A design method of asymmetric helical cylindrical gear pair based on coincidence degree

Abstract

The present application relates to cylindrical gear design technical field, specifically a kind of asymmetric helical cylindrical gear pair design method based on coincidence degree. Including definition parameter, draw the effective coincidence degree contour map of driving side, select design coincidence degree point, asymmetric helical cylindrical gear rack cutter parameter reverse, establish asymmetric helical cylindrical gear cylindrical gear tooth surface equation, adopt NX software to establish asymmetric helical cylindrical gear pair three-dimensional model, this method can meet the design requirement of driving side pressure angle, design asymmetric helical cylindrical gear pair to meet the demand design coincidence degree or maximum coincidence degree, without repeated check coincidence degree, gear undercut, meshing interference and other problems. The asymmetric helical cylindrical gear pair of large coincidence degree designed has the characteristics of transmission smooth, strong bearing capacity. And this design method can be applied to the occasion where the installation center distance changes.

Description

Technical Field

[0001] The invention relates to the technical field of cylindrical gear design, in particular to a design method for an asymmetric helical cylindrical gear pair based on overlap. Background Art

[0002] New energy is the future development trend for construction machinery and heavy-duty vehicles, driving the development of high-precision electric drive reducers toward high power and high speed. Gears, as the core and fundamental components of reducers, place higher demands on their transmission performance. Previous studies have shown that the pressure angle significantly influences the meshing performance of spur involute cylindrical gears. Increasing the pressure angle on the working side of the tooth surface increases the root thickness and the radius of curvature of the tooth profile, improving the contact and bending strength of spur gear teeth. However, spur gears typically have low contact and limited load-bearing capacity. A large pressure angle on the working side reduces contact and tooth top thickness, impacting transmission smoothness and noise levels.

[0003] Currently, the parameter design methods for asymmetric gears mostly predetermine the gear parameters, then calculate the overlap and determine whether it reaches the required value. This process requires repeated calculations and is very complicated. In addition, the verification of parameters such as overlap and strength is also relatively cumbersome.

[0004] In order to solve the above problems, the present invention provides a design method for an asymmetric helical cylindrical gear pair based on overlap design. This method can design an asymmetric helical cylindrical gear pair with large overlap under the conditions of satisfying a high pressure angle of the working tooth surface and preventing root cutting. At the same time, this design method allows the center distance of the gear pair to be appropriately adjusted. Summary of the Invention

[0005] The purpose of the present invention is to avoid the shortcomings of the existing technology and provide a design method for an asymmetric helical cylindrical gear pair based on overlap. The method adopts an asymmetric helical gear structure design, which has a greater overlap and load-bearing capacity than a spur gear, so that the gear teeth have higher contact strength and bending strength, realizes the design of a helical gear pair with large overlap, and solves the problems existing in the existing technology.

[0006] To achieve the above object, the technical solution adopted by the present invention is a design method for an asymmetric helical cylindrical gear pair based on overlap, comprising the following steps:

[0007] The first step is to define the parameters.

[0008] Determine the basic parameters of the asymmetric helical cylindrical gear pair, including the number of teeth z of the pinion p , the number of teeth of the large gear z g , normal modulus m n , asymmetry coefficient k, pinion tooth top thickness coefficient L pat, large gear tooth top thickness coefficient L gat , helix angle β, installation center distance a';

[0009] The second step is to draw the contour map of effective coincidence degree on the driving side.

[0010] Establish an analytical relationship for the end face tooth profile of an asymmetric helical cylindrical gear and derive the backlash-free meshing equation for an asymmetric helical cylindrical gear pair at the pitch circle. Establish equations for the gear and pinion tooth root pressure angles to be greater than or equal to zero, and for the gear and pinion tooth top pressure angles to be greater than or equal to the pitch circle pressure angle. Draw contour plots of the effective contact ratio of the drive side tooth profile.

[0011] Furthermore, the process of establishing the analytical relationship of the end face tooth profile of the asymmetric helical cylindrical gear is as follows:

[0012] The asymmetric coefficient of the tooth profile on both sides of the asymmetric helical cylindrical gear is expressed as,

[0013]

[0014] In the above formula: r bct —Radius of the sliding side base circle; r bdt —Drive side base circle radius; α oct —Pitch circle pressure angle on sliding side; α odt —Drive side pitch circle pressure angle;

[0015] The relationship between the tooth top thickness coefficient is:

[0016]

[0017] In the above formula: L at —Tooth tip thickness coefficient, L at The value is (0.25-0.4) / z, z is the number of gear teeth; inv is the involute function; α jdt —pressure angle at the intersection of the involutes on the driving side; α jct —pressure angle at the intersection of the involutes on the sliding side; α adt —pressure angle at the involute tooth top on the driving side; α act —pressure angle at the involute tooth top on the sliding side;

[0018] The formula for the end face overlap of an asymmetric helical cylindrical gear pair on the driving side is:

[0019]

[0020] Furthermore, the derivation of the backlash-free meshing equation of the asymmetric helical cylindrical gear pair at the pitch circle is:

[0021]

[0022] In the above formula: i—transmission ratio; z p —Number of teeth on the pinion;

[0023] Furthermore, the process of establishing the equation for the pressure angle of the tooth roots on the sliding side of the large gear and the small gear to be greater than zero includes:

[0024] For the no-interference condition, the pressure angle at the bottom of the sliding side of the pinion must be greater than or equal to zero.

