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Continuous generating grinding Material engagement in gear tooth root machiningBerend Denkena, Jens Kohler, Andreas Schindler *, Stephan WoiwodeInstitute ofProduction Engineering and Machine Tools, Gottfried Wilhelm Leibniz Universitat, An der Universitat2,30823 Hannover GermanyABSTRACTThe load carrying capacity of the tooth root mainly depends on its fillet geometry and subsurface integrity, which are affected by the hard finish processes. This paper analyzes the contact conditions in continuous generating grinding and aims to fill the knowledge gap concerning the elementary effects during penetration of tool tip and gear tooth root fillet. In order to obtain fundamental understanding of this process, the three-dimensional removal simulation software CutS was used. The gained results show that the simulated data correlate to experimental results concerning tool wear and thermal load on gear subsurface. Thereby, the reasonable use ofvitrified bond corundum-tools is severely restricted by grinding burn and macro-geometrical wear, which can be described by the tool surface normal feed rate vfn.max. An analytical approach to the calculation of vfn.max is presented, which can be applied on a practical scale. 2014 Elsevier Ltd. All rights reserved.1.Introduction1.1.Tooth root load carrying capacityThe resistance of the gear teeth to crack formation in the tooth root fillet area mainly depends on the tooth root fillet geometry and its subsurface integrity. This resistance is called tooth root load carrying capacity. Fatigue cracks which propagate under the influence of repeated alternating or cyclic stresses may end in tooth breakage 1. This means in general a gear transmission failure. Fatigue cracks result from high bending stresses which occur primarily when a small root fillet radius is generated. Thus, the optimization of the tooth root fillet geometry can substantially improve the load carrying capacity of the gear wheels 2. Grooves at the tooth root after hard finishing processes act like small root fillet radii and have to be avoided 3. High compressive residual stresses in the root fillet area have been proven beneficial, preventing the formation and restraining the growth of fatigue cracks 4-6. In comparison, grinding burn results in a decrease of the tooth root load carrying capacity whereas the influence of the root fillet surface roughness on the formation of fatigue cracks is negligible 7.In order to improve the wear resistance of the generated tooth flanks, most gears in modern transmissions are heat-treated. Oxidized surface layers formed by carburizing during heat treatment can result in reduced fatigue strength of the tooth root. Therefore, shot peening or blasting processes follow in order to clean the oxidized layer and to bring in compressive residual stresses into the gear subsurface 5,6. However, heat treatment and shot peening result in gear distortion as well as low surface quality. The resulting geometry deviation, consequently, requires a further finishing process 8.* Corresponding author. Tel.: +49 511 762 5940; fax: +49 511 762 5115. E-mail address: schindler_aifw.uni-hannover.de (A. Schindler)./10.1016/j.mechmachtheory.2014.06.008 0094-114X/ 2014Elsevier Ltd. All rights reserved.1.2.Gear hard finishingThe objectives of the hard finishing are the removal of oxidized surface layers and the achievement of suitable macro- and micro- geometrical tooth surface quality. Thereby, thermal damages and grinding burn are ineligible due to lowering of compressive residual stresses and accordingly inducing of tensile stresses.Gear hard finishing can be realized by means of several distinctive processes which can be classified in processes with defined and undefined cutting edges, continuous and discontinuous as well as generating and profiling processes. Gear shaving and skive hobbing are among the prime examples of continuous generating finishing processes with defined cutting edge. In comparison, continuous generating grinding and gear honing are continuous hard finishing processes with undefined cutting edge. Due to their high productivity, the continuous generating processes are typically chosen for large-scale production of automobile gears. However, as discontinuous profile gear grinding is characterized