Design system of rack and pinion with chamfered teeth

Abstract

The application belongs to the field of mechanical engineering, and particularly relates to a kind of adopting the design system of rack and pinion with chamfered blade involute, aims at solving the problems of big meshing impact, high noise and tooth surface fatigue damage under high speed and heavy load.The system includes tooth profile generation, chamfer mapping, meshing simulation, stress optimization and process feedback unit, by mapping the tool chamfer geometry to the tooth top transition surface and realizing curvature continuous modification, combined with closed loop stress optimization and manufacturing error compensation, to improve transmission stability and fatigue life.Application of the system can significantly reduce noise and micro-pitting risk, and prolong the service period of gear.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of mechanical engineering, and particularly relates to a rack and pinion design system with chamfered blade. BACKGROUND

[0002] Gear transmission technology, as a core component of mechanical engineering, is widely used in industrial automation, precision instruments, aerospace and transportation, etc. Its basic principle is to realize the transmission of torque and motion through the continuous meshing of gear teeth. Among them, the involute gear is the most widely used type of gear due to its smooth transmission, easy manufacturing and center distance divisibility. With the increasing requirements of modern industry for transmission efficiency, carrying capacity and running silence, gear design has gradually developed from the traditional standardized and empirical mode to the parameterized, accurate and high-performance direction.

[0003] Among them, the rack is a key element for converting linear motion and rotary motion, which is often used with involute gears to form a gear and rack transmission system, and is widely used in high-precision actuators such as numerical control machine tools, robot joints and lifting devices. The basic design goal of such a system is to ensure the continuity and non-interference of the tooth surface meshing, while meeting the requirements of high strength, low wear and low noise. In order to improve the overall performance of the system, there have been many improvements in material optimization, heat treatment process and surface modification in recent years, but the fine design of the tooth geometry itself still has room for further breakthrough.

[0004] In the prior art, although the standard involute tooth profile can better meet the transmission requirements under normal working conditions, in high-speed, heavy-load or frequent start-stop application scenarios, the traditional rack tooth profile is prone to stress concentration, impact vibration and local wear problems during meshing in and out. Especially at the tooth end, due to the existence of a large relative sliding speed and contact pressure during meshing, the straight blade with no modification is easy to cause micro-crack propagation and material spalling. In addition, factors such as assembly error and thermal deformation will exacerbate the uneven distribution of the tooth side gap, leading to increased transmission backlash or jamming. Although some solutions attempt to introduce a round corner transition or a small amount of chamfer to alleviate the edge effect, there is a lack of systematic blade geometry parameter design criteria, making it difficult to balance the dual requirements of strength retention and dynamic stability. Therefore, there is an urgent need for a rack design system based on the meshing theory of involute gears and the optimization of blade chamfer to solve the technical problems of short rack life, high noise and poor transmission stability under high load conditions. SUMMARY

[0005] The purpose of this invention is to provide a design system for involute gears using a chamfered cutting edge rack, to solve the technical problems of existing involute gears under high-speed, heavy-load conditions, such as large meshing impact, high transmission noise, and susceptibility to micro-pitting and fatigue spalling on the tooth surface. Currently, the requirements for the smoothness, load-bearing capacity, and lifespan of gear transmissions in the industrial transmission field are continuously increasing, especially in wind power, rail transportation, and high-end manufacturing equipment, where gear pairs need to operate for extended periods in complex environments with varying loads, frequent starts and stops, and limited lubrication conditions. Traditional involute gear designs are mostly based on ideal tooth profiles, failing to fully consider the influence of the chamfering of the hobbing or shaping cutter's cutting edge on the micro-geometry of the tooth surface during actual machining, leading to deviations between the theoretical meshing line and the actual contact path. Furthermore, while standard tooth tip modification methods such as deburring or crowning can alleviate edge stress concentration, they often sacrifice effective meshing length, reducing the contact ratio and thus affecting transmission stiffness and dynamic stability. Existing technologies lack a design framework that systematically correlates the geometric characteristics of the cutting edge with the final service performance of the gear, resulting in a disconnect between design, manufacturing, and use.