[0025] tan(α lpct )=(1+i)tan(α oct )-itan(α agct )≥0 (5)

[0026] In the above formula: α lpct —The pressure angle of the tooth root on the sliding side of the pinion; α agct —Pressure angle of tooth top on sliding side of large gear;

[0027] For the no-interference condition, the pressure angle at the bottom of the sliding side of the gear must be greater than or equal to zero.

[0028]

[0029] In the above formula: α lgct — tooth root pressure angle on the sliding side of the large gear; α agct —Pressure angle of tooth top on the sliding side of the pinion;

[0030] Furthermore, the process of establishing the constraint equation that the tooth top pressure angle of the large gear and the small gear is equal to the pitch circle pressure angle includes:

[0031] To meet the backlash-free meshing condition of the gear pair at the pitch circle, the tooth tip radius must be larger than the pitch circle radius, that is, the pressure angle at the tooth tip on the driving side must be larger than the pressure angle at the pitch circle.

[0032] The pressure angle of the addendum circle on the driving side of the pinion is greater than or equal to the pressure angle of the pitch circle.

[0033] α apdt -α odt ≥0 (7)

[0034] The pressure angle of the tooth top circle on the driving side of the large gear is greater than or equal to the pressure angle of the pitch circle.

[0035] α agdt -α odt ≥0 (8)

[0036] Furthermore, the process of drawing the effective contact contour map of the driving side tooth profile includes:

[0037] Driving side tooth profile coincidence isoline drawing: Solve the nonlinear equations composed of equations (1), (2), (3), and (4), and by pre-given α apdt A series of values, each given a value to solve the equations once, so that the coincidence contour line is drawn, by changing the ε in formula (3) sd The size of can be used to obtain contour lines with different degrees of coincidence;

[0038] The contour line of the pinion sliding side tooth root pressure angle is 0: Solve the nonlinear equations composed of equations (1), (2), (4), and (5), and by pre-given α apdt A series of values, each given a value to solve the equations once, you can get the pinion sliding side tooth root pressure angle 0 contour line;

[0039] The contour line of the gear sliding side tooth root pressure angle is 0: Solve the nonlinear equations composed of equations (1), (2), (4), and (6), and by pre-given α apdt A series of values, each given a value to solve the equations once, you can get the tooth top pressure angle contour line of the sliding side of the large gear with the root pressure angle of 0;

[0040] The pressure angle of the top circle of the driving side of the pinion is greater than the pressure angle of the pitch circle. The contour line is drawn: Solve the nonlinear equations composed of equations (1), (2), (4), and (7). By pre-given α apdt A series of values, each given a value by solving the equations once, we can get the pinion driving side tooth addendum pressure angle greater than the pitch circle pressure angle contour line;

[0041] The contour line of the tooth top circle pressure angle on the driving side of the large gear is greater than the pitch circle pressure angle is drawn: Solve the nonlinear equations composed of equations (1), (2), (4), and (8), and by pre-given α apdt A series of values, each given a value to solve the equations once, you can get the driving side of the gear tooth tip circle pressure angle greater than the pitch circle pressure angle contour line;

[0042] The area enclosed by the above-mentioned driving side tooth profile overlap contour line, the pinion sliding side tooth root pressure angle zero contour line, the gear sliding side tooth root pressure angle zero contour line, the pinion driving side tooth addendum pressure angle greater than the pitch circle pressure angle contour line, and the gear driving side tooth addendum pressure angle greater than the pitch circle pressure angle contour line is the effective overlap contour line diagram;

[0043] The third step is to select the design coincidence point.

[0044] According to the effective contact contour map obtained in the second step, the design contact point is selected. The horizontal coordinate corresponding to the design contact point is the pressure angle α of the tooth top on the driving side of the pinion. apdtThe vertical axis is the tooth top pressure angle on the driving side of the large gear. According to formula (3), the driving side pitch circle pressure angle parameter α is obtained. odt ;

[0045] The fourth step is to reverse the tool parameters of the asymmetric helical gear rack.

[0046] The rack tool normal surface parameters are inversely calculated based on the gear drive side tooth top pressure angle and pitch circle pressure angle parameters. The analysis process includes:

[0047] The end face pitch circle pressure angle of the sliding side of the asymmetric helical cylindrical gear is,

[0048] α oct =acos(k·cos(α odt )),

[0049] The normal pressure angle at the pitch line on the rack tool drive side is,

[0050]

[0051] The normal pressure angle at the pitch line of the rack tool sliding side is,

[0052]

[0053] In the above formula: a is the center distance of the standard gear pair; a′ is the installation center distance of the gear pair; β is the pitch circle helix angle;

[0054] The tooth thickness at the pitch line of the rack tool is,

[0055]

[0056] The normal modification coefficient of the asymmetric helical cylindrical gear is,

[0057]

[0058] The tooth root height of the rack cutter is,

[0059]

[0060] The tooth top height of the rack cutter is,

[0061]

[0062] In the above formula: c * —Head clearance coefficient; m n —Gear normal module;

[0063] The radius of the tooth tip circle of the rack cutter is,

[0064]

[0065] The distance from the center of the tool tooth top arc to the intersection of the rack centerline and the sliding side cutting edge is,

[0066] e rc =(h ra -r d +r d ·sin(α rc ))·tan(α rc )+r d ·cos(α rc ),

[0067] The distance from the center of the tool tooth top arc to the intersection of the rack centerline and the driving side cutting edge is,

[0068] e rd =(h ra -r d +r d ·sin(α rd ))·tan(α dd )+r d ·cos(α rd ).

