机械制造技术基础英文课件CHAPTER1

Chapter 1 Fundamentals of Cutting

Abstract

1.1 Basic definition1.2 material of the cutting tool

Absract

Two parts concerning the fundamental of metal cutting process are involved in this chapter

1 Basic definition——including basic concepts in cutting process,such as cutting motions,parameters, reference frame,marked angles, cutting layer parameters

2 cutting tool material——including the necessary performance of cutting tool material(hardness, wear

resistance,strength,toughness, hot hardness…), two kinds of normal material for cutting tool(HSS and carbide alloy) and the other material(coating,ceramics diamond and cubic boron Nitride)

1.1 Basic definition

1.1.1 cutting motion and parameters

1.1.2 basic definition of the cutting region

1.1.3 exchange of the cutting angles

1.1.4 work angles of the cutting tool1.1.5 cutting layer parameters and mode

1.1.1 cutting motions and parametersFor example,in turning,the workpiece rotates,the cutting tool moves longitudinally, the mixture of the two motions forms the external cylindrical surface.There are three surfaces created in turn during the new surface is forming（Figure1.1）：Surface to be machined：means the surface in which the material is to be removedMachining surface：means the surface is being machined by the cutting edgeMachined surface：means the surface in which the material has been removedFig 1.1cutting motions in turning1.1.1.1 cutting motionThe basic motion for a machine tool includes linear motion and rotational motion. If classified according to the functions of the cutting tool in relation with the workpiece, they are called the main motion and the feed motion,shown as Fig.1.1（1）the main motionthe main motion required to remove the metal. Usually it has the biggest velocity, and consumes most of the power（2）the feed motionIt brings the new metal into cutting constantly. It can be continuous or interrupted.

（3）resultant motion and velocityWhen the main motion and the feed motion take part in cutting simultaneously, the velocity in one point of the cutting edge relative to the workpiece is called resultant cutting motion, its size and direction can be represented with a vector ve, shown as Fig.1.3, and it equals the vector sum of the two motionsve=vc+vf(1.1)Fig.1.3 The resultant velocity in cutting

1.1.1.2 Three elements in cuttingve、f 、ap are called the three elements in cutting（1）Cutting speedMost of the main cutting motions are rotational motion.The velocity in one point of the rotating body(cutting tool or workpiece) can be calculated using the following formulavc= ?dnm/sor m/min (1.2)1000whered－the rotational diameter of one point in the workpiece or the cutting tool（mm)n－number of revolution per second or per minute (r/s or r/min). （r/s or r/min)（2）Feeding speed, feed and feed per tooth

Feeding speed vfis the feed in a unit time (m/sor m/min)

Feed is the relative displacement between the workpiece and the cutter along the direction of feeding motion per revolution or per stock (mm/r)。

For multiple teeth cutting tools, such as milling cutter, reamer, broach, gear hob etc. feed fzmay be measured in millimeters per tool tooth (mm/z). Obviously，

vf=f·n=fz·z·nmm/s or mm/min （1.3）

（3）Back engagement of the cutting edge

For turning and planing, the back engagement of the cutting edge apis equal to the normal distance between the machined surface and the workpiece surface to be cut(mm). For cylindrical turning,

ap=（dw-dm）/2 mm (1.4)

For drilling

ap=dm/2 mm (1.5)

where dm——diameter of machined surface（mm）

dw——diameter of workpiece surface to be cut（mm）

1.1.2 Essential definitions for the working parts of cutting tools

1.1.2.1The basicelements for the

working part of cutting tool

(1) Rake surface(2) Flank(3) Cutting edge(4) Tool nose

Fig.1.3 components of typical turning tool

(1) Rake face Rake face Aris the surface on which the chip acts directly and which can tools the direction of the chip flowing out . The part

adjoining the major cutting edge is referred to as the major rake face; the part adjoining the minor cutting edge is referred to as the minor rake face.