by high flexibility concerning profile modifications, it is generally used for hard finishing of diverse dimensioned gears even if it is less productive than the continuous processes 3,8,9.High productivity, the flexibility concerning topological gear tooth modifications and the process stability make continuous generating grinding widely spread machining process in industry. The kinematics of continuous generating grinding is similar to the rolling motion of two gears and determines the involute of the tooth flank and the tooth root 3,8,9. During the contact of the tool and the workpiece, a sliding motion occurs which defines the cutting speed vc. In order to machine the entire tooth width of the gear, an axial movement is required, which is specified by the feed rate vf (Fig. 1a).Grinding worms are predominantly made of vitrified bond corundum, which offers flexible tool geometry by the variation of the dressing process. In most cases, form rollers are used for the dressing of the grinding worms whereby the dressing process can be compared with thread turning (Fig. 1b). Also often used in generating gear grinding are non-dressable electroplated worms with cubic-boron-nitride abrasive (CBN). This tool type offers an increased tool lifetime at comparatively higher material removal rates but is also more expensive. Dressable vitrified bond CBN-worms are a compromise between dressable corundum wheels and electroplated CBN-tools. Investigations by10-12 concerning the dressing process revealed a higher performance of vitreous bonded CBN-worms in comparison to corundum-worms. However, compared to corundum-worms, vitrified bond CBN-worms are characterized by more than ten times higher tool costs as well as higher dressing tool wear which severely inhibits their industrial acceptance. Therefore, this works focuses on common vitrified bond corundum-worms.1.3. Characteristic values and process simulationIn order to describe the grinding processes, different process descriptive characteristic values have been investigated. In this context, types of chip thickness, stock removal rate and machining force models, have been analyzed. These values base mostly on the constancy of the inner and outer volumetric material flows 13.The complexity of the tooth geometry and the process kinematics complicate the transfer ofknown characteristic values to the continuous generating gear grinding. Thus, only a few scientific investigations exist, which focus on the development of specialized characteristic values 14-16.The first approach to the simulation of the continuous generating grinding process by a nonpublic simulation program is shown by 14. Thereby, a smaller chip thickness was investigated for this process in comparison to the discontinuous generating gear grinding. Thus, the less grinding burn by continuous generating ground gears could be explained.The calculation of the mean and local specific material removal rate related to the process-affected tool width is presented by15. In comparison to the mean specific material removal rate, the local specific material removal rate at the gear tooth addendum can be more than two times higher, which prevalently results in thermal damages. The geometrical analysis of the process shows that anincrease of the cutting speed or of the number of tool threads causes shorter contact times. Consequently, less heat flows in the gear subsurface.Furthermore, several characteristic values for tooth flank machining were calculated by16,17 by means of the three-dimensional material removal simulation software CutS. Thereby, the maximal single grain chip thickness hCumax correlates to the tool wear characterized by the gear profile angle deviation fHa. The area-specific removal rate Qw.max describes the summarized process forces. The simulated geometrical contact length lgmax normalized by the cutting speed correlates to the measured residual stresses in the cutting direction. Using a significance analysis method, the essential process as well as tool and gear parameters were identified in order to develop a simulation independent calculation method for the characteristic values hcu.max, Qw.max and lgmax. Furthermore, the simulation results show higher values of Qw.max during the plunge of the worm addendum into the tooth flank allowance near tooth root compared