CN116451384B - Gear forming method based on optimized reference rack tooth profile curve - Google Patents
Gear forming method based on optimized reference rack tooth profile curve Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 29
- 238000009825 accumulation Methods 0.000 claims abstract description 5
- 238000006073 displacement reaction Methods 0.000 abstract description 4
- 238000002474 experimental method Methods 0.000 abstract description 2
- 239000003921 oil Substances 0.000 description 7
- 230000010349 pulsation Effects 0.000 description 7
- 239000010720 hydraulic oil Substances 0.000 description 4
- 238000010586 diagram Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 239000007788 liquid Substances 0.000 description 1
- 238000003754 machining Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000005086 pumping Methods 0.000 description 1
- 230000011218 segmentation Effects 0.000 description 1
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- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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Abstract
The invention discloses a gear forming method based on an optimized reference rack tooth profile curve, wherein the reference rack tooth profile curve is formed by convolution or accumulation of two groups of model curves; the module curve can be a piecewise curve or a continuous curve, the piecewise curve is consistent and continuous at piecewise points, the method for obtaining the optimal solution is to establish a nonlinear programming equation based on the minimum acting force when the tooth profile curve of the reference rack and the reference gear are meshed after obtaining equations of two groups of model curves, and solve the nonlinear programming equation to obtain A and B; obtaining a reference rack through the tooth profile curve of the reference rack, and generating the tooth profile of a gear by utilizing the correction rack; the noise of the hydraulic system using the gear of the invention is very small, and experiments prove that the noise below 50 displacement is generally less than 56dB, and the pump noise of 50-100 displacement is generally less than 58 dB.
Description
Technical Field
The invention relates to the field of gear generating methods, in particular to a gear forming method for optimizing a tooth profile curve of a reference rack.
Background
One section of the involute of the traditional gear pump is a gear designed by the requirements of modulus, pressure angle, tooth number, reference circle and the like, and the gear is a pair of gears generated by generating gears formed by the requirements. The driving gear and the driven gear are meshed with the pump body shaft sleeve (or the side plate) to form two cavities, when the master gear and the slave gear rotate, the volumes of the oil inlet cavity and the oil pressing cavity are changed, hydraulic oil enters the oil inlet cavity from the oil tank under the action of atmospheric pressure, and the hydraulic oil is pressed into the oil outlet through the meshing of the driving gear and the driven gear, so that the function of pumping oil is formed.
Because the traditional gears are meshed only at the involute parts, discontinuous oil liquid can be generated by the meshing of the two gears, pulsation can occur to pressure, and at present, the demand of ultra-low noise gear pumps in the market is larger and larger, and the noise of the gear pumps manufactured by the traditional involute gears can not meet the demand.
Disclosure of Invention
The invention aims to solve the problems and provide a gear forming method for optimizing the tooth profile of a reference rack and a gear for generating the tooth profile of a spiral gear, wherein the gear pump gear formed by the method can provide hydraulic oil with small pulsation, and the noise is 15-30 dB smaller than that of the traditional gear pump.
In order to achieve the above purpose, the present invention is realized by the following technical scheme:
based on the positive correlation between pulsation noise and tangential force received during rotation of a gear, the method of the invention provides a gear forming method based on an optimized reference rack tooth profile curve, wherein the reference rack tooth profile curve is formed by convolution or accumulation of two groups of model curves, in order to limit that the gear has less tangential force in all directions during rotation, uniform stress on the curves is realized by accumulation or convolution of multiple curves, and the method for obtaining an optimal solution is that after equations of the two groups of model curves are obtained, a nonlinear programming equation is established based on the minimum acting force when the reference rack tooth profile curve and the reference gear are meshed, and the nonlinear programming equation is solved to obtain A and B; and then obtaining a reference rack through the tooth profile curve of the reference rack, and generating the tooth profile of a gear by utilizing the correction rack.
Compared with the prior art, the invention has the beneficial effects that:
the tooth profile of the invention is connected and meshed, and the generated pulsation is very small;
the tooth profile can be formed based on curve fitting of various models, and is suitable for generating requirements of spiral gears with various requirements;
the noise of the hydraulic system using the gear of the invention is very small, and experiments prove that the noise below 50 displacement is generally less than 56dB, and the pump noise of 50-100 displacement is generally less than 58 dB.
Drawings
FIG. 1 is a schematic diagram of the gear generation principle of the present invention;
FIG. 2 is a schematic view of a helical gear of the present invention;
FIG. 3 is a schematic view of a reference rack of the present invention;
FIG. 4 is a schematic diagram of a gear according to the present invention;
fig. 5 is an enlarged view of the gear K.
