【作者】 王佰超；

【导师】 杨兆军；

【作者基本信息】 吉林大学 ， 机械制造及其自动化， 2014， 博士

【摘要】 螺旋锥齿轮是传递相交轴运动及动力的基本元件，它具有重合系数大、传动平稳、强度高等优点，被广泛应用到航空、航天、船舶、军工、汽车等领域及机床、工程机械等重要装备中。螺旋锥齿轮的齿廓应该是理想的球面渐开线。在国内外被广泛应用的格里森体制螺旋锥齿轮采用工程近似的方法。由于齿形设计往往是在平面内进行设计，而球面不同于圆柱面或圆锥面，是不能展开成平面的。因此格里森体制螺旋锥齿轮采用背锥展开在平面上假想的当量圆柱齿轮的齿面齿形，近似代替球面渐开线齿形，这样就从原理上产生了误差，导致了两个齿轮不能正确啮合并造成齿面接触不良。为了获得较好的接触区，需要对一对齿轮进行成对加工、成对装配，同时还需对机床和刀具进行复杂的调整和反复的试切、检验等。由于其原理存在误差，使得设计计算与制造工艺极其复杂，导致加工效率低、制造周期长并且切齿设备昂贵。虽然格里森制齿轮经过上百年的历史，到目前为止仍然有大批学者在研究其设计及加工问题，但依然不能摆脱其切齿体制及原理误差问题。同时格里森始终保持技术垄断，虽然了解其使用规范但其核心技术密不外宣。在格里森齿制中，为了使刀盘能够进行连续回转切削，所以将螺旋锥齿轮的齿线设计成了圆弧形，因此弧齿锥齿轮几乎成了螺旋锥齿轮的代名词。斜齿螺旋锥齿轮作为螺旋锥齿轮的一种具有螺旋锥齿轮重合系数大、传动平稳、强度高等传动特性的全部优点。由于弧齿螺旋锥齿轮的垄断，以及尚未探索出高效、高精度的斜齿螺旋锥齿轮的加工方法与技术，故斜齿螺旋锥齿轮的加工理论与技术尚不成熟。课题组经过多年研究，提出了一种基于球面渐开线齿面生成原理的螺旋锥齿轮齿面成形新方法—产形线切齿法。利用产形线切齿法进行螺旋锥齿轮的齿面加工，能够获得无原理误差的球面渐开线齿形的螺旋锥齿轮。为了能够使产形线切齿法在更大的范围内发挥优势，本文在此基础之上将对斜齿螺旋锥齿轮设计及切齿加工进行深入研究，建立斜齿螺旋锥齿轮制造技术新方法，其研究工作如下：对斜齿螺旋锥齿轮齿面生成原理进行了分析。构造了螺旋锥齿轮基圆锥及与基圆锥相切的基平面，斜齿螺旋锥齿轮齿面是由基平面上的线段(即齿面发生线)在基平面与基圆锥相对纯滚动过程中扫掠形成的曲面所生成。通过调整发生线参数及基平面相对于基圆锥滚动的方向得到左、右旋齿轮的两侧齿面。推导了球面渐开线斜齿螺旋锥齿轮节圆锥与基圆锥相关的几何参数关系式。传统的螺旋锥齿轮从设计、加工到啮合都是与齿轮的节圆锥相联系，而基于产形线的新型切齿法的球面渐开线螺旋锥齿轮从设计到加工需从齿轮基圆锥入手，本文建立了节圆锥与基圆锥相关的参数方程，推导出关键的几何参数求解公式，为球面渐开线斜齿螺旋锥齿轮的齿面设计、加工机床、刀具设计及加工工艺设计提供理论依据。提出了以齿面发生线的极径及球面渐开线生成过程的基圆锥转角为参数的斜螺旋锥齿轮齿面建模方法。分别建立了左、右旋齿轮的左、右齿面的数学模型；推导了斜齿螺旋锥齿轮副啮合方程，对斜齿螺旋锥齿轮的齿面接触形式进行了分析。建立了基于产形线加工原理的斜齿螺旋锥齿轮齿面加工数学模型。以螺旋锥齿轮齿面生成原理为基础，以基平面上的齿面发生线为切齿刀刃，根据球面渐开线斜齿螺旋锥齿轮的齿面生成的展成运动进行切齿运动分析，建立了切齿加工的运动方程。提出了利用指状铣刀实现齿槽加工及通过圆盘铣刀实现齿面精铣加工相结合的三轴联动的切齿加工新方法。以圆盘铣刀刀刃端面圆与基平面相垂直相交得到的结交线为齿面发生线，根据齿面生成的相对运动关系，通过机床的三轴联动实现球面渐开线斜齿螺旋锥齿轮齿面的精加工，并建立了精铣加工运动方程；推导了影响加工精度的加工分度转角方程；在精铣削加工运动方案基础上，通过调整切削区获得不同的切削锥面，利用指状铣刀在切削锥面上沿着该锥面与齿面相交得到的螺旋线向前进给，实现齿槽的加工，建立了齿槽加工运动方程，由此加工出齿面的等距曲面，为齿面的精铣削预留等厚的切削余量。进行了机床的切齿加工运动仿真。在VERICUT环境中先后进行了齿槽及齿面虚拟加工，为最终的切齿实验提供参考；在VERICUT完成的机床切齿仿真基础上，进行了机床及刀具的结构设计。为确定斜齿螺旋锥齿轮新的切齿加工方法的切削参数，对指状铣刀及盘铣刀进行了刀具振颤的研究与分析。建立了铣削颤振稳定域解析模型，并通过实验模态分析与测试，进行了模态参数识别；绘制了两种刀具的主轴转速与径向切深的二维稳定域图，旨在找出齿轮加工的稳定的切削域。根据所选的一对齿轮的几何参数，设计并制造了齿轮的工装夹具，进行了切齿实验，并且对切齿实验得到的齿轮进行了齿廓精度的检测，结果显示：齿面法向偏差在-7.7μm-11.7μm之间，验证了利用该方法进行斜齿螺旋锥齿轮加工的可行性。更多还原