to the gear flank processing.Public research pertaining to the continuous generating gear grinding has been primarily focused on the processing of the tooth flank. Although profile grinding of the tooth root fillet can increase the gear lifetime up to 30% 6, so far, continuous generating grinding has been applied to it rather infrequently. The main reason for this could be the missing knowledge of the tool-workpiece contact conditions and the resulting thermo-mechanical loads on the gear in continuous generating grinding.14. Objectives ofthepaperTherefore, this work aims to analyze the material engagement conditions during the tooth root machining in the continuous generating grinding with focus on the grinding worm tip geometry. For this purpose, the basics of the characteristic values modeling are examined, and the relation between the values Qw.max, hcu.max and the worm surface normal feed rate vfe.max is investigated. The relevance of the value vfn.max for the machining process is verified by experiments regarding the grinding worm tip wear and the gear subsurface integrity. The analysis of the process kinematics enables the calculation of the value vfn.max without further simulations. Hence, a new tool for the process design is made available to research and praxis.2.Three-dimensional simulation using CutSThe simulation environment CutS 18 developed by the Institute of Production Engineering and Machine Tools (IFW) allows a detailed observation of the material engagement conditions in cutting processes. In order to analyze the worm-gear contact during tooth root machining in continuous generating grinding, the CutS simulation software has been adapted. The chosen source code modification enables variations of the grinding worm tip and the pre-cutting tool geometry realizing different gear tooth root fillet geometries. The simulation results are used below in order to explain some basic effects occurring during the real tooth root machining.2.1.Simulation procedureFor the simulation development of continuous generating grinding, four data sets have been specified: the geometry data of the gear wheel, the hob and the grinding worm as well as the coordinate system in which the machine axes and the relative movement of the affected partner in NC-Code are defined. In addition, the discretization of the process time has had to be specified.In theory, the grinding process is identical for each gear tooth; therefore, the gear blank can be modeled as a cylinder segment stump with an outer diameter equal to the gear cylinder diameter da and an apex angle equal to the gear angular pitch t. Consequently, the machining of one gear tooth can be simulated and used as a representative of all teeth. The hob is represented by a hob basic rack profile. The grinding worm is represented by a part of the worm thread. Used tool profiles can be varied with respect to the DIN standard 3972 19. Both tool geometries cover the gear width and, as a result, the contact zone completely.The simulation is realized in three steps. First step is pre-machining of the gear blank using the hob profile in order to create a tooth space with allowance. Thereby the pre-machined gear profile is a numerical approximation of the ideal involute. Geometrical deviations, caused by hobbing process or thermal treatment, are not focused in this work. At the second stage, an initial cut with the grinding worm profile follows succeeded by a progressive cut representing the material engagement conditions during the process. Hence, the generated material removal is used for further process analysis.2.2.Material engagement conditions during tooth root fillet machiningThe tooth space machining involves multiple areas of contact between the grinding worm and the gear wheel. The direction of movement is determined by the process kinematics and differs between the right and left flank ofthe grinding worm (Fig. 2a). In the case presented here, profiles of the gear and grinding worm move in the area of contact from top to bottom. The left flank is firstly touched by the worm tip close to the gear form radius rFf. The theoretical contact point splits up in two points. The flank involute is processed from the gear form radius rFf to the gear outer diameter. Simultaneously, the tooth root fillet is processed from the gear form radius