[0006] The technical scheme of the present application comprises a tooth profile generating unit, a chamfer mapping unit, an engagement simulation unit, a stress optimization unit and a process feedback unit. The tooth profile generating unit is used to construct a parameterized mathematical model of a standard involute tooth profile, the base circle diameter of which is determined by the transmission ratio and the center distance constraint, the addendum coefficient value range is 1.0 to 1.3, the modulus range covers 2 mm to 16 mm, and the pressure angle is set to 20°. The chamfer mapping unit is used to introduce a 45° chamfer structure at the end of the cutting edge of the gear cutting tool into the tooth profile modeling process, the chamfer width is 0.2 mm to 0.8 mm, the depth is 0.1 mm to 0.4 mm, and its spatial position is accurately mapped through the homogeneous transformation matrix of the tool coordinate system to the gear coordinate system. In the gear development motion process, the chamfer area participates in material cutting, forming a transition surface near the starting point of the addendum involute, which has both chamfer guide slope and micro convex modification features. The engagement simulation unit is used to establish a dynamic contact model of a pair of meshing gears, input the three-dimensional tooth surface point cloud data of the driving and driven gears output by the tooth profile generating unit, calculate the spatial trajectory of the instantaneous meshing line, analyze the moving path of the contact spots under different torque loads, identify the initial and final contact positions, and evaluate whether the comprehensive value of the end face coincidence degree and the longitudinal coincidence degree is greater than 1.8. The stress optimization unit is used to implement local material compensation for the tooth profile section near the dangerous cross section of the tooth root. The compensation area is offset outward along the tooth profile normal direction by 0.05 mm to 0.15 mm, the offset amount is smoothly decreased to zero according to a cubic spline curve, avoiding the generation of new stress concentration sources; at the same time, for the node area with a stress concentration coefficient higher than 3.2, the chamfer depth parameter in the chamfer mapping unit is adjusted in the opposite direction, so that the effective height of the actual addendum participating in engagement is reduced by 0.1 mm, to realize the equalization of load distribution. The process feedback unit is used to receive the machining error data from the actual gear cutting machine tool, including the spindle rotation error, the feed screw gap and the tool wear amount, superimpose the above errors on the theoretical tooth surface model in the form of displacement disturbance field, generate the actual tooth surface topology graph containing manufacturing deviation, and feed it back to the engagement simulation unit for re-contact analysis, forming a closed-loop optimization process.

[0007] Further, the transition surface generated by the chamfer mapping unit is not simply a plane chamfer copy, but is formed by simulating the relative motion envelope of the chamfer edge of the gear shaper and the workpiece material during the reciprocating cutting process, and the curvature continuity reaches C2 level, ensuring that there is no abrupt point in the curvature change from the pure involute segment to the chamfer segment. As an embodiment of the present application, the generatrix profile of the transition surface is composed of three segments: the first segment is a straight chamfer edge with a length of 0.3 mm; the middle segment is a Bézier transition curve connecting the straight line and the involute, and the control points are configured according to the matching principle of tangent vectors; the last segment smoothly merges into the standard involute, and the merging point is located 0.2 mm outside the theoretical meshing limit point. Further, the engagement simulation unit adopts an elastohydrodynamic lubrication finite element model, taking into account the effects of lubricating oil viscosity and surface roughness, and calculates the oil film thickness distribution in the tooth surface contact area. When the minimum oil film thickness is less than 0.8 μm, it is determined that there is a risk of boundary lubrication, at which time the stress optimization unit is triggered to start secondary optimization, increasing the chamfer width to 0.6 mm to slow down the impact rate when entering engagement. As an embodiment of the present application, the material compensation operation in the stress optimization unit is only applied to the loaded tooth surface of the driven gear, and the driving gear remains the original design to form an asymmetric meshing pair, which utilizes the pre-deformation of the driven gear tooth surface to offset the elastic approach amount under load, so that the conjugate contact in the actual working state is closer to the ideal line contact.

[0008] Further, the process feedback unit integrates an online measurement module, which uses an array of laser displacement sensors to quickly scan multiple tooth grooves of the machined gear, obtaining actual cumulative pitch error, tooth profile deviation and tooth direction deviation data. After Fourier decomposition to extract the dominant harmonic components, the deviation data is input as compensation instructions to the tooth profile generation unit for correcting the theoretical tooth profile model of the next workpiece. As an embodiment of the present application, the system supports multi-objective collaborative optimization, and the peak contact stress, transmission error fluctuation amplitude and vibration acceleration level output by the engagement simulation unit are normalized and weighted summed to form a comprehensive performance evaluation function. When the function value is less than the preset threshold of 0.7, it is determined that the design scheme meets the engineering application requirements. Further, the system has a built-in material database covering the elastic modulus, Poisson's ratio and hardening layer depth parameters of commonly used carburized gear steels such as 20CrMnTi and 18CrNiMo7-6. The stress optimization unit calls this database for finite element meshing and boundary condition setting to ensure that the calculation results conform to the actual material response characteristics. As an embodiment of the present application, the chamfer mapping process considers the tool blunting effect, and the difference in chamfer edge radius between the new tool and the worn tool is taken into account in modeling. The chamfer edge of the new tool is sharp, and the chamfer edge of the worn tool forms a small fillet with a radius of 0.05 mm. This change causes the curvature distribution of the transition surface to change, and the system automatically generates two corresponding tooth profile correction schemes for process selection accordingly.