[0069] The fifth step is to establish the tooth surface equation of the asymmetric helical cylindrical gear.

[0070] Define the rack cutter for the asymmetric helical cylindrical gear and establish the coordinate system for the rack to generate the asymmetric helical cylindrical gear; determine the meshing equation between the rack cutter and the gear; and establish the tooth surface equation of the asymmetric helical cylindrical gear.

[0071] Further: the rack cutter for defining the asymmetric helical cylindrical gear and establishing a coordinate system for generating the rack into the asymmetric helical cylindrical gear include:

[0072] The tooth profile on the normal section of the rack is divided into two parts. One part is the straight line ab on the sliding side and the straight line df on the driving side, which are used to generate the driving tooth surface of the asymmetric helical cylindrical gear; the other part is the arc bc on the sliding side and the arc cd on the driving side, which are used to generate the transition surface of the asymmetric helical cylindrical gear. The coordinate origin and y-axis of the coordinate system Sa are both on the straight line tooth profile on the sliding side of the rack tool, the coordinate origin and y-axis of the coordinate system Sc are both on the straight line tooth profile on the driving side of the rack tool, the y-axis of the coordinate system Sb is vertically downward and passes through the center point M of the tool tooth top arc, the origin Oa, Ob, and Oc are all located on the rack indexing line, and the tooth thickness on the rack tool indexing line is The y-axis of coordinate system So coincides with the y-axis of coordinate system Sb, and the distance between points Ob and O in the two coordinate systems is x·m n ;

[0073] The linear tooth profile ab on the sliding side of the rack normal section is in the coordinate system s aThe tooth surface equation and normal vector equation are as follows:

[0074]

[0075] Where,

[0076] The sliding side tooth top arc bc in the rack normal section is in the coordinate system s a The tooth surface equation and normal vector equation are as follows:

[0077]

[0078] Where,

[0079] The linear tooth profile df on the driving side of the rack normal section is in the coordinate system s c The tooth surface equation and normal vector equation are as follows:

[0080]

[0081] Where,

[0082] The sliding side tooth top arc cd in the rack normal section is in the coordinate system s c The tooth surface equation and normal vector equation are as follows:

[0083]

[0084] Where,

[0085] The tooth surface and normal vector of the driving side segments ab and bc expressed in the coordinate system Ss are:

[0086]

[0087] The tooth surface and normal vector of the sliding side cd and df segments expressed in the coordinate system Ss are:

[0088]

[0089] In the above formula, L sO , L Ob , L ba , L bc is the position coordinate transformation matrix M sO 、M Ob 、M ba 、M bc Remove the fourth row and fourth column to get it.

[0090] Further: The meshing equation for determining the rack cutter and the asymmetric helical cylindrical gear is:

[0091]

[0092] In the formula, the relative speed

[0093] Further: the establishment of the tooth surface equation of the asymmetric helical cylindrical gear includes:

[0094] The tooth surface of the asymmetric helical cylindrical gear is formed by the tooth profile of the rack cutter plane and the tooth top arc, which can be obtained by the following formula:

[0095]

[0096] Where;

[0097]

[0098] Where r ps —Pitch circle radius; —engagement angle;

[0099] Step 6: Use NX software to create a 3D model of the asymmetric helical cylindrical gear pair.

[0100] According to the tooth surface equation of the asymmetric helical cylindrical gear determined in step five, the single tooth surface point of the gear is obtained through programming solution, and the tooth surface point is imported into NX software for solid modeling to obtain the three-dimensional model of the asymmetric helical cylindrical gear pair.

[0101] The present invention provides a method for designing asymmetric helical gear pairs based on contact. This method can design asymmetric helical gear pairs that meet the required design contact or maximum contact while meeting the design requirements for the drive-side pressure angle, eliminating the need for repeated verification of contact, gear undercutting, meshing interference, and other issues. The resulting high-contact asymmetric helical gear pairs exhibit smooth transmission and strong load-bearing capacity. Furthermore, this design method is applicable to applications where the mounting center distance varies. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] Figure 1 It is a design flow chart of the present invention;

[0103] Figure 2 The involute profile of the end face of the asymmetric helical gear of the embodiment of the present invention;

[0104] Figure 3 is a value line diagram of the end face overlap according to an embodiment of the present invention;

[0105] Figure 4 is the cross-sectional profile of the rack tool method of an embodiment of the present invention;

[0106] Figure 5The rack tool and its coordinate system according to an embodiment of the present invention;

[0107] Figure 6 The rack cutter of the embodiment of the present invention generates a gear coordinate system;

[0108] Figure 7 is a three-dimensional model of an asymmetric helical cylindrical gear according to an embodiment of the present invention;

[0109] Figure 8 This is a three-dimensional model of an asymmetric helical cylindrical gear pair according to an embodiment of the present invention. DETAILED DESCRIPTION

[0110] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0111] In order to achieve the above object, the present invention provides the following specific implementation methods: Figure 1 As shown, the design method of an asymmetric helical cylindrical gear pair based on overlap comprises the following steps:

[0112] The first step is to define the parameters.

