Method for calculating wind resistance power loss under oil injection lubrication of spiral bevel gear pair

Abstract

The invention discloses a method for calculating wind resistance power loss under oil injection lubrication of a spiral bevel gear pair, and belongs to the field of aero-engine power transmission systems. The method comprises the following steps: constructing a gear tooth surface equation of the spiral bevel gear pair based on a Cartesian coordinate system; establishing a spiral bevel gear pair parameter model provided with an oil injection lubrication system; calculating tooth surface wind resistance power loss, large and small end surface wind resistance power loss, front and rear conical surface wind resistance power loss, tooth crest circumferential surface wind resistance power loss, tooth groove and tooth root wind resistance power loss and pump flow wind resistance power loss of the spiral bevel gear pair; and all the wind resistance power losses are added to obtain the total wind resistance power loss of the spiral bevel gear pair under oil injection lubrication. According to the method, a special analytical model is established for each region, regional modeling can be more suitable for an actual flow field, and the wind resistance power loss of the spiral bevel gear pair can be accurately calculated.

Description

Technical Field

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

[0002] Spiral bevel gears have the advantages of high load-carrying capacity, light weight, smooth transmission, and good lubricity, and play an irreplaceable role in the high-speed transmission system of helicopter main reducers. When spiral bevel gears rotate at high speed with oil injection lubrication, lubricating oil and air mix around the gears to form an oil-gas two-phase flow. The rotation of the gears drives the two-phase flow to generate strong vortices, high-speed fields, and centrifugal force fields. As a result, pressure difference forces and viscous forces are generated on the surfaces of the gears, and these forces will generate a torque opposite to the rotation direction of the gears, forming windage losses. In addition, when the gears rotate at high speed, they agitate the surrounding fluid to form intense turbulence, and the kinetic energy of the fluid is dissipated through turbulence and converted into heat energy, resulting in power losses, which also constitute windage losses. Windage loss is a load-independent power loss, which inevitably exacerbates the power loss of the gear transmission system. Windage is also the main source of heat generation, leading to a decrease in the viscosity of the lubricating oil, further increasing the wear of mechanical and bearing components, and shortening the service life. The windage effect of the gears will also deflect the movement 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 gears, which further exacerbates micro fractures and fatigue cracks on the gear surfaces. At the same time, windage will also cause gear vibration, noise, increase tooth surface wear, etc.

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

[0004] Technical Problem to be Solved In order to avoid the deficiencies of the prior art, the present invention provides a calculation method for windage power loss under oil injection lubrication of spiral bevel gear pairs. The windage loss of spiral bevel gear pairs is divided into 6 independent regions (tooth surface, large and small end faces, front and rear conical surfaces, tooth tip circumferential surface, tooth groove and tooth root, pump flow meshing position), and a dedicated analytical model is established for each region. Using regional modeling can be more in line with the actual flow field and can accurately calculate the windage power loss of spiral bevel gear pairs.

[0005] The technical solution of the present invention is: a calculation method for windage power loss under oil injection lubrication of spiral bevel gear pairs, and the specific steps are as follows: Construct the gear tooth surface equation of the spiral bevel gear pair based on the Cartesian coordinate system; Determine the preset parameters of the spiral bevel gear pair according to the gear tooth surface equation of the spiral bevel gear pair, and then establish 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, calculate the impact depth of the oil-gas two-phase flow on the tooth surface of the unit spiral bevel gear pair, and then establish a calculation model for the wind resistance power loss of the tooth surface of the spiral bevel gear pair to calculate the wind resistance power loss of the tooth surface 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, establish a calculation model for the wind resistance power loss of the large and small end faces of the spiral bevel gear pair to calculate the wind resistance power loss of the large and small end faces of the spiral bevel gear pair; According to the flow characteristics of the oil-gas two-phase flow on the front and rear conical surfaces of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the front and rear conical surfaces of the spiral bevel gear pair to calculate the wind resistance power loss of the front and rear conical surfaces of the spiral bevel gear pair; According to the flow characteristics of the oil-gas two-phase flow on the tooth top circumferential surface of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the tooth top circumferential surface of the spiral bevel gear pair to calculate the wind resistance power loss of the tooth top circumferential surface of the spiral bevel gear pair; According to the flow characteristics of the oil-gas two-phase flow at the tooth root of the tooth groove of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the tooth root of the tooth groove of the spiral bevel gear pair to calculate the wind resistance power loss of the tooth root of the tooth groove of the spiral bevel gear pair; According to the flow characteristics of the oil-gas two-phase flow at the meshing part of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the pump flow of the spiral bevel gear pair to calculate the wind resistance power loss of the pump flow of the spiral bevel gear pair; Add the wind resistance power loss of the tooth surface of the spiral bevel gear pair, the wind resistance power loss of the large and small end faces, the wind resistance power loss of the front and rear conical surfaces, the wind resistance power loss of the tooth top circumferential surface, the wind resistance power loss of the tooth root of the tooth groove, and the wind resistance power loss of the pump flow to obtain the total wind resistance power loss of the spiral bevel gear pair under oil injection lubrication. The expression is as follows:

[0006] In the formula, P w represents the total wind resistance power loss of the spiral bevel gear pair under oil injection lubrication, P t represents the wind resistance power loss of the tooth surface, P s represents the wind resistance power loss of the large and small end faces, P c represents the wind resistance power loss of the front and rear conical surfaces, P f represents the wind resistance power loss of the tooth top circumferential surface, P r represents the wind resistance power loss of the tooth root of the tooth groove, P b represents the wind resistance power loss of the pump flow; i Takeq represents the driving gear when i take g represents the driven gear when

[0007] A further technical solution of the present invention is that the gear tooth surface equation for constructing a spiral bevel gear pair based on a Cartesian coordinate system includes: Take the center of the processing machine tool as the origin of the Cartesian coordinate system; Based on the origin of the Cartesian coordinate system, obtain the unit position vector and unit normal vector of the generating surface, and perform multiple coordinate transformations on the unit position vector and unit normal vector respectively to obtain the gear tooth surface equations of the spiral bevel gear pair, including the gear tooth surface equation of the driving gear and the gear tooth surface equation of the driven gear.

