[47] Strain wave gearing design system

Fig.47.3 Property and basic rack（Cup type）
47.4 Dimension
Dimension display is shown in Figure 47.4 by using the example with
mn=0.3, zFS=100 ， zCS=102 ． Although the addendum modification
coefficient is shown as xn=0.2, it can be set to any value. Also, tip R canbe defined all the way to the addendum pointed limit．In basic rack root
R, the value specified in Figure 47.2 is taken as the standard value, but it
can be defined all the way to the established limit of basic rack profile.
The input range is shown below.
Module： 0＜mn＜10
Number of teeth ： 10＜zFS≦1000，zFS+2＜zCS≦1000
Profile shift： -2＜xn＜+3Face width： 0＜b ＜1000

Fig.47.1 Strain wave gearing design system
47.1 Overview
Strain wave gearing design system is a software that generates wave
gear tooth profile, based on basic rack or tool (hob). Meshing of thegenerated tooth profile and rendering can be displayed, and also
2D-DXF file output can be generated. Overall display is shown in Table
47.1.
47.2 Software configuration
Strain wave gearing design system configuration is shown in Table
47.1．

No.
1234567891011

Table 47.1 Software Configuration
Item
FigureBasic rack
47.3
Tool（HOB）----47.12
Type of Ring----Tool dimension----47.12
Gear dimension
47.4
47.12.2
Tooth profile
47.5
47.12.3
Tooth modification
47.6----2DTooth profile
47.7
47.12.3
Tooth rendering
47.8
47.12.3
FEM-Analysis
47.9
47.12.4
Hertzian stress
47.10
47.12.4
Output (Tooth profile)
47.11
47.12.5
Design-data management
47.13

Fig.47.4 Gear dimensions
47.5 Tooth profile calculation
The tooth profile calculation setup display is shown in Figure 47.5.
Flex spline thickness, device outer diameter and number of divisions for
tooth profile calculation set-up can be specified. After setting the values,
click
to proceed to tooth profile calculation.

47.3 Basic Rack（Property）
Basic rack (cup type) is shown in Figure 47.2. As basic rack can bechosen between full depth tooth, low tooth and special tooth, initialize
is used to set up special tooth with α=25°，hac=0.8, hfc=1.05, rc=0.375．
After basic rack is specified, actual basic rack can be displayed as shownby Figure 47.3, by clicking． (Hob-based tooth profile isshown in Figure 47.12)
Fig.47.5 Tooth Profile Set-up
47.6 Tooth profile modification
Generated flex spline tooth profile can be modified as shown in Figure
47.6. Tooth profile can be specified either by line of action or diameter,while the magnification of the tooth profile modification can be selectedfrom 50, 100, 200, 300, 400, 500, 1000.

Fig.47.2 Basic rack（Cup type）
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Fig.47.6 Tooth Profile Modification
The tooth profile modification can be applied by track-bar (shown at
the center of Figure 47.7) and table-entry on the right hand side of thescreen. In Figure 47.7, tooth profile is shown with 9 divisions, but it canbe specified up to 50 divisions. Also, connection of the tooth profile canbe spline (as shown by this example) or straight line connection.
Moreover, numerical value can be entered into the template figure asshown in Figure 47.8．

(a) Section[A](b) Section [B](c) Section [C](d) Section [D]Fig.47.10 Enlarged figure at each sectionFig.47.7 Profile modification setup
Fig.47.11 Distance measurement
47.8 Rendering
Tooth profile can be displayed as shown in Figure 47.12. Thisrendering can be enlarged, reduced and rotated by using.

Fig.47.8 Profile modification setup (Template)[E]47.7 Tooth Profile Figure (2D)
Generated tooth profile can be displayed as shown in Figure 47.9.
Enlarged sections [A] to [D] are shown in Figure 47.10. Also, distancecan be measured as shown in Figure 47.11. Moreover, rotation-related
tooth profile meshing can be checked by rotationin righthand corner of Figure 47.9.

[A]

Fig.47.12 Rendering and supplemental form

[B]
[C]

Fig.47.13 Rendering enlargement[E][D]
47.9 FEM Analysis (2D)
When load is applied to teeth, root stress in the teeth can be calculated.
FEM analysis setup display is shown in Figure 47.14, but in FEM
analysis, material is symbols only, as it is based on longitudinal elastic
modulus and Poisson's ratio. Vertical division number and horizontal

Fig.47.9 Tooth Profile & Supplemental Feature
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division number can be specified arbitrarily. The position of the load (2 inthe example: the second node from the tooth tip), less than 2 in thevertical division number can be specified. For the load applied in thiscase, please set the value per designer’s intension.

