CN116842664A - Tooth surface forward design method, device and medium for meshing performance requirements - Google Patents
Tooth surface forward design method, device and medium for meshing performance requirements Download PDFInfo
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Abstract
The invention discloses a tooth surface forward design method, a device and a medium for meshing performance requirements, wherein the method comprises the following steps: calculating mathematical expression of the gear engagement performance requirement; calculating the allowable limit deviation in the manufacturing process, and accounting for mathematical expression of the gear engagement performance requirement; carrying out tooth surface solving under a given actual meshing state to obtain an initial design tooth surface; performing performance check under the expected engagement state to obtain a further designed tooth surface; correcting the advanced design tooth surface according to manufacturing conditions and process requirements to obtain a perfect design result; the method for solving the tooth surface geometry based on the actual tooth surface meshing performance is defined under the condition of comprehensively considering the deviation of the gear to be processed by establishing the relation between the service performance and the gear meshing performance from the service performance, and on the basis, the design result is converted into the processable tooth surface parameters by comprehensively considering the processing and manufacturing conditions of the gear.
Description
Technical Field
The invention relates to the technical field of gear transmission design and manufacture, in particular to a tooth surface forward design method, a tooth surface forward design device and a tooth surface forward design medium for meshing performance requirements.
Background
Gears are an important component in transmission design and are widely applied to various transmission mechanisms; at present, the design mode of the gear is mainly to carry out macroscopic parameter design according to the actual use condition of the gear, and then carry out tooth surface modification optimization according to the processing and manufacturing condition of the gear on the basis of the macroscopic parameter design, and finally obtain a group of feasible microscopic parameters of the tooth surface so as to determine the tooth surface geometry of the gear for actual work.
The tooth surface geometry is obtained by adopting the traditional gear shaping optimization, the essence of the method is iterative optimization with performance as a target, no theoretical analysis exists, and the fracture exists between the tooth surface geometry and the product performance index, so the tooth surface geometry obtained by adopting the traditional method is not necessarily the optimal tooth surface geometry required by the product; the product performance in actual engineering is severely dependent on the experience of engineering technicians.
Tooth surface geometry is an important factor for determining gear transmission performance, and the gear transmission performance as an important component in a product directly affects the final performance of the product; with the improvement of living standard, the performance requirement of people on products is higher and higher, and the traditional design mode of gears can not meet the increasingly improved product performance requirement.
Disclosure of Invention
The invention aims to solve the problems in the prior art, and provides a tooth surface forward design method, a tooth surface forward design device and a tooth surface forward design medium for meshing performance requirements, so as to solve the problems that the tooth surface geometry and product performance indexes are split in the prior art, and the tooth surface geometry can not completely meet the use requirements; the current situation that the tooth surface geometric design can only be obtained by modifying and optimizing by experience of engineers in the past and the result is not unique is changed.
In order to solve the technical problems, the specific technical scheme of the invention is as follows:
in one aspect, the present invention provides a tooth surface forward design method for meeting meshing performance requirements, including the steps of:
calculating mathematical expression of the gear engagement performance requirement;
calculating allowable limit deviations during manufacturing and accounting for mathematical representations of the gear engagement performance requirements;
based on the mathematical expression of the gear engagement performance requirement, carrying out tooth surface solving under a given actual engagement state to obtain an initial design tooth surface;
performing performance check in a desired engagement state based on the initial design tooth surface to obtain a further design tooth surface;
and correcting the advanced design tooth surface according to manufacturing conditions and process requirements to obtain a perfect design result.
As an improvement, the calculating the mathematical expression of the gear engagement performance requirement includes: obtaining macroscopic parameters of a gear, design performance indexes of the product, actual running conditions of a gear pair, gear materials and heat treatment conditions, theoretical tooth surfaces of a large gear and a small gear, converting the macroscopic parameters and the product design performance indexes into gear meshing performance through calculation, and carrying out characterization in a mathematical mode to obtain mathematical expression of the gear meshing performance requirements.
As an improvement, the calculating the mathematical expression of the gear engagement performance requirement further includes: index conversion directly realized by gear transmission; switching boundary conditions required by gear operation; conversion of the influence of actual running conditions of the gears; the gear teeth themselves are transformed.
As an improvement, said calculating the limit deviation allowed during manufacture and accounting for a mathematical representation of said gear mesh performance requirement comprises: and calculating the limit deviation value of the gear teeth and correlating the limit deviation value with a deviation type, and converting the limit deviation value and the deviation type into input boundary conditions for calculating the meshing performance of the gear.
As an improved solution, the tooth surface solving under the given actual engagement state based on the mathematical expression of the gear engagement performance requirement to obtain an initial design tooth surface includes: in the gear engagement performance requirement, the gear engagement performance which is consistent with the given actual engagement state is matched, the limit deviation allowed in the manufacturing process is introduced, on the basis, the gear engagement principle is adopted, and the design tooth surface of the small wheel is solved on the basis of the theoretical tooth surface of the large wheel.
As an improved solution, the tooth surface solving is performed under a given actual engagement state based on the mathematical expression of the gear engagement performance requirement, to obtain an initial design tooth surface, and the method further includes: determining performance indexes and working conditions for tooth surface design; analyzing actual meshing performance indexes of the gear teeth; solving the comprehensive rigidity of the gear teeth; defining a gear motion rule; the method is characterized in that the designed tooth surface of the small wheel is solved by adopting a meshing principle on the basis of the theoretical tooth surface of the large wheel, the motion rule of the gear, the calculation condition corresponding to the motion rule of the gear and the tooth thickness reduction.