[0008] 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; The gear pair geometric parameter group includes: the helix direction of the driving gear, the helix direction of the driven gear, the total number of teeth of the driving gear, the total number of teeth of the driven gear, the module at the large end of the gear, the gear width, the pressure angle, the helix angle, the outer cone distance of the gear, the pitch cone angle of the driving gear, the pitch cone angle of the driven gear, the hub radius of the driving gear, the hub radius of the driven gear, the spoke radius at the small end of the driving gear, the spoke radius at the small end of the driven gear, the spoke radius at the large end of the driving gear, the spoke radius at the large end of the driven gear, the rim thickness of the front cone surface of the driving gear, the rim thickness of the back cone surface of the driving gear, the rim thickness of the front cone surface of the driven gear, the rim thickness of the back cone surface of the driven gear; The oil injection lubrication system parameter group includes: the coordinate of the oil outlet position of the oil injector ( x 0, y 0, z 0), the jet inclination angle, the jet azimuth angle.

[0009] 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 a unit spiral bevel gear pair includes the impact depth on the tooth surface of the unit driving gear and the impact depth on the tooth surface of the unit driven gear; The impact depth on the tooth surface of the unit driving gear The calculation formula is as follows:

[0010] In the formula, is the addendum circle radius of the unit driving gear; , is the coordinate of the collision point between the lubricating oil droplet and the tooth profile of the unit driving gear. The acquisition method is to take the derivative of the dynamic equation of the lubricating oil droplet during the jet flow movement on the tooth surface of the unit spiral bevel gear to obtain the acceleration equation, and then perform a second integration on the acceleration equation in combination with the initial velocity and initial displacement to obtain the coordinate of the collision point between the lubricating oil droplet and the tooth profile of the unit driving gear and ; The impact depth of the tooth surface of the unit driven gear The calculation formula is as follows:

[0011] In the formula, is the addendum circle radius of the unit driven gear; and are the coordinates of the collision point between the lubricating oil droplet and the tooth profile of the unit driven gear. The acquisition method is to take the derivative of the dynamic equation of the lubricating oil droplet during the jet flow movement on the tooth surface of the unit spiral bevel gear to obtain the acceleration equation, and then perform a second integration on the acceleration equation in combination with the initial velocity and initial displacement to obtain the coordinate of the collision point between the lubricating oil droplet and the tooth profile of the unit driven gear and .

[0012] A further technical solution of the present invention is that in the calculation model of the wind resistance power loss of the tooth surface of the spiral bevel gear pair, the wind resistance power loss of the driving gear tooth surface P tq The expression is as follows:

[0013] In the formula, B is the gear width; is the pitch cone angle of the driving gear; is the rotational angular velocity of the driving gear; ξ is the correction coefficient , indicating the number of teeth of the driving gear directly affected by the lubricating oil jet line at a certain moment accounting for the proportion of the total number of teeth of the driving gear ; is the impact depth on the tooth surface of the unit driving gear 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 gear housing around the gear; is the helix angle at the axial coordinate equal to z ; is the pressure angle at the impact depth of H in the local reference coordinate system; The wind resistance power loss of the driven gear tooth surface P tg The expression is as follows:

[0014] Wherein, is the pitch cone angle of the driven gear; is the rotational angular velocity of the driven gear; is the correction coefficient , representing the number of teeth of the driven gear directly affected by the lubricating oil jet streamline at a certain moment accounting for the total number of teeth of the driven gear ratio; is the impact depth on the tooth surface of the unit driven gear not directly affected by the jet streamline.

[0015] A further technical solution of the present invention is that in the calculation model of the wind resistance power loss of the large and small end faces of the spiral bevel gear pair, in the laminar flow regime: The expression of the wind resistance power loss of the large and small end faces of the driving gear is as follows:

[0016] Wherein, ν is the kinematic viscosity of the fluid; r shq is the large end spoke radius of the driving gear; r stq is the small end spoke radius of the driving gear; r hgq is the hub radius of the driving gear; The expression of the wind resistance power loss of the large and small end faces of the driven gear is as follows:

[0017] Wherein, r shg is the large end spoke radius of the driven gear; r stg is the small end spoke radius of the driven gear; r hgg is the hub radius of the driven gear; In the turbulent flow regime: The expression of the wind resistance power loss of the large and small end faces of the driving gear is as follows:

[0018] Wherein, r cq Transition radius of the fluid state on the end face of the driving gear from laminar flow to turbulent flow; The expression of the wind resistance power loss of the large and small end faces of the driven gear is as follows:

[0019] Wherein, r cgThe transition radius of the fluid state from laminar flow to turbulent flow on the end face of the driven gear.

[0020] A further technical solution of the present invention is that the expression of the calculation model of the wind resistance power loss on the front and rear conical surfaces of the spiral bevel gear pair is as follows: The expression of the wind resistance power loss on the front and rear conical surfaces of the driving gear is as follows:

[0021] In the formula, μ is the dynamic viscosity of the fluid; 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; The expression of the wind resistance power loss on the front and rear conical surfaces of the driven gear is as follows:

[0022] In the formula, l hg is the rim thickness of the back cone surface of the driven gear; l tg is the rim thickness of the front cone surface of the driven gear.

[0023] A further technical solution of the present invention is that the expression of the calculation model of the wind resistance power loss on the tip circumferential surface of the spiral bevel gear pair is as follows: The expression of the wind resistance power loss on the tip circumferential surface of the driving gear is as follows:

[0024] In the formula, r taq is the tip circle radius at the small end face of the driving gear; The expression of the wind resistance power loss on the tip circumferential surface of the driven gear is as follows:

[0025] In the formula, r tag is the tip circle radius at the small end face of the driven gear.

[0026] A further technical solution of the present invention is that the expression of the calculation model of the wind resistance power loss on the tooth groove and tooth root of the spiral bevel gear pair is as follows: The expression of the wind resistance power loss on the tooth groove and tooth root of the driving gear is as follows:

[0027] In the formula, is the coefficient of the biharmonic equation of the driving gear; is the addendum circle radius of the driving gear; is the dedendum circle radius of the driving gear; The expression of the wind resistance power loss of the tooth space root of the driven gear is as follows:

[0028] In the formula, is the coefficient of the biharmonic equation of the driven gear; is the addendum circle radius of the driven gear; is the dedendum circle radius of the driven gear.

[0029] A further technical solution of the present invention is that the expression of the calculation model of the pump flow wind resistance power loss of the spiral bevel gear pair is as follows:

[0030] In the formula, is the extrusion power loss of the control volume of the driving gear of the gear pair at the th discrete position, represents the serial number of the discrete position of the gear pair, and , where represents the total number of discrete positions within one base pitch; represents the th fluid control volume of the driving gear at the j th discrete position. The fluid control volume is the cavity formed during the meshing of the gear pair and is composed of the involute surfaces and the tooth root profiles of the two meshing teeth; , is the total number of control volumes of the driving gear at the th discrete position, and its value depends on the contact ratio of the gear pair; is the extrusion power loss of the control volume of the driven gear of the gear pair at the th discrete position; represents the th fluid control volume of the driven gear at the k th discrete position, , is the total number of control volumes of the driven gear at the th discrete position, and its value depends on the contact ratio of the gear pair.

