今天小编给大家整理了关于函数的计算方法，这应该对从事数控行业的你有所帮助，不会的赶紧学学吧

三角函数计算

角函数的关系

(正弦) Sin θ = 对边A / 斜边C

(余弦) Cosθ = 邻边B / 斜边C

(正切) Tanθ = 对边A / 邻边B

对边A = 斜边C * Sinθ

对边A = 邻边B * Tanθ

邻边B = 斜边C * Cosθ

邻边B = 对边A / Tanθ

斜边C = 对边A / Sinθ

斜边C = 邻边B / Cosθ

例题：已知斜边C=20, 角度θ=35度 求对边A及邻边B

对边A =斜边C * Sinθ= 20 * Sin (35) = 20 * 0.573576 = 11.471

邻边B =斜边C * Cosθ= 20 * Cos (35) = 20 * 0.81915 = 16.383

一般车床锥度与三角函数的关系

锥度比T=(大径D-小径d) / (长度L)

Tanθ= (大径D-小径d) / (2*长度L )

D= d + 2*L* Tanθ

d= D - 2*L* Tanθ

θ= Tan - ( (D-d) / 2L )

这里为你提供了sin,cos,tan不同角度的表值，精确度也很高了，相信对你有用

sin1=0.01745240643728351

sin2=0.03489949670250097

sin3=0.05233595624294383

sin4=0.0697564737441253

sin5=0.08715574274765816

sin6=0.10452846326765346

sin7=0.12186934340514747

sin8=0.13917310096006544

sin9=0.15643446504023087

sin10=0.17364817766693033

sin11=0.1908089953765448

sin12=0.20791169081775931

sin13=0.22495105434386497

sin14=0.24192189559966773

sin15=0.25881904510252074

sin16=0.27563735581699916

sin17=0.2923717047227367

sin18=0.3090169943749474

sin19=0.3255681544571567

sin20=0.3420201433256687

sin21=0.35836794954530027

sin22=0.374606593415912

sin23=0.3907311284892737

sin24=0.40673664307580015

sin25=0.42261826174069944

sin26=0.4383711467890774

sin27=0.45399049973954675

sin28=0.4694715627858908

sin29=0.48480962024633706

sin30=0.49999999999999994

sin31=0.5150380749100542

sin32=0.5299192642332049

sin33=0.544639035015027

sin34=0.5591929034707468

sin35=0.573576436351046

sin36=0.5877852522924731

sin37=0.6018150231520483

sin38=0.6156614753256583

sin39=0.6293203910498375

sin40=0.6427876096865392

sin41=0.6560590289905073

sin42=0.6691306063588582

sin43=0.6819983600624985

sin44=0.6946583704589972

sin45=0.7071067811865475

sin46=0.7193398003386511

sin47=0.7313537016191705

sin48=0.7431448254773941

sin49=0.7547095802227719

sin50=0.766044443118978

sin51=0.7771459614569708

sin52=0.7880107536067219

sin53=0.7986355100472928

sin54=0.8090169943749474

sin55=0.8191520442889918

sin56=0.8290375725550417

sin57=0.8386705679454239

sin58=0.848048096156426

sin59=0.8571673007021122

sin60=0.8660254037844386

sin61=0.8746197071393957

sin62=0.8829475928589269

sin63=0.8910065241883678

sin64=0.898794046299167

sin65=0.9063077870366499

sin66=0.9135454576426009

sin67=0.9205048534524404

sin68=0.9271838545667873

sin69=0.9335804264972017

sin70=0.9396926207859083

sin71=0.9455185755993167

sin72=0.9510565162951535

sin73=0.9563047559630354

sin74=0.9612616959383189

sin75=0.9659258262890683

sin76=0.9702957262759965

sin77=0.9743700647852352

sin78=0.9781476007338057

sin79=0.981627183447664

sin80=0.984807753012208

sin81=0.9876883405951378

sin82=0.9902680687415704

sin83=0.992546151641322

sin84=0.9945218953682733

sin85=0.9961946980917455

sin86=0.9975640502598242

sin87=0.9986295347545738

sin88=0.9993908270190958

sin89=0.9998476951563913

sin90=1

cos1=0.9998476951563913

cos2=0.9993908270190958

cos3=0.9986295347545738

cos4=0.9975640502598242

cos5=0.9961946980917455

cos6=0.9945218953682733

cos7=0.992546151641322

cos8=0.9902680687415704

cos9=0.9876883405951378

cos10=0.984807753012208

cos11=0.981627183447664

cos12=0.9781476007338057

cos13=0.9743700647852352

cos14=0.9702957262759965

cos15=0.9659258262890683

cos16=0.9612616959383189

cos17=0.9563047559630355

cos18=0.9510565162951535

cos19=0.9455185755993168

cos20=0.9396926207859084

cos21=0.9335804264972017

cos22=0.9271838545667874

cos23=0.9205048534524404

cos24=0.9135454576426009

cos25=0.9063077870366499

cos26=0.898794046299167

cos27=0.8910065241883679

cos28=0.882947592858927

cos29=0.8746197071393957

cos30=0.8660254037844387

cos31=0.8571673007021123

cos32=0.848048096156426

cos33=0.838670567945424

cos34=0.8290375725550417