Detailed Description
The invention is described in further detail below in connection with the embodiments in the drawings, but is not to be construed as limiting the invention in any way.
The present invention aims to reduce tangential force and thus pulsation of rotation pressure when rotating a gear, and referring to fig. 1, the generating method is also called generating method, which is a method for machining a gear 200 by using a principle of meshing a pair of gears or racks, wherein a rack-type cutter is shown, and when the gear hob 100 rotates around its axial direction, the axial section of the gear hob 100 corresponds to a rack translating along an axis, similar to the reference rack 300 of fig. 3; the generating method is to forcefully process the gear, and the accurate and uniform segmentation of the gear shape is realized between the cutter and the wheel blank according to the meshing motion relationship of the rack and the gear; the reference rack 300 of fig. 3, which has a plurality of basic tooth forms including a side 301, a crown 302, and a root 303; in combination with the gear of fig. 4, which has a gear outer diameter R1, a pitch diameter R3, and a tooth root diameter R2, it can be seen that the circle enclosed by the gear outer diameter R1 is tangent to the crown 302, the pitch diameter R3 passes through the midpoint of the side 301, the circle enclosed by the tooth root diameter R2 is tangent to the root 303, and thus the forcible meshing between the cutter and the wheel blank according to the rack and the gear is realized;
in order to enable the gear pump gear to provide hydraulic oil with small pulsation and cause minimum noise, the invention provides a gear forming method based on an optimized reference rack tooth profile curve, which specifically comprises the following steps:
step S100, obtaining the profile of the gear to be generated, the crown C and the pressure angle α of the reference gear, wherein the profile of the gear to be generated includes the outer diameter R of the gear to be generated 1 Root diameter R 2 The spiral angle beta and the tooth number n, wherein the profile and the pressure angle of the generating gear are preset, for example, the pressure angle alpha of the reference gear is 20 degrees in national standard, and the top clearance C is generally set to be 0;
step S200, calculating the tooth depth h and the tooth width S of the reference gear according to the outline of the gear to be generated, the top clearance C and the pressure angle alpha of the reference gear; the method for solving the tooth depth h and the tooth width s is the existing solving method as follows:；
step S300, selecting two groups of model curvesSolving an initial model curve equation based on the pressure angle alpha, the tooth depth h and the tooth width s of the reference gear;
step S400, fitting factors A, B are distributed to two groups of model curves; two sets of model curvesFitting factorMultiplication or->As reference rack profile, wherein>A convolution representing two curves;
step S500, a nonlinear programming equation is established based on the reference rack tooth profile curve and the minimum acting force when the gear is meshed, and the nonlinear programming equation is solved to obtain A and B;
step S600, obtaining a reference rack based on the obtained reference rack tooth profile curve, and generating a tooth profile of a gear by using the correction rack;
in embodiment 1, the model curve is selected as a continuous curve, and a cosine curve can be selected as an embodiment (this embodiment only serves as step S300 to solve the initial model curve equation):
setting upWherein x is an argument, < >>Are all unknowns due to model curvesTwo tangential points are arranged on the reference rack, as shown in the enlarged view of the gear K in fig. 5, a rectangular coordinate system is established by taking the middle point of the gear tooth width as the center, and a model curve ∈ ->At->,/>The pressure angle alpha of the reference gear is further determined by tangent to the reference rack>Is a value of (2);
in embodiment 2, the model curve is selected as the segment curve, and the segment curves of the circle and the straight line can be selected as the embodiment (this embodiment only solves the initial model curve equation as step S300):
setting upWherein x is an argument, < >>Are all unknowns due to the model curve +.>The reference rack is provided with two tangential points, as shown in the enlarged view of the gear K in FIG. 5, a rectangular coordinate system is established by taking the midpoint of the gear tooth width as the center, and the model curve is shown in the following,/>The pressure angle alpha of the reference gear determines the value of the unknown number;
the following improvements can thus be made in the above-described method:
step S100, obtainingThe profile of the gear to be generated, the top clearance C and the pressure angle alpha of the reference gear, the profile of the gear to be generated comprises the outer diameter R of the gear to be generated 1 Root diameter R 2 Helix angle beta and number of teeth n;
step S200, calculating the tooth depth h and the tooth width S of the reference gear according to the outline of the gear to be generated, the top clearance C and the pressure angle alpha of the reference gear;
step S300, selecting two groups of model curvesSolving an initial model curve equation based on the pressure angle, the tooth depth h and the tooth width s of the reference gear;
