surface windage power loss of the spiral bevel gear pair.

[0194] Specifically, the initial state parameters of the fluid in the box around the gear are: pressure is 1.0×10 5 Pa, the temperature is 298K, the specific heat capacity at constant volume is 717 J / (kg·K), the specific heat capacity at constant pressure is 1005 J / (kg·K), and the air density is 1.205 kg / m 3 , the dynamic viscosity is 1.81×10 -5 Pa·s, the density of lubricating oil is 998kg / m 3 , the dynamic viscosity is 6.04×10 -2 Pa·s, the initial volume fraction of the lubricating oil is 0, and the speed of the driving gear changes from 0 to about 27000 r / min.

[0195] Reference Figure 3 As shown in the figure, a droplet on the oil jet line is taken as the research object. According to the dynamic equation of the lubricating oil droplet when it is in the jet motion on the tooth surface of the spiral bevel gear and the above initial conditions, the impact depth of the oil-gas two-phase flow on the tooth surface is calculated, and the tooth surface windage power loss of the spiral bevel gear pair is obtained. P tq and P tg .

[0196] Step 104: Based on the flow state of the oil-gas two-phase flow on the large and small end faces of the spiral bevel gear pair, a calculation model for the windage power loss of the large and small end faces of the spiral bevel gear pair is established to calculate the windage power loss of the large and small end faces of the spiral bevel gear pair.

[0197] Specifically, refer to Figure 4 As shown in the figure, when calculating the windage power loss of the large and small end faces of the spiral bevel gear pair, the gear is simplified into a rotating disk. The fluid motion state on the rotating disk is determined according to the gear speed and gear geometry. Then, the continuity equation of the disk flow and the NS equation group are established based on the rotating disk flow theory, and then the windage power loss of the large and small end faces of the spiral bevel gear pair in the laminar flow state is calculated. and , wind resistance power loss of large and small end faces of spiral bevel gear pair in turbulent flow state and .

[0198] Step 105: Based on the flow characteristics of the oil-gas two-phase flow on the front and rear conical surfaces of the spiral bevel gear pair, a calculation model for the windage power loss of the front and rear conical surfaces of the spiral bevel gear pair is established to calculate the windage power loss of the front and rear conical surfaces of the spiral bevel gear pair.

[0199] Specifically, refer to Figure 5 As shown in the figure, the front and rear cones of the spiral bevel gear pair are divided into many small cones. When the width of the division is small enough, the microelement cone is regarded as a unit cylinder. The fluid continuity equation and NS equation are established according to the circular flow theory, and then the wind resistance power loss of the front and rear cone surfaces of the spiral bevel gear pair is calculated. p cq and p cg .

[0200] Step 106: Based on the flow characteristics of the oil-gas two-phase flow on the tooth tip circumferential surface of the spiral bevel gear pair, a calculation model for the windage power loss on the tooth tip circumferential surface of the spiral bevel gear pair is established to calculate the windage power loss on the tooth tip circumferential surface of the spiral bevel gear pair.

[0201] Specifically, since the tooth top circle surface of the spiral bevel gear is a cone surface, the calculation principle of the wind resistance power loss of the tooth top circle surface is the same as the wind resistance power loss of the front and rear cone surfaces. The wind resistance power loss of the tooth top circle surface of the spiral bevel gear pair is calculated as follows: p fq and p fg .

[0202] Step 107: Based on the flow characteristics of the oil-gas two-phase flow at the tooth root of the spiral bevel gear pair, a tooth root windage power loss calculation model of the spiral bevel gear pair is established to calculate the tooth root windage power loss of the spiral bevel gear pair.

[0203] Specifically, refer to Figure 6 As shown in the figure, the fluid motion at the tooth root of the spiral bevel gear pair is modeled as the flow of fluid through the annular cavity, and the windage power loss at the tooth root of the spiral bevel gear pair is calculated based on the biharmonic equation of fluid motion. p rq and p rg .

[0204] Step 108: Based on the flow characteristics of the oil-gas two-phase flow at the meshing point of the spiral bevel gear pair, a pump flow windage power loss calculation model of the spiral bevel gear pair is established to calculate the pump flow windage power loss of the spiral bevel gear pair.

[0205] Specifically, refer to Figure 7 As shown in the figure, the spiral bevel gear pair is equivalent to a spur gear pair. During the meshing process of the gear pair, multiple cavities (fluid control bodies) are formed. First, the end area and side clearance area of ​​a fluid control body are calculated. Then, the dynamic equation of the fluid in the control body is established based on compressible flow to calculate the pump flow windage power loss of the spiral bevel gear pair. P b .