【Abstract】 Spiral bevel gears are the key components for transmitting speed and power betweenninterseeting axes and they are widely used in fields of aviation and space, ships, nationaldefense equipment, automotive vehicle and kinds of machines such as machine tools,engineering machine because of the advantages of large coincidence degree, steadytransmission and high strength. However, manufacturing technology of spiral bevel gearsbecomes a research hotspot in both domestic and overseas due to the complexity of thedesign process the difficulties in machining.The tooth profile of spherical involute is ideal profile of spiral bevel gear. In the cuttingprocess of spiral bevel gear, the machining method is the method of engineeringapproximation about gleason system spiral bevel gears that are widely used at home andabroad. Tooth profile design is always in-plane, but different from cylindrical surface and thecone surface, spherical surface can’t spread in-plane. So the tooth profile of bevel gear isapproximated by the profile of equivalent cylindrical gear which is unwrapped on the backcone. That the principium error which will be producted may lead to incorrect mesh and badcontact of gear surface. And process and assemble of a pair of mesh gear must be carried outin pairs. But the above method need be modified repeatedly. Although gleason gear has beenstudied more than one century. Up to now, many scholars take on the research of this field,and they have achieved many good results. However the question of theory error still couldnot be got rid of and complex design and manufacture can result in low efficiency, longperiod and high cost. In addition, gleason keep technological monopoly all along and thecore technology can not be shared to the external world.In the gleason system, toothed portion of spiral bevel gears is designed as a circular-arcin order to make cutter head cut continuous rotary. therefore, circular-arc bevel gear has beenthe pronoun of spiral bevel gears. One of spiral bevel gears-skew bevel gears have alladvantage of spiral bevel gear such as large coincidence degree, steady transmission andhigh strength. Up to now, high precision processing method of skew bevel gears has not beendeveloped and processing theory and technology of skew bevel gears are not enough mature.Based on the research practice of my group, new processing method-tracing line wasput forward to breach the current theoretical and this method can realize tooth machining atthe same time can obtain spiral bevel gears without principle errors. In this paper, study isimplemented on design and machining of skew bevel gears and manufacturing technologysystem will be established. The main research works in this dissertation are as follows. The generating principle of tooth surface was analyzed. Basic cone and basic planewere constructed. The tooth surface of spiral bevel gear with spherical involute was formedby the arc generating-line’s pure rolling on the base cone both sides tooth surface aregenerated by adjusting generating-line parameter and rolling direction.The relation of geometrical parameters between base cone and pitch cone were studied.Traditional design, machining and meshing are based on pitch cone. However, the newmachining method is related with base cone. In this paper, parameters equation of base coneand pitch cone are established and key geometry formula are deduced. Theoreticalfoundation are provided for design of gear surface, machine, cutting tool, process by theparameters equation.New method of gear surface was put forward based on two parameter which are polarradius and base cone corner. Mathematic model of left and right gears surface were setup. And meshing formula of spiral bevel gears was deduced. At the same time, consistencyof generating-line and meshing line were demonstrated.Mathematical model of gear surface about skew bevel gears was set up according totracing line. Based on generating theory of spiral bevel gears, gear surface of skew bevelgears are formed throught relative motion between gear blank and cutting which is used asedge generating line of base plane. And motion equation was set up finally.Three axes linkage method of cutting gear surface is put forward that gear groove areprocessed by finger milling cutter and finish machining of gear surface is carried out by discmilling tool. Head face edge of disc milling tool and base plane vertical intersect at thegenerating line. And the relative motion between gear blank and cutting follows thegenerating theory of gear surface. Finally, finish machining of gear surface was realized bythree axes linkage,and motion equation of finish machining was set up.Second,outer cornerformula was established. Based on finish machining project, processing of gear groove isaccomplished through finger milling cutter feed along spiral line of conical surface which isobtained by adjusting cutting section corner. And motion equation of gear groove was set up.The movement simulation and of NC machine working was carried out. Processing ofgear groove and finish machining of gear surface were accomplish accomplished.based onthe simulation, structure of machine and cutter were designed.Research of rremble was developed about disc milling tool and finger milling cutter inorder to determinate cutting parameters with new processing method. Analytical model offlutter instability is established and experimental modal parameter identification was carriedout. the figure of spindle speed and radial cutting depth were rendered about two cutters. Assembly technology clamp was designed and machined on the basis of a couple ofgears parameter and practical manufacture was carried. Gear profile of gear was measuredthe results showed that: gear surface normal error between-7.7μm-11.7μm, the performanceof this method is verified by experimental results.更多还原