BEVEL-GEAR-CALCULATION (BEVEL-GEAR-PAIR)

1 KISS soft Release 03/2015 F. KISS soft evaluation File Name : BevelGear 1 (Klingelnberg). Description: KISS soft example Changed by: kspl on: at: 10:50:06. BEVEL-GEAR-CALCULATION ( bevel - gear -PAIR). Drawing or article number: gear 1: gear 2: Calculation method bevel gear Klingelnberg Cyclo-Palloid KN3028/KN3030 Geometry calculation according ISO 23509:2006, method 3. Uniform depth, fig 3 (Klingelnberg). Manufacture process: ground/hard-cut Spiral toothing Face hobbing (continuing indexing method). ------- gear 1 -------- gear 2 ------- Power (kW) [P] Speed (1/min) [n] Rotation direction, wheel 1, viewed on cone tip: left Torque (Nm) [T] Application factor [KA] Power distribution factor [Kgam] Required service life [H] gear driving (+) / driven (-) + - 1. TOOTH GEOMETRY AND MATERIAL. ------- gear 1 -------- gear 2 ------- Hypoid offset (mm) [a] Shaft angle ( ) [Sigma] Mean normal module (mm) [mmn] Pressure angle at normal section ( ) [alfn] Mean spiral angle ( ) [betm] Hand of gear left right Number of teeth [z] 11 54.

2 Facewidth (mm) [b] 1/13. Assumed and measured contact pattern width (mm) [be] Accuracy grade according to DIN 3965 [Q-DIN3965] 6 6. Internal diameter gearbody (mm) [di] Pitch apex to front of gear blank (mm) [yi] Pitch apex to back of gear blank (mm) [yo] H misalignment (P misalignment) ( m) [DeltaH] G misalignment ( m) [DeltaG] V misalignment (E misalignment) ( m) [DeltaV] Material gear 1: 18 CrNiMo7-6, Case-carburized steel, case-hardened ISO 6336-5 Figure 9/10 (MQ), core strength >=25 HRC Jominy J=12mm<HRC28. gear 2: 18 CrNiMo7-6, Case-carburized steel, case-hardened ISO 6336-5 Figure 9/10 (MQ), core strength >=25 HRC Jominy J=12mm<HRC28. Surface hardness HRC 61 HRC 61. Fatigue strength. tooth root stress (N/mm ) [sigFlim] Fatigue strength for Hertzian pressure (N/mm ) [sigHlim] Tensile strength (N/mm ) [Rm] Yield point (N/mm ) [Rp] Young's modulus (N/mm ) [E] 206000 206000.

3 Poisson's ratio [ny] Roughness average value DS, flank ( m) [RAH] Roughness average value DS, root ( m) [RAF] Mean roughness height, Rz, flank ( m) [RZH] Mean roughness height, Rz, root ( m) [RZF] gear reference profile 1: Reference profile / / Cyclo-Palloid Dedendum coefficient [hfP*] Root radius factor [rhofP*] (rhofPmax*=. ). Addendum coefficient [haP*] Tip radius factor [rhoaP*] Protuberance height factor [hprP*] Protuberance angle [alfprP] Tip form height coefficient [hFaP*] Ramp angle [alfKP] not topping gear reference profile 2: Reference profile / / Cyclo-Palloid Dedendum coefficient [hfP*] 2/13. Root radius factor [rhofP*] (rhofPmax*=. ). Addendum coefficient [haP*] Tip radius factor [rhoaP*] Protuberance height factor [hprP*] Protuberance angle [alfprP] Tip form height coefficient [hFaP*] Ramp angle [alfKP] not topping Summary of reference profile gears: Dedendum reference profile [hfP*] Tooth root radius Refer.

4 Profile [rofP*] Addendum Reference profile [haP*] Protuberance height factor [hprP*] Protuberance angle ( ) [alfprP] Tip form height coefficient [hFaP*] Ramp angle ( ) [alfKP] Type of profile modification: none (without running-in). Tip relief ( m) [Ca] Tip alteration, outside, height (mm) [hake] Tip alteration, outside, length (mm) [l_hake] Tip alteration, inside, height (mm) [haki] Tip alteration, inside, length (mm) [l_haki] Reduction of tooth contact area through tip alteration (%). [delF] Notice: Tip alteration are used only for 3D geometry and measurement grid generation. The strength calculation will ignore the input. Lubrication type oil injection lubrication Type of oil Oil: BP XP 100. Lubricant base Mineral-oil base Kinem. viscosity oil at 40 C (mm /s) [nu40] Kinem. viscosity oil at 100 C (mm /s) [nu100] FZG test ( ISO 14635-1:2006) [FZGtestA] 12.