[0206] Step 109: Add the calculated tooth surface windage power loss, large and small end surface windage power loss, front and rear cone surface windage power loss, tooth top circumferential surface windage power loss, tooth groove root windage power loss, and pump flow windage power loss of the spiral bevel gear pair to obtain the total windage power loss of the spiral bevel gear pair under oil injection lubrication.

[0207] Specifically, the total windage power loss of the spiral bevel gear pair under oil injection lubrication is the sum of the windage power loss on each surface of the driving gear and the driven gear and the pump flow loss when the gear pair is meshing. Therefore, the calculation formula for the total windage power loss of the spiral bevel gear pair under oil injection lubrication is as follows:

[0208]

[0209] Where, P w It represents the total windage power loss of the spiral bevel gear pair under oil injection lubrication. P t Indicates the power loss of tooth surface windage resistance, P s Indicates the windage power loss at the large and small end faces. P c Indicates the power loss of front and rear cone wind resistance, P f Indicates the windage power loss on the tooth tip circle. P r It represents the windage power loss at the tooth root. P b It represents the power loss of gear pair pump flow resistance; i Pick q When is the driving gear, i Pick g : represents the driven gear.

[0210] Step 110: Verify the accuracy by comparing the calculated total windage power loss of the spiral bevel gear pair under oil injection lubrication with the experimental value. The comparison results are as follows: Figure 8 As shown in the figure, the calculated value of total windage power loss is close to the experimental value, and the relative error is basically between 4.29% and 8.37%.

[0211] The low error stems from the refined modeling of fluid motion and geometric characteristics in this embodiment, as well as consideration of the meshing extrusion power loss of the gear pair. Consequently, the calculated value is relatively reasonable. Verification results demonstrate that the proposed method for calculating windage power loss in spiral bevel gear pairs can reasonably predict windage power loss under oil-spray lubrication conditions, enabling a relatively accurate calculation of the gear system's transmission efficiency.

[0212] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A method for calculating windage power loss of spiral bevel gear pairs under oil injection lubrication, characterized in that The specific steps are as follows: Construct the gear tooth surface equation of the spiral bevel gear pair based on the Cartesian coordinate system; Determining preset parameters of the spiral bevel gear pair according to the gear tooth surface equation of the spiral bevel gear pair, and then establishing a parameter model of the spiral bevel gear pair equipped with an oil injection lubrication system; Based on the gear tooth surface equation of the spiral bevel gear pair and the parameter model of the spiral bevel gear pair equipped with an oil injection lubrication system, the impact depth of the oil-gas two-phase flow on the unit tooth surface of the spiral bevel gear pair is calculated, and then a calculation model for the tooth surface windage power loss of the spiral bevel gear pair is established to calculate the tooth surface windage power loss of the spiral bevel gear pair; According to the flow state of the oil-gas two-phase flow on the large and small end faces of the spiral bevel gear pair, a calculation model for the large and small end face windage power loss of the spiral bevel gear pair is established to calculate the large and small end face windage power loss of the spiral bevel gear pair; Based on the flow characteristics of the oil-gas two-phase flow on the front and rear conical surfaces of the spiral bevel gear pair, a calculation model for the windage power loss of the front and rear conical surfaces of the spiral bevel gear pair is established to calculate the windage power loss of the front and rear conical surfaces of the spiral bevel gear pair; Based on the flow characteristics of the oil-gas two-phase flow on the tooth top circumferential surface of the spiral bevel gear pair, a calculation model for the windage power loss on the tooth top circumferential surface of the spiral bevel gear pair is established to calculate the windage power loss on the tooth top circumferential surface of the spiral bevel gear pair; Based on the flow characteristics of the oil-gas two-phase flow at the tooth root of the spiral bevel gear pair, a tooth root windage power loss calculation model of the spiral bevel gear pair is established to calculate the tooth root windage power loss of the spiral bevel gear pair; Based on the flow characteristics of the oil-gas two-phase flow at the meshing point of the spiral bevel gear pair, a pump flow windage power loss calculation model of the spiral bevel gear pair is established to calculate the pump flow windage power loss of the spiral bevel gear pair; The total windage power loss of the spiral bevel gear pair under oil injection lubrication is obtained by adding the tooth surface windage power loss, large and small end surface windage power loss, front and rear cone surface windage power loss, tooth top circumference surface windage power loss, tooth root windage power loss, and pump flow windage power loss of the spiral bevel gear pair. The expression is as follows: Where, P w It represents the total windage power loss of the spiral bevel gear pair under oil injection lubrication. P t Indicates the power loss of tooth surface windage resistance, P s Indicates the power loss of wind resistance at large and small ends. P c Indicates the power loss of front and rear cone wind resistance, P f Indicates the windage power loss on the tooth tip circle. P r It represents the windage power loss at the tooth root. P b Indicates the pump flow windage power loss; i Pick q When is the driving gear, i Pick g : represents the driven gear.