[0031] Beneficial effects The beneficial effects of the present invention are as follows: In the calculation process of the wind resistance power loss of the aero high-speed spiral bevel gear pair under oil spray lubrication, the present invention considers the influence of the interaction between the lubricating oil and the flow field around the gear on the wind resistance power loss of the spiral bevel gear, and also considers the influence of the pump flow effect of the gear pair meshing effect on the wind resistance power loss, making the finally calculated total wind resistance power loss of the spiral bevel gear pair closer to the actual situation and having higher calculation accuracy (as Figure 8 shown). The specific effect analysis is as follows: 1. The present invention constructs a sub-region physical analysis model (tooth surface, large and small end faces, front and rear conical surfaces, tooth tip circumferential surface, tooth groove and tooth root, pump flow meshing area), replacing the traditional CFD full flow field simulation. While ensuring the accuracy, the calculation speed is improved. For example, if the traditional CFD full flow field simulation uses 2 nodes for full-core operation, it takes about 50 hours to complete the calculation of one example; while using the analysis model proposed by the present invention, it takes about 3 minutes to complete one example.

[0032] 2. A special model is proposed for the complex geometric characteristics of the spiral bevel gear pair. Among them, the tooth surface impact depth model combines jet dynamics to quantify the lubricating oil distribution, accurately quantify the influence of jet lubrication on wind resistance, and solve the problem that the traditional model ignores the oil film distribution; the wind resistance power loss calculation model for the large and small end faces simplifies the gear into a rotating disk, determines the fluid motion state on the rotating disk according to the gear rotation speed and the gear geometric dimensions, and distinguishes the laminar flow state and the turbulent flow state to reduce the calculation error; the wind resistance power loss calculation model for the front and rear conical surfaces divides the front and rear cones of the spiral bevel gear pair into several small cones. When the divided width is small enough, the micro-element cone is regarded as a unit cylinder to solve the problem of non-uniform flow field distribution caused by the conical surface curvature; the wind resistance power loss calculation model for the tooth tip circumferential surface takes the tooth tip circle radius as the characteristic dimension and establishes an equivalent rotating cylinder model to simplify the complex conical surface flow into an equivalent two-dimensional problem; the tooth groove and tooth root creeping 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 volumes, which is more suitable for the transient effect under high-speed working conditions.

[0033] 3. The present invention reveals the influence mechanism of jet parameters on wind resistance loss by introducing the equivalent density of the oil-gas two-phase flow and the dynamic impact depth, and at the same time supports the optimization of the nozzle layout.

[0034] 4. The present invention can predict the hot spot area of the temperature rise of the gear system by accurately calculating the wind resistance power loss, and avoid problems such as lubricating oil failure and tooth surface scuffing caused by wind resistance overheating. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic flow chart of the calculation method for the wind resistance power loss of the aero high-speed spiral bevel gear pair under oil spray lubrication in the embodiment of the present invention; Figure 2Schematic diagram of the spiral bevel gear pair model equipped with an oil injection lubrication system in the embodiment of the present invention; Figure 3 Schematic diagram of the principle for calculating the windage power loss of the tooth surface of the spiral bevel gear pair in the embodiment of the present invention; Figure 4 Schematic diagram of the principle for calculating the windage power loss of the large and small end faces of the spiral bevel gear pair in the embodiment of the present invention; Figure 5 Schematic diagram of the principle for calculating the windage power loss of the front and rear cone surfaces of the spiral bevel gear pair in the embodiment of the present invention; Figure 6 Schematic diagram of the principle for calculating the windage power loss of the tooth groove and tooth root of the spiral bevel gear pair in the embodiment of the present invention; Figure 7 Schematic diagram of the principle for calculating the windage power loss of the pump flow of the spiral bevel gear pair in the embodiment of the present invention; Figure 8 Comparison diagram of the calculated value and experimental value of the windage power loss of the spiral bevel gear pair in the embodiment of the present invention. Detailed implementation manners

[0036] The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the present invention, and should not be construed as a limitation to the present invention.

[0037] In an aircraft high-speed transmission system, spiral bevel gear pairs are widely used in the main reducer due to their advantages such as high load-carrying capacity and low noise. When the gears rotate at high speed in an oil injection lubrication environment, the gears interact with the surrounding oil-gas mixture, resulting in significant windage power loss, which seriously reduces the transmission efficiency. At the same time, the resulting temperature rise causes the lubricating oil viscosity to fail, increasing the risk of tooth surface scuffing, micropitting and other faults. The current windage loss prediction technologies have the following defects: 1. CFD simulation method (such as CN114547789B): It depends on the meshing of the three-dimensional fluid domain grid. The calculation for a single working condition takes several hours, which cannot meet the rapid design iteration requirements of aircraft gears; and the resolution of micro-scale flow fields such as tooth grooves and meshing areas is insufficient, with an error > 15%.

[0038] 2. Empirical formula method (such as CN116108652A): Based on the simplified models of spur gears / face gears, the spatial curved surface geometry of spiral bevel gears (such as spherical involute, back cone angle) is ignored, resulting in distorted prediction of the cone surface flow field; 3. Windage-churning coexistence model (such as CN116187081B): It is only applicable to the oil immersion lubrication scenario and does not consider the dynamic impact effect of the oil injection jet. The error is as high as 40% in the aircraft oil injection lubrication environment.

[0039] Based on the existing defects, the present invention for the first time proposes a physical analysis model for different regions of the wind resistance loss of an aviation spiral bevel gear pair under oil spray lubrication, solving the problems of low CFD simulation efficiency and inapplicability of coexistence models.