cos35=0.8191520442889918

cos36=0.8090169943749474

cos37=0.7986355100472928

cos38=0.7880107536067219

cos39=0.7771459614569709

cos40=0.766044443118978

cos41=0.754709580222772

cos42=0.7431448254773942

cos43=0.7313537016191705

cos44=0.7193398003386512

cos45=0.7071067811865476

cos46=0.6946583704589974

cos47=0.6819983600624985

cos48=0.6691306063588582

cos49=0.6560590289905074

cos50=0.6427876096865394

cos51=0.6293203910498375

cos52=0.6156614753256583

cos53=0.6018150231520484

cos54=0.5877852522924731

cos55=0.5735764363510462

cos56=0.5591929034707468

cos57=0.5446390350150272

cos58=0.5299192642332049

cos59=0.5150380749100544

cos60=0.5000000000000001

cos61=0.4848096202463371

cos62=0.46947156278589086

cos63=0.4539904997395468

cos64=0.43837114678907746

cos65=0.42261826174069944

cos66=0.4067366430758004

cos67=0.3907311284892737

cos68=0.3746065934159122

cos69=0.35836794954530015

cos70=0.3420201433256688

cos71=0.32556815445715675

cos72=0.30901699437494745

cos73=0.29237170472273677

cos74=0.27563735581699916

cos75=0.25881904510252074

cos76=0.24192189559966767

cos77=0.22495105434386514

cos78=0.20791169081775923

cos79=0.19080899537654491

cos80=0.17364817766693041

cos81=0.15643446504023092

cos82=0.13917310096006546

cos83=0.12186934340514749

cos84=0.10452846326765346

cos85=0.08715574274765836

cos86=0.06975647374412523

cos87=0.052335956242943966

cos88=0.03489949670250108

cos89=0.0174524064372836

cos90=0

tan1=0.017455064928217585

tan2=0.03492076949174773

tan3=0.052407779283041196

tan4=0.06992681194351041

tan5=0.08748866352592401

tan6=0.10510423526567646

tan7=0.1227845609029046

tan8=0.14054083470239145

tan9=0.15838444032453627

tan10=0.17632698070846497

tan11=0.19438030913771848

tan12=0.2125565616700221

tan13=0.2308681911255631

tan14=0.24932800284318068

tan15=0.2679491924311227

tan16=0.2867453857588079

tan17=0.30573068145866033

tan18=0.3249196962329063

tan19=0.34432761328966527

tan20=0.36397023426620234

tan21=0.3838640350354158

tan22=0.4040262258351568

tan23=0.4244748162096047

tan24=0.4452286853085361

tan25=0.4663076581549986

tan26=0.4877325885658614

tan27=0.5095254494944288

tan28=0.5317094316614788

tan29=0.554309051452769

tan30=0.5773502691896257

tan31=0.6008606190275604

tan32=0.6248693519093275

tan33=0.6494075931975104

tan34=0.6745085168424265

tan35=0.7002075382097097

tan36=0.7265425280053609

tan37=0.7535540501027942

tan38=0.7812856265067174

tan39=0.8097840331950072

tan40=0.8390996311772799

tan41=0.8692867378162267

tan42=0.9004040442978399

tan43=0.9325150861376618

tan44=0.9656887748070739

tan45=0.9999999999999999

tan46=1.0355303137905693

tan47=1.0723687100246826

tan48=1.1106125148291927

tan49=1.1503684072210092

tan50=1.19175359259421

tan51=1.234897156535051

tan52=1.2799416321930785

tan53=1.3270448216204098

tan54=1.3763819204711733

tan55=1.4281480067421144

tan56=1.4825609685127403

tan57=1.5398649638145827

tan58=1.6003345290410506

tan59=1.6642794823505173

tan60=1.7320508075688767

tan61=1.8040477552714235

tan62=1.8807264653463318

tan63=1.9626105055051503

tan64=2.050303841579296

tan65=2.1445069205095586

tan66=2.246036773904215

tan67=2.355852365823753

tan68=2.4750868534162946

tan69=2.6050890646938023

tan70=2.7474774194546216

tan71=2.904210877675822

tan72=3.0776835371752526

tan73=3.2708526184841404

tan74=3.4874144438409087

tan75=3.7320508075688776

tan76=4.0107809335358455

tan77=4.331475874284153

tan78=4.704630109478456

tan79=5.144554015970307

tan80=5.671281819617707

tan81=6.313751514675041

tan82=7.115369722384207

tan83=8.144346427974593

tan84=9.514364454222587

tan85=11.43005230276132

tan86=14.300666256711942

tan87=19.08113668772816

tan88=28.636253282915515

tan89=57.289961630759144

tan90=(无限)