As an improved solution, the performance checking is performed in a desired engagement state based on the initial design tooth surface to obtain a further design tooth surface, including: and checking and calculating the gear meshing performance in the expected meshing state by adopting the theoretical tooth surface of the large wheel and the design tooth surface of the small wheel, and if the gear meshing performance does not meet the product requirement, carrying out iterative calculation by modifying the gear movement rule and the tooth thickness thinning amount until the gear meshing performance meets the product requirement.
As an improved solution, the correcting the advanced design tooth surface according to the manufacturing condition and the process requirement to obtain a perfect design result includes:
Selecting the processing conditions and the processing technology of the designed gear; the instantaneous tooth surface meshing characteristic is not changed into a principle, and the tooth thickness thinning amount of each meshing phase is distributed among the sizes according to the selected processing conditions and process;
determining limit deviation generated in the tooth surface geometry manufacturing process according to the selected processing conditions and process, and adopting the tooth surface geometry containing the limit deviation to check and calculate the performance index; if the requirements cannot be met, the machining conditions or the process are selected again, and if the requirements can be met, the limit deviation allowed by the tooth surface geometry is given;
and integrating the tooth surface geometry, the limit deviation, the corresponding machining conditions and the process requirements to obtain and output the perfect design result.
On the other hand, the invention also provides a tooth surface forward direction design device facing to the engagement performance requirement, which comprises the following components: a mathematical expression calculation unit for calculating a mathematical expression of the gear engagement performance requirement;
the limit deviation conversion unit is used for calculating the limit deviation allowed in the manufacturing process and accounting for mathematical expression of the gear engagement performance requirement;
the tooth surface geometric solving unit is used for carrying out tooth surface solving under a given actual meshing state based on the mathematical expression of the gear meshing performance requirement to obtain an initial design tooth surface;
The tooth surface geometry checking unit is used for performing performance checking in an expected meshing state based on the initial design tooth surface to obtain a further design tooth surface;
and the tooth surface geometric output unit is used for correcting the advanced design tooth surface according to manufacturing conditions and process requirements to obtain a perfect design result.
In another aspect, the present invention also provides a computer readable storage medium having a computer program stored thereon, which when executed by a processor, implements the steps of the tooth surface forward design method for meshing performance requirements.
The technical scheme of the invention has the beneficial effects that:
1. according to the tooth surface forward design method facing the meshing performance requirement, from the point of product service performance, the relation between the product service performance and the gear meshing performance is established, and under the condition of comprehensively considering the deviation of a processed gear, a method for solving tooth surface geometry based on the actual meshing performance of the tooth surface is defined; on the basis, the machining and manufacturing conditions of the gear are comprehensively considered, and the design result is converted into a machinable tooth surface parameter; the application of the method lays a foundation for realizing the forward design of the tooth surface geometry, changes the situation that the tooth surface geometry and the product performance index are cracked, and the tooth surface geometry can not completely meet the use requirement; the problems that the geometrical design of the tooth surface can only be modified and optimized by depending on the experience of engineers in the past and the result is not unique are solved; the tooth surface geometric design realizes further improvement of the meshing performance under the same condition, simultaneously provides a theoretical and realized basis for the design of the high-performance gear transmission device, has great practical value, and makes up the defects of the prior art.
2. The tooth surface forward design device facing the meshing performance requirement can realize the starting from the product service performance through the mutual matching of the mathematical expression calculation unit, the limit deviation conversion unit, the tooth surface geometric solving unit, the tooth surface geometric checking unit and the tooth surface geometric output unit, and defines a method for solving the tooth surface geometric based on the actual meshing performance of the tooth surface under the condition of comprehensively considering the deviation of the gear to be processed by establishing the relation between the product service performance and the gear meshing performance; on the basis, the machining and manufacturing conditions of the gear are comprehensively considered, the design result is converted into the machinable tooth surface parameters, and a foundation is laid for realizing the forward design of the tooth surface geometry.
3. The computer readable storage medium can realize the coordination of a guided mathematical expression calculation unit, a limit deviation conversion unit, a tooth surface geometric solving unit, a tooth surface geometric checking unit and a tooth surface geometric output unit, further, after the product requirement is converted into the actual meshing performance requirement of the gear from the product use performance requirement, the tooth surface geometric design is carried out according to the actual meshing performance requirement by adopting the meshing principle, the elastic mechanics and other forward theories, the basic thought from the tooth surface geometry to the processing and manufacturing realization is provided, the theoretical basis is provided for the high-performance gear transmission design, the current situation that the tooth surface geometric design depends on the experience of engineering technicians is solved, and meanwhile, a feasible method and a feasible way are provided for improving the gear transmission performance.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the present invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a tooth surface forward design method for meeting meshing performance requirements according to example 1 of the present invention;
FIG. 2 is a schematic representation of the single tooth peripheral node in the gear motion diagram in the tooth surface forward design method facing the engagement performance requirement according to embodiment 2 of the present invention;
FIG. 3 is a schematic illustration of the definition of the geometry of the contact in the tooth surface in the positive design method for tooth surface facing the engagement performance requirement according to example 2 of the present invention;
fig. 4 is a schematic diagram showing the change of torsional stiffness of a single tooth in the tooth surface forward design method facing the requirement of engagement performance according to embodiment 2 of the present invention.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making clear and defining the scope of the present invention.
In the description of the present invention, it should be noted that the described embodiments of the present invention are some, but not all embodiments of the present invention; all other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The terms "initial," "advanced," "complete," and the like in the description and claims herein and in the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments described herein may be capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, apparatus, article, or device that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed or inherent to such process, method, article, or device.
