面齿轮设计案例解析

塑料面齿轮计算案例

目录

1 案例数据 ................................................................................................................ 3 2 修改建议Modified Suggestion ............................................................................... 3 2.1 ABOUT THE PINION小齿轮部分 ..................................................................... 3 2.2 ABOUT THE FACE GEAR 面齿轮部分............................................................ 5 3 软件界面输入 ......................................................................................................... 5 4 软件输出报告 ......................................................................................................... 6

1 案例数据

2 修改建议Modified Suggestion

2.1 ABOUT THE PINION小齿轮部分

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To get the correct root diameter df and tip diameter da, you need to consider the profile shift of x*=0.2 on the pinion.

为了得到确切的齿根圆直径d f 和齿顶圆直径d a ，需要考虑调整变位系数为0.2；

Change the tip diameter tolerance of the pinion. 改变小齿轮上的齿顶圆公差；

To get the correct tooth thickness M on the pinion, you need to change the tooth thickness tolerances like this:

为获得确切的小齿轮上的齿厚，需要改动齿厚公差为如下所示：

In the tab “Tolerances”, adjust the data as per the drawing (for the pinion):

在“公差”内，对于小齿轮可以按照图纸上的要求改动为球直径0.35mm ；

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Then, you can check in the KISSsoft report the data for the pinion

之后根据KISSsoft 的计算报告和图纸上的信息进行比对，发现两个结果高度一致！

o Module is same in KISSsoft and in drawing, 0.20mm； o 图纸上模数和KISSsoft 中计算出的一致，都为0.2mm ； o Pressure angle is same in KISSsoft and in drawing, 20deg； o 图纸上压力角和KISSsoft 软件中的一致，都为20度； o Pitch diameter is same in KISSsoft and in drawing, 1.60mm o 图纸上节圆直径和KISSsoft 软件中的一致，为1.6mm ； o Tip diameter is same in KISSsoft and in drawing, 2.08mm； o 图纸上齿顶圆和KISSsoft 软件中一致，为2.08mm ；

o Root diameter is same in KISSsoft and in drawing 1.18mm； o 图纸上齿根圆和KISSsoft 软件一致，为1.18mm ；

o Total tooth height is same in KISSsoft and in drawing, 0.45mm； o 图纸上总齿长度和KISSsoft 中一致，为0.45mm ；

o Addendum factor reference profile is same in KISSsoft and in drawing, 1.00*Mn； o 基准齿廓中齿顶高系数和KISSsoft 软件和图纸上的值一致，为1.0Mn ； o Profile shift factor is same in KISSsoft and in drawing, x*1=0.20； o 变位系数为x*1=0.2，软件和图纸上一致；

o Tooth thickness M (on drawing) = MdK (in KISSsoft) is same in KISSsoft and in drawing,

2.1319 (it is 2.132 in KISSsoft)；

o 图纸上和KISSsoft 软件中跨棒距的值一致（在选择球直径为0.35mm 情况下），

为2.1319mm （KISSsoft 中为2.132mm ）。

2.2 ABOUT THE FACE GEAR 面齿轮部分

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Go to tab “Basic data”. Press button “Details”. Enter height of face gear (it is 1.1mm on the drawing) ；

在“基本数据”界面中，点击“细节”按钮，输入面齿轮齿长度（1.1mm 齿长）；

- - -

There are also some changes needed for the offset bv； 同时，对于偏心距bv 也需要做一些调整；

3 软件界面输入

4 软件输出报告

KISSsoft evaluation Name : Face-Gear-Henry Changed by: Henry Xu am: 23.08.2013 um: 11:42:41

1-> An exact calculation of the center distance is not possible.

2-> facewidth of the crown gear is incorrect: 齿宽出现一定问题 (b= 0.4500 mm, dPi= 4.3000 mm, dPe= 5.2000 mm) Limit: dPi > 4.5105 mm ... dPe

3-> UNDERCUT gear 1 存在根切现象

Notice: Increase profile shift coefficient to at least 0.5321

4-> Tooth thickness at face gear is too small: 面齿轮齿厚过小：

(

Adjust tip height of face gear by, at least haki= 0.0131 mm, l_haki= 0.3465 mm

(current input: haki= 0.0000 mm, l_haki= 0.0000 mm)

5-> Calculation of plastics according to DIN3990 or ISO6336: 塑料齿轮强度校核警告：

An exact calculation taking into account the actual Woehler line (S-N curve) and the temperature dependence can only be executed according to VDI2545.