[0040] A calculation method for the wind resistance power loss of a spiral bevel gear pair under oil spray lubrication provided by the present invention is as follows: Construct the gear tooth surface equation of the spiral bevel gear pair based on the Cartesian coordinate system; Determine the preset parameters of the spiral bevel gear pair according to the gear tooth surface equation of the spiral bevel gear pair, and then establish a parameter model of the spiral bevel gear pair equipped with an oil spray 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 spray lubrication system, calculate the impact depth of the oil-gas two-phase flow on the tooth surface of a unit spiral bevel gear pair, and then establish a calculation model for the wind resistance power loss of the tooth surface of the spiral bevel gear pair to calculate the wind resistance power loss of the tooth surface 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, establish a calculation model for the wind resistance power loss of the large and small end faces of the spiral bevel gear pair to calculate the wind resistance power loss of the large and small end faces of the spiral bevel gear pair; According to the flow characteristics of the oil-gas two-phase flow on the front and rear conical surfaces of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the front and rear conical surfaces of the spiral bevel gear pair to calculate the wind resistance power loss of the front and rear conical surfaces of the spiral bevel gear pair; According to the flow characteristics of the oil-gas two-phase flow on the circumferential surface of the tooth tip of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the circumferential surface of the tooth tip of the spiral bevel gear pair to calculate the wind resistance power loss of the circumferential surface of the tooth tip of the spiral bevel gear pair; According to the flow characteristics of the oil-gas two-phase flow at the tooth root of the tooth groove of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the tooth root of the tooth groove of the spiral bevel gear pair to calculate the wind resistance power loss of the tooth root of the tooth groove of the spiral bevel gear pair; According to the flow characteristics of the oil-gas two-phase flow at the meshing part of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the pump flow of the spiral bevel gear pair to calculate the wind resistance power loss of the pump flow of the spiral bevel gear pair; Add the wind resistance power loss of the tooth surface, the wind resistance power loss of the large and small end faces, the wind resistance power loss of the front and rear conical surfaces, the wind resistance power loss of the circumferential surface of the tooth tip, the wind resistance power loss of the tooth root of the tooth groove, and the wind resistance power loss of the pump flow of the spiral bevel gear pair to obtain the total wind resistance power loss of the spiral bevel gear pair under oil spray lubrication, and the expression is as follows:

[0041] In the formula, P wIndicates the total wind resistance power loss of the spiral bevel gear pair under oil spray lubrication. P t Indicates the wind resistance power loss of the tooth surface. P s Indicates the wind resistance power loss of the large and small end faces. P c Indicates the wind resistance power loss of the front and rear cone surfaces. P f Indicates the wind resistance power loss of the circumferential surface of the tooth tip. P r Indicates the wind resistance power loss of the tooth space and tooth root. P b Indicates the wind resistance power loss of the pump flow. i Take q Indicates the driving gear when i Take g Indicates the driven gear when

[0042] In one embodiment, the gear tooth surface equation of the spiral bevel gear pair constructed based on the Cartesian coordinate system includes: Take the center of the machining machine tool as the origin of the Cartesian coordinate system; Based on the origin of the Cartesian coordinate system, obtain the unit position vector and unit normal vector of the generating surface, and perform multiple coordinate transformations on the unit position vector and unit normal vector respectively to obtain the gear tooth surface equation of the spiral bevel gear pair, including the gear tooth surface equation of the driving gear and the gear tooth surface equation of the driven gear.

[0043] In one embodiment, in the gear tooth surface equation of the spiral bevel gear pair, the expression of the tooth surface equation of the driving gear is as follows:

[0044] In the formula, the following are the respective coordinate transformation matrices: , , , , , , , , ,

[0045] In the formula, is the current rotation angle of the machined driving gear, , is the radius of the cutter head of the driving gear; is the current rotation angle of the generating coordinate system of the driving gear and the swing table; is the root cone angle of the driving gear machine tool; is the bed position of the driving gear; is the vertical position of the driving gear; is the axial position of the driving gear; is the angular tool position of the driving gear; is the radial tool position of the driving gear; and represents the surface coordinates of the conical surface of the driving gear; is the tool profile angle of the driving gear; is the unit position vector of the generating surface of the driving gear; is the unit normal vector of the generating surface of the driving gear; is the unit position vector of the tooth surface of the driving gear, is the unit normal vector of the tooth surface of the driving gear; The expression of the tooth surface equation of the driven gear is as follows:

[0046] In the formula, the coordinate transformation matrices are as follows: , , , , , , , , ,

[0047] In the formula, is the current rotation angle of the driven gear to be machined, , is the cutter head radius of the driven gear, is the current rotation angle of the generating coordinate system of the driven gear and the rotary table; is the root cone angle of the driven gear machine tool; is the bed position of the driven gear; is the angular tool position of the driven gear; is the radial tool position of the driven gear; and are the surface coordinates of the conical surface of the driven gear; is the tool profile angle of the driven gear; is the unit position vector of the generating surface of the driven gear, is the unit normal vector of the generating surface of the driven gear; is the unit position vector of the tooth surface of the driven gear, is the unit normal vector of the tooth surface of the driven gear; In one embodiment, start the spiral bevel gear pair, install the oil injection lubrication system inside the spiral bevel gear pair, determine the preset parameters of the spiral bevel gear pair according to the gear tooth surface equation of the spiral bevel gear pair, and then establish a parameter model of the spiral bevel gear pair with an oil injection lubrication system, including the following steps: Obtain the parameters of the oil injection lubrication system of the spiral bevel gear pair and establish an oil injection lubrication system model; Obtain the geometric parameters of the spiral bevel gear pair and the oil injection lubrication system model, and establish a parameter model of the spiral bevel gear pair with an oil injection lubrication system.

[0048] The parameter model of the spiral bevel gear pair 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: helix direction of the driving gear, helix direction of the driven gear, total number of teeth of the driving gear, total number of teeth of the driven gear, module at the large end of the gear, gear width, pressure angle, helix angle, outer cone distance of the gear, pitch cone angle of the driving gear, pitch cone angle of the driven gear, hub radius of the driving gear, hub radius of the driven gear, spoke radius at the small end of the driving gear, spoke radius at the small end of the driven gear, spoke radius at the large end of the driving gear, spoke radius at the large end of the driven gear, rim thickness of the front cone surface of the driving gear, rim thickness of the back cone surface of the driving gear, rim thickness of the front cone surface of the driven gear, rim thickness of the back cone surface of the driven gear; The oil injection lubrication system parameter group includes: position coordinates of the oil outlet of the oil injector ( x 0, y 0, z 0), jet inclination angle, jet azimuth angle.

