齿轮传动及测量理论

,Hier klicken zur Titeleingabe,Hier klicken, um Master-Textformat zu bearbeiten.,Zweite Ebene,Dritte Ebene,Vierte Ebene,Fnfte Ebene,Gearing and Measurement,Verzahnung und Messung,Brner, TR-G, Folie,31,Copyright ZF Friedrichshafen AG 2001,Presentation,介绍,Theory of Gearing and Measurement,齿轮传动及测量理论,Dr. Jrg Brner,Corporate R&D,Zentrale Forschung,ZF Friedrichshafen AG,Gearing and Measurement,Verzahnung und Messung,d,a,齿顶圆直径,tip,diameter,d,Na,d,Fa,d,ab,有效齿顶圆直径,effective tip,diameter,d,Fa,min,最小有效齿顶圆直径,min. effective tip,diameter,d,Nf,max,最大有效齿顶圆直径,max. SAP,diameter,d,Nf,SAP,直径,SAP,diameter,d,Ff,齿根形状直径,root form,diameter,d,f,根圆直径,root,diameter,dfv,砂轮齿顶位置,（假想齿根圆直径）,SAP: start of active profile,SAP:,有效齿形的起点,Diameters,直径,d,a,d,Na,d,Fa,prefinished contour,预加工轮廓,d,Fa,min,d,Nf,d,f,d,Ff,d,Nf,max,finished contour,精加工轮廓,df,v,Gearing and Measurement,Verzahnung und Messung,Thread model,Step 1: Wrap a thread around the,base circle,Step 2: Unwind the thread from thebase circle,Step 3: Fixed to the thread, a pen paintsthe,involute,.,Fadenmodel,第一步: 沿基圆绕线,第二步: 将线展开拉直,第三步: 将笔固定于线，可画出渐开线,Developing,展成,Gearing and Measurement,Verzahnung und Messung,Standard geometry of gear teeth,Flanks = involutes.,Tooth thickness,s,b,.,Tip circle,and,root circle,limit the standard tooth.,轮齿的标准几何外形,齿侧面 = 渐开线,齿厚,s,b,.,齿顶圆和齿根圆限定了标准齿的形状,.,Standard tooth,标准齿,Gearing and Measurement,Verzahnung und Messung,Roll distance,Each circle segment belongsto an involute segment,Length of the circle segments= length of the thread= roll distance,滚动距离,每段圆弧都属于一个渐开线段,圆弧长度= 线的长度 = 滚动距离,Roll distance,滚动距离,Gearing and Measurement,Verzahnung und Messung,One,base circle generatesmany inolutes.,Base pitch,= distancebetween the involutes.,一个基圆展成许多渐开线,基节,= 渐开线间的距离,Base pitch,基节,Gearing and Measurement,Verzahnung und Messung,Main advantageof involute gears:,Independent from the changeof the center distance,渐开线齿轮的主要优点:,与中心局的改变无关,Change of center distance,中心距的改变,Gearing and Measurement,Verzahnung und Messung,Working pressure,angle,a,w,工作压力角,a,w,only defined for a gear pair,只对一对齿轮定义,a,w,depends on the center distance,a,w,取决于中心距,Working pressure angle,工作压力角,a,w,a,w,Gearing and Measurement,Verzahnung und Messung,Path of contact (POC),during mesh, the point of contactmoves along the path of contact (POC),POC is tangential to the base circles,Length of action = Distance on thePOC between the tip circles,啮合轨迹,啮合过程中，接触点沿啮合轨迹移动,啮合轨迹与基圆相切,啮合长度 = 齿顶圆之间啮合轨迹线的距离,Path of contact (POC),啮合轨迹,POC,啮合轨迹,Gearing and Measurement,Verzahnung und Messung,Base tangent length,公法线长度,Base tangent length,W,k,公法线长度,W,k,dependent on the number of,取决于测量的齿数,K,measuring teeth,k,(picture:,k,= 5),(,图中,k = 5),Gearing and Measurement,Verzahnung und Messung,Prefinished contour,预加工轮廓,Prefinished gears,Root geometry is manufacturedby hobbing or cutting,Base tangent length of prefinishedgears is different to finished gears,Attention,:Change of hob or cuttercan make problems,预加工的齿轮,滚齿或铣齿加工得到齿根轮廓,预加工后的基圆切线长度与最终的,基圆切线长度是不一样的,注意,:更换滚刀或铣刀可能出现问题,finished contour,最终轮廓（精加工后）,hobbed contour,滚齿后轮廓,Gearing and Measurement,Verzahnung und Messung,Rolling a basic rackgenerates a gear,Thats the principle of,hobbing,worm grinding,滚动齿条可以生成齿轮,这就是滚齿和蜗杆磨的原理,Basic rack,齿条,base circle,基圆,Gearing and Measurement,Verzahnung und Messung,The root fillet is a cycloid,generated by the tool tip,Tool of prefinish process:hob or cutter,Undercut is a special gear design,齿根修形是由刀头加工得到的圆滚线,粗加工的刀具：滚刀或铣刀,根切是一种特殊的齿轮设计,Root fillet,齿根修形,Cycloid,圆滚线,Tool tip,刀头,r,a,r,a,r,a,Gearing and Measurement,Verzahnung und Messung,One basic rack can generate several gears,with the same base circle,with the same involute, but,different parts,of the involute,changing addendum modification (profile shift),一个齿条可以生成多个齿轮,有同样的基圆,有相同的渐开线，但属于渐开线的不同部分,更换变位系数（齿形改变）,Addendum