[0113] Determine the basic parameters of the asymmetric helical cylindrical gear pair, including the number of teeth z of the pinion p , the number of teeth of the large gear z g , normal modulus m n , asymmetry coefficient k, pinion tooth top thickness coefficient L pat , large gear tooth top thickness coefficient L gat , helix angle β, installation center distance a', the specific values ​​are shown in Table 1;

[0114] Table 1 Basic design parameters of asymmetric helical cylindrical gear pairs

[0115]

[0116] The second step is to draw the contour map of effective coincidence degree on the driving side.

[0117] Establish an analytical relationship for the end face tooth profile of an asymmetric helical cylindrical gear and derive the backlash-free meshing equation for an asymmetric helical cylindrical gear pair at the pitch circle. Establish equations for ensuring that the root pressure angle on the sliding side of the gear and pinion is greater than zero, and establish equations for limiting the tooth tip pressure angle on the gear and pinion to be equal to the pitch circle pressure angle. Draw contour plots of the effective contact ratio of the drive side tooth profile.

[0118] Furthermore, the analytical process of establishing the end face tooth profile analytical relationship of the asymmetric helical cylindrical gear includes:

[0119] The end face tooth profile of the asymmetric helical cylindrical gear is as follows Figure 2As shown, r ft is the tooth root radius, r pt is the pitch circle radius, r at is the radius of the tooth tip circle, r jt is the radius at the intersection of the involutes, and the asymmetric coefficient of the tooth profile on both sides of the asymmetric helical cylindrical gear is expressed as,

[0120]

[0121] In the above formula: r bct —Radius of the sliding side base circle; r bdt —Drive side base circle radius; α oct —Pitch circle pressure angle on sliding side; α odt —Drive side pitch circle pressure angle;

[0122] The relationship between the tooth top thickness coefficient is:

[0123]

[0124] In the above formula: L at —Tooth tip thickness coefficient, L at The value is (0.25-0.4) / z, z is the number of gear teeth; inv is the involute function; α jdt —pressure angle at the intersection of the involutes on the driving side; α jct —pressure angle at the intersection of the involutes on the sliding side; α adt —driving side involute tip circle pressure angle; α act —pressure angle at the involute tooth top on the sliding side;

[0125] The formula for the end face overlap of an asymmetric helical cylindrical gear pair on the driving side is:

[0126]

[0127] Furthermore, the analysis process of deriving the backlash-free meshing equation of the asymmetric helical cylindrical gear pair at the pitch circle includes:

[0128] The backlash-free meshing equation at the pitch circle is:

[0129]

[0130] In the above formula: i—transmission ratio; z p —Number of teeth on the pinion;

[0131] Furthermore, the analysis process of establishing the equation for the pressure angle of the tooth roots on the sliding side of the large gear and the small gear to be greater than zero includes:

[0132] For the no-interference condition, the pressure angle at the bottom of the sliding side of the pinion must be greater than or equal to zero.

[0133] tan(α lpct )=(1+i)tan(α pct )-itan(α agct )≥0 (5)

[0134] In the above formula: α lpct —The pressure angle of the tooth root on the sliding side of the pinion; α agct —Pressure angle of tooth top on sliding side of large gear;

[0135] For the no-interference condition, the pressure angle at the bottom of the sliding side of the gear must be greater than or equal to zero.

[0136]

[0137] In the above formula: α lgct — tooth root pressure angle on the sliding side of the large gear; α agct —Pinion sliding side tooth top pressure angle Further, the establishment of the constraint equation of the gear and pinion tooth top pressure angle being equal to the pitch circle pressure angle, the analysis process includes:

[0138] In order to meet the backlash-free meshing condition of the gear pair at the pitch circle, the radius of the tooth tip circle must be larger than the radius of the pitch circle, that is, the pressure angle at the tooth tip on the driving side must be larger than the pressure angle at the pitch circle.

[0139] The pressure angle of the addendum circle on the driving side of the pinion is greater than or equal to the pressure angle of the pitch circle.

[0140] α apdt -α pdt ≥0 (7)

[0141] The pressure angle of the tooth top circle on the driving side of the large gear is greater than or equal to the pressure angle of the pitch circle.