for selecting two sets of model curvesThe method of (2) is as follows: in order to ensure that the tooth profile of the invention is in continuous engagement, the modular curve should be a segmented curve or a continuous curve, the segmented curve being consistently continuous at the segmented points; the continuous curve is one or two of elliptic curve, cubic curve, four-time curve and cosine function curve; the piecewise curve is one or two of a piecewise curve of a circle and a straight line, a piecewise curve of an ellipse and a straight line, a piecewise curve of a circle and a cubic curve, and an elliptic and cosine function curve;
step S400, fitting factors A, B are distributed to two groups of model curves; two sets of model curvesFitting factorMultiplication or->As reference rack profile, wherein>A convolution representing two curves;
in order to limit that the gears have less tangential force in all directions when rotating, uniform stress on the curves is realized by accumulating or convoluting multiple curves, the convolution of the two curves ensures the characteristics of the gears and is more uniform, and the accumulation of the two curves can be more outstanding in characteristics and can also have other outstanding characteristics;
step S500, a nonlinear programming equation is established based on the reference rack tooth profile curve and the minimum acting force when the gear is meshed, and the nonlinear programming equation is solved to obtain A and B; the nonlinear programming equation here may be:
wherein the method comprises the steps ofIs the axial force applied during the rotation of the tooth form, +.>For tangential forces experienced by the tooth form as it rotates, const represents a constant independent of A, B; and then in->The tangential force is minimum under the condition that the axial force applied to the tooth form during rotation is constant (the rotation force pulsation source and the tangential force of the gear are independent of the distributed fitting factors);
and S600, obtaining a reference rack based on the obtained tooth profile curve of the reference rack, and generating the tooth profile of a gear by using the correction rack, so as to realize the generation of the gear under the condition that the tangential force is limited to be minimum.
The above examples are provided for convenience of description of the present invention and are not to be construed as limiting the invention in any way, and any person skilled in the art will make partial changes or modifications to the invention by using the disclosed technical content without departing from the technical features of the invention.
Claims (4)
1. A gear forming method based on optimized reference rack tooth profile curve is characterized in that,
the reference rack tooth profile curve is formed by convolution or accumulation of two groups of model curves;
the model curve is a segmented curve or a continuous curve, and the segmented curve is consistent and continuous at segmented points;
the continuous curve is one or two of an elliptic curve, a cubic curve, a quadric curve and a cosine function curve;
the segmented curve is one or two of a segmented curve of a circle and a straight line, a segmented curve of an ellipse and a straight line, a segmented curve of a circle and a cubic curve, and an elliptic and cosine function curve;
the forming method comprises the following steps:
step S100, obtaining the profile of the gear to be generated, the crown C and the pressure angle α of the reference gear, wherein the profile of the gear to be generated includes the outer diameter R of the gear to be generated 1 Root diameter R 2 Helix angle beta and number of teeth n;
step S200, calculating the tooth depth h and the tooth width S of the reference gear according to the outline of the gear to be generated, the top clearance C and the pressure angle alpha of the reference gear;
step S300, selecting two groups of model curvesSolving an initial model curve equation based on the pressure angle alpha, the tooth depth h and the tooth width s of the reference gear;
step S400, fitting factors A, B are distributed to two groups of model curves; two sets of model curvesFitting factorMultiplication or->As reference rack profile, wherein>A convolution representing two curves;
step S500, a nonlinear programming equation is established based on the reference rack tooth profile curve and the minimum acting force when the gear is meshed, and the nonlinear programming equation is solved to obtain A and B;
step S600, a reference rack is obtained based on the obtained reference rack tooth profile curve, and then the tooth profile of a gear is generated by using the reference rack.
2. A method of forming a gear based on an optimized reference rack profile as defined in claim 1, wherein: the step S200 calculates the tooth depth h and the tooth width S of the reference gear by,。
3. a method of forming a gear based on an optimized reference rack profile as defined in claim 1, wherein: the step S300 is a method for solving an initial model curve equation based on the pressure angle, the tooth depth h and the tooth width S of the reference gear, and is to calculate the model curve equation by taking the tooth depth h, the tooth width S and two tangent points of the model curve on the reference rack as initial conditions.
4. A method of forming a gear based on an optimized reference rack profile as defined in claim 1, wherein: in the step S500, a nonlinear programming equation is established based on the minimum acting force when the reference rack tooth profile curve and the reference gear mesh, and the nonlinear programming equation is solved to obtain nonlinear programming equations of a and B as follows:
；
wherein the method comprises the steps ofIs the axial force applied during the rotation of the tooth form, +.>Const represents a constant independent of A, B, which is the tangential force experienced by the tooth form as it rotates.
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