[0049] In one embodiment, based on the parameter model of the spiral bevel gear pair with an oil injection lubrication system, calculate the impact depth of the oil-gas two-phase flow on the tooth surface of the unit spiral bevel gear pair, and then establish a calculation model of the wind resistance power loss of the tooth surface of the spiral bevel gear pair. The steps for calculating the wind resistance power loss of the tooth surface of the spiral bevel gear pair are as follows: According to the spiral bevel gear pair with an oil injection lubrication system, establish a dynamic equation for the jet flow motion of the lubricating oil droplets on the tooth surface of the spiral bevel gear, and the expression is as follows:

[0050] In the formula, C D is the fluid resistance coefficient, determined according to the fluid rotational Reynolds number; d o is the diameter of the lubricating oil droplet; v rz , v tz are the velocity components of the lubricating oil droplet along the direction respectively, are the acceleration components of the lubricating oil droplets along the direction; v g is the tangential velocity of the gear; and are the force values of the lubricating oil droplets along the direction, respectively; ρ is the equivalent density of the oil-gas two-phase fluid in the housing around the gear, and its calculation formula is as follows:

[0051] In the formula, is the volume fraction of the lubricating oil; is the density of the lubricating oil; is the density of the air; Derive the dynamic equation of the lubricating oil droplets during the jet motion on the tooth surface of the unit spiral bevel gear to obtain the acceleration equation, and then perform a second integral on the acceleration equation in combination with the initial velocity and initial displacement to obtain the coordinates and of the collision point of the lubricating oil droplets and the tooth profile of the unit driving gear, and the coordinates and of the collision point of the lubricating oil droplets and the tooth profile of the unit driven gear; Calculate the impact depth of the tooth surface of the unit spiral bevel gear pair, including the impact depth of the tooth surface of the unit driving gear and the impact depth of the tooth surface of the unit driven gear; The impact depth of the tooth surface of the unit driving gear has the following calculation formula:

[0052] In the formula, is the addendum circle radius of the unit driving gear; The impact depth of the tooth surface of the unit driven gear has the following calculation formula:

[0053] In the formula, is the addendum circle radius of the unit driven gear; Construct a calculation model for the wind resistance power loss of the tooth surface of the spiral bevel gear pair, and calculate the wind resistance power loss P tq of the tooth surface of the driving gear. The expression is as follows:

[0054] In the formula, B is the gear width; is the pitch cone angle of the driving gear; is the rotational angular velocity of the driving gear; ξis the correction coefficient , representing the number of driving gear teeth directly affected by the lubricating oil jet streamline at a certain moment accounting for the total number of driving gear teeth ratio; is the impact depth on the tooth surface of the unit driving gear not directly affected by the jet streamline; is the density of the lubricating oil; ρ is the equivalent density of the oil-gas two-phase fluid in the housing around the gear; is the helix angle at the axial coordinate equal to z ; is the pressure angle when the impact depth in the local reference coordinate system is H ; Calculate the wind resistance power loss of the driven gear tooth surface P tg The expression is as follows:

[0055] In the formula, δ g is the pitch cone angle of the driven gear; ω g is the rotational angular velocity of the driven gear; is the correction coefficient , representing the number of driven gear teeth directly affected by the lubricating oil jet streamline at a certain moment accounting for the total number of driven gear teeth ratio; is the impact depth on the tooth surface of the unit driven gear not directly affected by the jet streamline.

[0056] In one embodiment, in the calculation model of the wind resistance power loss of the large and small end faces of the spiral bevel gear pair, in the laminar flow regime: The expression for the wind resistance power loss of the large and small end faces of the driving gear is as follows:

[0057] In the formula, ν is the kinematic viscosity of the fluid; r shq is the large-end spoke radius of the driving gear, r stq is the small-end spoke radius of the driving gear, r hgq is the hub radius of the driving gear; The expression for the wind resistance power loss of the large and small end faces of the driven gear is as follows:

[0058] In the formula, r shg is the large-end spoke radius of the driven gear,r stg is the radius of the spoke at the small end of the driven gear, r hgg is the radius of the hub of the driven gear; In the turbulent flow regime: The expression for the power loss due to wind resistance on the large and small end faces of the driving gear is as follows:

[0059] Where, r cq is the transition radius of the fluid state from laminar to turbulent on the end face of the driving gear; The expression for the power loss due to wind resistance on the large and small end faces of the driven gear is as follows:

[0060] Where, r cg is the transition radius of the fluid state from laminar to turbulent on the end face of the driven gear.

[0061] In one embodiment, the expression for the calculation model of the power loss due to wind resistance on the front and rear conical surfaces of the spiral bevel gear pair is as follows: The expression for the power loss due to wind resistance on the front and rear conical surfaces of the driving gear is as follows:

[0062] Where, μ is the dynamic viscosity of the fluid; l hq is the rim thickness of the back cone of the driving gear, l tq is the rim thickness of the front cone of the driving gear, δ B is the back cone angle of the spiral bevel gear; The expression for the power loss due to wind resistance on the front and rear conical surfaces of the driven gear is as follows:

[0063] Where, l hg is the rim thickness of the back cone of the driven gear, l tg is the rim thickness of the front cone of the driven gear.

[0064] In one embodiment, the expression for the calculation model of the power loss due to wind resistance on the circumferential surface of the tooth tip of the spiral bevel gear pair is as follows: The expression for the power loss due to wind resistance on the circumferential surface of the tooth tip of the driving gear is as follows:

[0065] Where, r taqis the radius of the tooth tip circle at the small end face of the driving gear; The expression of windage power loss on the top circle of the driven gear is as follows:

[0066] In the formula, r tag It is the radius of the tooth top circle at the small end face of the driven gear.

[0067] 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: The power loss expression of the wind resistance at the root of the active gear tooth groove is as follows:

[0068] In the formula, is the coefficient of the biharmonic equation of the driving gear, is the addendum radius of the driving gear, is the root circle radius of the driving gear; The power loss expression of the windage resistance at the root of the driven gear tooth groove is as follows:

[0069] In the formula, 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; In one embodiment, the pump flow windage power loss calculation model expression of the spiral bevel gear pair is as follows:

[0070] In the formula, For the Discrete position 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; Indicated in The first discrete position of the driving gear j A fluid control body, which is a 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 pair; For the The extrusion power loss of the meshing pair of the gear pair on the driven gear control body at discrete positions ; Denote the th fluid control volume of the driven gear at the k th discrete position, , and is the total number of control volumes of the driven gear at the

[0071] th discrete position, and its value depends on the contact ratio of the gear pair. In one embodiment, as shown in reference to Figure 1 , the calculation method of the wind resistance power loss under oil spray lubrication of the aviation high-speed spiral bevel gear pair specifically includes the following steps: Step 101: Construct the gear tooth surface equation of the spiral bevel gear pair based on the Cartesian coordinate system.

[0072] Specifically, determine the machining parameters of the driven gear, and then the machining parameters of the driving gear can be determined by the local synthesis method, so as to establish the tooth surface equations of the driving gear and the driven gear. Taking the left-handed driving gear of the 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 cutting parameters include: the surface coordinates of the cone surface, the tooth profile angle of the tool, 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 generating coordinate system and the oscillating table, and the current rotation angle of the gear to be machined.