[0142] α agdt -α pdt ≥0 (8)

[0143] Furthermore, the analysis process of drawing the effective coincidence contour map of the driving side tooth profile includes:

[0144] Driving side tooth profile coincidence isoline drawing: Solve the nonlinear equations composed of equations (1), (2), (3), and (4), and by pre-given α apdt A series of values, each given a value to solve the equations once, so that the coincidence contour line is drawn, by setting the coincidence degree ε in formula (3) sd The values ​​of are 1.4, 1.5, 1.7, and 1.8, and the contour lines under four degrees of coincidence can be obtained, such as Figure 3 A1(ε d =1.4), A2(ε d =1.5), A3(ε d=1.7), A4(ε d =1.8);

[0145] The contour line of the pinion sliding side tooth root pressure angle is 0: Solve the nonlinear equations composed of equations (1), (2), (4), and (5), and by pre-given α apdt A series of values, each given a value to solve the equations once, you can get the pinion sliding side tooth root pressure angle 0 tooth top pressure angle contour line, such as Figure 3 B1(α lpct =0);

[0146] The contour line of the gear sliding side tooth root pressure angle is 0: Solve the nonlinear equations composed of equations (1), (2), (4), and (6), and by pre-given α apdt A series of values, each given a value to solve the equations once, you can get the gear sliding side tooth root pressure angle 0 tooth top pressure angle contour line, such as Figure 3 B2(α lgct =0);

[0147] The pressure angle of the top circle of the driving side of the pinion is greater than the pressure angle of the pitch circle. The contour line is drawn: Solve the nonlinear equations composed of equations (1), (2), (4), and (7). By pre-given α apdt A series of values, each given a value to solve the equations once, you can get the pinion drive side tooth top circle pressure angle greater than the pitch circle pressure angle isoline, such as Figure 3 C1(α apdt =α odt );

[0148] The contour line of the tooth top circle pressure angle on the driving side of the large gear is greater than the pitch circle pressure angle is drawn: Solve the nonlinear equations composed of equations (1), (2), (4), and (8), and by pre-given α apdt A series of values, each given a value to solve the equations once, you can get the driving side of the large gear tooth tip circle pressure angle is greater than the pitch circle pressure angle isoline, such as Figure 3 C2(α agdt =α odt );

[0149] The above curve A1(ε d =1.4), B1(α lpct =0), B2(α lgct =0), C1(α apdt =α odt )、C2(α agdt =α odt ) is the effective coincidence contour map.

[0150] The third step is to select the design coincidence point.

[0151] Furthermore, the analysis process of selecting and designing the coincidence points includes:

[0152] According to the effective contact contour map obtained in the second step, the design contact point is selected. The horizontal coordinate corresponding to the design contact point is the pressure angle α of the tooth top on the driving side of the pinion. apdt The vertical axis is the tooth top pressure angle on the driving side of the large gear. According to formula (3), the driving side pitch circle pressure angle parameter α is obtained. odt ;

[0153] The fourth step is to reverse the tool parameters of the asymmetric helical gear rack.

[0154] Furthermore, the inverse determination of the rack tool normal surface parameters, based on the gear drive side tooth top pressure angle and pitch circle pressure angle parameters, includes:

[0155] The normal cross-section profile of the rack tool is as follows Figure 4 As shown;

[0156] The end face pitch circle pressure angle of the sliding side of the asymmetric helical cylindrical gear is,

[0157] α oct =acos(k·cos(α odt )) (1)

[0158] The normal pressure angle at the pitch line on the rack tool drive side is,

[0159]

[0160] The normal pressure angle at the pitch line of the rack tool sliding side is,

[0161]

[0162] In the above formula: a is the center distance of the standard gear pair; a′ is the installation center distance of the gear pair; β is the pitch circle helix angle;

[0163] The tooth thickness at the pitch line of the rack tool is,

[0164]

[0165] The normal modification coefficient of the helical cylindrical gear is,

[0166]

[0167] The tooth root height of the rack cutter is,

[0168]

[0169] The tooth top height of the rack cutter is,

[0170]

[0171] In the above formula: c * —Head clearance coefficient; m n —Gear normal module;

[0172] The radius of the tooth tip circle of the rack cutter is,

[0173]

[0174] The distance from the center of the tool tooth top arc to the intersection of the rack centerline and the sliding side cutting edge is,

[0175] e rc =(h ra -r d +r d ·sin(α rc ))·tan(α rc )+r d ·cos(α rc ) (9)

[0176] The distance from the center of the tool tooth top arc to the intersection of the rack centerline and the driving side cutting edge is,

[0177] e rd =(h ra -r d +r d ·sin(α rd ))·tan(α rd )+r d ·cos(α rd ) (10)

[0178] The fifth step is to establish the tooth surface equation of the asymmetric helical cylindrical gear.

[0179] Define the rack cutter for the asymmetric helical cylindrical gear and establish the coordinate system for the rack to generate the asymmetric helical cylindrical gear; determine the meshing equation between the rack cutter and the gear; and establish the tooth surface equation of the asymmetric helical cylindrical gear.

[0180] Further: the rack cutter for defining the asymmetric helical cylindrical gear and establishing a coordinate system for generating the rack into the asymmetric helical cylindrical gear include:

[0181] Rack tool and its coordinate system as Figure 5 shown. Figure 5(a) is the rack cutter normal section. The tooth profile on the rack normal section is divided into two parts. One part is the ab straight line tooth profile on the sliding side and the df straight line tooth profile on the driving side, which are used to generate the driving tooth surface of the asymmetric helical cylindrical gear; the other part is the bc arc tooth profile on the sliding side and the cd arc tooth profile on the driving side, which are used to generate the transition surface of the asymmetric helical cylindrical gear. Figure 5 (b) is the rack pitch plane. The coordinate origin and y-axis of the coordinate system Sa are both on the linear tooth profile on the sliding side of the rack tool. The coordinate origin and y-axis of the coordinate system Sc are both on the linear tooth profile on the driving side of the rack tool. The y-axis of the coordinate system Sb is vertically downward and passes through the center point M of the tool tooth top arc. The origins Oa, Ob, and Oc are all located on the rack indexing line. The tooth thickness on the rack tool indexing line is The y-axis of coordinate system So coincides with the y-axis of coordinate system Sb, and the distance between points Ob and O in the two coordinate systems is x·m n .