（2）Flank There are a major flank and a minor flank. The major flank Aαis the surface which is opposite to the surface on the workpiece; the minor flank A’αis the surface which is opposite to the machined surface on the workpiece

（3）Cutting edge Cutting edges are the edges engaged in cutting on rake face. There

are major cutting edge and the minor cutting edge. The major cutting edge is an intersecting line between the rake face and major flank, it performs the principal work of metal removal. The minor cutting edge is an intersecting line between the rake face and the minor flank, it plays a subsidiary role in cutting.

（4）Tool nose The tool nose may be an intersecting point of major and minor cutting edges, or an intermediate straight line or a circular arc.

1.1.2.2Reference system for the marked angles of cutting tools

predetermined motion condition：first, predetermine the direction of main motion and the direction of feeding motion of the tool, then, assume that the feeding speed is very low so that the main motion vector vccan substitute for the combined speed vector veapproximately, then the reference system can be

composed of coordinate planes that are parallel or perpendicular to the direction of the main motion.

Predetermined condition for setup: assume the planes in reference system are parallel or perpendicular to the base plane of the tool which is easy for grinding and setup

The reference system consists of the following planes：

Tool reference plane Pris a plane which passes

through a designated point on the cutting edge and is perpendicular to the vector veof combined speed. Usually it is parallel or normal to the setup plane or axis of the tool arbor. For instance, in Fig.1.6, Pr is the reference plane for turning tool or planing tool,it is parallel

（1）Tool reference plane Pr

to the base plane of the cutting tool.

(2) Tool cutting edge plane Ps

Tool cutting edge plane Psis a plane which passes through a designated point on the cutting edge and is tangential to the cutting surface,namely, the plane formed by vector veof combined speed and the tangent line of a designated point on the cutting edge

Fig.1.6 the reference plane Prof an ordinary turning tool

（3）Main section P0and main section reference system

Main section Pois a plane which passes through a designated point on the cutting edge and is perpendicular to the tool reference plane Prand the tool cutting edge plane Ps

simultaneously. Fig.1.8 shows a main section reference system composed of Pr－Ps －P0

（4）Normal section Pn and normal section reference system

Normal section Pnis a plane which passes through a designated point on the cutting edge and is perpendicular to the cutting edge. The normal section reference system is composed of Pr—Ps—Pn,shown as Fig 1.8

Fig.1.8 main section and normal section reference system

(5) Transverse section Pf, longitudinal section Pp, transverse section or

longitudinal section system

Pr －Pf－Pp

Fig.1.9 Transverse section Pf,

longitudinal section Pp

TransversesectionPfisaplanepassingthroughadesignatedpointoncuttingedgeandparalleltothedirectionoffeedingmotionandperpendiculartothetoolreferenceplanePr..Normally,Pfisasectionparallelornormaltoacertainplaneoraxisofthetooleasyforgrindingandsetup,shownasFig.1.9.LongitudinalsectionPpisaplanepassingthroughadesignatedpointonthecuttingedgeandperpendiculartothetoolreferenceplanePrandthetransversesectionPf.

1.1.2.3 Reference system for the working angles of cutting tools

In the definition of tool reference plane Prthe feeding motion is not considered, i.e. the marked angles of the cutting tool is determined under the predetermined conditions . It is no true in practice,where only the resultant ve reflects the situation. For example，Fig.1.10 shows three tools having the same marked angles,but the practical conditions,like the contact and friction,are very different

It is same considering the affection of the tool setup position, except that veis replaced by vc，where vcis the practical feeding direction instead of the predetermined direction.

Fig.（a）it is normal, where there is clearance between the flank and the workpiece.

