Design method of asymmetric helical cylindrical gear pair based on contact ratio

Abstract

The invention relates to the technical field of cylindrical gear design, in particular to an asymmetric helical cylindrical gear pair design method based on the contact ratio. Comprising the steps of defining parameters, drawing a driving side effective contact ratio contour map, selecting design contact ratio points, reversely solving parameters of an asymmetric helical spur gear rack tool, establishing a tooth surface equation of an asymmetric helical spur gear, and establishing a three-dimensional model of the asymmetric helical spur gear pair by adopting NX software. According to the method, the asymmetric helical cylindrical gear pair meeting the requirement for designing the overlap ratio or the maximum overlap ratio can be designed under the condition that the design requirement for the pressure angle of the driving side is met, and the overlap ratio, gear undercutting, meshing interference and other problems do not need to be repeatedly checked. The designed large-overlap-ratio asymmetric helical cylindrical gear pair has the advantages of being stable in transmission and high in bearing capacity. And the design method can be suitable for occasions 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 of engineering machinery and heavy vehicles, which promotes the development of high-precision electric drive reducers towards high power and high speed. As the core basic parts of reducers, gears have put forward higher requirements on the transmission performance of gears. Studies have shown that the pressure angle has a great influence on the meshing performance of spur involute cylindrical gears. By increasing the pressure angle of the tooth surface on the working side, the root thickness of the tooth increases, and the radius of curvature of the tooth profile increases, which can improve the contact strength and bending strength of the spur gear teeth. However, the overlap of spur gears is usually small and the load-bearing capacity is limited. The large pressure angle on the working side will also reduce the overlap and the thickness of the tooth top, affecting the transmission stability and noise level.

[0003] At present, the parameter design method for asymmetric gears is mostly to pre-set the gear parameters, then calculate the overlap and determine whether it reaches the required value. This process requires repeated calculations many times, the process is very complicated, and 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 a large overlap under the conditions of satisfying a high pressure angle of the working tooth surface and no 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 prior art and provide a design method for an asymmetric helical cylindrical gear pair based on overlap, which adopts an asymmetric helical gear structure design, has a greater overlap and load-bearing capacity than spur gears, makes 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 prior art.

[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 is 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 the analytical relationship of the end face tooth profile of the asymmetric helical cylindrical gear, derive the backlash-free meshing equation of the asymmetric helical cylindrical gear pair at the pitch circle; establish the equation that the tooth root pressure angle of the sliding side of the large gear and the small gear is greater than or equal to zero, and establish the equation that the tooth top pressure angle of the large gear and the small gear is greater than or equal to the pitch circle pressure angle; draw the contour diagram of the effective overlap of the driving 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 asymmetry 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 base circle on the sliding side; 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] Further, 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 root of the sliding side of the large gear and the small gear being 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 pinion tooth top on sliding side;

[0030] Furthermore, the process of establishing the limiting 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 condition of gear pair meshing without backlash at the pitch circle, the radius of the tooth tip circle should be larger than the radius of the pitch circle, that is, the pressure angle at the tooth tip on the driving side of the gear should be larger than the pressure angle at the pitch circle.

[0032] The pressure angle of the tooth top 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 coincidence contour diagram of the driving side tooth profile includes:

[0037] Driving side tooth profile overlap contour 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 coincidence degrees;

[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) by pre-given α apdt A series of values, each given a value to solve the system of 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 gear with the root pressure angle of 0;

[0040] The pressure angle of the pinion tooth top circle on the driving side 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, solve the equations once, and you can get the contour line where the pressure angle of the addendum circle on the driving side of the pinion is greater than the pressure angle of the pitch circle;

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

[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 top circle pressure angle greater than the pitch circle pressure angle contour line, and the gear driving side tooth top circle 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 pinion driving side tooth top. apdt, the ordinate is the tooth top pressure angle on the driving side of the large gear, and the driving side pitch circle pressure angle parameter α is further obtained according to formula (3): odt ;