[0182] The linear tooth profile ab on the sliding side of the rack normal section is in the coordinate system s a The tooth surface equation and normal vector equation are as follows:

[0183]

[0184] Where,

[0185] The sliding side tooth top arc bc in the rack normal section is in the coordinate system s a The tooth surface equation and normal vector equation are as follows:

[0186]

[0187] Where,

[0188] The linear tooth profile df on the driving side of the rack normal section is in the coordinate system s c The tooth surface equation and normal vector equation are as follows:

[0189]

[0190] Where,

[0191] The sliding side tooth top arc cd in the rack normal section is in the coordinate system s c The tooth surface equation and normal vector equation are as follows:

[0192]

[0193] Where,

[0194] The tooth surface and normal vector of the driving side segments ab and bc expressed in the coordinate system Ss are:

[0195]

[0196] The tooth surface and normal vector of the sliding side cd and df segments expressed in the coordinate system Ss are:

[0197]

[0198] In the above formula, L sO , L Ob , L ba , L bc is the position coordinate transformation matrix M sO 、M Ob 、M ba 、M bc Remove the fourth row and fourth column to get;

[0199] Further: The meshing equation for determining the rack cutter and the asymmetric helical cylindrical gear includes:

[0200] The meshing equation between the rack cutter and the asymmetric helical cylindrical gear is:

[0201]

[0202] In the formula, the relative speed

[0203] Further: the establishment of the tooth surface equation of the asymmetric helical cylindrical gear includes:

[0204] The tooth surface of the asymmetric helical cylindrical gear is formed by the tooth profile of the rack tool plane and the tooth top arc. The meshing coordinate system is as follows: Figure 6 As shown, the tooth surface equation can be obtained by the following formula:

[0205]

[0206] Where;

[0207]

[0208] Where r ps —The pitch circle radius of asymmetric helical gears; —Asymmetric helical gear meshing angle, such as Figure 6 As shown;

[0209] Step 6: Use NX software to create a 3D model of the asymmetric helical cylindrical gear pair.

[0210] UG software is used to establish a 3D model of an asymmetric helical cylindrical gear pair. According to the calculation results of step 4, the small gear tooth width is taken as 56mm and the large gear tooth width is taken as 51mm. The end face profile and tooth surface coordinate points of a single tooth groove of the asymmetric helical cylindrical gear are obtained through programming. The tooth surface points are imported into UG software for surface fitting. The fitted surface is then trimmed on the gear blank. The tooth groove is further annularly arrayed to obtain a 3D geometric model of a single gear, as shown in the figure. Figure 7 As shown, the asymmetric helical cylindrical gear pair model is obtained, as shown in Figure 8 shown.