rFf to the tooth root surface. Since the machining process occurs inversely at the right flank, the two contact points converge at the transitional area between the flank involute and the tooth root fillet.Due to the grinding allowance in the real process, contact areas occur instead of contact points. Projected on a plane, the contact areas form halves of ellipses during the initial cut (Fig. 2b). The lengths of the ellipse axes are determined by the curvature of the affected partners as well as by the depth of cut normal to the finished gear surface an. During the progressive cut, the size of the triangular contact areas is additionally determined by the feed per gear revolution f (Fig. 2c). When increasing f, the contact areas expandFig. 2. Material engagement conditions during tooth root fillet machining. (a) Movement of the theoretical contact point in the transverse plane of the spur gear (b) influence of the depth of cut on the contact area range and (c) influence of the feed per gear revolution on the contact area shape.(Fig. 2c, bottom). The presented simplification enables a geometrical description of the contact situation in continuous generating grinding. Moreover, this simplification can be used for the analytical modeling of the contact area in further research.2.3.Material removal model and calculation of characteristic valuesThe gear wheel segment is represented by512 x 512 parallel arranged dexel, which are distributed equidistantly in the Y direction (AY = 0.035 mm) and Z (AZ = 0.039 mm) direction of the gear coordinate system. Thereby, one dexel is the line section defined by two three-dimensional points with equal Y and Z and differentXvalues. For the realization of the material removal, the tool segment is generated as a composition of triangular facets (Fig. 3a).The tool and the workpiece reposition step by step accordingly to the process kinematics. When the material engagement takes place, the intersection point between the tool facet and the dexel is calculated. The calculated intersection point splits the dexel into two, the removed and the remaining dexel (Fig. 3b). The removed dexel defines the material removal in the considered time interval (At 0.19 ms). The remaining dexel defines the actual geometry of the tooth surface and can be involved in the material engagement in subsequent steps. The calculation of the characteristic values is realized in the programming environment Matlab by means of a specifically developed routine. The calculation oflocal characteristic values is based on the consideration of four parallel dexels. This 4-dexel-tuple spans a square rod, which is machined with a tool surface (Fig. 3b,c).Fig. 3. Schematic illustration of the material removal model. a) Workpiece and tool structure b) removal element defined by four dexels and c) volumetric equivalence of three hexahedrons.The local volume V(At) dependent from the considered time increment is removed in the form of a hexahedral volume element, which is defined by removed dexel q. As the size of removed dexel q may vary, the local volume elementV(At) has to be calculated using the “right prism approximation” (1)V(At) - AY AZ 0ci(1)where AY and AZ are perpendicular transversal distances of neighbored dexel in two directions and 0q is the average value of the dexel removed in the X direction in the gear coordinate system. The sides a and b of the local contact area at the current time step ti are defined by the coordinates of the related dexel points. Thus, the area-specific removal rate Qw can be determined by dividing the volume V(At) by the local contact area a b and the associated time increment At (2). This value equals the time increment dependent height h(At) of the oblique prism with the volume V(At), base area a b and oblique edges 0q. Thus, the area-specific removal rate Qw has velocity units.q =寧)=h(t)r7、Q w _ a b t _ t (2)Strictly speaking the value Qw is the local average material engagement velocity of the grinding wheel into the material normal to the local grinding wheel surface. It can be defined as the local, tool surface normal feed rate vfn in Eq. (3).V h(t)Vfn _j (3)The workpiece volume is described by 262,144 dexels. In the process the cutting volume is composed by few tens up to 12 thousand hexahedrons each time step. Thus for each time step and for