47.10 Tooth contact stress
The calculation of Hertzian stress acting on tooth surface is shown in
Figure 47.19. The purpose of this feature is to compare the Hertzianstress due to tooth profile differences, so the load acting on one toothshould be designer’s intended value.

Fig.47.14 FEM analysis setupFEM analysis results are shown in Figure 47.15 to 47.20. The analysis
items are, and flex spline max
main stress is found to be σ1max=24.0MPa as shown in Figure 47.15. Also,displacement figure is shown in Figure 47.17 while stress summary(selective results only) is shown in Figure 47.18.

Fig.47.19 Hertzian Stress47.11 Tooth profile output
The resulting F/S (perfect circle), F/S (ellipse) and C/S tooth profile
output can be generated. F/S tooth profile output display is shown inFigure 47.20 while CAD drawing sample is shown in Figure 47.21.

Fig.47.20 F/S Tooth profile output setup
Fig.47.15 Flex Spline, σ1max=14.4MPa(a) F/S(perfect circle)
F/S(Ellipse)
Fig.47.21 CAD Drawing sample(c) C/S

47.12 Tooth profile made by hob
47.12.1 Hob dimensions
When hob blade profile is known, the hob profile can be defined by
selecting cup
in reducer type property in Figure
47.32.

Fig.47.16 Circular spline，σ1max=13.4MPa

Fig.47.17 Flex Spline displacement, δmax=0.08μm
Fig.47.32 Property, Cup type (Special tool)
Hob dimension input sample is shown in Figure 47.33. In this sample,
pitch=0.9425 is used to achieve module 0.3, but any value can bespecified. After input entry, true hob profile can be displayed by clicking
profile. The hob profile is based on gear front surface.
Fig. 47.18 Stress Summary (selective results)
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Figure 47.37. Also, there is 22μm of gap between tooth tips in [F], andthere is 2.6μm of gap between teeth in [G]. The clearance is 0.07mm asshown in Figure 47.40, and F/S tip area is found to be arc-shape of
0.359mm as calculated in Figure 47.41. When gear is specified asover-pin, tooth profile and pin are contacting as shown in Figure 47.42,
and F/S contact diameter is found to be dc=33.01mm.

[G][E]
Fig.47.33 Hob dimensions[F]

Fig.47.37 Tooth profile
Fig.47.34 Hob profile
47.12.2 Gear Dimensions
In Figure 47.4, module was entered, but module, pressure angle androot diameter cannot be entered in Figure 47.35 because pitch is alreadyentered in Figure 47.33 (background is grayed out).
(a) [E] section(b) [F] section
Fig. 47.38 Enlarged tooth profile

Fig.47.39 Enlarged tooth profile [G] section, distance measurement
Fig. 47.35 Gear dimensions
47.12.3 Tooth profile
After gear dimensions are specified, tooth profile calculation isperformed based on rim thickness and outer diameter as shown in Figure
47.36.

Fig.47.40 Distance measurement

Fig.47.41 Arc measurement

Fig.47.36 Rim thickness and outer diameter
After tooth profile calculation is completed, transverse tooth profile
can be displayed as shown in Figure 47.37. However, tooth profile
modification cannot be performed when it is based on hob. Since C/Stooth profile is generated to mesh with F/S tooth profile, both gears arecontacting without any gaps as shown in the enlarged view of [E] in(a) F/S & Pin(b) C/S & Pin
Fig.47.42 Pin positions
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After tooth profile is generated, tooth profile rendering can bedisplayed as shown in Figure 47.43. This figure can be rotated just like2D tooth profile, while changing observation angle in the supplementalform.

47.12.5 CAD drawing sample
Drawing samples are shown in Fig. 47.48 to Fig. 47.50.

F/S(circle)

F/S(ellipse)
Fig.47.48 CAD drawing sample,

Fig.47.43 Rendering & supplemental form
47.12.4 FEM analysis & Hertzian stress
Analysis results are shown in Fig.47.44 to Fig. 47.47.
Fig.47.50 CAD drawing sample, C/S
47.13 Design data management
Design data can be managed as shown in Figure 47.51, while it can bealso imported and exported as shown in Figure 47.52.

Fig.47.44 FEM analysis setup

Fig.47.51 Design data management

Fig.47.45 Flex spline, σ1max=11.5MPa

Fig.47.52 File management

Fig.47.46 Circular spline, σ1max=472MPa

Fig.47.53 Ring type, m=0.15, z1=z3=200, z2=204◆日本語版カタログは別途お申しつけください．

Fig.47.47 Hertzian stress
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