[0211] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A design method for an asymmetric helical cylindrical gear pair based on contact ratio, characterized in that: The following steps are involved: The first step is to define the parameters. Determine the basic parameters of the asymmetric helical cylindrical gear pair, including the number of teeth z of the pinion p , the number of teeth of the large gear z g , normal modulus m n , asymmetry coefficient k, pinion tooth top thickness coefficient L pat , large gear tooth top thickness coefficient L gat , helix angle β, installation center distance a'; The second step is to draw the contour map of effective coincidence degree on the driving side. Establish an analytical relationship for the end face tooth profile of an asymmetric helical cylindrical gear, and derive the backlash-free meshing equation for an asymmetric helical cylindrical gear pair at the pitch circle. Establish equations for the sliding side root pressure angle of the gear and pinion to be greater than or equal to zero, and for the gear and pinion tooth top pressure angle to be greater than or equal to the pitch circle pressure angle. Draw the contour diagram of the effective contact ratio of the tooth profile on the driving side; The process of drawing the effective contact contour diagram of the driving side tooth profile includes: Driving side tooth profile overlap contour drawing: solve the nonlinear equations consisting of the asymmetric coefficient of the tooth profile on both sides of the asymmetric helical cylindrical gear, the relationship between the tooth top thickness coefficient, the end face overlap formula of the asymmetric helical cylindrical gear pair on the driving side, and the derivation of the backlash-free meshing equation of the asymmetric helical cylindrical gear pair at the pitch circle. A series of values, each given a value to solve the equations once, so that the coincidence contour line is drawn, by changing the end face coincidence formula of the asymmetric helical cylindrical gear pair on the driving side The size of , that is, the contour lines under different coincidence degrees are obtained; in, is the pressure angle of the pinion tooth top on the driving side, is the end face overlap of the asymmetric helical cylindrical gear pair on the driving side; Draw the contour line of the pinion sliding side tooth root pressure angle of 0: solve the nonlinear equations consisting of the asymmetric coefficient of the tooth profile on both sides of the asymmetric helical cylindrical gear, the relationship between the tooth top thickness coefficient, the derivation of the backlash-free meshing equation of the asymmetric helical cylindrical gear pair at the pitch circle, and the equation of the pinion sliding side tooth root pressure angle greater than zero, by pre-given A series of values, each time a value is given, the equation system is solved once, and the tooth top pressure angle contour line with the root pressure angle of the pinion sliding side being 0 is obtained; Drawing the contour line of the tooth root pressure angle of the sliding side of the large gear is 0: Solve the nonlinear equations consisting of the asymmetric coefficient of the tooth profile on both sides of the asymmetric helical cylindrical gear, the relationship between the tooth top thickness coefficient, the derivation of the backlash-free meshing equation of the asymmetric helical cylindrical gear pair at the pitch circle, and the equation consisting of the pressure angle of the tooth root on the sliding side of the large gear is greater than zero. A series of values, each time a value is given, the equation system is solved once, and the tooth top pressure angle contour line with the root pressure angle of the sliding side of the large gear is 0 is obtained; Drawing of contour lines of the pressure angle of the tooth top circle on the driving side of the pinion gear is greater than the pressure angle of the pitch circle: Solve the nonlinear equations consisting of the asymmetric coefficient of the tooth profile on both sides of the asymmetric helical gear, the relationship between the tooth top thickness coefficient, the derivation of the backlash-free meshing equation of the asymmetric helical gear pair at the pitch circle, and the equation of the pressure angle of the pinion gear tooth top is greater than or equal to the pressure angle of the pitch circle. A series of values, each given a value to solve the equations once, to obtain the pinion driving side tooth addendum pressure angle is greater than or equal to the pitch circle pressure angle contour line; The contour line of the tooth top circle pressure angle on the driving side of the large gear is greater than the pitch circle pressure angle is drawn: solve the nonlinear equations composed of the asymmetric coefficient of the tooth profile on both sides of the asymmetric helical cylindrical gear, the relationship between the tooth top thickness coefficient, the derivation of the backlash-free meshing equation of the asymmetric helical cylindrical gear pair at the pitch circle, and the equation of the large gear tooth top pressure angle being greater than or equal to the pitch circle pressure angle. A series of values, each given a value to solve the equations once, to obtain the driving side of the gear tooth tip circle pressure angle is greater than or equal to the pitch circle pressure angle contour line; The area enclosed by the above-mentioned driving side tooth profile overlap contour line, the pinion sliding side tooth root pressure angle contour line of 0, the gear sliding side tooth root pressure angle contour line of 0, the pinion driving side tooth addendum pressure angle greater than the pitch circle pressure angle contour line, and the gear driving side tooth addendum pressure angle greater than the pitch circle pressure angle contour line is the effective overlap contour line diagram; The third step is to select the design coincidence point. According to the effective contact contour map obtained in the second step, the design contact point is selected. The horizontal coordinate corresponding to the design contact point is the pressure angle of the tooth top on the driving side of the pinion. , the vertical axis is the tooth top pressure angle on the driving side of the large gear , and further obtain the driving side pitch circle pressure angle parameter according to the end face overlap formula of the driving side of the asymmetric helical cylindrical gear pair ; The fourth step is to reverse the tool parameters of the asymmetric helical gear rack. Inversely calculate the normal surface parameters of the rack tool according to the gear drive side tooth top pressure angle and pitch circle pressure angle parameters; The fifth step is to establish the tooth surface equation of the asymmetric helical cylindrical gear. Define the rack cutter for the asymmetric helical cylindrical gear and establish the coordinate system for the rack to generate the asymmetric helical cylindrical gear; determine the meshing equation between the rack cutter and the gear; and establish the tooth surface equation of the asymmetric helical cylindrical gear. Step 6: Use NX software to create a 3D model of the asymmetric helical cylindrical gear pair; According to the tooth surface equation of the asymmetric helical cylindrical gear determined in step five, the single tooth surface point of the gear is obtained through programming solution, and the tooth surface point is imported into NX software for solid modeling to obtain the three-dimensional model of the asymmetric helical cylindrical gear pair.