2. The method for calculating windage power loss of a spiral bevel gear pair under oil injection lubrication according to claim 1, characterized in that: The gear tooth surface equations of the spiral bevel gear pair constructed based on the Cartesian coordinate system include: The center of the machining center is taken as the origin of the Cartesian coordinate system; Based on the origin of the Cartesian coordinate system, the unit position vector and the unit normal vector of the generating surface are obtained, and multiple coordinate transformations are performed on the unit position vector and the unit normal vector respectively to obtain the gear tooth surface equations of the spiral bevel gear pair, including the gear tooth surface equations of the driving gear and the gear tooth surface equations of the driven gear.

3. The method for calculating windage power loss of a spiral bevel gear pair under oil injection lubrication according to claim 2, characterized in that: The parameter model of the spiral bevel gear pair equipped with an oil injection lubrication system includes a gear pair geometric parameter group and an oil injection lubrication system parameter group; The gear pair geometric parameter group includes: driving gear rotation direction, driven gear rotation direction, total number of driving gear teeth, total number of driven gear teeth, gear big end module, gear width, pressure angle, helix angle, gear outer cone distance, driving gear partial cone angle, driven gear partial cone angle, driving gear hub radius, driven gear hub radius, driving gear small end spoke radius, driven gear small end spoke radius, driving gear big end spoke radius, driven gear big end spoke radius, driving gear front cone surface rim thickness, driving gear back cone surface rim thickness, driven gear front cone surface rim thickness, driven gear back cone surface rim thickness; The oil injection lubrication system parameter group includes: the oil injection nozzle oil outlet position coordinates ( x 0, y 0, z 0), jet inclination angle, jet azimuth.

4. The method for calculating windage power loss of a spiral bevel gear pair under oil injection lubrication according to claim 3, characterized in that: The impact depth of the oil-gas two-phase flow on the tooth surface of the unit spiral bevel gear pair includes the impact depth of the unit driving gear tooth surface and the impact depth of the unit driven gear tooth surface; The impact depth of the unit driving gear tooth surface The calculation formula is as follows: Where, is the addendum circle radius of the unit driving gear; 、 The coordinates of the point where the lubricating oil droplet collides with the tooth profile of the unit active gear are obtained by differentiating the dynamic equation of the lubricating oil droplet in the jet motion on the tooth surface of the unit spiral bevel gear to obtain the acceleration equation. The acceleration equation is then quadratically integrated based on the initial velocity and initial displacement to obtain the coordinates of the point where the lubricating oil droplet collides with the tooth profile of the unit active gear. 、 ; The impact depth of the unit driven gear tooth surface The calculation formula is as follows: Where, is the tooth tip circle radius of the unit driven gear; 、 The coordinates of the point where the lubricating oil droplet collides with the unit driven gear tooth profile are obtained by differentiating the dynamic equation of the lubricating oil droplet in the jet motion on the tooth surface of the unit spiral bevel gear to obtain the acceleration equation. The acceleration equation is then quadratically integrated based on the initial velocity and initial displacement to obtain the coordinates of the point where the lubricating oil droplet collides with the unit driven gear tooth profile. 、 .

5. The method for calculating windage power loss of a spiral bevel gear pair under oil injection lubrication according to claim 4, characterized in that: In the calculation model of the tooth surface wind resistance power loss of the spiral bevel gear pair, the tooth surface wind resistance power loss of the active gear is The expression is as follows: Where, B is the gear width; is the cone angle of the driving gear; is the rotational angular velocity of the driving gear; ξ Correction factor , which indicates the number of active gear teeth directly affected by the lubricating oil jet line at a certain moment Total number of teeth on the driving gear proportion; is the impact depth on the tooth surface of the unit driving gear that is not directly affected by the jet line; is the density of the lubricating oil; ρ is the equivalent density of the oil-gas two-phase fluid in the box around the gear; The axial coordinate is equal to z The helix angle at The impact depth in the local reference coordinate system is H The pressure angle at Power loss from windage on the driven gear tooth surface P tg The expression is as follows: Where, is the cone angle of the driven gear; is the rotational angular velocity of the driven gear; Correction factor , which indicates the number of driven gear teeth directly affected by the lubricating oil jet line at a certain moment Total number of driven gear teeth proportion; It is the impact depth on the tooth surface of the unit driven gear that is not directly affected by the jet line.