The invention mainly starts from the requirement of product service performance, provides a method from the requirement of gear engagement actual performance to the geometric forward design of the tooth surface, and simultaneously provides a basic thought for processing and manufacturing the designed tooth surface, thereby laying a foundation for high-performance gear transmission design and manufacturing.
Embodiment 1. This embodiment provides a tooth surface forward design method for meeting the engagement performance requirement, as shown in fig. 1, comprising the following steps:
s100, calculating mathematical expression of gear engagement performance requirements;
the mathematical expression of the gear engagement performance requirement is based on the determined gear macroscopic design and the theoretical tooth surfaces of the large and small wheels, and the product use performance is converted into the gear engagement performance through calculation according to the product use performance requirement and the actual working conditions of the gear pair such as dislocation quantity, temperature and the like and is characterized in a mathematical mode;
in particular, the product performance requirements are mainly expressed for the gear transmission: the volume is smaller, the weight is lighter, the noise is lower, the service life is longer, the reliability is more reliable, and the like; the product service performance requirement is reflected to the gear meshing performance, and the main manifestation is: and under the conditions of dislocation quantity, temperature and the like, the bearing capacity of the gear teeth, transmission errors and the like.
Because the corresponding relation between the service performance requirements of different products and the gear meshing performance is complex, in order to realize the conversion of the service performance requirements of the products, the following aspects are needed to be analyzed and specific work is carried out in the step:
s101, directly realizing index conversion by gear transmission;
the product use performance indexes such as volume requirement, weight requirement, service life requirement, reliability requirement, noise requirement and the like are converted into corresponding gear tooth engagement performance indexes such as bearing capacity, transmission error and the like;
s102, converting boundary conditions required by gear operation;
the conditions of the boundary required by the working of the gear, such as working rotation speed, torque, ambient temperature, lubrication condition and the like, are converted into the calculation conditions of the gear meshing performance, such as load spectrum, heat balance condition, lubricating oil (grease) viscosity and the like;
s103, converting the influence of actual running conditions of the gears;
the actual running conditions of the gears such as system deformation generated under external load, deformation generated by centrifugal force, heat dissipation and cooling and the like are converted into calculation conditions of gear meshing performance such as dislocation quantity, thermal deformation and the like of gear teeth;
s104, converting the conditions of the gear teeth;
the conditions of the gear teeth themselves include: material heat treatment conditions, macroscopic parameters of gears, theoretical tooth surfaces, single tooth rigidity of gear teeth, theoretical meshing tracks and the like.
S200, calculating the allowable limit deviation in the manufacturing process, and accounting in mathematical expression of the gear engagement performance requirement;
the allowable limit deviation and conversion in the manufacturing process refers to the allowable limit deviation value of the tooth surface according to the use condition and the design experience in the actual processing of the designed tooth surface, and the allowable limit deviation value is converted into the input boundary condition required by the positive design of the tooth surface according to the influence on the meshing performance of the gear and the deviation type;
specifically, the errors generated in the manufacturing and assembling process can be considered in two parts, namely, the errors generated in the manufacturing and assembling process of the gear teeth are eliminated, and the errors generated in the manufacturing and assembling process of the gear teeth are eliminated.
S201, removing the conversion of errors generated by manufacturing and assembling of the gear teeth;
the error generated in the manufacturing and assembling process of the product mainly changes the boundary and working conditions of the actual work of the gear teeth, such as the deviation of the supporting shaft holes, the non-concentric deviation of the supporting shafts, the play of the bearings, the matching of the supporting pieces and the like, and can be directly converted into the boundary and working conditions required by the calculation of the meshing performance in the actual calculation.
S202, converting errors generated by gear tooth manufacturing;
the effects of errors in the gear tooth manufacturing process can be categorized into three categories: firstly, the geometrical design of the tooth surface does not change the influence caused by the error, such as dynamic response caused by radial runout, and aiming at the deviation, the deviation needs to be comprehensively considered in the performance index conversion, and the deviation is defined as a first type of error in the document; secondly, the geometrical design of the tooth surface can improve the influence caused by the error, such as the impact of meshing in and out caused by a single tooth peripheral section, and the deviation needs to be comprehensively considered as an input condition when the geometrical design of the tooth surface is required, and is defined as a second type of error in the document; thirdly, manufacturing errors of tooth surface geometry, such as errors of tooth shape, tooth direction, tooth surface topology and the like, and when the tooth surface design result is output on the basis of analyzing the influence of the errors, limit deviation values meeting requirements are given, and the errors are defined as third type errors in the document.
S300, carrying out tooth surface solving under a given actual meshing state based on mathematical expression of the gear meshing performance requirement to obtain an initial design tooth surface;
the tooth surface solving under the given actual meshing state is to solve the pinion tooth surface by adopting the gear meshing principle on the basis of the theoretical tooth surface of the large wheel according to the gear meshing principle on the basis of giving the gear meshing performance under the unique determined condition in the actual meshing performance requirements of all gears and introducing the limit deviation of the manufacturing process.
Specifically, the solution of the tooth surface in the actual engagement state can be carried out as follows:
s301, determining performance indexes and working conditions for tooth surface design;
in actual engineering, no matter the use performance index or the working condition of the product, the normal condition is not the only determination, but a section with a certain value range is provided, and on the other hand, the geometrical surface of the tooth surface for realizing power and motion transmission is the only determination;
in view of the above, factors such as product performance indexes, product performance index requirements, redundancy degrees of different engagement performance indexes and the like of different engagement performance indexes are comprehensively considered, and determination conditions for solving tooth surface geometry are defined according to experience.
