[3] involute Σ Worm Gear Design System
Fig. 3.1 involute Σ Worm Gear Design System
3.1 Introduction
The involute Σ Worm Gear Design System  is a complete design system for worm gear sets (consisting of a worm and a worm wheel). For worm and helical gear combinations, please use the involute Σ Worm and Helical Gear Design System .
3.2. Software Features
Table 3.1 shows the available software features.
Table 3.1. Software Features
Item Page  Applicable
<1> Basic Rack Setting
13 ○
<2> Worm Tooth Profile (Type 1) 13 ○
<3> Worm Tooth Profile (Types 3 and 4) 13 ◎ <4> Hob Setting
13 ○ <5> Tooth Profile Calculation (Standard) 14 ○ <6> Tooth Profile Calculation (Interference)
14 ◎ <7> Gear Dimension
14 ○ <8> Gear Meshing Drawing (2D-DXF, 3D-DXF) 14 ○
<9> Tooth Profile Rendering (Image Display) 14
◎ <10> Tooth Profile Rendering (Mounting Error Adjustment)
14
◎
<11> Tooth Profile Rendering (Backlash Angle) 14
◎ <12> Tooth Profile Data File Output (2D-DXF, 3D-DXF)
14
○
<13> Tooth Profile Data File Output (3D-IGES) 14 ◎ <14> Strength Calculation (Metal) 14 ○ <15> Strength Calculation (POM) 14 ○ <16> Strength Calculation (PA) 15 ◎ <17> Gear Accuracy
--- ○ <18> 2D-FEM Tooth Profile Stress Analysis 15 ◎ <19> Transmission Error Analysis 15 ◎ <20> Sliding Speed Graph 15 ◎ <21> Hertzian Stress Graph 16 ◎ <22> Fourier Analysis 16 ◎ <23> Design Data Management -- ○ <24> Tooth Contact Analysis 16 ◎ <25> Bearing Load Calculation 16 ○ <26> Center Distance Variation Analysis 16 ◎ <27> Tooth Profile Modification 16
◎
○ (Supported as standard)    ◎ (Optional)
3.3 Icon Buttons
The toolbar contains 17 icon buttons including [Dimension], [Tooth Profile], [Strength], [FEM], and [Transmission].
3.4 Basic Rack Setting
Before using the System, the user needs to configure the basic rack settings by selecting: (1) basic rack type (full depth, stub gear, or special), (2) worm tooth profile (Type 1, 3, or 4), (3) tooth profile reference (cross-sectional or normal), and (4) worm wheel shape. Fig. 3.2 shows the Initial dimension setting screen.
Fig. 3.2 Initial Dimension Settings
3.5 Gear Dimension Setting
Fig. 3.3 shows the Gear dimension setting screen. The user may change items such as the gorge radius, tip diameter, root diameter, and center distance. For the tooth thickness reduction and the tooth surface thinning factor , specifying one automatically sets the other.
Fig. 3.3 Gear Dimension Settings
3.6 Tool Setting and Gear Dimension Calculation
Specify the specifications of the hob for cutting the worm wheel. The default setting angle of the hob is determined to match the axial pitch. The diameter and setting angle of the hob affect the tooth profile of the worm wheel to be cut. For the Type 3 worm, however, the diameter of the grinding wheel affects the tooth profile. Fig. 3.4 shows the Tool dimension setting screen and Fig. 3.5 shows the calculated worm gear dimensions.
Fig.3.4 Hob specification Settings
Fig. 3.5 Calculated Worm Gear Dimensions
3.7 Tooth Profile Calculation
(1) Standard Tooth Profile Analysis
The System calculates the tooth profile of the worm wheel using the hob specifications specified in Fig. 3.4. (2) Interference Analysis
Setting a large lead angle prevents the worm from contacting the worm wheel at the center of the tooth flank because of the lead difference between the worm and the hob. The Interference Analysis feature analyzes the tooth profile of the hob to help the user eliminate interference. For details, refer to Section 3.20.
Fig. 3.6 Tooth Profile Calculation
3.8 Gear Meshing Drawing
Fig. 3.7 shows the cross-sectional tooth profiles of the worm and the wheel meshed at the axial center of the worm. Even if the teeth seem to be meshed correctly in this 2D drawing, interference may occur in other sections. Incorrect tooth contact due to interference or assembly errors can be checked using the Tooth Profile Rendering feature in Section 3.9.