6. The method for calculating windage power loss of a spiral bevel gear pair under oil injection lubrication according to claim 5, characterized in that: In the calculation model of windage power loss of the large and small end faces of the spiral bevel gear pair, in laminar flow state: The expression for windage power loss of the large and small end faces of the driving gear is as follows: Where, ν is the kinematic viscosity of the fluid; r shq is the spoke radius of the big end of the driving gear; r stq is the spoke radius of the small end of the driving gear; r hgq is the radius of the driving gear hub; The power loss expression of windage resistance on the large and small end faces of the driven gear is as follows: Where, r shg is the spoke radius of the big end of the driven gear; r stg is the spoke radius of the small end of the driven gear; r hgg is the driven gear hub radius; In turbulent flow: The expression for windage power loss of the large and small end faces of the driving gear is as follows: Where, r cq The transition radius of the fluid state from laminar flow to turbulent flow on the end face of the driving gear; The power loss expression of windage resistance on the large and small end faces of the driven gear is as follows: Where, r cg The transition radius of the fluid state from laminar flow to turbulent flow on the end face of the driven gear.

7. The method for calculating windage power loss of a spiral bevel gear pair under oil injection lubrication according to claim 6, characterized in that: The calculation model expression of the windage power loss of the front and rear cone surfaces of the spiral bevel gear pair is as follows: The expression for wind resistance power loss of the front and rear cone surfaces of the driving gear is as follows: Where, μ is the fluid dynamic viscosity; l hq The rim thickness of the back cone surface of the driving gear; l tq The rim thickness of the front cone surface of the driving gear; δ B is the back cone angle of the spiral bevel gear; The expression for windage power loss on the front and rear cone surfaces of the driven gear is as follows: Where, l hg The rim thickness of the back cone surface of the driven gear; l tg It is the rim thickness of the front cone surface of the driven gear.

8. The method for calculating windage power loss of a spiral bevel gear pair under oil injection lubrication according to claim 7, characterized in that: The calculation model expression of the windage power loss on the tooth tip circle of the spiral bevel gear pair is as follows: The expression of wind resistance power loss on the tooth top circle of the driving gear is as follows: Where, r taq is the radius of the tooth tip circle at the small end face of the driving gear; The expression for the windage power loss on the tooth tip circle of the driven gear is as follows: Where, r tag is the radius of the tooth top circle at the small end face of the driven gear.

9. The method for calculating windage power loss of a spiral bevel gear pair under oil injection lubrication according to claim 8, characterized in that: The calculation model expression of the windage power loss of the tooth root of the spiral bevel gear pair is as follows: The power loss expression of the tooth root windage of the active gear is as follows: Where, is the coefficient of the biharmonic equation of the driving gear; is the radius of the tooth tip circle of the driving gear; is the root circle radius of the driving gear; The power loss expression of the windage resistance at the tooth root of the driven gear is as follows: Where, is the coefficient of the biharmonic equation of the driven gear; is the addendum radius of the driven gear; is the root circle radius of the driven gear.

10. The method for calculating windage power loss of a spiral bevel gear pair under oil injection lubrication according to claim 9, characterized in that: The calculation model expression of the pump flow windage power loss of the spiral bevel gear pair is as follows: Where, For the discrete positions of the gear pair meshing on the active gear control body The extrusion power loss, represents the discrete position number of the gear pair, and ,in, represents the total number of discrete positions within a base segment; Indicates in discrete position of the driving gear j A fluid control body, which is the cavity formed during the meshing process of the gear pair, and is composed of the involute surface and tooth root profile of the two meshing teeth; , For the The total number of active gear control bodies at discrete positions depends on the overlap of the gear pairs; For the discrete positions of the gear pair meshing with the driven gear control body Extrusion power loss; Indicates in discrete position of the driven gear k A fluid control body, , For the The total number of driven gear control bodies at discrete positions depends on the degree of overlap of the gear pair.

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