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

[0046] The normal surface parameters of the rack tool 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 pitch circle pressure angle of the sliding side of the asymmetric helical 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 standard gear pair; a′ is the center distance of gear pair installation; β is the pitch circle helix angle;

[0054] The tooth thickness at the pitch line of the rack cutter 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 tip 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 tip 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 of the asymmetric helical cylindrical gear, establish the coordinate system of the rack developed into the asymmetric helical cylindrical gear; determine the meshing equation between the rack cutter and the gear; establish the tooth surface equation of the asymmetric helical cylindrical gear;

[0071] Further: the rack cutter of the asymmetric helical cylindrical gear is defined, and the coordinate system of the rack developed into the asymmetric helical cylindrical gear is established, including:

[0072] The tooth profile on the normal section of the rack 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 develop 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 develop 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 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 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, 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 the 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 under are:

[0074]

[0075] In the formula,

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

[0077]

[0078] In the formula,

[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 under are:

[0080]

[0081] In the formula,

[0082] The arc cd of the tooth tip on the sliding side in the normal section of the rack is in the coordinate system s c The tooth surface equation and normal vector equation under are:

[0083]

[0084] In the formula,

[0085] The tooth surface and normal vector of the driving side segments ab and bc 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] In the formula, r ps — Pitch circle radius; — engagement angle;

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

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

[0101] The beneficial effects of the present invention are as follows: the present invention provides a design method for an asymmetric helical cylindrical gear pair based on overlap, which can design an asymmetric helical cylindrical gear pair that meets the required design overlap or maximum overlap while meeting the design requirements of the driving side pressure angle, without repeatedly checking overlap, gear undercutting, meshing interference and other issues. The designed asymmetric helical cylindrical gear pair with large overlap has the characteristics of stable transmission and strong load-bearing capacity. And the design method can be applied to occasions where the installation center distance changes. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

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

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

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

[0107] Figure 6 is a gear coordinate system generated by a rack tool according to an embodiment of the present invention;

[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 It 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 in conjunction with 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 asymmetric helical cylindrical gear pair design method 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 is 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 the analytical relationship of the end face tooth profile of the asymmetric helical cylindrical gear, derive the backlash-free meshing equation of the asymmetric helical cylindrical gear pair at the pitch circle; establish the equation that the tooth root pressure angle of the sliding side of the large gear and the small gear is greater than zero, and establish the limiting equation that the tooth top pressure angle of the large gear and the small gear is equal to the pitch circle pressure angle; draw the contour map of the effective overlap of the driving 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 an 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 base circle on the sliding side; 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 derivation of the backlash-free meshing equation of the asymmetric helical cylindrical gear pair at the pitch circle includes the following analysis process:

[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 root of the sliding side of the large gear and the small gear being 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 gear 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 condition of gear pair meshing without backlash at the pitch circle, it is necessary to make the radius of the tooth tip circle larger than the radius of the pitch circle, that is, the pressure angle at the tooth tip on the driving side of the gear tooth should be larger than the pressure angle at the pitch circle.

[0139] The pressure angle of the tooth top 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 diagram of the driving side tooth profile includes:

[0144] Driving side tooth profile overlap contour 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 equation system 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 we can get the contour lines under four degrees of coincidence, 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) 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 pinion tooth top circle on the driving side 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 contour line, such as Figure 3 C1(α apdt =α odt );

[0148] The contour line of the pressure angle of the tooth top circle on the driving side of the large gear is greater than the pressure angle of the pitch circle: Solve the nonlinear equations composed of equations (1), (2), (4), and (8) and give α in advance. apdt A series of values, each given a value to solve the equations once, you can get the driving side of the gear tooth top circle pressure angle greater than the pitch circle pressure angle contour line, 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 point 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 pinion driving side tooth top. apdt , the ordinate is the tooth top pressure angle on the driving side of the large gear, and the driving side pitch circle pressure angle parameter α is further obtained according to formula (3): odt ;

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

[0154] Further, the inverse determination of the normal surface parameters of the rack tool comprises:

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

[0156] The end pitch circle pressure angle of the sliding side of the asymmetric helical 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 standard gear pair; a′ is the center distance of gear pair installation; β is the pitch circle helix angle;

[0163] The tooth thickness at the pitch line of the rack cutter 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 tip 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 tip 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 of the asymmetric helical cylindrical gear, establish the coordinate system of the rack developed into the asymmetric helical cylindrical gear; determine the meshing equation between the rack cutter and the gear; establish the tooth surface equation of the asymmetric helical cylindrical gear;

[0180] Further: the rack cutter of the asymmetric helical cylindrical gear is defined, and the coordinate system of the rack developed into the asymmetric helical cylindrical gear is established, including:

[0181] Rack tool and its coordinate system are as follows 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 develop 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 develop the transition surface of the asymmetric helical cylindrical gear. Figure 5 (b) is the rack pitch plane. The origin and y-axis of the coordinate system Sa are on the linear tooth profile on the sliding side of the rack tool, the origin and y-axis of the coordinate system Sc are 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 origin Oa, Ob, 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 the 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 under are:

[0183]

[0184] In the formula,

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

[0186]

[0187] In the formula,

[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 under are:

[0189]

[0190] In the formula,

[0191] The arc cd of the tooth tip on the sliding side in the normal section of the rack is in the coordinate system s c The tooth surface equation and normal vector equation under are:

[0192]

[0193] In the formula,

[0194] The tooth surface and normal vector of the driving side segments ab and bc 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 of 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 cutter 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] In the formula, 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 an asymmetric helical cylindrical gear pair.

[0210] The UG software is used to establish the 3D model of the asymmetric helical cylindrical gear pair. According to the calculation results of step 4, the small gear tooth width is 56mm and the large gear tooth width is 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 the UG software for surface fitting, and then the fitted surface is trimmed on the gear blank. The tooth groove is further arrayed to obtain the 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 principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A design method for an asymmetric helical cylindrical gear pair based on overlap, 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 is 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 the analytical relationship of the end face tooth profile of the asymmetric helical cylindrical gear, derive the backlash-free meshing equation of the asymmetric helical cylindrical gear pair at the pitch circle; establish the equation that the root pressure angle of the sliding side of the large gear and the small gear is greater than or equal to zero, and establish the equation that the top pressure angle of the large gear and the small gear is greater than or equal to the pitch circle pressure angle; draw the contour diagram of the effective overlap of the driving side tooth profile, 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 α of the pinion driving side tooth top. apdt , the ordinate is the tooth top pressure angle α on the driving side of the large gear agdt , and further obtain the driving side pitch circle pressure angle parameter α according to the end face overlap formula of the driving side of the asymmetric helical cylindrical gear pair odt ; The fourth step is to reverse the tool parameters of the asymmetric helical cylindrical 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 of the asymmetric helical cylindrical gear, establish the coordinate system of the rack developed into the asymmetric helical cylindrical gear; determine the meshing equation between the rack cutter and the gear; establish the tooth surface equation of the asymmetric helical cylindrical gear; Step 6: Use NX software to build 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, a single tooth surface point of the gear is obtained by programming, and the tooth surface point is imported into NX software for solid modeling, thereby obtaining a three-dimensional model of the asymmetric helical cylindrical gear pair.