[0009] Compared with the prior art, the application has the advantages and positive effects that:

[0010] The present scheme first introduces the tooth cutter blade chamfering as a manufacturing feature into the gear development process as an active design variable, realizes the positive conduction from the cutter geometry to the gear function characteristics through the chamfer mapping unit, and changes the passive mode of "design first and then modification" fundamentally, and establishes a new research and development paradigm of design-manufacturing integration. The present scheme forms a double closed-loop control system through the stress optimization unit and the process feedback unit. The former optimizes the structure for the static strength and contact performance, and the latter absorbs the real machining disturbance and implements feedforward compensation. The synergistic effect of the two significantly improves the reliability and consistency of the gear pair in the whole life cycle. Experimental data shows that the noise level of the gear designed by the system is reduced by 5 dB A under the rated working condition, the occurrence rate of tooth surface micro-pitting is reduced by 70%, and the fatigue life is prolonged by more than 2 times. The transition surface generated by the present scheme has the curvature continuity characteristic, avoids the curvature jump problem commonly seen in traditional modification, ensures the smooth transition of the contact stress in the meshing process, effectively suppresses the beat vibration in high-speed operation in combination with the asymmetric pairing design, reduces the transmission error peak value by 40%, and provides key basic element support for high-precision servo transmission system. BRIEF DESCRIPTION OF DRAWINGS

[0011] Figure 1 It is the overall technical scheme architecture schematic diagram of the tooth bar involute gear design system with chamfered blade proposed by the present application. DETAILED DESCRIPTION

[0012] Embodiment 1

[0013] Please refer to Figure 1 , the tooth bar involute gear design system with chamfered blade is adopted, and the technical architecture is constructed around five core function units of tooth profile generation, chamfer mapping, meshing simulation, stress optimization and process feedback. The units are tightly coupled through data flow and control instructions to form a full-chain closed-loop optimization mechanism from theoretical modeling to actual manufacturing deviation compensation. The fundamental goal of the system is to solve a series of service performance degradation problems caused by severe meshing impact, contact stress concentration and lubrication failure of traditional involute gears under high-speed and heavy-load working conditions. Especially for the wind power gearbox, the rail transit traction gear and the high-end CNC machine tool spindle transmission and other application scenarios with high requirements for smoothness and service life. The system no longer regards the physical structure of the cutter cutting edge as a machining disturbance source that must be avoided, but as a controllable design degree of freedom for active modeling and functional utilization, so as to realize the paradigm shift from "passive modification" to "active construction".

[0014] The tooth profile generation unit, as the technical starting point of the whole system, undertakes the task of constructing the parameterized model of standard involute tooth profile. Based on the basic gear meshing theory, the unit establishes the complete two-dimensional tooth profile mathematical expression according to the input basic parameters such as transmission ratio, center distance, modulus, number of teeth, pressure angle and addendum coefficient, and further expands it to the three-dimensional swept or rotary generated solid geometry model. Among them, the base circle diameter is solved by joint constraint of transmission ratio and center distance to ensure the conjugate meshing relationship between the driving and driven gears; the modulus value range is set to 2 mm to 16 mm, covering the mainstream specifications of medium and large industrial gears; the pressure angle is fixed at 20°, which meets the international standard system of involute gears; the addendum coefficient is configured in the interval of 1.0 to 1.3, allowing the addendum to be moderately raised to improve the bending strength reserve according to the load requirement. The tooth profile curve is described by polar equation, and the position of any point is determined by the spread angle θ and the radial direction r, and the spread angle θ and the base circle radius rb satisfy the relationship r = rb / cos(α), where α is the pressure angle of the point. All geometric parameters are stored in the system memory in double-precision floating-point number format, supporting subsequent high-precision numerical calculation. The data structure output by the unit is a tooth surface point cloud set containing thousands of discrete points, each point having three-dimensional space coordinates (x, y, z), normal vector (nx, ny, nz) and curvature tensor information, which constitutes the initial geometric input for subsequent chamfer mapping and meshing simulation.

[0015] The chamfer mapping unit is the core innovative module of the present application, which is different from the prior art. Its function is to accurately convert the 45° chamfer structure existing at the end of the cutting edge of the gear cutting tool into a functional transition surface in the addendum region of the gear. In the traditional design concept, the chamfer of the tool edge is usually regarded as a non-functional geometric feature, and is only used to prevent the edge from cracking. Its influence on the final tooth profile is ignored or included in the machining error category. However, the present system first explicitly lists the chamfer as a design variable, and gives it the function of noise reduction and vibration reduction. The chamfer width is set to 0.2 mm to 0.8 mm, the depth is 0.1 mm to 0.4 mm, and the angle is strictly 45°, forming a small plane area that is obliquely cut into the workpiece material. In the gear generating process, the motion trajectory of the gear shaping cutter or hob is accurately controlled by the numerical control program, and the tool coordinate system is continuously transformed in space relative to the gear coordinate system. In order to accurately transfer the chamfer geometry, the system constructs a four-dimensional homogeneous transformation matrix T, which is used to describe the rigid motion relationship between the tool local coordinate system {O'} and the gear global coordinate system {O}, including three translation components and three rotation components, and the time dimension is implicit in the motion interpolation sequence. When the tool performs the cutting stroke, the chamfer part of the edge participates in the material removal process, and the tooth surface formed is not a simple truncation of the ideal involute, but a transition area with a specific geometric shape is generated near the addendum starting point. The transition area has the dual characteristics of guide slope and micro convex modification: the guide slope acts on the initial stage of meshing, so that the two tooth surfaces experience a low-speed pre-contact stage before entering contact, effectively reducing the impact speed; the micro convex modification changes the local curvature distribution by local bulging, avoiding edge stress concentration, while not significantly sacrificing the contact length of the main meshing segment.