5 Specific density at 15 C (kg/dm ) [roOil] Oil temperature ( C) [TS] ------- gear 1 -------- gear 2 ------- Overall transmission ratio [itot] gear ratio [u] Outer spiral angle ( ) [bete] 3/13. Mean spiral angle ( ) [betm] Inner spiral angle ( ) [beti] Pinion offset angle in axial plane ( ) [zetm] Pinion offset angle in pitch plane ( ) [zetmp] Offset in pitch plane (mm) [ap] Outer normal module (mm) [men] Outer transverse module (mm) [met] Mean normal module (mm) [mmn] Mean transverse module (mm) [mmt] Inner normal module (mm) [min] Inner transverse module (mm) [mit] Sum of profile shift coefficients [xhm1+xhm2] Profile shift coefficient [xhm] Undercut boundary [xGrenz] Profile shift coef. for balanced sliding [xGleit] Tooth thickness modification coefficient [xsmn] Outer pitch diameter (mm) [de] Outer tip diameter (mm) [dae] Outer root diameter (mm) [dfe] Mean pitch diameter (mm) [dm] Mean tip diameter (mm) [dam] Mean root diameter (mm) [dfm] Inner pitch diameter (mm) [di] Inner tip diameter (mm) [dai] Inner root diameter (mm) [dfi] Addendum (mm) [hae] (mm) [ham] (mm) [hai-haki] Dedendum (mm) [hfe] (mm) [hfm] (mm) [hfi] Tooth height (mm) [he] (mm) [hm] (mm) [hi] Working depth (mm) [whe] (mm) [whm] (mm) [whi] Tip clearance (mm) [ce] (mm) [cm] (mm) [ci] Outer cone distance (mm) [Re] Mean cone distance (mm) [Rm] Inner cone distance (mm) [Ri] Pitch angle ( ) [delta] 4/13.

6 Face angle ( ) [dela] Addendum angle ( ) [thea=dela-delta] Root angle ( ) [delf] Dedendum angle ( ) [thef=delta-delf] Distance along axis to crossing point (mm) [txo] (mm) [txi] Distance apex to crossing point (mm) [tz] (mm) [tzF] (mm) [tzR] Distance in axial direction to the cone tip (mm) [ye] (mm) [yae] (mm) [yai] Theoretical tip clearance (mm) [c] Effective tip clearance (mm) [ ] / / According to Klingelnberg instruction for bevel gears: Transverse contact ratio [epsa] Overlap ratio [epsb] ** Virtual cylindrical gear toothing **. Pressure angle at normal section ( ) [alfvn] Pressure angle at pitch circle ( ) [alfvt] Helix angle at reference circle ( ) [betv] Base helix angle ( ) [betvb] Virtual centre distance (mm) [av] Working transverse pressure angle ( ) [alfvwt] Number of teeth [zv] gear ratio [uv] Generating Profile shift coefficient [ ] / / -0.

7 4000. Theoretical tip clearance (mm) [c] Effective tip clearance (mm) [ ] / / Reference diameter (mm) [dv] Base diameter (mm) [dvb] Tip diameter (mm) [dva] Tip form diameter (mm) [dvFa] Active tip diameter (mm) [dvNa] Operating pitch diameter (mm) [dvw] Root diameter (mm) [dvf] Root form diameter (mm) [dvFf] Active root diameter (mm) [dvNf] Reserve (dNf-dFf)/2 (mm) [cF] Normal-tooth thickness at tip circle (mm) [svan] Normal-tooth thickness on tip form circle (mm) [svFan] 5/13. Virtual gear no. of teeth [zvn] Maximum sliding speed at tip (m/s) [vga] Pitch on reference circle (mm) [pvt] Base pitch (mm) [pvbt] Transverse pitch on contact-path (mm) [pvet] Length of path of contact (mm) [gva] Virtual cylindrical gear toothing (. ISO 10300:2001, Annex A): Referenced to facewidth [bveff] Transverse contact ratio [epsva] Overlap ratio [epsvb] Total contact ratio [epsvg] (DIN 3991: epsva = , epsvb = , epsvg = ).