S302, analyzing actual meshing performance indexes of the gear teeth;
the actual meshing performance indexes of the gear teeth comprise: tooth surface contact stress, tooth surface bending stress, law of motion, tooth surface normal force distribution, tooth surface relative velocity distribution, tooth surface power loss, tooth surface temperature, and the like. The essence of high performance gear transmission is that all the above indexes can meet the use requirement under the condition that the requirement is determined, and the redundancy is minimum.
The engagement performance index analysis is to solve the needed engagement performance index determination process of the tooth surface according to the product use performance requirement under the determined calculation condition. In general, the index with the smallest redundancy is used as an input variable of the tooth surface geometric forward design, meanwhile, the influence of the first type of errors is comprehensively considered to correct the index, and other meshing performance indexes are checked or iterated under the condition.
S303, solving the comprehensive rigidity of the gear teeth;
defining a calculation reference point: the points of the large gear tooth width middle section falling on the instantaneous shaft surface (the curved surface formed by the instantaneous sliding shaft of the gear pair around the respective rotation center) are usually selected, and other gear surface points on the large gear tooth surface can be selected according to actual conditions.
Defining a meshing track: from the reference point, the engagement track is defined under the condition of satisfying the engagement principle while considering the engagement performance and the requirement of the designed tooth surface conjugation, and in general, a theoretical engagement track can be adopted.
Single tooth stiffness solution: along the defined meshing track, the single tooth stiffness of the large and small wheels is calculated at each meshing phase (if no other calculation conditions can be adopted for theoretical contact length).
Single tooth comprehensive rigidity solving: and calculating the single-tooth comprehensive rigidity of the gear pair at each meshing phase point along the defined meshing track, and drawing a relation curve between the working phase or the meshing track of the gear and the single-tooth comprehensive rigidity if necessary.
S304, defining a gear motion rule;
defining a gear tooth idle motion rule function under the calculation condition: based on the uniform speed motion of the small wheel, a functional relation, such as a polynomial relation, of undetermined coefficients between the difference between the actual angular displacement and the theoretical angular displacement of each meshing phase and the meshing phase of the large wheel is defined.
Interdental load distribution calculation: under the constraint conditions of overall consideration of a second type of errors, gear overlap ratio, idle motion law of gear teeth (initial value is given according to experience if first iteration) and the like, external load is converted into concentrated load along a meshing track from a reference point, then a gear tooth load distribution calculation equation is built on the basis of load balance, deformation coordination and Hooke's law, and the equation is solved to obtain gear tooth concentrated load converted onto a fitting track at each meshing phase and macroscopic deformation of the gear teeth under the phase.
Calculating geometrical characteristic parameters of each point on the meshing track according to the meshing characteristics: along the defined meshing track, the geometrical contact characteristic parameters of the tooth surface, such as the curvature radius in the direction of the meshing track, the curvature radius in the direction perpendicular to the meshing track and the like, are calculated at each meshing phase point according to the meshing characteristic requirement.
Determining a motion rule: and iterating the steps by taking macroscopic deformation of the gear teeth, curvature radius in the direction perpendicular to the meshing track, continuous phase and the like as constraint conditions, and solving the undetermined coefficient of the motion rule function to obtain the motion rule under the calculation condition.
S305, solving a pinion tooth surface;
the function definition of the tooth thickness reduction amount of the vertical meshing track is as follows: starting from a reference point, along the meshing track, according to the calculated geometrical characteristic parameters of each point on the meshing track, and according to the meshing performance requirements of each point on the track, defining a tooth thickness thinning quantity function of each point on the track perpendicular to the track direction.
Tooth surface engagement EASEOFF curve inspection: and defining a tooth surface engagement EASEOFF curved surface function based on the obtained motion rule and tooth thickness thinning amount function, and continuously and convexly checking the EASEOFF curved surface in the engagement boundary, if the correction motion rule or the tooth thickness thinning amount is not satisfied.
Pinion tooth surface solving: the tooth surface of the small wheel is solved by adopting the meshing principle based on the theoretical tooth surface of the large wheel, the motion rule, the calculation conditions (such as dislocation amount) corresponding to the motion rule, the tooth thickness thinning amount and the like.
S306, analyzing a calculation result;
in the initial design process, the gear tooth rigidity is calculated by adopting a theoretical tooth surface and a theoretical contact state, and if the calculation accuracy is further improved, the obtained tooth surface can be used for iterative calculation by repeating S303-S305.
S400, performing performance check in an expected engagement state based on the initial design tooth surface to obtain a further design tooth surface;
the expected engagement state refers to other actual engagement states except the given actual engagement state, performance check is performed under the other actual engagement states, according to actual engagement requirements of gears and manufactured limit deviation conditions, checking calculation is performed on engagement performance under all conditions by adopting a theoretical tooth surface of a large wheel and a design tooth surface of a small wheel, if a condition that the product requirements are not met occurs, the process returns to the step S400, and the design of the tooth surface of the small wheel is performed after the calculation conditions required by the step S400 are properly corrected until the requirements are met.
Specifically, based on the tooth surface geometry obtained by calculation, respectively calculating whether the performance of other actual meshing states meets the product requirement, if not, carrying out iterative calculation by modifying the motion rule and the tooth thickness thinning amount until the requirement is met.