[0073] After a series of coordinate transformations on the unit position vector and the unit normal vector of the generating surface, 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.

[0074] Step 102: Establish a parameter model of the spiral bevel gear pair equipped with an oil spray lubrication system according to the preset parameters of the spiral bevel gear pair.

[0075] Specifically, as shown in reference to Figure 2 , the parameter model of the spiral bevel gear pair equipped with an oil spray lubrication system includes: the driving gear has a left-handed helix, the driven gear has a right-handed helix, the total number of teeth of the driving gear z q is 27, the total number of teeth of the driven gear z g is 81, the module at the large end of the gear m is 3.85 mm, the gear width b is 38 mm, the pressure angle α p is 20°, and the helix angle βis 35°, the outer cone distance of the gear R em is 164.31 mm, the pitch cone angle of the driving gear δ q is 16.91°, the pitch cone angle of the driven gear δ g is 52.86, the hub radius of the driving gear r hgq is 20 mm, the hub radius of the driven gear r hgg is 35 mm, the spoke radius at the small end of the driving gear r stq is 27 mm, the spoke radius at the small end of the driven gear r stg is 106.6 mm, the spoke radius at the large end of the driving gear r shq is 35 mm, the spoke radius at the large end of the driven gear r shg is 148.4 mm, the rim thickness of the front cone surface of the driving gear l tq is 3.6 mm, the rim thickness of the back cone surface of the driving gear l hq is 10 mm, the rim thickness of the front cone surface of the driven gear l tg is 6 mm, the rim thickness of the back cone surface of the driven gear l hg is 20 mm, the coordinate of the fuel injection nozzle outlet position ([[]] x 0, y 0, z 0) is (120, 90, 50) mm, the jet inclination angle η is 100°, the jet azimuth angle φ is 90°.

[0076] Step 103: Combine the gear tooth surface equation and the spiral bevel gear pair parameter model installed with the fuel injection lubrication system, calculate the impact depth of the oil-gas two-phase flow on the tooth surface of the unit spiral bevel gear pair, and then establish a calculation model for the tooth surface wind resistance power loss of the spiral bevel gear pair, and calculate the tooth surface wind resistance power loss of the spiral bevel gear pair.

[0077] Specifically, the initial state parameters of the fluid in the gear housing are: the pressure is 1.0×10 5 Pa, the temperature is 298 K, the specific heat capacity at constant volume is 717 J / (kg·K), the specific heat capacity at constant pressure is 1005 J / (kg·K), the air density is 1.205 kg / m 3 ³, the dynamic viscosity is 1.81×10 -5 ⁻⁵ Pa·s, the lubricating oil density is 998 kg / m³3 The dynamic viscosity is 6.04×10 -2 Pa·s, the initial volume fraction of the lubricating oil is 0, and the rotational speed of the driving gear changes from 0 to approximately 27,000 r / min.

[0078] Refer to Figure 3 As shown, taking a certain droplet on the oil injection lubrication jet line as the research object, according to the dynamic equation of the lubricating oil droplet during the jet flow movement on the tooth surface of the spiral bevel gear and the above initial conditions, the impact depth value of the oil-gas two-phase flow on the tooth surface is calculated, and the wind resistance power loss of the tooth surface of the spiral bevel gear pair is obtained P tq and P tg .

[0079] Step 104: According to the flow states of the oil-gas two-phase flow on the large and small end faces of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the large and small end faces of the spiral bevel gear pair, and calculate the wind resistance power loss of the large and small end faces of the spiral bevel gear pair.

[0080] Specifically, refer to Figure 4 As shown, when calculating the wind resistance power loss of the large and small end faces of the spiral bevel gear pair, the gear is simplified as a rotating disk. According to the rotational speed of the gear and the geometric dimensions of the gear, the fluid motion state on the rotating disk is determined, and then the continuity equation and N-S equations of the disk flow are established based on the rotating disk flow theory, and further the wind resistance power loss of the large and small end faces of the spiral bevel gear pair in the laminar flow state is calculated and , and the wind resistance power loss of the large and small end faces of the spiral bevel gear pair in the turbulent flow state and .

[0081] Step 105: According to the flow characteristics of the oil-gas two-phase flow on the front and rear conical surfaces of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the front and rear conical surfaces of the spiral bevel gear pair, and calculate the wind resistance power loss of the front and rear conical surfaces of the spiral bevel gear pair.

[0082] Specifically, refer to Figure 5 As shown, the front and rear cones of the spiral bevel gear pair are divided into many small cones. When the divided width is small enough, the micro-element cone is regarded as a unit cylinder, and the fluid continuity equation and N-S equation are established based on the circumferential flow theory, and further the wind resistance power loss of the front and rear conical surfaces of the spiral bevel gear pair is calculated p cq and p cg .

[0083] Step 106: Based on the flow characteristics of the oil-gas two-phase flow on the tip circumference surface of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss on the tip circumference surface of the spiral bevel gear pair, and calculate the wind resistance power loss on the tip circumference surface of the spiral bevel gear pair.

[0084] Specifically, since the tip circumference surface of the spiral bevel gear is a conical surface, the calculation principle of the wind resistance power loss on its tip circumference surface is the same as that of the front and rear conical surfaces, and the wind resistance power loss on the tip circumference surface of the spiral bevel gear pair is calculated. p fq and p fg 。

[0085] Step 107: Based on the flow characteristics of the oil-gas two-phase flow at the tooth root of the tooth space of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss at the tooth root of the tooth space of the spiral bevel gear pair, and calculate the wind resistance power loss at the tooth root of the tooth space of the spiral bevel gear pair.

[0086] Specifically, as shown in Figure 6 , model the fluid motion at the tooth root of the tooth space of the spiral bevel gear pair as the flow of fluid through an annular cavity, and calculate the wind resistance power loss at the tooth root of the tooth space of the spiral bevel gear pair according to the biharmonic equation of fluid motion. p rq and p rg 。

[0087] Step 108: Based on the flow characteristics of the oil-gas two-phase flow at the meshing part of the spiral bevel gear pair, establish a calculation model for the pump flow wind resistance power loss of the spiral bevel gear pair, and calculate the pump flow wind resistance power loss of the spiral bevel gear pair.