the total process, the maximum and total values ofthe cutting volumes and resulting characteristic values can be calculated.With knowledge of the Qw.max respectively of the vfn.max, the single grain chip thickness hcu.max can be calculated. For this purpose, equations for Q_w.max and hcu.max developed by the regression method presented in 15, are mathematically transposed and compared to each other in Eqs. (4), (5). Thereby factor afn is realized depth ofcut normal to the new surface. In flat grinding afn is equal to depth of cut ae.Qw.max _ vfn: max _ 150 、 a (4)afn0 3 f| (5)Neglecting the small exponent difference (0.3 to 1/3) of the flank normal allowance afn, the terms in the brackets of Eqs. (4) and (5) are equal. Consequently, the parentheses in Eq. (5) can be replaced by Qw.max divided by the coefficients 150 and vc. Thus following relationship results between the two values:hn /Qw.max、Influence of vta on the grinding processBased on the theoretical models presented above, it has been established that the value vfe.max has significant importance for the thermo-mechanical load spectrum of the machining process. This will be illustrated below by the correlation of the simulated and measured data.4.1.Influence on the macro-geometrical tool wearThe macro-geometrical wear of the worm profile after one gear grinding has been evaluated taking into consideration the measured gear profile deviations (Fig. 5a). The lowest deviation of the measured gear profile from the calculated geometry of the spur gear (Table 1, gear 1) APmax = 0.045 mm correlates to the smallest value for normal feed rate vfe,max = 61 mm/s (Fig. 5b). With increasing vfn.max, the deviation values APmax increase exponentially. The worm tip fillet radius pao has a significant influence on the maximal normal feed rate and, thus, on the local load of the worm profile. The resulting excessive loading of the grains and the bonding leads to increased tool wear. Consequently, the affected areas flatten cumulatively with each worm revolution. Thereby, 0 14 /Qw.maxV 0 14 /vfnmax V心hcu.眶=0 14 AiswmaxJ 一 pffi一 pffi AV-J (6)The speed ratio vfn.max to vc describes the maximal chip thickness hcu.max, which is established between two subsequent grains with one millimeter spacing. This ratio is independent of the grinding wheel specification and is adjusted by the model of grain distribution to the grinding wheel specification developed by 20. As vfe.max describes the material feed rate in the direction of the tool, this model is conforming to the general order of 13. The essential advantage of vfn.max compared to a simple workpiece Table 1Data of the machined gears and used grinding tools as well as process parameters.order to characterize the grinding tool macro-geometrical wear, the profile of the ground gear tooth space was measured by the precision coordinate measuring machine Leitz PMM 866. In order to detect grinding burn the analysis of polished tooth cross sections as well as temper etch inspection with respect to the ISO standard 14104 21 has been made.The variation of the tool tip geometry has been defined with respect to the DIN standard 3972 19 (Fig. 4a). In order to generate the worm profile, a double-tapered dressing roller with a defined profile radius has been used. While dressing the worm tooth flanks, the dressing roller has been used as a profile roller, whereas the conditioning of the worm tooth tip has been realized by a path controlled profiling using the profile radius of the dressing tool (Fig. 4b). The advantage of this method is the time saving profiling of the flank profile. At the same time, a high flexibility for the generation of the addendum profiles is assured(a) correlation method(b) max. norma! feed rate Vfn.max(c) max. normal feed rate Vfp.Sci/64653 IFWFig. 5. Influence of the maximal normal feed rate vfn.max on maximal gear profile deviations APmax (a) method of correlation (b) influence of maximal normal feed rate vfn.max on maximal profile deviations APmax measured on spur gears and (c) influence of maximal normal feed rate vfnmax on maximal profile deviations APmax measured on helical gears.the local load of the grinding worm surface declines in the process. Thus, when using grinding worms with small tip fillet radii pa and large worm addenda ha。