An approximately determination of service life can be executed in KISSsoft according to DIN3990 or ISO6336. The permissible material data sigFlim and sigHlim have to be examined, sigFlim and sigHlim should be valid for a cycle number of approximate 10^8.

(The values in database are valid for a temperature of 70° and a number of load changes of 10^8.)

6-> Gear 2:

Notch parameter qs (8.751403) outside RANGE (1.0...8.0).

Please consult part 3 of the standard. YS is calculated with qs = 8.000000.

7-> Gear 1 :

You have entered a effective roller diameter ( 0.3500 mm) which deviates considerable from the best value ( 0.4216 mm)!

图纸上规定为量球为0.35mm ，软件推荐为0.4216mm ，测量的位置会更准确！

Drawing or article number: Gear 1: 0.000.0 Gear 2: 0.000.0

Calculation method Method ISO 6336:2006-B/ Literature The calculated facewidth will be inserted:

Flank: The minimum length of contact line Lcont (case Lcont

Root: The length of contact in the direction of facewidth bcont Tot*+2*mn (where bcontTot*+2*mn

Power (W) [P] 0.00 Speed (1/min) [n] 100.0 33.3 Rotation seen onto crown gear toothing : left Torque (Nmm) [T] 0.1 0.3 Gear driving (+) / driven (-) + - Application factor [KA] 1.25 Required service life [H] 20.00

------ PINION ----------- FACE GEAR ------ Center distance (mm) [a] 0.000 Shaft angle (°) [Sigma] 90.00 Normal module (mm) [mn] 0.2000 Pressure angle at normal section (°) [alfn] 20.0000 Helix angle at reference circle (°) [beta] 0.0000 Hand of gear Spur gear Number of teeth [z] 8 24 Facewidth (mm) [b] 1.300 0.450 Tooth width adjustment [bv] -0.025 Accuracy grade [Q-ISO1328:1995] 9 10 Internal diameter gearbody (mm) [di] 0.00 0.00 Material Gear 1: POM, Thermoplastic (POM, PPA, etc.), untreated VDI2736 [SBWd] Gear 2: POM, Thermoplastic (POM, PPA, etc.), untreated VDI2736 [SBWd] ------- PINION ----------- FACE GEAR ---- Fatigue strength. tooth root stress (N/mm²) [sigFlim] 29.00 29.00 Fatigue strength for Hertzian pressure (N/mm²) [sigHlim] 0.00 0.00 Tensile strength (N/mm²) [Rm] 50.00 50.00 Young's modulus (N/mm²) [E] 2800 2800 Poisson's ratio [ny] 0.400 0.400 Mean roughness, Ra, tooth flank (µm) [RAH] 1.05 1.05 Mean roughness height, Rz, flank (µm) [RZH] 8.00 8.00 Mean roughness height, Rz, root (µm) [RZF] 8.00 8.00

Tool or reference profile of gear 1 : Reference profile (Own input) Dedendum coefficient [hfP*] 1.250 Root radius factor [rhofP*] 0.380 Addendum coefficient [haP*] 1.000 Tip radius factor [rhoaP*] 0.000 Tip form height coefficient [hFaP*] 0.000 Protuberance height factor [hprP*] 0.000 Protuberance angle [alfprP] 0.000 Ramp angle [alfKP] 0.000 not topping

Tool or reference profile of gear 2 : Pinion type cutter (Own input) Number of teeth

Profile shift coefficient Addendum coefficient Dedendum coefficient Tip form: Radius Root radius factor

Root form height coefficient Protuberance angle (°) Protuberance height factor Ramp angle (°) Tip diameter (mm)

Tip form diameter (mm) Root form diameter (mm) Root diameter (mm)

Addendum coeff. ref. profile

Summary of reference profile gears: Dedendum reference profile (in module) Root radius reference profile (in module) Addendum reference profile (in module) Protuberance height coefficient (in module) Protuberance angle (°)

Tip form height coefficient (in module) Ramp angle (°)

[z] [x*] [haP0*] [hfP0*] [rhoaP0*] [rhofP0*] [hFfP0*] [alfprP0] [hprP0*] [alfKP0] [da0] [dFa0] [dFf0] [df0]

not topping

[haP*]

13 0.000 1.250 1.250 0.140 0.000 0.000 0.000 0.000 0.000 3.100 3.078 2.509 2.100 1.000