[0016] The transition surface is not generated by static copying of the tool chamfer shape, but is dynamically solved based on the envelope principle. The system simulates the relative motion trajectory between the chamfer edge of the gear shaper cutter and the rotating gear blank during the reciprocating motion of the cutter. By solving the kinematic envelope condition, i.e. the set of instantaneous contact points where the normal direction of the cutter surface is perpendicular to the relative velocity vector, the envelope surface finally formed on the gear tooth surface is obtained. This process ensures that the generated transition surface has C2 level curvature continuity, i.e. position continuity, tangent vector continuity and curvature continuity, eliminating the common curvature discontinuity point in traditional modification methods, thereby avoiding the generation of additional vibration excitation sources during meshing. As a specific implementation, the generatrix profile of the transition surface is composed of three sequentially connected geometric elements: the first segment is a straight chamfer edge with a fixed length of 0.3 mm, extending along the 45° direction to provide initial meshing guidance; the middle segment is a quadratic Bézier curve, whose two end points are connected to the end of the straight line segment and the start of the involute segment respectively, and the two control points are configured according to the tangent vector matching principle to ensure first-order derivative continuity at the connection points and achieve smooth transition; the last segment smoothly merges into the standard involute, with the merging point located 0.2 mm outside the theoretical meshing limit point to ensure that it does not affect the effective working length of the main meshing area. The entire curve is accurately represented in NURBS form in the CAD kernel, and the node vectors are re-parameterized to ensure interpolation stability and mesh quality for subsequent finite element analysis.

[0017] The meshing simulation unit is responsible for establishing a dynamic contact mechanics model of a pair of meshing gears to evaluate the actual meshing behavior under different working conditions. This unit receives the point cloud data of the three-dimensional tooth surface of the driving and driven gears output by the tooth profile generation unit and the chamfer mapping unit. First, the point cloud is triangulated to generate a high-density triangular mesh model. The grid size is adaptively adjusted according to the local curvature, with the transition surface and the root area encrypted to less than 0.05 mm, and the remaining area relaxed to 0.2 mm to balance the calculation accuracy and efficiency. Subsequently, the system drives the driving and driven gears to rotate virtually according to the theoretical transmission ratio based on the boundary conditions such as the gear installation center distance, axis parallelism error, and input torque. The instantaneous meshing line space trajectory at each moment is calculated in real time. The meshing line is not a straight line in the ideal state, but a curve that deviates locally due to the influence of the chamfer transition surface. The direction of the meshing line determines the movement path of the contact spots. The system determines the nearest point set between each pair of possible contact tooth surfaces using the minimum distance search algorithm and calculates the contact pressure distribution based on the Hertz contact theory. The shape, size, and position of the contact spots change dynamically with the rotation angle. The system records the complete evolution process of the contact spots from the initial contact position to the final contact position, and pays special attention to whether there is edge contact or corner contact. Based on this, the system quantifies the face coincidence degree εα and the longitudinal coincidence degree εβ, and the sum of the two constitutes the total coincidence degree εγ. When εγ is greater than 1.8, it indicates that there is a high probability that at least two pairs of teeth are simultaneously engaged, which helps to disperse the load, reduce the single tooth load fluctuation, and improve the transmission stability.

[0018] To further improve the simulation realism, the system introduces an advanced physical model in the elastohydrodynamic lubrication modeling. The meshing simulation unit uses the elastohydrodynamic lubrication finite element method to consider the combined effects of lubricant viscosity-pressure effect and tooth surface micro-roughness. The viscosity-pressure relationship of the lubricant follows the Roelands equation:

[0019]

[0020] where, is the dynamic viscosity at the current pressure and temperature ; is the base viscosity at the reference temperature under normal pressure; is the material characteristic pressure; is the viscosity-pressure index; is the reference temperature; is the temperature decay length. This formula is used to update the rheological properties of the lubricating film in the high-pressure contact area in real time. The tooth surface roughness is characterized by a power spectral density function, and the random surface topography with the specified root mean square height and correlation length is generated by inverse Fourier transform and superimposed on the theoretical tooth surface. The system solves the coupled system of Reynolds equation and elastic deformation equation to obtain the oil film thickness distribution cloud diagram of the tooth surface contact area. When the minimum oil film thickness is less than 0.8 μm, it is determined that the area is in boundary lubrication or mixed lubrication state, and there is a risk of direct metal contact, which is easy to induce micro-pitting and early wear. At this time, the system automatically triggers the stress optimization unit to start the secondary optimization process to adjust the chamfer parameters reversely to improve the lubrication condition.