S500, correcting the advanced design tooth surface according to manufacturing conditions and process requirements to obtain a perfect design result and obtain a tooth surface geometric design output capable of realizing machining;
the geometrical design output of the tooth surface capable of realizing processing is realized, firstly, the processing conditions and the process of the designed tooth surface are selected, then, the actual microscopic parameters of the large and small tooth surfaces can be redistributed on the basis of the processing conditions and the process on the basis that the instantaneous meshing characteristics of the tooth surface do not become the principle, so that the design of the tooth surface morphology of the large and small wheels meeting the product requirement is obtained.
Specifically, first, the manufacturing conditions, processing process, and the like of the designed gear are determined. The tooth thickness reduction of each meshing phase is reasonably distributed among the sizes according to the specific and requirements of the adopted manufacturing conditions and process, so that the processing requirements are met.
And secondly, determining limit deviation possibly generated in the manufacturing process of the tooth surface geometry according to the selected processing conditions and process, and performing check calculation on each performance index by adopting the tooth surface geometry containing the limit deviation. If the requirements cannot be met, the machining conditions or processes are re-selected, and if the requirements can be met, the limit deviation allowed by the tooth surface geometry is given.
And finally, finishing the design result, and finishing the output of the tooth surface geometry, the limit deviation and the result corresponding to the manufacturing conditions and the process requirements.
Embodiment 2. This embodiment is based on the same inventive concept as a tooth surface forward direction design method facing engagement performance requirements as described in embodiment 1, and further provides a tooth surface forward direction design method facing engagement performance requirements, which is applied to a tooth surface design process of which design indexes of a product are input rotational speed, input torque, operating time and noise, and in which gear macroscopic parameters are determined; correspondingly, the method in the embodiment 1 is further perfected by the embodiment 2, and further the specific implementation of the method is described in detail.
In the specific embodiment of step S100 to step S500, there are further implementation steps according to the conditions of the given tooth surface geometric design, compared to the tooth surface forward design method for engagement performance requirements in embodiment 1.
As shown in fig. 2 to 4, the tooth surface forward design method facing the engagement performance requirement in the embodiment 2 mainly includes the following steps:
S100, calculating mathematical expression of gear engagement performance requirements;
acquiring and carding the conditions of given tooth surface geometric design:
input rotation speed:the rotation/min is the working rotation speed of the small wheel;
input torque:nm, small wheel working torque;
the working time is as follows:hours;
noise:decibels;
macroscopic parameters of gear: number of small and large gear teeth；
Modulus of mm；
Pressure angleA degree;
coefficient of displacement ；
Helix angleA degree;
tooth top mm；
Full tooth height mm；
Tooth width mm；
Gear materials, heat treatment conditions, machining precision grade and the like.
S101, directly realizing index conversion by gear transmission;
in this embodiment 2, step S101 specifically includes:
ratio of transmission:；
load carrying capacity (contact for example):in MPa, units of the total weight of the product,
in the method, in the process of the invention,the method is characterized in that the tooth surface contact stress is used for designing performance indexes for products; />The allowable contact stress limit of the tooth surface is calculated according to the gear material, the heat treatment condition, the SN curve and the cycle time; />The safety coefficient is defined according to industry requirements;
transmission error:the unit μm, the transmission error is the displacement folded onto the engagement line;
the transmission error is obtained by establishing a system dynamics model under the condition of considering the gear tooth machining error, possible vibration response generated by the system and other factors.
S102, converting boundary conditions required by gear operation;
as an embodiment of the present invention, in this embodiment 2, step S102 specifically includes:
tooth surface contact normal force:the unit N is obtained through calculating the working torque T of the small wheel and the macroscopic geometric parameters of the small wheel;
cycling for a round:in the formula, n is the rotation speed of the small wheel, and H is the working time.
S103, converting the influence of the actual running conditions of the gears;
in this embodiment 2, step S103 specifically includes:
amount of misalignment:and (3) building a system deformation calculation model in units of mum under the conditions of considering machining errors, bearing play, system deformation under working load and the like, and obtaining the system deformation calculation model through calculation.
S104, converting the conditions of the gear teeth;
as an embodiment of the present invention, in this example 2, step S104 specifically includes;
material conditions:unit MPa, according to material, heat treatment, SN curve and cyclic cycle N calculation determination;
macroscopic parameters of gear: number of small and large gear teeth；
Modulus of mm；
Pressure angleA degree;
coefficient of displacement ；
Helix angleA degree;
tooth top mm；
Full tooth height mm；
Tooth width mm；
Theoretical tooth surface: calculating a tooth surface equation of a tooth surface working area according to the macroscopic parameters of the gear and the involute equation;
Single tooth stiffness: selecting single tooth stiffness according to calculation accuracy requirementA calculation method;
theoretical meshing trace: perpendicular to the instantaneous contact line in the engagement surface, and forms an included angle with the tooth width directionStraight line (units: degrees),>is the base circle helix angle.
S200, calculating the allowable limit deviation in the manufacturing process, and accounting in mathematical expression of the gear engagement performance requirement;
in this step S200, the conversion of errors generated in the manufacturing and assembling of the gear teeth themselves specifically includes:
s201, errors generated in the manufacturing and assembling process of the product comprise: manufacturing deviation of the box body, play of the bearing and deviation of the gear teeth relative to the rotation center of the support bearing.
The deviation of the box body and the gear teeth relative to the rotation center of the support bearing is half of the limit deviation value and is converted into the rotation center of the support bearing, rigid body deflection angle calculation is carried out according to the span of the support bearing on the basis, and the calculated value is directly and linearly superimposed on the gear dislocation.
The bearing play is taken into account in the system deformation calculation model in terms of a gap displacement which is shifted in the bearing-carrying direction by half the play value, in order to take account of the influence of the bearing play on the operating conditions of the gear.