[hfP*] [rofP*] [haP*] [hprP*] [alfprP] [hFaP*] [alfKP] 1.250 0.380 1.000 0.000 0.000 0.000 0.000 1.250 0.140 1.000 0.000 0.000 0.000 0.000

Type of profile modification: none (only running-in) Tip relief (µm) [Ca] 20.4 20.4

Lubrication type Grease lubrication Type of grease Grease: Microlube GB 00 Lubricant base Mineral-oil base Kinem. viscosity base oil at 40 °C (mm²/s) [nu40] 700.00 Kinem. viscosity base oil at 100 °C (mm²/s) [nu100] 35.00 FZG-Test A/8.3/90 step [FZGtestA] 12 Specific density at 15 °C (kg/dm³) [roOil] 0.900 Grease temperature (°C) [TS] 70.000 ------ PINION ----------- FACE GEAR ------ Overall transmission ratio [itot] -3.000 Gear ratio [u] 3.000 Transverse module (mm) [mt] 0.200 Pressure angle at normal section (°) [alfn] 20.000 Pressure angle at pitch circle (°) [alft] 20.000 Base helix angle (°) [betab] 0.000 Pitch angle (°) [delta] 0.000 89.999 Face gear pressure angle at Height hdFG (calculated according to the theory): Inside (°) [alfn_i,L/R] 0.0000 / 0.0000 Middle (°) [alfn_m,L/R] 18.2710 / 18.2710 Outside (°) [alfn_e,L/R] 29.8411 / 29.8411 Inside (°) [alft_i,L/R] 0.0000 / 0.0000 Middle (°) [alft_m,L/R] 18.2710 / 18.2710 Outside (°) [alft_e,L/R] 29.8411 / 29.8411

Sum of profile shift coefficients [Summexi] 0.2000 Profile shift coefficient [x] 0.2000

0.0000

Diameter of face gear: External diameter (mm) [dPe] Mean diameter (mm) [dPm] Inner diameter (mm) [dPi] 'Reference diameter' (mm) [dPd] Heights of face gear: Height of bolt head (mm) [haFG] No modification at tip circle 'Height reference line' (mm) [hdFG] Dedendum (mm) [hfFG] Assembly distance (mm) [aFG] Manufacturing distance without tooth thickness allowance (mm) [aFG0]

Reference diameter (mm) [d] Base diameter (mm) [db] Tip diameter (mm) [da] Tip form diameter (mm) [dFa] Tip diameter allowances (mm) [Ada.e/i] Root diameter (mm) [df] Theoretical tip clearance (mm) [c] Generating Profile shift coefficient [xE.e/i] Manufactured root diameter with xE (mm) [df.e/i] Root form diameter (mm) [dFf] [dFf.e/i] Roll angle at dFa (°) [xsi_dFa.e/i] Roll angle at dFf (°) [xsi_dFf.e/i] Tooth height (mm) [H] Virtual gear no. of teeth [zn] Normal tooth thickness at tip cyl. (mm) [san] (mm) [san.e/i] Normal spacewidth at root cylinder (mm) [efn] Pitch on reference circle (mm) [pt] Base pitch (mm) [pbt] Transverse pitch on contact-path (mm) [pet] Axial pitch (mm) [px]

Contact ratio, contact lines, calculated facewidth:

(mne= 0.217) (mnm=0.108) (mni= 0.000) (mn = 0.200) 5.2000 4.7500 4.3000 4.8000 1.1000 0.9000 0.6500 1.7400 2.2000

1.600 1.504 2.080 2.080 0.000 / -0.030

1.180 0.050 0.1313 / 0.1313 1.153 / 1.153

1.504 1.504 / 1.504 54.773 / 53.105 0.209 / 0.209

0.450 8.000 0.076 0.090 / 0.063

0.000 0.628 0.590 0.590 0.000

0.000 / -0.010

0.050

Length of contact line (average) (mm) [Lcont] 0.404 0.404 (mm) [Lcont.e/i] 0.494 / 0.179 0.494 / 0.179 Length (centered in the direction of facewidth) (mm) [bcont] 0.321 0.321 [bcont.e/i] 0.401 / 0.090 0.401 / 0.090 Contact line outer single contact BB: Length (in direction facewidth) (mm) [bcont*] 0.000 0.000 Total length (multiple contacts) (mm) [bcontTot*] 0.090 0.090 Fictive helix angle (°) [beta'] 0.000 beta' = ArcTan(d1/2/bcont*(Tan(alf1max= 57.296)-Tan(alf1min= 0.000)) Transverse contact ratio (middle of facewidth) [eps.am] 1.616 Overlap ratio (from beta') [eps.bm] 0.000 (eps.bm calculated with normal module in the middle of the facewidth of the face gear ( 0.108 mm)) Total contact ratio [eps.gm] 1.616