modification,齿顶修形,Gearing and Measurement,Verzahnung und Messung,Table of addendum modifications,变位系数表,Copyright ZF Friedrichshafen AG 2001,Gearing and Measurement,Verzahnung und Messung,Variation of profile angle,压力角的变化,Gearing and Measurement,Verzahnung und Messung,Due to the geometric generation,The probe moves,linear,in the,transvers plane,The gear rotates,Diagram of a true involuteis a vertical line,根据几何结构,探头在横截面线性移动,齿轮转动,一条无误差的渐开线的图是一条垂线,Measurement of involute profiles,渐开线齿形的测量,Gearing and Measurement,Verzahnung und Messung,Profile angle deviation,f,H,a,齿形角误差,f,H,a,Deviation in micrometer m,千分尺的误差 ,m,Related to the measurement range,与测量范围有关,Profile form deviation,f,f,a,齿形轮廓误差,f,f,a,Deviation in micrometer m,千分尺误差 ,m,Profile deviations,齿形误差,f,H,a,f,H,a,-,+,f,f,a,f,f,a,-,+,Gearing and Measurement,Verzahnung und Messung,Evaluation range is usuallyequal to 80% of the profile length,Evaluation range is not equalto the required measurement range,计量范围通常在齿形长度的80%以内,计量范围不等同于要求的测量范围,Evaluation range,计量范围,profile measurement,齿形测量,100%,80%,Gearing and Measurement,Verzahnung und Messung,Typical profile charts,典型齿形图,Examples of profile measurement,齿形测量的实例,Gearing and Measurement,Verzahnung und Messung,Under load,加载时,deformation of the gear teeth,轮齿变形,entry impact,啮入冲击,modifications are used to avoid,通过修形来避免啮入冲击,the entry impact,Profile under load,加载时的齿形,主动轮,从动轮,主动轮,从动轮,Gearing and Measurement,Verzahnung und Messung,Helical gears,Screwed transverse cut.,involute in each transverse cut.,same K sheet as spur gears.,斜齿轮,螺旋横切.,各个横截面中的渐开线.,同直齿轮一样的跨测齿数表（,K,表）,Helical gears,斜齿轮,Gearing and Measurement,Verzahnung und Messung,Transverse cut,Base circle,d,b,depends on helix angle,b,.,Different,b,generates different involutesin the transvers cuts.,Picture shows transverse cuts withsame basic rack but different helix angles,横截面,基圆,d,b,取决于螺旋角,b,不同的,b,在横截面上生成不同的渐开线,如图所示，横截面上有相同的齿条，但是螺旋角不同,Influence of helix angle,螺旋角的影响,Gearing and Measurement,Verzahnung und Messung,Two gears in mesh,啮合的一对齿轮,two base cylinders,两个基圆柱,closed thread,绕圆柱，有闭合的曲线,wrapped around the cylinders,Base cylinder,基圆柱,Gearing and Measurement,Verzahnung und Messung,Helical gears,斜齿轮,Properties of the cylinder surface,圆柱面的特征可以展开到平面上,can be transformed into a plane,The cylinder can be the,这个圆柱可以是节圆，也可以是基圆,pitch cylinder or base cylinder,Developing into the plane,展开到平面,Gearing and Measurement,Verzahnung und Messung,Helical gear,斜齿轮,The contact lines are straight lines.,啮合线是直线,Advantage: smooth entrance,优点：啮入平稳,Contact ratio is part of gear design,啮合比是齿轮设计的重要部分,Contact line,啮合线,Gearing and Measurement,Verzahnung und Messung,Measurement kinematics,测量运动学,probe moves,linear,探头线性运动,The gear rotates,齿轮旋转,Diagram of an ideal helix,理想的螺旋线图是一条直线,is a line,Measurement of the lead,齿向的测量,Gearing and Measurement,Verzahnung und Messung,Profile contact ratio,e,a,齿形接触比,e,a,=,g,a,/p,et,b -Face width,齿宽,g,a,- Path of contact,啮合轨迹,p,et,- base pitch,基节,p,et,g,a,p,et,g,a,e,a,=,1,6,e,a,=,2,b,b,Gearing and Measurement,Verzahnung und Messung,Overlap ratio,e,b,重合比,e,b,=,1,p,et,g,a,b,b,s,b,p,et,g,a,b,b,s,b,e,b,=,0,8,b -Face width,齿宽,b,- helix angle,螺旋角,b,b,- base helix angle,基圆螺旋角,m,n,-Normal module,法向模数,p,et,- base pitch,基节,Gearing and Measurement,Verzahnung und Messung,Contact lines at helical gear,斜齿轮的啮合线,Start of contact,啮合起点,End of contact,啮合终点,Gear rotation (driving gear),齿轮转动（主动轮）,Contact line,啮合线,Field of action,作用面,Contact starts at the root on the acute edge of driver,and at the tip on the obtuse edge of the driven gear,啮合始于主动轮的齿根尖端和从动轮的齿顶钝端,Gearing and Measurement,Verzahnung und Messung,Helical gear with,斜齿轮，参数为：,e,a,=2 e,b,=2,g,a,p,et,b,b,total contact ratio,e,g,is equal to the,average number of teeth in contact,总重合度,e,g,等于啮合齿数的平均数,Gearing and Measurement,Verzahnung und Messung,