,the profile deviations APmax are smaller than expected when considering vfmax values.Experiments performed on helical gears (Table 1, gear 2) have been added to the grinding and simulation experiments on spur gears. The measured maximal deviations continue the exponential trend of the deviation curve observed by spur gears (Fig. 5c). It can be clearly seen that decreasing of vfn.max values leads to smaller gear profile deviations. The whole curve progression shows that, for values of vfn,max between 50 mm/s and 75 mm/s, a strong increase of the deviation values APmax occurs. This suggests a critical threshold of the mechanical wheel loading which is consistent with the increasing grain loss. About the featured link between vfn,max and hcu.max in Eq. (6), the single grain chip thickness from 0.011 jjmto 0.014 jjm yields. This range corresponds nearly to the results of Stimpel in 16,17 where corundum tools with a grain size between 90 jim and 130 jjm were used as well. Stimpel determines in his work a critical maximum single grain chip thickness with hcu.max 0.02 jjm.4.2.Influence on gear subsurface integrityMetallographic analysis shows marginal structural transformations in the flank area of the spur gears (Fig. 6a). These occur in the range of normal feed rates vfn from12.5 to 25 mm/s. Values of vfn above 45 mm/s have been calculated for the thermally non-damaged tooth root. The occurrence of thermal damage at lower values for vfn can be found in the context of this value with the single grain chip thickness hcu in Eq. (6). The undershooting of a critical single grain chip thickness leads to friction and plowing effects without effective chip removal 22,23. Consequently, more energy flows as heat energy into the gear subsurface.For the same process parameters (Table 1), the helical gear flank subsurface is more thermally damaged in contrastto the spur gear flanks (Fig. 6b). The tooth root fillet remains, as in the case of spur gears, uncolored. The vfn during the processing of the helicalFig. 7. Influence of vfn on gear subsurface integrity and tool wear.ujnq 6u!pu!jo)to maximally 11.5 mm/s. Thus, it is below the normal feed rate values at the flanks of machined spur gears i a further reduction of the single grain chip thickness hcu resulting in higher thermal gear flank subsurface e tool diameter and the number of threads are kept constant, the smaller normal modulus (mn = 2 helical eads to smaller lead angle of the grinding tool. This results in the one third lower gear speed of the helical )ur gear. Consequently, the contact time between the grinding worm and the gear flank per gear revolution he helical gears so that thermal subsurface load increases. In the tooth root fillet of the helical gear profile e calculated (Fig. 6b). Thus, no grinding burn has been detected in this area.en measured profile deviations, thermal load visualized by temper etch inspection and vfn are summarized ting optimum between vfn = 25 mm/s and vfn = 60 mm/s result for the used grinding wheel. ermal effects in the conventional grinding processes often relies on geometric contact length which has no :he continuous generation grinding. Despite doubling of the contact lengths by using grinding worm pro- o thermally induced changes has been observed in the gear tooth root fillet subsurface. This confirms the al feed velocity vfn,max, which is directly related to the single grain chip thickness and the contact time. of 16,17, the experimental verification of the parameter vfnmax during the tooth root machining confirms ling process. In order to make this value applicable the next logical step is the detachment of vfn.max fromthe normal feed rate vtamaxhe local thermo-mechanical effects, it is necessary to analyze the velocity state during the continuous s. Since the contact conditions during the flank and tooth root machining always differ, two models for are required. The basic modeling approach without detailed mathematical calculations is explained below. nstruction of normal feed rate vfn.max in the axial cross-section for the tooth flank and tooth root fillet hown. In the two-dimensional view of two time-discrete machining steps in the gear coordinate system, ween the two worm flank positions within the allowance is spanned (Fig. 8a).of contact between the tool and final gear flank involute normal feed rate equals zero since only sliding distance to the theoretical contact point along the worm flank, the normal feed rate increases. This isFig. 