[0088] Specifically, as shown in Figure 7 , equivalent the spiral bevel gear pair to a spur cylindrical gear pair. During the meshing process of the gear pair, multiple cavities (fluid control volumes) are formed. First, calculate the end area and side clearance area of a fluid control volume, and then establish the dynamic equation of the fluid in the control volume based on compressible flow to calculate the pump flow wind resistance power loss of the spiral bevel gear pair. P b 。

[0089] Step 109: Add the calculated tooth surface wind resistance power loss, large and small end face wind resistance power loss, front and rear conical surface wind resistance power loss, tip circumference surface wind resistance power loss, tooth root of tooth space wind resistance power loss, and pump flow wind resistance power loss of the spiral bevel gear pair to obtain the total wind resistance power loss of the spiral bevel gear pair under oil injection lubrication.

[0090] Specifically, the total windage power loss of a spiral bevel gear pair under oil injection lubrication is the sum of the windage power losses on the surfaces of the driving gear and the driven gear and the pump flow loss during the meshing of the gear pair. Therefore, the calculation formula for the total windage power loss of a spiral bevel gear pair under oil injection lubrication is as follows:

[0091] In the formula, P w represents the total windage power loss of the spiral bevel gear pair under oil injection lubrication, P t represents the windage power loss of the tooth surface, P s represents the windage power loss of the large and small end faces, P c represents the windage power loss of the front and rear conical surfaces, P f represents the windage power loss of the circumferential surface of the tooth tip, P r represents the windage power loss of the tooth groove and tooth root, P b represents the pump flow windage power loss of the gear pair; i When taking q it represents the driving gear, i When taking g it represents the driven gear.

[0092] Step 110: Verify the accuracy. Compare the calculated value of the total windage power loss of the spiral bevel gear pair under oil injection lubrication with the experimental value. The comparison result is as Figure 8 shown. The calculated value of the total windage power loss is relatively close to the experimental value, and the relative error is basically between 4.29% and 8.37%.

[0093] The low error is due to the refined modeling of the fluid motion characteristics and geometric features in the method of this embodiment, and the meshing extrusion power loss of the gear pair is considered. Therefore, its calculated value is relatively reasonable. The verification result shows that the calculation method of the windage power loss of the spiral bevel gear pair proposed by the present invention can reasonably predict the windage power loss of the gear pair under the oil injection lubrication condition, and thus can calculate the transmission efficiency of the gear system more accurately.

[0094] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principle and purpose of the present invention.

Claims

1. A calculation method for the air resistance power loss under oil spray lubrication of a spiral bevel gear pair, 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; Determine the preset parameters of the spiral bevel gear pair according to the gear tooth surface equation of the spiral bevel gear pair, and then establish 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, calculate the impact depth of the oil-gas two-phase flow on the tooth surface of the unit spiral bevel gear pair, and then establish a calculation model for the wind resistance power loss of the tooth surface of the spiral bevel gear pair, and calculate the wind resistance power loss of the tooth surface 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, establish a calculation model for the wind resistance power loss of the large and small end faces of the spiral bevel gear pair, and calculate the wind resistance power loss of the large and small end faces of the spiral bevel gear pair; According to the flow characteristics of the oil-gas two-phase flow on the front and rear conical surfaces of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the front and rear conical surfaces of the spiral bevel gear pair, and calculate the wind resistance power loss of the front and rear conical surfaces of the spiral bevel gear pair; According to the flow characteristics of the oil-gas two-phase flow on the circumferential surface of the tooth tip of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the circumferential surface of the tooth tip of the spiral bevel gear pair, and calculate the wind resistance power loss of the circumferential surface of the tooth tip of the spiral bevel gear pair; According to the flow characteristics of the oil-gas two-phase flow at the tooth root of the tooth groove of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the tooth root of the tooth groove of the spiral bevel gear pair, and calculate the wind resistance power loss of the tooth root of the tooth groove of the spiral bevel gear pair; According to the flow characteristics of the oil-gas two-phase flow at the meshing position of the spiral bevel gear pair, establish a calculation model for the wind resistance power loss of the pump flow of the spiral bevel gear pair, and calculate the wind resistance power loss of the pump flow of the spiral bevel gear pair; Add the wind resistance power loss of the tooth surface of the spiral bevel gear pair, the wind resistance power loss of the large and small end faces, the wind resistance power loss of the front and rear conical surfaces, the wind resistance power loss of the circumferential surface of the tooth tip, the wind resistance power loss of the tooth root of the tooth groove, and the wind resistance power loss of the pump flow of the spiral bevel gear pair to obtain the total wind resistance power loss of the spiral bevel gear pair under oil injection lubrication. The expression is as follows: In the formula, P w represents the total wind resistance power loss of the spiral bevel gear pair under oil spray lubrication, P t represents the wind resistance power loss of the tooth surface, P s represents the wind resistance power loss of the large and small end faces, P c represents the wind resistance power loss of the front and rear conical surfaces, P f represents the wind resistance power loss of the circumferential surface of the tooth tip, P r represents the wind resistance power loss of the tooth groove and tooth root, P b represents the wind resistance power loss of the pump flow; i When taking q it represents the driving gear, i When taking g it represents the driven gear.

2. The calculation method for the air resistance power loss under oil spray lubrication of a spiral bevel gear pair according to claim 1, wherein: The construction of the gear tooth surface equation of the spiral bevel gear pair based on the Cartesian coordinate system includes: Take the center of the processing machine tool as the origin of the Cartesian coordinate system; Based on the origin of the Cartesian coordinate system, obtain the unit position vector and unit normal vector of the generating surface, and perform multiple coordinate transformations on the unit position vector and unit normal vector respectively to obtain the gear tooth surface equation of the spiral bevel gear pair, including the gear tooth surface equation of the driving gear and the gear tooth surface equation of the driven gear.

3. The calculation method for the air resistance power loss under oil spray lubrication of a spiral bevel gear pair 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 geometric parameter group of the gear pair includes: helix direction of the driving gear, helix direction of the driven gear, total number of teeth of the driving gear, total number of teeth of the driven gear, module at the large end of the gear, gear width, pressure angle, helix angle, outer cone distance of the gear, pitch cone angle of the driving gear, pitch cone angle of the driven gear, hub radius of the driving gear, hub radius of the driven gear, spoke radius at the small end of the driving gear, spoke radius at the small end of the driven gear, spoke radius at the large end of the driving gear, spoke radius at the large end of the driven gear, rim thickness of the front cone surface of the driving gear, rim thickness of the back cone surface of the driving gear, rim thickness of the front cone surface of the driven gear, rim thickness of the back cone surface of the driven gear; The parameters of the oil injection lubrication system include: the position coordinates of the oil outlet of the injector nozzle ( x 0, y 0, z 0), the jet inclination angle, and the jet azimuth angle.