(a)

Fig.1.10 the working angle of the tool

Fig.（b）, two surfaces are completely contacted, causing serious friction；

(b)

Fig.1.10 Working angles of the tool

in Fig.（c）,the cutting edge can not enter into the metal.Therefore, only consider the main motion is not proper. The working angles of the tool must be decided by the working reference system, i.e.,consider the direction of the resultant motion

刀具工作角度示意图

Fig.1.10 the working angles of the tool

1.1.2.4 How to mark the tool angleThe azimuth angles between the cutting edgeand the tool surfacedetermined in the reference system for the marked angles are called ―marked angles of cutting tool‖ .If the cutting edge is curved, or the rake surface or flank surface is curved, a tangential line or surface passing through a point in the edge is used to define the angles.Fig.1.11shows the name, symbol and definition of the marked angles in the main section reference systemRakeγ0clearance angleα0Cutting edge angle κrκrinclination angleλsλsLikewise, there are four angles related with the minor cutting edge, which are, minor cutting edge angleκ?r ，minor inclination angleλ ?s，minor rakeγ ?0，minor clearance angleα ?0. The definition is similar to that of the main cutting edgerakeγ0：the angle between the rake surface and the reference plane（measured in main section ）。Fig.1.11(a) the tool angle marked in the main section systemClearance angleα0：angle between flank and cutting edge plane（measured in main section)Fig.1.11(b) the tool angle marked in the main section systemkrCutting edge angle κr, measured in the reference plane,formed by the cutting edge and feed directionFig.(c) the tool angle marked in the main section systemInclination angle λs：measured in the cutting edge plane, formed by cutting edge and reference planeFig.1.11(d) the tool angle marked in the main section system

When the cutting edge and minor cutting edge are all on the rake face, like Fig.1.11, γ?0、λ ?s can be educed from γ0、λs、κr、κ ?r，and it is called derived angles. There are 6 independent marked angles for lathe cutting tool. In addition，as required in analysis, there are some other derived angles, which are：

wedge angleβ0：measured in main section,formed by rake face and flank.

β0＝90°－（γ0＋α0）

（1.6）

tool tip(nose) angleεr：the angle formed by cutting edge and minor cutting edge in the reference plane.

εr＝180 °－（κr＋κ’r ）

（1.7）

The sign of γ0、α0 、λs、κr、κ’ris specified as in Fig.1.12：in the main section, if rake face is parallel to the reference plane, γ0=0, ，if the angle is less than 90°, it is positive, otherwise, it is negative. The sign of the inclination angle is shown in Fig.1.12 .

(a)λs＝0

(b)－λs

Fig.1.12 the sign of inclination angle

(c)+ λs

1.1.3 Tool angle conversion in different system

It is necessary to convert the marked angle from one system to another system in tool design and manufacturing. i.e, among main section system,normal

section system, transverse system and longitudinal system

1.1.3.1 tool angle conversion from main section to normal section

This conversion is used in tool design, manufacturing,tool grinding and inspection,especially for large inclination tool, the angles must be marked in normal section system.

tanγn=tanγ0.cosλscotαn=cotα0.cosλs

1.1.3.1 conversion from main section to normal sectionTaketherakeangleconversionasexample,itiseducedas：tan?n?tan?o?acMaabMatan?nacMaac????cos?stan?oMaababtan?n?tan?o?cos?s1.1.3.2 angle conversion from main section to any sectionrake angle γθin any section Pθ：tanγθBD?DCBCEF?DC???ABABABAEtan?0?DCtan?s?ABAEDF?.tan?0?.tan?sABABthentanγθ＝tanγ0.sinθ+tanλs.cosθ （1.10）

1.1.3.2angle conversion from main section to any sectionWhen θ＝0: tanγθ=tanλs，γθ＝λswhenθ＝90°－kr，the longitudinal rake angleγp:tanγp=tan γ0.cos kr＋tan λs.sin kr whenθ＝180°－kr，the transverse rake angleγf:（1.11）tanγf=tan γ0.sin kr＋tan λs.coskr（1.12）the maximum rake angleγg obtained by differential quotient of formula 1.10tan γg＝tan2?0?tan2?sor tan γg＝（1.13）（1.14）tan?f?tan?p221.1.3.2angle conversion from main section to any sectionThe angle formed by the plane where the maximum angle is and the cutting edge projected on the reference plane θmax：tan?0tan θmax＝tan?swhenθ＝90°－kr：whenθ＝180°－kr:（1.15）similarly，the clearance angle of any given sectionαθ：cot?p?cot?0.coskr?tan?s.sinkr(1.17)cot?f?cot?0.sinkr?tan?s.coskr(1.18)1.1.4 working angles