In this step S200, the conversion of the error generated by the gear tooth manufacturing specifically includes:
S202, a first type error: radial runoutSimplified to amplitude +.>The period is a sine function of the frequency of the gear rotating shaft, and the period is converted into the transmission error by using the sine function as an excitation source through a system dynamics model>In (a) and (b);
the second type of error: single tooth peripheral joint of small wheelSingle tooth peripheral node of large wheel->When the small wheel rotates at uniform speed, the large wheel rotation angle error caused by the cycle error,
using the formulaAnd performing conversion calculation, wherein the expression in the motion law relation diagram is shown in figure 2.
S300, carrying out tooth surface solving under a given actual meshing state based on mathematical expression of the gear meshing performance requirement to obtain an initial design tooth surface;
the solving of the tooth surface in the actual engagement state in this step specifically includes:
s301, determining performance indexes and working conditions for tooth surface design;
as an embodiment of the present invention, in this embodiment 2, step S301 specifically includes: the given calculation condition of the tooth surface only has single rotational speed and torque, so that the working condition is unique, and the calculated gear working condition and the gear engagement performance index are uniquely determined and calculated under the calculation condition; the boundary conditions required for tooth surface design are as described above and will not be described in detail here.
S302, analyzing actual meshing performance indexes of the gear teeth;
as an embodiment of the present invention, in the present embodiment 2, step S302 specifically includes:
the performance index of tooth surface engagement comprises two items of contact bearing capacity and transmission error, and the specific mathematical expression is as follows:
according to given requirements, the contact bearing capacity is adopted as a subsequent tooth surface design basis, and the transmission error is adopted as a checking index.
S303, solving the comprehensive rigidity of the gear teeth;
as an embodiment of the present invention, in this embodiment 2, step S303 specifically includes:
defining a calculation reference point: selecting the intersection point of the wide middle section of the large gear tooth and the pitch cylinder as a reference point M, wherein the position in the meshing surface is shown in figure 3;
defining a meshing track: in the engagement surface, the joint cylinder curve is selected to beIs the meshing line, see fig. 3;
single tooth stiffness solution: calculating the single tooth stiffness of the large and small wheels at each meshing phase (if no other calculation conditions can be adopted for theoretical contact length) along the defined meshing track;
for the three-dimensional gear teeth, the single-tooth loading rigidity can be calculated by adopting a slicing method. The rigidity of each piece can be divided into bending rigidity, shearing rigidity, extrusion rigidity and contact rigidity, and the slicing rigidity of the ith piece of gear teeth is as follows:
The single tooth stiffness at one contact instant is
N is the number of slices that are engaged instantaneously by contact;
at each meshing phase point, the single tooth comprehensive rigidity of the gear pair is as follows:
this gives rise to a single tooth integrated stiffness profile from engaged to engaged as shown in fig. 4.
S304, defining a gear motion rule;
as an embodiment of the present invention, in the present embodiment 2, step S304 specifically includes:
defining a gear tooth idle motion rule function under the calculation condition, and taking a polynomial as an example for design:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,is the angle error of the large wheel; />Is a coefficient to be determined; />Is the phase of the large wheel rotation angle;
interdental load distribution calculation, the following interdental load distribution equation can be established:
: large wheel rotation angle
: the large wheel transmitting torque
It should be noted that: in actual calculation, the first calculation is iterated according to the initial value of the undetermined coefficient given empirically.
S305, solving a pinion tooth surface;
as an embodiment of the present invention, in the present embodiment 2, step S305 specifically includes:
defining a tooth thickness reduction function of a vertical meshing track, and taking a polynomial as an example for design:
: is a coefficient to be determined; />
: tooth thickness reduction.
The normal force of the contact position can be obtained according to the result of the last step; according to the thinning amount and the motion rule, the comprehensive curvature of the tooth surface can be calculated; according to the normal force and the comprehensive curvature, the contact stress of the contact position can be calculated by adopting a Hertz contact algorithm; and according to the design stress index, iterating the thinning coefficient, and determining the thinning coefficient to be determined.
It should be noted that: in actual calculation, the initial value of the coefficient to be determined is given and thinned according to experience in the first calculation.
Completing computation of an ase-off curved surface on the basis, and judging the concave-convex property of the ase-off curved surface according to the Gaussian curvature;
k, curved Gaussian curvature;
detII is determinant of curved surface second basic form;
detI: is a determinant of a curved first basic form.
Pinion tooth surface solving: the method is characterized in that the tooth surface of the small wheel is solved by adopting a meshing principle on the basis of a theoretical tooth surface of the large wheel, a motion rule, calculation conditions (such as dislocation amount) corresponding to the motion rule, tooth thickness thinning amount and the like; the solving formula is as follows:
n: the normal direction of the contact point is related to the tooth thickness reduction amount;
v pw the relative speed of the wheels with the contact points is related to regular motion, calculation conditions and the like.
S306, analyzing a calculation result;
and repeating the steps S303-S305 to perform iterative calculation according to the requirements of the margin between the calculated stress and the allowable stress and the motion law.
S400, performing performance check in an expected engagement state based on the initial design tooth surface to obtain a further design tooth surface;
as an embodiment of the present invention, the desired engagement state refers to other actual engagement states than the given actual engagement state, and in this example 2, only one load condition is involved, and no performance check calculation in other actual engagement states is involved.