2. The design method of an asymmetric helical cylindrical gear pair based on contact ratio according to claim 1, characterized in that: In the second step, the analytical relationship of the end face tooth profile of the asymmetric helical cylindrical gear is established, and the process is as follows: The asymmetric coefficient of the tooth profile on both sides of the asymmetric helical cylindrical gear is expressed as, (1) In the above formula: —Radius of base circle on sliding side; —Drive side base circle radius; —Pitch circle pressure angle on sliding side; —Drive side pitch circle pressure angle; The relationship between the tooth top thickness coefficient is: （2） In the above formula: —tooth tip thickness coefficient, The value is (0.25-0.4) / z, where z is the number of gear teeth; is an involute function; —Pressure angle at the intersection of the involutes on the driving side; —pressure angle at the intersection of the involutes on the sliding side; —pressure angle at the involute tooth top on the driving side; —pressure angle at the involute tooth top on the sliding side; The formula for the end face overlap of an asymmetric helical cylindrical gear pair on the driving side is: (3) Furthermore, the derivation of the backlash-free meshing equation of the asymmetric helical cylindrical gear pair at the pitch circle is: (4) In the above formula: i — transmission ratio; —Number of teeth on the pinion; α pjdt —Pressure angle at the intersection of the involutes on the driving side of the pinion; α pjct —Pressure angle at the intersection of the involutes on the sliding side of the pinion; α gjdt —Pressure angle at the intersection of the involutes on the driving side of the large gear; α gjct —Pressure angle at the intersection of the involutes on the sliding side of the large gear; Furthermore, the process of establishing the equation for the pressure angle of the tooth roots on the sliding side of the large gear and the small gear to be greater than zero includes: For the no-interference condition, the pressure angle at the bottom of the sliding side of the pinion must be greater than or equal to zero. (5) In the above formula: —Root pressure angle of pinion sliding side; —Pressure angle of tooth top on sliding side of large gear; For the no-interference condition, the pressure angle at the bottom of the sliding side of the gear must be greater than or equal to zero. (6) In the above formula: — tooth root pressure angle on the sliding side of the large gear; —Pressure angle of tooth top on the sliding side of the pinion; Furthermore, the process of establishing the equations for the tooth top pressure angles of the large gear and the small gear to be greater than or equal to the pitch circle pressure angles includes: To meet the backlash-free meshing condition of the gear pair at the pitch circle, the tooth tip radius must be larger than the pitch circle radius, that is, the pressure angle at the tooth tip on the driving side must be larger than the pressure angle at the pitch circle. The pressure angle of the addendum circle on the driving side of the pinion is greater than or equal to the pressure angle of the pitch circle. (7) The pressure angle of the tooth top circle on the driving side of the large gear is greater than or equal to the pressure angle of the pitch circle. (8)。 3. The design method of an asymmetric helical cylindrical gear pair based on contact ratio according to claim 2, characterized in that: In the fourth step, the rack tool normal surface parameters are inversely calculated based on the gear drive side tooth top pressure angle and pitch circle pressure angle parameters, and the process includes: The end face pitch circle pressure angle of the sliding side of the asymmetric helical cylindrical gear is, ， The normal pressure angle at the pitch line on the rack tool drive side is, ， The normal pressure angle at the pitch line of the rack tool sliding side is, ， In the above formula: a —Standard gear pair center distance; —Gear pair installation center distance; is the pitch circle helix angle; The tooth thickness at the pitch line of the rack tool is, ， The normal modification coefficient of the asymmetric helical cylindrical gear is, ， The tooth root height of the rack cutter is, ， The tooth top height of the rack cutter is, ， In the above formula: —Head clearance coefficient; —Gear normal module; The radius of the tooth tip circle of the rack cutter is, ， The distance from the center of the tool tooth top arc to the intersection of the rack centerline and the sliding side cutting edge is, ， The distance from the center of the tool tooth top arc to the intersection of the rack centerline and the driving side cutting edge is, 。 4. The design method of an asymmetric helical cylindrical gear pair based on contact ratio according to claim 3, characterized in that: The fifth step defines the rack cutter of the asymmetric helical cylindrical gear and establishes a coordinate system for generating the rack into the asymmetric helical cylindrical gear, including: The tooth profile on the normal section of the rack is divided into two parts. One part is the straight line ab on the sliding side and the straight line df on the driving side, which are used to generate the driving tooth surface of the asymmetric helical cylindrical gear; the other part is the arc bc on the sliding side and the arc cd on the driving side, which are used to generate the transition surface of the asymmetric helical cylindrical gear. The coordinate origin and y-axis of the coordinate system Sa are both on the straight line tooth profile on the sliding side of the rack tool, the coordinate origin and y-axis of the coordinate system Sc are both on the straight line tooth profile on the driving side of the rack tool, the y-axis of the coordinate system Sb is vertically downward and passes through the center point M of the tool tooth top arc, the origin Oa, Ob, and Oc are all located on the rack indexing line, and the tooth thickness on the rack tool indexing line is The y-axis of coordinate system So coincides with the y-axis of coordinate system Sb, and the distance between points Ob and O in the two coordinate systems is ; The linear tooth profile ab on the sliding side of the rack normal section is in the coordinate system The tooth surface equation and normal vector equation are as follows: ， Where, ; The sliding side tooth top arc bc in the rack normal section is in the coordinate system The tooth surface equation and normal vector equation are as follows: ， Where, ; ; The linear tooth profile df on the driving side of the rack normal section is in the coordinate system The tooth surface equation and normal vector equation are as follows: ， Where, ; The sliding side tooth top arc cd in the rack normal section is in the coordinate system The tooth surface equation and normal vector equation are as follows: ， Where, ; ; The tooth surface and normal vector of the driving side segments ab and bc expressed in the coordinate system Ss are: ， The tooth surface and normal vector of the sliding side cd and df segments expressed in the coordinate system Ss are: ， In the above formula, 、 、 、 is transformed by the position coordinate matrix 、 、 、 Remove the fourth row and fourth column to get; Further: The meshing equation for determining the rack cutter and the asymmetric helical cylindrical gear is: ， In the formula, the relative speed ; Further: the establishment of the tooth surface equation of the asymmetric helical cylindrical gear includes: The tooth surface of the asymmetric helical cylindrical gear is formed by the tooth profile of the rack cutter plane and the tooth top arc, which can be obtained by the following formula: ， Where; ， Where, —Pitch circle radius; —Engagement angle.

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