8. Geometrical construction of normal feed rate vfn.max, a) tooth flank machining and b) tooth root fillet machining.due to the tilt of the contact surface, which leads to the penetration between grinding worm and gear flank allowance. As an approximation of the normal feed rate vfn,max, the time increment dependent height of the triangle can be used. Thereby, the worm flank at time ti + ! is used as the base side. Thus, the value vfe,max is determined by the gear speed nw, the radius of the gear flank curvature p and the flank normal depth of cut am in Eq. (7).vfn max 2 . n . nw . P . sin cos-1-(7)For modeling of the normal feed rate during the tooth root machining, a position in the rolling motion is considered, in which the tool firstly touches the final geometry of the flank plunging into the flank allowance (Fig. 8b). The position of the grinding worm profile relative to the gear tooth is defined by the grinding worm form addendum hFa0 and the gear tooth root form radius rFf 24. The rotational velocity vp at the form circle equals the velocity of the tool profile normal to the flank surface vpano. These values are defined by the gear speed and the gear tooth root form radius rFf. Thus, the sliding velocity vt tangential to the involute curve can be calculated. In the theoretical point of contact between tool and workpiece only sliding tangential to the final involute occur. Here, vfn,max applies 0 mm/s. With increasing distance from the contact point in the direction of the tooth flank allowance surface, the direction of the normal feed vector changes. This leads to increase of the normal feed rate value. The main factors in the tooth root machining are thus the gear speed nw, the normal depth of cut at the tooth flank near tooth root afn, the grinding worm tip radius pa0 as well as the form addendum hFa0 and the angle of pressure an in Eq. (8).vfn 2 . n . nw . hFa0 . tan-1 (a) cos (an) cos 0:5 . n cos-M 1 j (8)LV pa0/JThe calculation of v max relates to the initial cut and correlates with the coefficient of determination of R2 = 0.99 with the simulated values of the vfn.max (Fig. 9). Thus, the basic validity of the model is confirmed. The feed per gear revolution was not reflected in this model jet. The influence of the feed per gear revolution f can be taken into account by mathematical analysis of the above presented ellipse segments (Fig. 2) as a simplification of the contact areas. By use of a factor of 0.5 the analytical model correlates with the simulated progressive cut values by the coefficient of determination of R2 = 0.95 (Fig. 9). Consequently, it seems to be sufficient to derive a numerical factor from the ellipse segment to transfer the presented initial cut model to the progressive cut generated by a user-defined feed per gear revolution value.In order to describe the process for helical gear grinding further model extension is needed. These are objectives of future studies, combined with the feed per gear revolution factor.6. SummaryThis paper has analyzed the meshing conditions in continuous generating grinding with a focus on the gear tooth root. For this purpose the three dimensional simulation software CutS was used to obtain some fundamental understanding and characteristic values of the process. In order to verify simulated data, two different gear geometries have been examined. Experiments show that the tool surface normal feed rate vfn,max is suitable for describing the thermo-mechanical loads acting on the grinding worm and the gear surface. The range of the reasonable use ofvitrified bond corundum-tools is closely restricted. These tools exhibit a poor wear behavior at normal feed rates over vmax = 60 mm/s. Thermal damages of the gear surface occur at normal feed rates less than vfe,max = 25 mm/s. Grinding tests have shown that the generation grinding of the tooth root is less susceptible to thermal damage than that of the gear flanks.In order to make simulation independent calculation of vfc.max for continuous generating grinding possible, the velocity state during the process has been analyzed. Analytically calculated values of vfn,max correlate to simulated values of vfn,max with a determination coefficient of R2 = 0.99 for