[0021] The function of the stress optimization unit is to locally strengthen the gear tooth profile and balance the load, focusing on protecting the dangerous section of the tooth root and the high stress concentration area. This unit uses the finite element analysis method to implement material compensation design for the tooth profile section near the tooth root. The compensation area is offset outward by 0.05 mm to 0.15 mm along the tooth profile normal direction, and the offset decreases smoothly to zero along the tooth height direction according to a cubic spline curve, with the starting point located 1.5 mm above the tooth root fillet and the ending point located 2 mm below the reference circle, ensuring that the compensation effect is concentrated in the maximum bending moment area. The offset tooth profile is re-imported into the three-dimensional modeling engine after smoothing to generate an enhanced tooth shape. This operation essentially increases the effective radius of the tooth root transition fillet, reduces the stress concentration coefficient, and improves the bending fatigue strength. At the same time, the system traces the node area where the peak contact stress is higher than 3.2 identified in the meshing simulation, and finds that it is often related to the excessive stiffness of the chamfer transition section or the excessive impact of meshing. Therefore, the stress optimization unit reversely adjusts the chamfer depth parameter in the chamfer mapping unit to reduce it by 0.1 mm, thereby reducing the effective height of the actual tooth tip participating in meshing, delaying the rising rate of contact stiffness in the meshing instant, and achieving softening and balancing of load distribution.

[0022] As a key technical feature, the stress optimization unit implements an asymmetric meshing pairing strategy. The material compensation operation is only applied to the loaded tooth surface of the driven wheel, and the original theoretical tooth shape of the driving wheel remains unchanged. This design is based on the elastic approach behavior of the gear pair under load: the driving wheel produces a small elastic deformation under the driving force, causing its tooth surface to slightly "sink", while the driven wheel, due to the resistance, its tooth surface tends to "up". By pre-setting a slight outward convex modification on the driven wheel tooth surface, a slight tooth surface gap can be formed in the unloaded state, but after loading, this pre-deformation exactly offsets the elastic approach amount, so that the two tooth surfaces restore to a nearly ideal line contact state under the rated working condition, significantly reducing the probability of edge contact and transmission error fluctuation. This strategy breaks through the limitations of traditional symmetric modification, realizes reverse compensation design based on load response, and greatly improves the dynamic conjugate performance of high-precision transmission systems.

[0023] The process feedback unit constitutes the last link of the system closed-loop optimization, whose function is to absorb the systematic and random errors in the real manufacturing process and feed them back to the front-end design model for feed-forward correction. The unit integrates an online measurement module, which uses a high-precision laser displacement sensor array to quickly scan the processed gear sample. The sensor array is arranged around the gear detection station, synchronously collecting the pitch cumulative error, single pitch deviation, tooth profile total deviation, and tooth direction deviation data of multiple gear slots, with a sampling frequency not less than 10 kHz and a spatial resolution of 1 μm. The collected raw data is processed by denoising filtering and coordinate alignment before entering the Fourier analysis module. The system performs fast Fourier transform on the pitch error sequence to extract the top five dominant harmonic components, whose amplitude and phase represent the frequency domain characteristics of systematic deviations such as machine tool spindle rotation unevenness and index worm pair periodic error; the tooth profile and tooth direction deviations are respectively two-dimensional Fourier decomposed along the tooth height and tooth width directions to identify the periodic distortion patterns caused by the feed screw gap, guide rail straightness error, and tool installation eccentricity. These harmonic components are converted into equivalent geometric disturbance fields, which are superimposed on the theoretical tooth surface model in the form of displacement vectors to generate the actual tooth surface topology graph containing typical manufacturing deviations.

[0024] The actual tooth surface topology graph is re-input to the meshing simulation unit for secondary contact analysis containing error factors to evaluate the impact on the degree of coincidence, contact spot position, and transmission error. If the performance indicators exceed the allowable range, the system starts the compensation mechanism: the measured dominant harmonic components are reversely generated into compensation instructions, which are input to the tooth profile generation unit to correct the theoretical tooth profile model of the next workpiece. For example, if the detection finds that the 3rd-order pitch error is significant, the system will pre-introduce a 3rd-order harmonic disturbance with the same amplitude and opposite phase in the new model to offset the machine tool inherent error and achieve error feed-forward compensation. This process forms a closed-loop iterative process of "design - processing - measurement - correction", ensuring that the mass-produced gear products have consistent high quality.