4. The calculation method for the air resistance power loss under oil spray lubrication of a spiral bevel gear pair according to claim 3, wherein: 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 on the tooth surface of the unit driving gear and the impact depth on the tooth surface of the unit driven gear; The impact depth of the tooth surface of the unit driving gear The calculation formula is as follows: In the formula, is the addendum circle radius of the unit driving gear; , are the coordinates of the collision point between the lubricating oil droplet and the tooth profile of the unit driving gear. The obtaining method is to take the derivative of the dynamic equation of the lubricating oil droplet during the jet flow movement on the tooth surface of the unit spiral bevel gear to obtain the acceleration equation, and then perform a second integral on the acceleration equation in combination with the initial velocity and initial displacement to obtain the coordinates of the collision point between the lubricating oil droplet and the tooth profile of the unit driving gear , ; The impact depth of the tooth surface of the unit driven gear The calculation formula is as follows: Wherein, is the addendum circle radius of the unit driven gear; , are the coordinates of the collision point between the lubricating oil droplet and the tooth profile of the unit driven gear. The obtaining method is to take the derivative of the dynamic equation of the lubricating oil droplet during the jet flow movement on the tooth surface of the unit spiral bevel gear to obtain the acceleration equation, and then perform a second integral on the acceleration equation in combination with the initial velocity and initial displacement to obtain the coordinates of the collision point between the lubricating oil droplet and the tooth profile of the unit driven gear , .

5. The calculation method of air resistance power loss under oil injection lubrication for a spiral bevel gear pair according to claim 4, characterized in that: In the calculation model of the wind resistance power loss of the tooth surface of the spiral bevel gear pair, the wind resistance power loss of the tooth surface of the driving gear The expression is as follows: In the formula, B is the gear width; is the pitch cone angle of the driving gear; is the rotational angular velocity of the driving gear; ξ is the correction coefficient , indicating the number of teeth of the driving gear directly affected by the lubricating oil jet streamline at a certain moment accounting for the total number of teeth of the driving gear ratio; is the impact depth on the tooth surface of the unit driving gear not directly affected by the jet streamline; is the density of the lubricating oil; ρ is the equivalent density of the oil-gas two-phase fluid in the housing around the gear; is the axial coordinate equal to z helix angle at the place; is the pressure angle when the impact depth in the local reference coordinate system is H ; Wind resistance power loss of the driven gear tooth surface P tg The expression is as follows: In the formula, is the pitch cone angle of the driven gear; is the rotational angular velocity of the driven gear; is the correction coefficient , representing the number of teeth of the driven gear directly affected by the lubricating oil jet streamline at a certain moment accounting for the total number of teeth of the driven gear ratio; is the impact depth on the tooth surface of the unit driven gear not directly affected by the jet streamline.

6. The calculation method of the air resistance power loss under oil injection lubrication of a spiral bevel gear pair according to claim 5, characterized in that: In the calculation model of wind resistance power loss at the large and small end faces of the spiral bevel gear pair, in the laminar flow regime: The expression of wind resistance power loss at the large and small end faces of the driving gear is as follows: In the formula, ν is the kinematic viscosity of the fluid; r shq is the radius of the spoke at the large end of the driving gear; r stq is the radius of the spoke at the small end of the driving gear; r hgq is the hub radius of the driving gear; The expression of wind resistance power loss at the large and small end faces of the driven gear is as follows: In the formula, r shg is the spoke radius at the large end of the driven gear; r stg is the spoke radius at the small end of the driven gear; r hgg is the hub radius of the driven gear; In the turbulent flow regime: The expression of wind resistance power loss at the large and small end faces of the driving gear is as follows: In the formula, r cq The transition radius of the fluid state from laminar flow to turbulent flow on the end face of the driving gear; The expression of wind resistance power loss at the large and small end faces of the driven gear is as follows: In the formula, 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 calculation method for the air resistance power loss under oil spray lubrication of a spiral bevel gear pair according to claim 6, wherein: The expression of the calculation model of wind resistance power loss at the front and back cone surfaces of the spiral bevel gear pair is as follows: The expression of wind resistance power loss at the front and back cone surfaces of the driving gear is as follows: In the formula, μ is the hydrodynamic 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; The expression of wind resistance power loss at the front and back cone surfaces of the driven gear is as follows: In the formula, l hg is the rim thickness of the back cone surface of the driven gear; l tg is the rim thickness of the front cone surface of the driven gear.

8. The calculation method for the air resistance power loss under oil spray lubrication of a spiral bevel gear pair according to claim 7, wherein: The expression of the calculation model of wind resistance power loss at the circumferential surface of the tooth tip of the spiral bevel gear pair is as follows: The expression of wind resistance power loss at the circumferential surface of the tooth tip of the driving gear is as follows: In the formula, r taq is the addendum circle radius at the small end face of the driving gear; The expression of wind resistance power loss at the circumferential surface of the tooth tip of the driven gear is as follows: In the formula, r tag is the addendum circle radius at the small end face of the driven gear.

9. The calculation method for the air resistance power loss under oil spray lubrication of a spiral bevel gear pair according to claim 8, wherein: The expression of the calculation model of wind resistance power loss at the tooth root of the tooth groove of the spiral bevel gear pair is as follows: The expression of wind resistance power loss at the tooth root of the tooth groove of the driving gear is as follows: In the formula, is the coefficient of the biharmonic equation of the driving gear; is the addendum circle radius of the driving gear; is the dedendum circle radius of the driving gear; The expression of wind resistance power loss at the tooth root of the tooth groove of the driven gear is as follows: In the formula, is the coefficient of the biharmonic equation of the driven gear; is the addendum circle radius of the driven gear; is the dedendum circle radius of the driven gear.

10. The calculation method for wind resistance power loss under oil spray lubrication of a spiral bevel gear pair according to claim 9, characterized in that: The expression of the calculation model of wind resistance power loss of the pump flow of the spiral bevel gear pair is as follows: wherein, is the squeeze power loss of the control volume of the driving gear of the gear pair at the th discrete position, ; represents the serial number of the discrete position of the gear pair, and , where represents the total number of discrete positions within one base pitch; represents the th fluid control volume of the driving gear at the j th discrete position. The fluid control volume is the cavity formed during the meshing of the gear pair and is composed of the involute surfaces and the root profiles of the two meshing teeth; , is the total number of control volumes of the driving gear at the th discrete position, and its value depends on the contact ratio of the gear pair; is the squeeze power loss of the control volume of the driven gear of the gear pair at the th discrete position, ; represents the th fluid control volume of the driven gear at the k th discrete position, , is the total number of control volumes of the driven gear at the th discrete position, and its value depends on the contact ratio of the gear pair.

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