the initial cut. The determination coefficient of R2 = 0.95 results for the progressive cut, if calculated data are multiplied by factor of 0.5. Calculating the vfe.max allows comparing the levels of gear flank and tooth root loading and respectively of grinding worm flank and tip fillet in the gear machining. This way extensive local, mechanical tool profile loading can be omitted. The danger of grinding burn can be evaluated before gear processing. The results presented are a basis for further investigations aiming to refine the model and ensure its higher generality degree.AcknowledgmentThe research work described in this paper was undertaken with support of the German Research Foundation (DFG) within the project DE 447/74-1 “Material engagement conditions during continuous generating grinding of gear tooth root”.齿轮齿形加工中连续产生磨削的材料啮合denkena Berend,Jens Khler,安德烈亚斯,斯蒂芬Woiwode生产工程与机床研究所Gottfried Wilhelm莱布尼茨大学,在大学T 2、30823德国汉诺威2014 Elsevier公司版权所有。摘要齿根承载能力主要取决于其角的几何形状和表面的完整性,它受到硬终点过程的影响。本文分析了连续产生磨削的接触条件,并旨在填补关于刀具尖端和齿轮齿形角的渗透过程中所涉及的基本效应知识缺口。为了获得这一过程的基本理解,采用三维仿真软件CutS。所获得的结果表明,模拟数据与关于齿轮表面刀具磨损与热载荷的研究的实验结果相关。因此,陶瓷结合剂工具的合理用法是由磨削烧伤和宏观几何磨损严重限制,可以通过工具表面正常进给速度vfn.max描述。提出的vfn.max计算分析的方法,可以应用于一个实际的规模。关键词:齿轮磨削;加工仿真;齿根1. 简介1.1 齿根承载能力齿轮齿对齿形角区裂纹形成的阻力主要取决于齿形角的几何形状及其表面的完整性。这种抗力称为齿根承载能力。反复交替或循环应力的影响下扩展的疲劳裂纹,可能会最终以轮齿断裂告终 1 。这一般意味着齿轮的传动故障。疲劳裂纹是起因于主要在小的根圆角半径时产生的高的弯曲应力。因此,优化的齿根角的几何形状,可以大大改善的齿轮的承载能力 2 。在硬化整理过程后齿根的凹槽,如小的根圆角半径,必须避免 3 。在根圆角区的高压缩残余应力已被证明是有益的,它抑制疲劳裂纹形成和增长 4 6 。相比之下,磨削烧伤导致的牙齿根部承载能力下降,而根角的表面粗糙度对疲劳裂纹的形成的影响可以忽略不计 7 。为了提高生成的齿面耐磨性,在现代变速箱中的大多数齿轮都是热处理过的。在热处理过程中形成的表面氧化层,可以导致齿根疲劳强度减少。因此,喷丸或喷砂过程以清理氧化层和引入齿轮表层残余压应力为准5,6。然而,热处理和喷丸处理导致齿轮变形以及表面质量低。因此,由此产生的几何偏差,需要进一步的整理过程 8 。通讯作者。电话:+ 49 511 762 5940;传真:+ 49 511 762 5115。电子邮件地址:schindler_aifw.uni-hannover.de(A. Schindler)。/10.1016/j.mechmachtheory.2014.06.008 0094-114x /2014 Elsevier公司保留所有权利。12 B denkena等人。/机构和机器理论81(2014)11 - 201.2 齿轮精加工硬化处理的目标是去除氧化层表面层和实现合适的宏观和微观几何齿面质量。因此,由于压缩残余应力降低和相应的拉伸应力和磨削烧伤产生的热损伤与磨削烧伤是不合格的。齿轮硬化处理,可以通过可分类的过程,与定义和未定义的切削刃,连续和不连续的,以及产生和分析过程等几个独特的过程来实现。剃齿和滚齿是具有定义切削刃的连续产生精加工工艺最好的例子之一。相比之下,连续的磨削和齿轮的研磨加工是用未定义的切削刃的连续硬加工过程。由于其生产率高,连续产生的过程通常被选择用于大规模生产的汽车齿轮。然而,作为不连续面齿轮磨削的特点是灵活性高,对配置文件的修改,它一般用于精加工不同尺寸的齿轮,尽管它比连续过程3,8,9少生产。高生产率,拓扑齿轮齿形修改和加工稳定性的灵活性,使连续磨削加工在工业中广泛应用。运动学连续展成磨削是相似的两齿轮滚动运动,确定齿面、齿根3,8,9渐开线。在工具和工件的接触过程中,出现了一个滑动运动,它定义了切削速度vc。为了加工齿轮全齿宽,轴向运动是必需的,这是由指定的进给速度Vf(图1A)。磨削蜗杆主要是用陶瓷结合剂制成,它提供了修整过程变化的灵活的刀具几何参数。在大多数情况下,形成辊用于修整磨削蜗杆,选矿工艺可与螺纹车削相比(图1B)。也经常用于蜗杆是非修整电镀立方氮化硼(CBN)磨料的展成磨齿。此工具类型拥有较高的刀具寿命和相对较高的材料去除率,但也更昂贵。修整陶瓷结合剂CBN蜗杆是修整陶瓷结合剂砂轮和电镀CBN工具之间折中的工具。关于修整工艺的研究显示1012CBN蜗杆在与陶瓷结合剂蜗杆相比性能更高。然而,相比于陶瓷结合剂蠕虫,陶瓷结合剂CBN蠕虫超过十倍刀具成本以及较高的修整工具的严重磨损,使它难以被行业接受。因此,这部作品主要集中在普通陶瓷结合剂蜗杆。1.3。特征值与过程模拟为了描述磨削过程,对不同的工艺描述特征值进行了研究。在这方面,对切削厚度,常备去除率和切削力模型的类型,进行了分析。这些标准基于内在和外部的体积物质流的恒定性 13 。齿形与过程运动学的复杂性使关于连续齿轮磨削已知特性的传递更复杂。因此,只有少数的科学调查,专注于专业化特征值的发展 14,16 。对模拟的连续展成磨削过程的仿真程序,第一种方法是公开表明 14 。因此,对一个较小的切削厚度在这一过程中与不连续的齿轮研磨进行了比较研究。因此,连续生成研磨齿轮引起较少的磨削烧伤可以解释。与受影响过程的宽度相关的平均和局部特定的材料去除率的计算被显示出来 15 。与平均材料去除率相比较,在齿轮的齿顶的具体的材料去除率可以超过高两倍,而普遍导致热损伤。对切削速度或刀具螺纹的数量的过程的几何分析表明,切削速度或刀具螺纹的数量的增加会导致更短的接触时间。因此,在齿轮表面的热量较少。此外,对齿面加工的几个特征值16,17,通过三维材料去除仿真软件 CutS计算。因此,最大单粒芯片厚度hcu.max与刀具磨损的特点齿廓偏差角FH相关。特定区域的去除率Qw.max描述总结过程的力量。模拟几何接触长度lg.max切削速度的相关测量的残余应力在切削方向的归一化。使用重要性分析法、基本过程、刀具和基本参数确定来开发一个独立模拟计算方法来描述特征值。此外,仿真结果显示在蜗杆齿顶齿向齿面附近的齿形齿向齿面加工中的齿齿向齿面加工中高 Qw.max值。关于连续产生齿轮磨削的公共性研究主要集中于齿面加工。虽然齿形磨削的齿形磨削可以增加齿轮寿命高达30% 6 ,到目前为止,连续产生研磨已经很少用到。主要原因可能是刀具工件接触条件和在齿轮上连续产生磨削中产生的机械热而产生的热机械载荷。NW工件主轴转速vccj蜗杆修整速度VD梳妆台切削速度vc切削VF磨削进给速度vfacj轴向修整进给速度1.4 论文的目的因此,这项工作的目的是分析齿形加工中齿面加工中的啮合条件与刃形几何的研究。因此,需要解释特征值模型的基础和研究值w.max Q,hcu.max和蜗杆表面正常进给速度vfn.max之间的关系。对加工过程中的值vfn.max的相关性已经被关于磨削蜗杆的磨损和齿轮表面的完整性的实验验证。过程运动学分析使不需要进一步仿真进行vfn.max值的计算成为可能。因此,一种新的程序设计工具是在研究与实践中可以使用。2 用CutS三维模拟仿真。由生产工程与机床研究所(IFW)开发的仿真环境CutS,允许详细观察在切削中的材料接触条件。为了分析在连续磨削齿根加工中的蜗轮蜗杆的接触,采用CutS三维仿真软件。选择的源代码改造使磨削蜗杆齿顶和预刀具几何实现不同齿轮的齿根圆角的几何形状的变化。仿真结果被用来解释一些发生在真正的牙齿根加工中的基本影响。2.1 仿真过程由于连续产生磨削的仿真发展,具体说明了四个数据集:齿轮的几何数据,滚刀和砂轮的坐标系,在这个坐标系中定义了受影响的数控代码的机器轴和相对运动。另外,必须已经指定了过程时间的离散化。理论上,磨削过程中每个齿轮的齿是相同的;因此,齿轮毛坯可以建模为一个外径等于齿轮滚筒直径大、顶角等于齿轮角间距筒节的树桩。因此,一个轮齿的加工可以模拟和作为所有轮齿的代表。滚刀是由一个滚刀基本齿条代表。研磨蜗杆是由一个部分的蜗杆螺纹表示。使用的工具,公司可以根据DIN 3972标准 19 变化。这两种工具几何形状包含齿轮的宽度,和完全接触区。仿真由三个步骤实现。第一步是使用滚刀齿廓以创建一个允许的齿空间的齿轮毛坯的预加工。因此,预加工的齿轮齿廓是一个理想的渐开线的数值逼近。采用滚齿加工或热处理引起的几何偏差,在这步不做讨论。在第二阶段,用研磨齿轮初步切削之后,紧接着是在这个过程中代表着材料接触条件的进一步切削。因此,所产生的材料去除用于进一步的过程分析。2.2 齿形角加工中的材料啮合条件齿面加工涉及磨轮与齿轮之间的多个接触区域。运动的方向是由运动学过程和蜗杆砂轮的右侧和左侧之间的差异决定的
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