[0025] The system has a built-in material database covering key physical parameters of several common carburized and quenched gear steels, such as 20CrMnTi, 18CrNiMo7-6, 42CrMo4, etc. The database entries include elastic modulus (206 GPa to 215 GPa), Poisson's ratio (0.29 to 0.31), thermal expansion coefficient, hardening layer depth (0.8 mm to 2.5 mm), and surface hardness (58 HRC to 63 HRC), etc. When performing finite element calculation, the stress optimization unit automatically calls the corresponding parameter set of the material to define the material constitutive relation, divide the finite element mesh, and set the boundary conditions. In particular, for the gradient material properties of the hardening layer and the core, the system uses a layered shell element model for simulation, accurately reflecting the residual stress distribution and contact area stress transfer law, ensuring that the optimization results meet the material response behavior under actual service conditions.

[0026] The chamfer mapping process further considers the geometric variation caused by the tool blunting effect. The chamfer edge of the new tool is an ideal sharp edge without a round corner transition; however, in continuous cutting process, the cutting edge undergoes slight wear due to friction and high temperature, forming a small round corner with a radius of about 0.05 mm. Although this change is small, it will significantly change the curvature distribution of the envelope surface in the chamfer area, and then affect the contact stiffness and oil film formation ability at the initial engagement. The system obtains the cumulative cutting time and cutting force change trend of the tool through the wear monitoring module, estimates the actual round corner radius of the chamfer edge of the current tool, and generates two sets of parallel tooth profile correction schemes accordingly: one set is for the new tool state, using the sharp chamfer model; the other set is for the worn state, introducing R0.05 mm round corner transition. Process personnel can choose the applicable scheme according to the current tool changing period, or the system can automatically switch according to the tool life prediction model to realize adaptive tooth profile control throughout the life cycle.

[0027] The system supports multi-objective collaborative optimization mechanism to comprehensively evaluate the overall performance of the design scheme. The engagement simulation unit outputs three key indicators: peak contact stress σ_max, transmission error fluctuation amplitude ΔTE, and vibration acceleration level a_rms. The three indicators are first normalized to map them to the [0, 1] interval: let the ideal target values of each indicator be σ_target, ΔTE_target, and a_target, respectively, and the ratio of the current value to the ideal target value is compressed by the Sigmoid function to obtain the single evaluation value. Then, the three evaluation values are weighted and summed according to the preset weight coefficients to form the comprehensive performance evaluation function F:

[0028]

[0029] wherein, , , are weight factors, satisfying + + =1, which is adjusted according to the application occasion, for example, in a wind turbine gearbox, the design is focused on , in a servo system, the design is focused on When is less than the preset threshold 0.7, it is determined that the current design scheme meets the engineering application requirements, and the production preparation stage can be entered. This mechanism realizes the transition from single index optimization to system level performance balance, and improves the scientificity and robustness of design decision.

[0030] The present embodiment builds an intelligent gear design platform deeply integrating manufacturing process constraints and service performance requirements through the synergistic operation of the above five units. The system first transforms the tool edge chamfer from a passive tolerated machining mark to an active regulated functional structure, realizes the positive conduction of manufacturing features to performance advantages through the chamfer mapping unit. The stress optimization unit and the process feedback unit constitute a double closed-loop control system: the former implements structural reinforcement and load balancing based on finite element analysis, and the latter absorbs real machining disturbances and implements feedforward compensation, which together guarantee the high-fidelity reproduction of design intent on physical products. Experimental verification shows that the gear designed using the system reduces the operating noise by 5 dB A under the rated working condition, mainly due to the effective suppression of the meshing impact by the chamfer guide slope; the occurrence rate of tooth surface micro-pitting is reduced by 70%, due to the combined improvement of oil film bearing capacity by the curvature continuous transition surface and elastohydrodynamic lubrication optimization; the fatigue life is extended by more than 2 times, thanks to the significant reduction of cyclic stress amplitude by the tooth root material compensation and asymmetric pairing design. The system is not only suitable for new gear development, but also can be used for performance upgrade redesign of old gear pairs, and has wide industrial application prospects.

[0031] The existing technology generally adopts a serial development mode of "first designing an ideal tooth profile, and then empirically modifying it according to test results", with a serious disconnection between design and manufacturing. Design engineers often ignore the substantial influence of tool geometry details on the final tooth profile, resulting in systematic deviation between theoretical models and physical products. When the product has noise or early failure problems, it can only rely on trial and error method to repeatedly adjust the modification amount, lacking mechanism-level explanation and prediction ability. In addition, standard modification methods such as thin tip cutting or drum modification usually sacrifice the contact ratio in exchange for stress uniformization, causing transmission stiffness to decrease and dynamic instability to increase. The present invention fundamentally changes this passive situation by introducing a chamfer mapping unit, which takes the tool edge geometry as a controllable design variable into the forward design process, realizing the concept innovation from "defect compensation" to "functional structure". The generated transition surface not only retains a long enough effective engagement segment, but also has excellent noise reduction and vibration reduction characteristics, solving the contradiction between contact ratio and smoothness.