8 Characteristic values for sizing [Re2/b2] [b2/mmn] 2. FACTORS OF GENERAL INFLUENCE. ------- gear 1 -------- gear 2 ------- Nominal circum. force at pitch circle (N) [Fmt] 20739..6. Drive side Axial force (N) [Fa] 6150..9. Radial force (N) [Fr] 13472..9. Normal force (N) [Fnorm] 25485..0. Axial force (%) [Fa/Ft] 29..658. Radial force (%) [Fr/Ft] 64..962. Remarks: Forces if rotation goes in opposite direction (coast side): Axial force (N) [Fa] 10931..1. Radial force (N) [Fr] -9993..3. Normal force (N) [Fnorm] 25485..0. Axial force (%) [Fa/Ft] 52..706. Radial force (%) [Fr/Ft] -48. 6/13..184. at mm (N/mm) (N/mm) [w] Circumferential speed reference circle (m/s) [v] Singular tooth stiffness (N/mm* m) [c'] Meshing stiffness (N/mm* m) [cg] Single pitch deviation ( m) [fp] 14..00. Running-in value ( m) [ya] Reduced mass (kg/mm) [mRed] Resonance speed (min-1) [nE1] 33432.

9 Under critical range - resonance ratio [N] Dynamic factor [KV] Mounting factor [KHbbe] Face load factor - flank [KHb] - Tooth root [KFb] - Scuffing [KBb] Transverse load factor - flank [KHa] - Tooth root [KFa] - Scuffing [KBa] Helical load factor scuffing [Kbg] Number of load cycles (in mio.) [NL] 354..444. 3. TOOTH ROOT STRENGTH. ------- gear 1 -------- gear 2 ------- Calculation of Tooth form coefficients according method: C. Manufacture process: generated Calculated with profile shift [x] Tooth form factor [YF] Stress correction factor [YS] Bending lever arm (mm) [hF] Working angle (deg) [alfh] Tooth thickness at root (mm) [sFn] Tooth root radius (mm) [roF] (hF* = sFn* = roF* = ). Contact ratio factor [Yeps] Helix angle factor [Ybet] 7/13. Effective facewidth (mm) [b] bevel gear factor (root) [YK] Nominal stress at tooth root (N/mm ) [sigF0] Tooth root stress (N/mm ) [sigF] Permissible bending stress at root of Test- gear Notch sensitivity factor [YdrelT] Surface factor [YRrelT] size factor (Tooth root) [YX] Finite life factor [YNT] [YdrelT*YRrelT*YX*YNT] Alternating bending factor (mean stress influence coefficient).

10 [YM] Stress correction factor [Yst] Yst*sigFlim (N/mm ) [sigFE] Permissible tooth root stress (N/mm ) [sigFP=sigFG/SFmin] Limit strength tooth root (N/mm ) [sigFG] Required safety [SFmin] Safety for Tooth root stress [SF=sigFG/sigF] 4. SAFETY AGAINST PITTING (TOOTH FLANK). ------- gear 1 -------- gear 2 ------- Zone factor [ZH] Elasticity coefficient ( N/mm) [ZE] Contact ratio factor [Zeps] Helix angle factor [Zbet] bevel gear factor (flank) [ZK] Nominal flank pressure (N/mm ) [sigH0] Effective flank pressure (N/mm ) [sigH] Lubrication coefficient at NL [ZL] Speed coefficient at NL [ZV] Roughness coefficient at NL [ZR] Work hardening factor at NL [ZW] Finite life factor [ZNT] [ZL*ZV*ZR*ZNT] Small no. of pittings permissible: no Size factor (flank) [ZX] Permissible surface pressure (N/mm ) [sigHP=sigHG/SHmin] Limit strength pitting (N/mm ) [sigHG] Safety for surface pressure at operating pitch circle [SHw] Single tooth contact factor [ZB/ZD] Flank pressure (N/mm ) [sigHB/D] 8/13.