KISSsoft instructions: Crossed helical gear pair, combination of a steel worm with a plastic gear and deep tooth form

Transcription

1 KISSsoft instructions: Crossed helical gear pair, combination of a steel worm with a plastic gear and deep tooth form Release 10/2008 Last correction :49:00 Calculation example Project No KISSsoft instructions 1.1 Task Presetting: Because of the different E-modules concerning the material (steel MPa, and 3000 MPa for plastics) there is an uneven distribution of the tooth thickness. Thus the tooth thickness has to be reduced for the worm and enlarged the gear. A common breakdown of the tooth thickness proportions for the worm is % and for the crossed helical gear 60-80%. For toothing without profile modification normal tooth thickness constitutes π x m n /2, that means 50% for each worm and gear. The normal tooth thickness s n has to be reduced by s n 0.5x m n what relates to a tooth thickness distribution of ca 34% for the worm compared to 66% for the gear. The root strength of the plastic gear may be significantly enlarged by reducing the steel worm so the gear teeth get larger. In the meanwhile, the root and tip circle are kept approximately equal. Therefore, the used formula of the standard DIN 3960 are: - Tooth thickness at the reference circle of a gear with profile shift: s n = m n (π/2+2 x tan α n ) - Root diameter: d f = d + 2 x m n 2 h fp Calculation procedure Open the calculation module for the crossed helical gear calculation. Enter the following values for a crossed helical gear pair. 1 / C:\HD\EES\KISSsoft\31-Worm-Crossedaxis-Face-Gear\Instructions_KISSsoft.doc

2 Figure 1.1-1: Input tab Basic date Figure 1.1-2: Input tab Reference profile 2 / 8

3 (file: z2_z49_m08_step1.z17) Figure 1.1-3: Input tab Tolerances Results of calculation with normal tooth thickness Centre distance (mm) [a] Centre distance tolerance DIN j10 Axis angle ( ) Normal module (mm) [mn] Normal module in pitch circle (mm) [msn] Helix angle at reference diameter ( ) [beta] Pressure angle at normal section ( ) [alfn] Lead angle at pitch diameter ( ) [gamma] Helix angle at pitch circle ( ) [betas] Number of teeth [z] 2 49 Shape of flank: ZI Helix right right Sum of the Addendum modification [Summexi] Profile shift coefficient [x] Generating Profile shift coefficient [x.e/i] / / Tooth thickness (chordal) in pitch diameter (mm) ['sn] (mm) ['sn.e/i] / / / 8

4 1.2 Required modification of tooth thickness, given sn (e.g. 0.5 x mn) First calculate the profile shift factor: x = s n /(2 m n tan α n ); the result in the example: x = x has to be set as follows: x= Alteration of calculation data Figure 1.2-1: Activate flaged checkboxes Correct the previous calculation (section 1.1.2) x1= -1.0, i.e. reduce the worm: x1(new) = x1(previous) - x x1= = and enlarge the gear x2(new) = x2(previous) + x x2= = : Figure 1.2-2: Enter the Profile shift coefficient x1 Run the calculation and confirm the warning message. 4 / 8

5 Figure 1.2-3: Enter the Root radius factor as follows: ρ* fp2 = Reference profile changes, so that the root and tip circle stay the same. Figure 1.2-4: New Reference profile According to the chosen settings derived from the previous calculation there apply following results: hfp 1 (new) = h* fp1 (previous) - x (dedendum) h* fp1 = = 0.50 hap 1 (new) = h* ap1 (previous) + x (addendum) h* fp1 = = 2.30 hfp 2 (new) = h* fp2 (previous) + x (dedendum) h* fp2 = = 2.50 hap 2 (new) = h* ap2 (previous) - x (addendum) h* fp2 = = 0.30 Tooth thickness (chordal) in pitch diameter (mm) ['sn] (mm) ['sn.e/i] / / The results show that the tooth thickness factor changed: s n =0.5 m n = 0,414 mm. That relates to a distribution of ca 34% (for the worm) compared to ca 66% (for the gear). 5 / 8

6 So the root strength of the crossed helical gear improved from to what relates to an amelioration of ca 45%. (File: z2_z49_m08_step2.z17) 1.3 Additional possibilities as profile correction Profile corrections may improve the run properties (acoustic) even more. The future manufacturing process has to be considered, so the properties can be consequently enhanced by driving into a blocksituation. The chosen values are just an example to show the various possibilities. For an exact value definition experience and a certain strategy are demanded. Furthermore, all conditions must be known which have to be fulfilled by the gearbox. A sharp-edged tooth tip of the worm inserts into the root of the crossed helical gear. Stress optimized elliptic root modification reduces stress peaks in the root region. 6 / 8

7 Elimination of manufacturing errors leads to better acoustic. (File: z2_z49_m08_step3.z17) Necessary addition for the manufacturing of injection molding. 1.4 Consider the mutated tolerances under extreme working temperatures The large length expansion of plastics may lead to jamming under differing and extreme working temperatures (-40 C /+80 C). 1.5 Calculation test Finally, check the automatic entries for the diameters of pins or balls for the measurement. 7 / 8

8 (File: z2_z49_m08_step4.z17) 8 / 8