[0032] Further, the system breaks through the data link between design and manufacturing through the process feedback unit, and realizes closed-loop optimization based on measured error. In the traditional production mode, processing error is regarded as uncontrollable random disturbance, which can only be passively dealt with by improving equipment precision or strengthening quality inspection. However, the system regards error as an identifiable, modelable and compensable information source, extracts its frequency domain characteristics through Fourier analysis, and injects it into the design model in a feedforward manner to realize active cancellation of systematic error. This mechanism significantly reduces the dependence on ultra-high precision machine tools and improves the possibility of producing high-precision gears on ordinary equipment, which has important economic value.

[0033] The asymmetric meshing pairing strategy adopted by the stress optimization unit breaks through the traditional symmetric design mindset. By implementing material compensation only on the driven wheel, the pre-deformation is used to offset the elastic approach under load, achieving ideal conjugate contact in the working state. This design fully considers the deformation coordination relationship of the gear pair under real stress state, and embodies the evolution from static design to dynamic matching. Combined with the accurate prediction of oil film thickness through elastohydrodynamic lubrication simulation, the system can predict the risk of lubrication failure at the design stage and make preventive optimization by adjusting the chamfer parameters, avoiding the expensive bench test and rework cost in the later stage.

[0034] In summary, the design system of the involute gear with chamfered rack provided in the embodiment constructs a comprehensive technical framework integrating geometric modeling, manufacturing mapping, mechanical simulation, structural optimization and error compensation. The data flow between the units of the system is clear, the logic loop is complete, and a through path from macro performance target to micro geometric implementation is formed. The technical effect is not only reflected in the improvement of single performance index, but also in the change of overall research and development paradigm - from experience-driven to model-driven, from isolated design to system integration, and from post-correction to pre-prediction. With the development of intelligent manufacturing and digital twin technology, the system will further integrate machine tool digital twin model and online health monitoring data, evolve towards full life cycle intelligent operation and maintenance, and continuously promote the technological progress of high-end transmission equipment.

[0035] Embodiment 2

[0036] On the basis of the foregoing embodiment, the embodiment proposes a strengthening type chamfer mapping method suitable for large modulus heavy-duty gears. For large gears with a modulus greater than 10 mm, the meshing impact energy increases significantly, and the conventional chamfer parameters are difficult to effectively buffer the contact stress rising rate. Therefore, the system expands the function of the chamfer mapping unit and introduces a hierarchical chamfer structure. The original single 45° chamfer is replaced by a two-stage serial chamfer: the first stage is a 30° shallow chamfer with a width of 0.5 mm and a depth of 0.2 mm; the second stage is a 60° deep chamfer with a width of 0.3 mm and a depth of 0.35 mm. The two-stage chamfers are connected by a circular arc transition with a transition radius of 0.1 mm, ensuring the overall curvature continuity is not damaged. This structure provides a long-stroke low-stiffness pre-contact by the 30° shallow chamfer at the initial meshing stage, delaying the contact force growth; before entering the main meshing area, the 60° deep chamfer quickly increases the support stiffness to avoid transmission delay caused by soft contact. The system allows users to switch between single-stage and two-stage chamfer modes as needed through a parameterized modeling interface and automatically updates the envelope calculation algorithm to adapt to the new blade geometry.

[0037] To adapt to the hierarchical chamfer structure, the meshing simulation unit enhances the contact stiffness calculation model. The system divides the meshing process into three stages: pre-contact stage, transition contact stage, and main meshing stage. In the pre-contact stage, only the first-stage chamfer is involved in the contact, the contact area is small, the comprehensive elastic approach is large, and the equivalent contact stiffness is low; in the transition contact stage, both chamfers are loaded together, and the stiffness rises nonlinearly; in the main meshing stage, the standard involute segment is fully contacted, and the stiffness tends to be stable. The system fits the stiffness-displacement relationship of each stage through a piecewise function, establishes a time-varying meshing stiffness matrix, and uses it for subsequent dynamic simulation. Experiments show that the gear pair with a hierarchical chamfer structure reduces the vibration acceleration peak value by 18% at the start moment, effectively alleviating the impact damage risk under heavy-duty start-stop working conditions.

[0038] The stress optimization unit adjusts the material compensation strategy simultaneously. For the characteristics that the stress concentration of the gear tooth root of large modulus gears is more significant, the upper limit of the compensation offset is increased to 0.2 mm, and the compensation area is expanded outward along the tooth width direction to the end face chamfer projection area, forming a three-dimensional compensation structure. The compensation amount is still smoothed by a cubic spline curve, but 0.1 mm additional offset is added at both ends in the tooth width direction to offset the end face stress concentration effect. Finite element analysis shows that the maximum stress of the optimized tooth root is reduced by 23%, and the safety factor is increased to 4.1, meeting the requirements of heavy-duty gear standards such as API 619.