Theoretical tip clearance (mm) [c] 0.050 0.050 Effective tip clearance (mm) [c.e/i] 0.050 / 0.050 0.050 / 0.050 Tooth height (mm) [H] 0.450 0.450 Virtual gear no. of teeth [znv] 8.000

Max. sliding velocity at tip (m/s):

Circumferential force (N) Axial force (N) Radial force (N) Normal force (N)

Tangent.load at p.c.d.per mm (N/mm) (N/mm) Circumferential speed pitch d.. (m/sec) Singular tooth stiffness (N/mm*µm) Meshing stiffness (N/mm/µm) Meshing stiffness (N/mm/µm)

The formula for c' and cg at w*KA

Dynamic factor

User specified factor KHb: Face load factor - flank - Tooth root - Scuffing

User specified factor KHa: Transverse load factor - flank - Tooth root - Scuffing

Helical load factor scuffing

Number of load cycles (in mio.)

Note special calculation (Graphic)

[Ft] [Fa] [Fr] [Fnorm] [w] [v] [c'] [cgalf] [cgbet]

------ PINION ----------- FACE GEAR ------

0.1

0.0 0.0 0.0 0.0

0.1 0.31 0.01 0.169 0.247 0.210

[fpt] [ya] [mRed] [nE1] [N] [KV]

0.00

0.00 0.000 489248

0.000

1.00

42.00

[KHb] [KFb] [KBb] 1.50 1.50 1.50

[KHa] [KFa] [KBa] [Kbg] [NL]

0.120

1.10 1.10 1.10 1.00

0.040

Calculation of Tooth form coefficients according method: C (Calculate tooth shape coefficient YF with addendum mod. x) Tooth form factor [YF] Stress correction factor [YS] Bending lever arm (mm) [hF] Working angle (grd) [alfFen] Tooth thickness at root (mm) [sFn] Tooth root radius (mm) [roF]

Contact ratio factor [Yeps] Helical load factor [Ybet] Deep tooth factor [YDT]

------ PINION ----------- FACE GEAR ------

3.50

1.46 0.41 41.63 0.34 0.11

0.714 1.000 1.000

2.03 2.65 0.41 20.00 0.49 0.03

Gear rim factor [YB] 1.000 Facewidth for calculation (mm) [beff] 0.49 Nominal stress at tooth root (N/mm²) [sigF0] 4.71 Tooth root stress (N/mm²) [sigF] 9.72

Permissible bending stress at root of Test-gear Support factor [YdrelT] 1.000 Surface factor [YRrelT] 1.007 Size coefficient (Tooth root) [YX] 1.000 Finite life factor [YNT] 1.677 [YdrelT*YRrelT*YX*YNT] 1.688 Alternating bending coefficient [YM] 1.000 Stress correction factor [Yst] 2.00 Yst*sigFlim (N/mm²) [sigFE] 58.00 Permissible tooth root stress (N/mm²) [sigFP=sigFG/SFmin] 163.18 Limit strength tooth root (N/mm²) [sigFG] 97.91 Required safety [SFmin] 0.60 Safety for Tooth root stress [SF=sigFG/sigF] 10.07

Zone factor [ZH] Elasticity coefficient (N.5/mm) [ZE] Contact ratio factor [Zeps] Helix angle factor [Zbet] Facewidth for calculation (mm) [beff] Nominal flank pressure (N/mm²) [sigH0] Surface pressure at operating pitch circle (N/mm²) [sigHw]

Lubrication coefficient at NL [ZL] Speed coefficient at NL [ZV] Roughness coefficient at NL [ZR] Material pairing coefficient at NL [ZW] Finite life factor [ZNT] [ZL*ZV*ZR*ZNT] Small amount of pitting permissible (0=no, 1=yes) Size coefficient (flank) [ZX] Permissible surface pressure (N/mm²) [sigHP=sigHG/SHmin] Limit strength pitting (N/mm²) [sigHG]

Safety for surface pressure at operating pitch circle [SHw]

As information:

Calculation of the flank pressure with minimum contact line length Facewidth for calculation (mm) [beff] Safety for surface pressure on flank [SH]