2. The design method of an asymmetric helical cylindrical gear pair based on overlap as claimed in 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 asymmetry coefficient of the tooth profile on both sides of the asymmetric helical cylindrical gear is expressed as, In the above formula: r bct —Radius of the base circle on the sliding side; r bdt —Drive side base circle radius; α oct —Pitch circle pressure angle on sliding side; α odt —Drive side pitch circle pressure angle; The relationship between the tooth top thickness coefficient is: 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; The formula for the end face overlap of an asymmetric helical cylindrical gear pair on the driving side is: Further, the derivation of the backlash-free meshing equation of the asymmetric helical cylindrical gear pair at the pitch circle is: In the above formula: i—transmission ratio; z p —Number of teeth on the pinion; Furthermore, the process of establishing the equation for the pressure angle of the tooth root of the sliding side of the large gear and the small gear being 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. tan(α lpct )=(1+i)tan(α oct )-it(α agct )≥0 (5) 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; 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. In the above formula: α lgct — tooth root pressure angle on the sliding side of the large gear; α agct —Pressure angle of pinion tooth top on sliding side; Furthermore, the process of establishing the equation that the tooth top pressure angle of the large gear and the small gear is greater than or equal to the pitch circle pressure angle includes: To meet the condition of gear pair meshing without backlash at the pitch circle, the radius of the tooth tip circle should be larger than the radius of the pitch circle, that is, the pressure angle at the tooth tip on the driving side of the gear should be larger than the pressure angle at the pitch circle. The pressure angle of the tooth top circle on the driving side of the pinion is greater than or equal to the pressure angle of the pitch circle. α apdt -α odt ≥0 (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. α agdt -α odt ≥0 (8)； Furthermore, the process of drawing the effective coincidence contour diagram of the driving side tooth profile includes: Driving side tooth profile overlap contour 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 coincidence degrees; 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) by pre-given α apdt A series of values, each given a value to solve the system of equations once, you can get the pinion sliding side tooth root pressure angle 0 contour line; 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 gear with the root pressure angle of 0; The pressure angle of the pinion tooth top circle on the driving side 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, solve the equations once, and you can get the contour line where 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; The contour line of the pressure angle of the tooth top circle on the driving side of the large gear is greater than the pressure angle of the pitch circle: Solve the nonlinear equations composed of equations (1), (2), (4), and (8) and give α in advance. apdt A series of values, each given a value, solve the equations once, and you can get the contour line where the pressure angle of the addendum circle on the driving side of the large gear is greater than or equal to the pressure angle of the pitch circle; The area enclosed by the above-mentioned driving side tooth profile overlap contour lines, the pinion sliding side tooth root pressure angle of 0 contour lines, the large gear sliding side tooth root pressure angle of 0 contour lines, the pinion driving side tooth top circle pressure angle greater than the pitch circle pressure angle contour lines, and the large gear driving side tooth top circle pressure angle greater than the pitch circle pressure angle contour lines is the effective overlap contour line diagram.

3. The design method of an asymmetric helical cylindrical gear pair based on overlap as claimed in claim 1, 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 pitch circle pressure angle of the sliding side of the asymmetric helical cylindrical gear is, a oct =acos(k·cos(α odt )), 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 is the center distance of standard gear pair; a′ is the center distance of gear pair installation; β is the pitch circle helix angle; The tooth thickness at the pitch line of the rack cutter 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: c * —Head clearance coefficient; m n —Gear normal module; The radius of the tooth tip circle of the rack cutter is, The distance from the center of the tool tooth tip arc to the intersection of the rack centerline and the sliding side cutting edge is, e rc =(h ra -r d +r d ·sin(a rc ))·tan(a rc )+r d ·cos(α rc ), The distance from the center of the tool tooth tip arc to the intersection of the rack centerline and the driving side cutting edge is, e rd =(h ra -r d +r d ·sin(a rd ))·tan(a dd )+r d ·cos(α rd )。 4. A design method for an asymmetric helical cylindrical gear pair based on overlap as claimed in any one of claims 1 to 3, characterized in that: In the fifth step, the rack cutter of the asymmetric helical cylindrical gear is defined, and the coordinate system of the rack developed into the asymmetric helical cylindrical gear is established, including: The tooth profile on the normal section of the rack 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 develop 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 develop 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 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 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, 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 the points Ob and O in the two coordinate systems is x·m n ; 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 under are: In the formula, The arc bc of the tooth top on the sliding side in the normal section of the rack is in the coordinate system s a The tooth surface equation and normal vector equation under are: In the formula, 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 under are: In the formula, The arc cd of the tooth tip on the sliding side in the normal section of the rack is in the coordinate system s c The tooth surface equation and normal vector equation under are: In the formula, The tooth surface and normal vector of the driving side segments ab and bc 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, 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; 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: In the formula, r ps — Pitch circle radius; —Engagement angle.

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