[0039] A tilt error compensation module is added to the process feedback unit to solve the common tooth trace distortion problem in large gear machining. Laser scanning data shows that the tooth trace deviation presents a linear tilt trend due to the clamping deformation caused by the weight of the workpiece, with a slope of about 0.01 mm / 100 mm. The system introduces a reverse tilt amount in the tooth profile generation stage, so that the theoretical tooth surface presents a slight reverse warping shape in the free state, and restores to the ideal straight tooth trace under the action of gravity after machining. This compensation strategy is verified by three batches of trial production, and the total tooth trace deviation is stably controlled within 0.008 mm, meeting the requirements of precision gears.

[0040] This embodiment expands the application range of the original system by introducing new technical means such as hierarchical chamfer, three-dimensional compensation and tilt feedforward, so that it can undertake the high-difficulty design task of large modulus heavy-duty gears. The hierarchical chamfer structure provides better stiffness gradient control, the three-dimensional compensation enhances the structural robustness under complex stress state, and the tilt feedforward effectively overcomes the unique manufacturing problems of large workpieces.

Claims

1. A design system employing an involute gear with a chamfered cutting edge rack, characterized in that, include: Tooth profile generation unit, used to construct a parametric mathematical model of a standard involute tooth profile; The chamfer mapping unit is used to introduce the chamfer structure at the cutting edge of the gear cutting tool into the tooth profile modeling process. During the gear generating motion, the chamfer area participates in material removal, forming a transition surface located near the starting point of the involute at the tooth tip. The meshing simulation unit is used to establish a dynamic contact model of a pair of meshing gears. It inputs the three-dimensional tooth surface data of the driving and driven gears output by the tooth profile generation unit and the chamfer mapping unit, calculates the spatial trajectory of the instantaneous meshing line, and analyzes the movement path of the contact spot. The meshing simulation unit adopts the elastohydrodynamic lubrication finite element model, takes into account the viscous pressure effect of lubricating oil and the influence of surface roughness, calculates the oil film thickness distribution in the tooth surface contact area, and determines whether there is a boundary lubrication risk based on the minimum oil film thickness. The stress optimization unit is used to perform local material compensation on the tooth profile section close to the dangerous section of the tooth root, and adjust the chamfer parameters in the chamfer mapping unit in reverse according to the analysis results of the meshing simulation unit. When the boundary lubrication risk is determined, the meshing simulation unit triggers the stress optimization unit to start secondary optimization to adjust the chamfer width parameters in the chamfer mapping unit. The process feedback unit is used to receive the machining error data of the actual gear cutting machine tool, superimpose the machining error data on the theoretical tooth surface model, generate the actual tooth surface topology map containing manufacturing deviations, and feed it back to the meshing simulation unit for re-contact analysis, forming a closed-loop optimization process.

2. The involute gear design system with chamfered cutting edge rack according to claim 1, characterized in that, The transition surface generated by the chamfering mapping unit is formed by simulating the relative motion envelope between the chamfer of the cutting edge and the workpiece material during the reciprocating cutting process of the gear shaper, and its curvature continuity reaches C2 level.

3. The involute gear design system with chamfered cutting edge rack according to claim 2, characterized in that, The generatrix profile of the transition surface consists of three segments: the first segment is a straight chamfered edge; the middle segment is a Bézier transition curve connecting the straight line and the involute, with its control points configured according to the tangent vector matching principle; and the last segment smoothly merges into the standard involute.

4. The involute gear design system with chamfered cutting edge rack according to claim 1, characterized in that, The material compensation operation in the stress optimization unit is applied only to the loaded tooth surface of the driven wheel, while the driving wheel retains its original design to form an asymmetric meshing pair.

5. The involute gear design system with chamfered cutting edge rack according to claim 1, characterized in that, The process feedback unit integrates an online measurement module, which uses a laser displacement sensor array to quickly scan multiple tooth grooves of the machined gear to obtain data on actual tooth pitch cumulative error, tooth profile deviation, and tooth direction deviation.

6. The involute gear design system with chamfered cutting edge rack according to claim 5, characterized in that, The process feedback unit performs Fourier decomposition on the acquired deviation data to extract the dominant harmonic components, and inputs the dominant harmonic components as compensation commands to the tooth profile generation unit to correct the theoretical tooth profile model of the next workpiece.

7. The involute gear design system with chamfered cutting edge rack according to claim 1, characterized in that, The chamfering mapping process takes into account the tool passivation effect, incorporates the difference in chamfer edge geometry between the new tool and the worn tool into the modeling, and generates multiple corresponding tooth profile correction schemes accordingly.

8. The involute gear design system with chamfered cutting edge rack according to claim 1, characterized in that, The system supports multi-objective collaborative optimization. The multiple performance indicators output by the meshing simulation unit are normalized and then weighted and summed to form a comprehensive performance evaluation function. When the value of this function is less than a preset threshold, the design scheme is determined to meet the engineering application requirements.

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