Calculation of the flank pressure with full facewidth [b]: Facewidth for calculation (mm) [beff] Safety for surface pressure on flank [SH]

Note special calculation (Graphic) END WITHOUT IF

1.000 0.45 5.37 11.09

1.000 1.004 1.000 2.001 2.008 1.000 58.00 194.12 116.47

0.60 10.50

------ PINION ----------- FACE GEAR ------

2.49 23.03 0.891 1.000

0.40 0.40

22.65 32.55 1.005 0.995 0.991 1.000 1.578 1.564 0

1.000 0.00 0.00

0.00

1.000 1.000 1.000 1.000 1.600 1.600 0

1.000 0.00 0.00

0.00

[Lcont.i]:

0.18 0.00

0.18 0.00

0.45 0.00 0.45 0.00

------ PINION ----------- FACE GEAR ------ Tooth thickness deviation Own Input Own Input Tooth thickness allowance (normal section) (mm) [As.e/i] -0.010 / -0.010 -0.040 / -0.060

Number of teeth spanned [k] 2.000 Base tangent length (no backlash) (mm) [Wk] 0.935 Actual base tangent length ('span') (mm) [Wk.e/i] 0.926 / 0.926 Diameter of contact point (mm) [dMWk.m] 1.766

Theoretical diameter of ball/pin (mm) [dm] 0.422 Eff. Diameter of ball/pin (mm) [DMeff] 0.350 Theor. dim. centre to ball (mm) [MrK] 1.066 Actual dimension centre to ball (mm) [MrK.e/i] 1.057 / 1.057 Diameter of contact point (mm) [dMMr.m] 1.609 Diametral measurement over two balls without clearance (mm) [MdK] 2.132 Actual dimension over balls (mm) [MdK.e/i] 2.114 / 2.114 Actual dimension over rolls (mm) [MdR.e/i] 2.114 / 2.114

Tooth thickness (chordal) in pitch diameter (mm) ['sn] 0.341 (mm) ['sn.e/i] 0.331 / 0.331 Reference chordal height from da.m (mm) [ha] 0.251 Tooth thickness (Arc) (mm) [sn] 0.343 (mm) [sn.e/i] 0.333 / 0.333

Centre distance allowances (mm) [Aa.e/i] 0.000 / 0.000 Circumferential backlash (transverse section) (mm) [jt] 0.070 / 0.050

According to ISO 1328:1995: Accuracy grade [Q-ISO1328] Single pitch deviation (µm) [fpt] Base circle pitch deviation (µm) [fpb] Cumulative circular pitch deviation over k/8 pitches (µm) [Fpk/8] Profile form deviation (µm) [ffa] Profile slope deviation (µm) [fHa] Total profile deviation (µm) [Fa] Helix form deviation (µm) [ffb] Helix slope deviation (µm) [fHb] Total helix deviation (µm) [Fb] Total cumulative pitch deviation (µm) [Fp] Concentricity deviation (µm) [Fr] Total radial composite deviation (µm) [Fi"] Radial tooth-to-tooth composite deviation (µm) [fi"] According to DIN 3965:1986: Accuracy grade according to DIN 3965 [Q-DIN3965] Single pitch deviation (µm) [fp] Total cumulative pitch deviation (µm) [Fp] Concentricity deviation (µm) [Fr] Total tangential composite deviation (µm) [Fi'] Tangential tooth-to-tooth composite deviation (µm)

------ PINION ----------- FACE GEAR ------ 9 17.00 16.00 17.00 7.50 6.50 9.50 14.00 14.00 20.00 35.00 28.00 35.00 7.00

10

42.00 76.00 47.00 91.00

Data for the tooth form calculation : Data not available.

[fi'] 56.00

Weight - calculated with da (g) [Mass] 0.01

REMARKS:

- Specifications with [.e/i] imply: Maximum [e] and Minimal value [i] with consideration of all tolerances

Specifications with [.m] imply: Mean value within tolerance

- The specification of circumferential backlash (as well as the backlash-free center distance for the tooth thickness check) is not exact and serves only as a guide.

0.01

For the calculation of face gears no standard is available..

The calculation will be carried out analogous to the cylindrical gear calculation according to the literature (Roth/Bastein). The results should be verified by tests..

Calculation according to ISO6336:2006, however YF acc. method C in ISO 6336:1996 cg according to method B KV according to method B

(Literature: Guus Bastein, Sizing face gears, "Antriebstechnik" 32, (1993), nr.11) End of Report lines: 395