切削速度的计算

Ｖc＝(π*Ｄ*Ｓ)／１０００

Vc：线速度(m/min) π：圆周率(3.14159) D：刀具直径(mm)

S：转速(rpm)

例题. 使用Φ25的铣刀Vc为(m/min)25求S=?rpm

Vc=πds/1000

25=π*25*S/1000

S=1000*25/ π*25

S=320rpm

进给量(F值)的计算

Ｆ＝Ｓ＊Ｚ＊Ｆz

F：进给量(mm/min) S：转速(rpm) Z：刃数

Ｆz：(实际每刃进给)

例题.一标准2刃立铣刀以2000rpm)速度切削工件，求进给量(F

值)为多少？(Ｆz=0.25mm)

Ｆ＝Ｓ＊Ｚ＊Ｆz

Ｆ＝2000*2*0.25

Ｆ＝1000(mm/min)

残料高的计算

Scallop＝（ae＊ae）／8R

Scallop：残料高(mm) ae：XYpitch(mm) R刀具半径(mm)

例题.Φ20R10精修2枚刃，预残料高0.002mm，求Pitch为多

少？mm

Scallop=ae2/8R

0.002=ae2/8*10

ae=0.4mm

逃料孔的计算

Φ＝√２Ｒ2　　　　　　Ｘ、Ｙ＝Ｄ／４

　　Φ：逃料孔直径(mm) R刀具半径(mm) D：刀具直径(mm)

例题. 已知一模穴须逃角加工(如图)，

所用铣刀为ψ10；请问逃角孔最小

为多少？圆心坐标多少？

Φ=√２Ｒ2

Φ=√２＊５２

Φ=7.1(mm)

Ｘ、Ｙ＝Ｄ／４

Ｘ、Ｙ＝１０／４

Ｘ、Ｙ＝2.5 mm

圆心坐标为(2.5,-2.5)

取料量的计算

Ｑ＝（ae＊ap＊Ｆ）／１０００

Ｑ：取料量(cm3/min)　　　ae：XYpitch(mm)ap：Zpitch(mm)

例题. 已知一模仁须cavity等高加工，Φ35R5的刀XYpitch是刀具的60%，每层切1.5mm，进给量为2000mm/min，求此刀具的取料量为多少？

Ｑ＝（ae＊ap＊Ｆ）／１０００

Ｑ＝35*0.6*1.5*2000／1000

Ｑ＝63 cm3/min

每刃进给量的计算

Ｆz＝ｈm * √(Ｄ／ap )

Ｆz：实施每刃进给量 ｈm：理论每刃进给量ap：Zpitch(mm)

D：刀片直径(mm)

例题(前提depo XYpitch是刀具的60%)

depoΦ35R5的刀，切削NAK80材料ｈm为0.15mm，Z轴切深1.5mm，求每刃进给量为多少？

Ｆz＝ｈm * √(Ｄ／ap )

Ｆz＝0.2*√10/1.5

Ｆz＝0.5mm

冲模刀口加工方法

刀口加工深度＝板厚－刀口高＋钻尖（０．３Ｄ）

Ｄ表示刀径

钻头钻孔时间公式

Ｔ（ｍｉｎ）＝Ｌ（ｍｉｎ）／Ｎ（ｒｐｍ）＊ｆ（ｍｍ／ｒｅｖ）

＝πＤＬ／１０００ｖｆ

Ｌ：钻孔全长　　　Ｎ：回转数　　　ｆ：进刀量系数　　

Ｄ：钻头直径　　　ｖ：切削速度

如图　　孔深ｌ　　钻头孔全长Ｌ　　　则Ｌ＝ｌ＋Ｄ／３

Ｔ＝Ｌ／Ｎｆ＝πＤＬ／１０００ｖｆ

系数表ｆ 直径ｍｍ　　　进刀ｍｍ／ｒｅｖ

1.6~3.2 0.025~0.075

3.2~6.4　　　　 0.05~0.15

6.4~12.8　　 0.10~0.25

12.8~25　　　　 0.175~0.375

25以上　　　　　 0.376~0.625　　

管牙计算公式

１英寸＝２５．４ｍｍ＝８分

２５．４／牙数＝牙距　　　　　　　　

例如　　　２５．４／１８＝１．４１４　　　牙距为５／１６丝攻

马力（枪钻）

Ｗ＝Ｍｄ＊Ｎ／９７．４１０

Ｗ：所要动力（ＫＷ）

Ｍｄ：扭矩（ｋｇ－ｃｍ）

Ｎ：回转数（ｒ.ｐ.ｍ）

扭矩计算公式如下：

Ｍｄ＝１／２０＊ｆ＊ｐｓ＊

ｆ为进给量ｍｍ／ｒｅｖ系数

ｒ为钻头半径赛（ｍｍ）

α：切削抵抗比值ｐｓ．在小进给时，一般钢为５００ｋｇ／ｍ㎡；一般铸铁为３００ｋｇ／ｍ㎡；

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