1.1.1.4 working angles influenced by feed motion

(1) Transverse turning shown as Fig.5.15:

In cut-off turning, without

considering feed motion，the cutting path is circular,while considering the feed motion, it becomes helical, and cutting edge plane changes from Ps to Pse，the angle variation is η。The working angles in the reference

system（Pre、Pse、P0e）are：γ0e ＝γ0+η; α0e=α0－η。

(1) Transverse turningη is the resultant cutting speed angle，formed by the main cutting speed and resultant speed. From the definition：tanη＝vfvcf= (1.19)?dWheredistheworkpiecediameterchangedwiththetoolfeeding.ηbecomesbiggerwhenthecuttingtoolapproachesthecenterofthework；whenthecuttingtoolis1mmfarawayfromtheworkcenterundernormalfeedrate,η＝1°40′；goingfurther,ηincreasessuddenly,andclearanceanglebecomes negative.（2）Longitudinal turning

Similarly, the working angles will change because of the resultant speedη

in longitudinal turning ，shown as 1.16，supposing λs＝0，

without considering feed motion, the marked angles are γ0、α0；otherwise the

working cutting edge plane Pse is

tangent to the helical surface and the tool working system （Pse、Pre）has an inclination angleη，the

working angles in working feed section are：γfe＝γf+η；ααf－η

fe＝

（2）Longitudinal turningAccording to the definition of the resultant speedη：ftanη= ?dwwhere f－feed ratedw－the diameter of the surface to be machined on the designated point A of the cutting toolConverse it to the main section：tanη0＝tanη.sinkr；γ0e＝γ0＋η0（1.20）We know from formula 1.20：η is not only related with feed rate f, but also related with the work diameter dw；the smaller dw，the bigger of the angle variation.1.1.4.2 Working angles influenced by tool setup（1）Influenced by tool tip setupWhen the tool tip is higher than the center of the work, the working cutting edge plane will be turned into Pse，working reference plane into Pre，working angleγpebecomes increases，αpedecreases。In the longitudinal plane P－P, the variation hof θpis ：tanθp＝?dw?2???h?2?2（1.21）Where h－the deviation from the tool tip to the work center line（mm）；dw－diameter of the work（1）Influenced by tool tip setupThe working angles ：γpe＝γp＋θpor αpe＝αp－θp（1.22）The above angles are marked in the system（Pp－Pp），they should be converted into the working main section plane：tanθ0＝h?dw?2?h???2?2coskr（1.23）?0e??0??0；or a0e?a0??0（1.24）（2）Influenced by the tool bar setup

If the tool bar is not perpendicular to the feed direction,the working cutting edge angle kreand minor cutting edge angle k’rewill change：

k0e?kr?G；

k're?k'r?G（1.25）

Where G—angle formed by predetermined feed section and working feed section，measured on the reference plane。It is also the angle formed by the normal line of feed direction and the center line of the tool bar

1.1.5 parameters of the cutting layer and cutting mode1.1.5.1 cutting layerAll the cutting parameters can be explained by the typical cylindrical turning,shown as Fig.1.19. The motional path of any designated point on the cutting edge relative to the workpiece is a spatial helix .The definition and explanation are as follows：Feed, the move distance of the cutting tool per workpiece revolution（f，mm/r）.Cutting layer,the layer where the metal is being cuttedIn longitudinal turning, and when k?r＝0、λs＝0，the the cutting layer geometry is parallelogramUnder special situation（kr＝90°）it is rectangle.

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