S500, correcting the advanced design tooth surface according to manufacturing conditions and process requirements to obtain a perfect design result, and outputting a geometric design of the tooth surface capable of realizing machining;
as an embodiment of the present invention, in the present embodiment 2, the step S500 specifically includes:
s501, determining the comprehensive modification amount of each meshing phase according to an ase-off curved surface;
s502, reasonably distributing the shape correction amount of the large and small wheels according to principle errors generated by the manufacturing process conditions of the designed gear and the shape correction mode which can be realized；
S503, determining the limit deviation of the large and small wheels possibly generated in the manufacturing process of the tooth surface geometry according to the selected processing conditions and process；
S504, according to the limit deviation sumThe thinning amount obtains a group of design tooth surfaces with different error distributions of the large and small wheels；
S505, calculating the gear engagement performance under different deviation conditions based on the designed tooth surface;
s506, if the motion error coefficient and the tooth thickness reduction coefficient in the step S300 are adjusted to be calculated iteratively;
s507, finishing the design result, and finishing the output of the tooth surface geometry, the limit deviation and the result corresponding to the manufacturing conditions and the process requirements.
Embodiment 3. This embodiment provides a tooth surface forward design device for engagement performance requirements, comprising: a mathematical expression calculation unit for calculating a mathematical expression of the gear engagement performance requirement;
the limit deviation conversion unit is used for calculating the limit deviation allowed in the manufacturing process and accounting for mathematical expression of the gear engagement performance requirement;
the tooth surface geometric solving unit is used for carrying out tooth surface solving under a given actual meshing state based on the mathematical expression of the gear meshing performance requirement to obtain an initial design tooth surface;
the tooth surface geometry checking unit is used for performing performance checking in an expected meshing state based on the initial design tooth surface to obtain a further design tooth surface;
and the tooth surface geometric output unit is used for correcting the advanced design tooth surface according to manufacturing conditions and process requirements to obtain a perfect design result.
Embodiment 4. This embodiment provides a computer-readable storage medium comprising:
the storage medium is used for storing computer software instructions for implementing the tooth surface forward design method for meshing performance requirements described in the above embodiment 1/embodiment 2, and the computer software instructions include a program for executing the above program set for the tooth surface forward design method for meshing performance requirements; specifically, the executable program may be built in the tooth surface forward direction designing device for engagement performance requirements described in embodiment 3, so that the tooth surface forward direction designing device for engagement performance requirements can implement the tooth surface forward direction designing method for engagement performance requirements described in embodiment 1/embodiment 2 by executing the built-in executable program.
Further, the computer readable storage medium provided in the present embodiment may be any combination of one or more readable storage media, where the readable storage media includes an electric, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof.
Compared with the prior art, the tooth surface forward design method, the tooth surface forward design device and the tooth surface forward design medium for the meshing performance requirement are adopted, forward theories such as meshing principle, elastic mechanics and the like are adopted after the product requirement is converted into the gear actual meshing performance requirement from the product use performance requirement, the tooth surface geometric design is carried out according to the actual meshing performance requirement, the basic thought from the tooth surface geometric to the processing and manufacturing realization is provided, the theoretical basis is provided for the high-performance gear transmission design, the current situation that the tooth surface geometric design depends on the experience of engineering technicians is solved, and meanwhile, a feasible method and a feasible way are provided for improving the gear transmission performance.
It should be understood that, in the various embodiments herein, the sequence number of each process described above does not mean the sequence of execution, and the execution sequence of each process should be determined by its functions and internal logic, and should not constitute any limitation on the implementation process of the embodiments herein.
It should also be understood that in embodiments herein, the term "and/or" is merely one relationship that describes an associated object, meaning that three relationships may exist. For example, a and/or B may represent: a exists alone, A and B exist together, and B exists alone. In addition, the character "/" herein generally indicates that the front and rear associated objects are an "or" relationship.
Those of ordinary skill in the art will appreciate that the elements and algorithm steps described in connection with the embodiments disclosed herein may be embodied in electronic hardware, in computer software, or in a combination of the two, and that the elements and steps of the examples have been generally described in terms of function in the foregoing description to clearly illustrate the interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure.
It will be clear to those skilled in the art that, for convenience and brevity of description, specific working procedures of the above-described systems, apparatuses and units may refer to corresponding procedures in the foregoing method embodiments, and are not repeated herein.
In the several embodiments provided herein, it should be understood that the disclosed systems, devices, and methods may be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative, e.g., the division of the units is merely a logical function division, and there may be additional divisions when actually implemented, e.g., multiple units or components may be combined or integrated into another system, or some features may be omitted or not performed. In addition, the coupling or direct coupling or communication connection shown or discussed with each other may be an indirect coupling or communication connection via some interfaces, devices, or elements, or may be an electrical, mechanical, or other form of connection.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the elements may be selected according to actual needs to achieve the objectives of the embodiments herein.
In addition, each functional unit in the embodiments herein may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit. The integrated units may be implemented in hardware or in software functional units.
The integrated units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the technical solutions herein are essentially or portions contributing to the prior art, or all or portions of the technical solutions may be embodied in the form of a software product stored in a storage medium, including several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in the embodiments herein. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
The foregoing description is only illustrative of the present invention and is not intended to limit the scope of the invention, and all equivalent structures or equivalent processes or direct or indirect application in other related technical fields are included in the scope of the present invention.
Claims (10)
1. The tooth surface forward design method facing the engagement performance requirement is characterized by comprising the following steps of:
calculating mathematical expression of the gear engagement performance requirement;
calculating allowable limit deviations during manufacturing and accounting for mathematical representations of the gear engagement performance requirements;
based on the mathematical expression of the gear engagement performance requirement, carrying out tooth surface solving under a given actual engagement state to obtain an initial design tooth surface;
performing performance check in a desired engagement state based on the initial design tooth surface to obtain a further design tooth surface;
and correcting the advanced design tooth surface according to manufacturing conditions and process requirements to obtain a perfect design result.
2. The tooth surface forward design method for meeting the engagement performance requirement according to claim 1, wherein: the calculating a mathematical representation of gear mesh performance requirements includes: obtaining macroscopic parameters of a gear, design performance indexes of the product, actual running conditions of a gear pair, gear materials and heat treatment conditions, theoretical tooth surfaces of a large gear and a small gear, converting the macroscopic parameters and the product design performance indexes into gear meshing performance through calculation, and carrying out characterization in a mathematical mode to obtain mathematical expression of the gear meshing performance requirements.
3. The tooth surface forward design method for meeting the engagement performance requirement according to claim 2, wherein: the mathematical representation of the calculated gear mesh performance requirement further comprises: index conversion directly realized by gear transmission; switching boundary conditions required by gear operation; conversion of the influence of actual running conditions of the gears; the gear teeth themselves are transformed.
4. A tooth surface forward direction design method for meeting meshing performance requirements according to claim 3, wherein: the calculating of the allowable limit deviation during manufacturing and accounting for the mathematical expression of the gear mesh performance requirement includes: and calculating the limit deviation value of the gear teeth and correlating the limit deviation value with a deviation type, and converting the limit deviation value and the deviation type into input boundary conditions for calculating the meshing performance of the gear.
5. The tooth surface forward direction design method for meeting the meshing performance requirement according to claim 4, wherein: the mathematical expression based on the gear engagement performance requirement is used for carrying out tooth surface solving under a given actual engagement state to obtain an initial design tooth surface, and the method comprises the following steps: in the gear engagement performance requirement, the gear engagement performance which is consistent with the given actual engagement state is matched, the limit deviation allowed in the manufacturing process is introduced, on the basis, the gear engagement principle is adopted, and the design tooth surface of the small wheel is solved on the basis of the theoretical tooth surface of the large wheel.
6. The tooth surface forward direction design method for meeting the meshing performance requirement according to claim 5, wherein the tooth surface forward direction design method comprises the following steps: the method for solving the tooth surface under the given actual engagement state based on the mathematical expression of the gear engagement performance requirement to obtain an initial design tooth surface further comprises the following steps: determining performance indexes and working conditions for tooth surface design; analyzing actual meshing performance indexes of the gear teeth; solving the comprehensive rigidity of the gear teeth; defining a gear motion rule; the method is characterized in that the designed tooth surface of the small wheel is solved by adopting a meshing principle on the basis of the theoretical tooth surface of the large wheel, the motion rule of the gear, the calculation condition corresponding to the motion rule of the gear and the tooth thickness reduction.
7. The tooth surface forward direction design method for meeting the meshing performance requirement according to claim 6, wherein: performing performance check in a desired engagement state based on the initial design tooth surface to obtain a further design tooth surface, including: and checking and calculating the gear meshing performance in the expected meshing state by adopting the theoretical tooth surface of the large wheel and the design tooth surface of the small wheel, and if the gear meshing performance does not meet the product requirement, carrying out iterative calculation by modifying the gear movement rule and the tooth thickness thinning amount until the gear meshing performance meets the product requirement.
8. The tooth surface forward direction design method for meeting the meshing performance requirement according to claim 7, wherein: the step-by-step design tooth surface is corrected according to manufacturing conditions and process requirements to obtain a perfect design result, which comprises the following steps:
selecting the processing conditions and the processing technology of the designed gear; the instantaneous tooth surface meshing characteristic is not changed into a principle, and the tooth thickness thinning amount of each meshing phase is distributed among the sizes according to the selected processing conditions and process;
determining limit deviation generated in the tooth surface geometry manufacturing process according to the selected processing conditions and process, and adopting the tooth surface geometry containing the limit deviation to check and calculate the performance index; if the requirements cannot be met, the machining conditions or the process are selected again, and if the requirements can be met, the limit deviation allowed by the tooth surface geometry is given;
and integrating the tooth surface geometry, the limit deviation, the corresponding machining conditions and the process requirements to obtain and output the perfect design result.
9. A tooth face forward direction design device for meeting meshing performance requirements, comprising:
a mathematical expression calculation unit for calculating a mathematical expression of the gear engagement performance requirement;
The limit deviation conversion unit is used for calculating the limit deviation allowed in the manufacturing process and accounting for mathematical expression of the gear engagement performance requirement;
the tooth surface geometric solving unit is used for carrying out tooth surface solving under a given actual meshing state based on the mathematical expression of the gear meshing performance requirement to obtain an initial design tooth surface;
the tooth surface geometry checking unit is used for performing performance checking in an expected meshing state based on the initial design tooth surface to obtain a further design tooth surface;
and the tooth surface geometric output unit is used for correcting the advanced design tooth surface according to manufacturing conditions and process requirements to obtain a perfect design result.
10. A computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program when executed by a processor implements the steps of the tooth surface forward design method for meeting the engagement performance requirement of any one of claims 1 to 8.
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Address after: Room 201, Building 28, No. 618, Wharf West Street, Kunlun Street, Liyang City, Changzhou City, Jiangsu Province, 213300 Patentee after: Liyang Jiankai Machinery Transmission Technology Co.,Ltd. Country or region after: China Address before: Building 34, No. 118, Zhennu Road, Kunlun Street, Liyang City, Changzhou City, Jiangsu Province, 213300 Patentee before: Liyang Jiankai Machinery Transmission Technology Co.,Ltd. Country or region before: China |