Fig. 3.7 Gear Meshing Drawing
3.9 Tooth Profile Rendering
Using the Tooth Profile Rendering feature may reveal severe interference on some tooth flanks of the wheel as shown in Fig. 3.8 and Fig. 3.9, even if it seems that there is no interference in this 2D drawing in Fig. 3.7. Fig. 3.10 shows the control form used for Tooth Profile Rendering. The user can not only change the viewing angle by specifying the X-, Y-, and Z-axis rotation angles, but also scale the image by entering the Z-axis travel distance. It is also possible to observe how the meshing state changes by varying the angle and position of the worm shaft.
The control form also offers optional features: The first feature provides (1) worm shaft angle, (2) worm shaft position, and (3) center distance
adjustments. The second feature is used to display the backlash angle.
Fig. 3.8 Tooth Profile Rendering (Left)  Fig. 3.9 Tooth Profile Rendering (Right)
Fig 3.10 Tooth Profile Rendering Control Form
3.10 Tooth Profile Data File Output
As shown in Fig. 3.11, the user can choose to output worm and wheel tooth profile data into four kinds of CAD-format files. Fig. 3.12 is an example of a 3D worm wheel tooth profile displayed in a CAD system.
File 3.11 Tooth Profile File  Fig. 3.12 3D Tooth Profile Data in a  CAD System (IGES)
3.11 Initial Strength Calculation Setting
Fig. 3.13 shows the Initial strength calculation settings screen, in which the user can select the material used for the worm wheel. Clicking the [Select material] button displays the Metal material selection screen as
shown in Fig. 3.14.
Fig. 3.13 Initial Strength Calculation Settings (with [Select Material] button)
Fig. 3.14 Metal Material Selection
3.12 Strength Calculation
Fig. 3.15 shows the strength setting screen for resin (PA) materials. The results of the strength calculation for the resin and metal materials are shown in Fig. 3.16 and Fig. 3.17, respectively.
Fig. 3.16 Strength Calculation Result for Resin Material (PA)
Fig. 3.17 Strength Calculation Result for Metal Material
3.13 FEM Tooth Profile Stress Analysis
Stress analysis can be easily performed by simply clicking the [FEM] button after strength calculation. Fig. 3.18 shows the FEM analysis setting screen. The user may change the Young modulus, Poisson ratio, number of partitions, and load values. Fig. 3.19 and Fig. 3.20 show the results of FEM analysis on the worm and the wheel, respectively.
Fig. 3.18 FEM Analysis Settings
Fig. 3.15 Strength Specification Settings for Resin Material (PA)
Fig. 3.19 FEM Analysis on Worm  Fig. 3.20 FEM Analysis on Wheel            (Stress=ó1)            (Stress=
ó1)
3.14 Transmission Error Analysis
Fig. 3.21 and Fig. 3.22 show the setting screens for transmission error analysis. The graphs in Fig. 3.23 and Fig. 3.24 show the results of analysis on the rotation transmission error and wow and flatter, respectively. These errors were raised by assembling the worm and wheel pair to have pitch and radial runout errors and rotating the worm by one turn. The graphs in Fig. 3.25 and Fig. 3.26 also show the results of analysis on the rotation transmission error and wow and flatter, respectively, but they were raised by rotating the wheel by one turn.
Fig. 3.21 Transmission Error Analysis  Fig. 3.22 Transmission Error  Settings (Worm)  Analysis Settings (Wheel)
Fig. 3.23 Rotation Transmission      Fig. 3.24 Wow & Flatter 1          Error 1
Fig. 3.25 Rotation Transmission Fig. 3.26 Wow & Flatter 2    Error 2
3.15 Frequency Analysis
Fig. 3.27 shows the result of analysis on the frequency measured when the worm is rotated by one turn; Fig. 3.28 shows the result of analysis on the frequency measured when the wheel is rotated by o
ne turn.
Fig. 3.27 Fourier Analysis 1 Fig. 3.28 Fourier Analysis 2
3.16 Hertzian Stress and Sliding Speed Graphs
Fig. 3.29 shows the Hertzian stress exerted on the tooth flank surface when the worm is rotated by one turn; the graph in Fig. 3.30 shows the sliding speed measured during that time.
These graphs are useful after the transmission error analysis.
Fig. 3.29 Hertzian Stress Graph  Fig. 3.30 Sliding Speed Graph
3.17 Center Distance Variation
This feature simulates how the center distance changes when, like on a double-flank gear rolling tester, the worm and the wheel rotate while mutually pressing each other's tooth flanks. The results of this simulation are shown in Fig. 3.31 (circle graph) and Fig. 3.32 (line graph), respectively.
Fig. 3.31 Center Distance Variation  Fig. 3.32 Center Distance Variation      Graph 1    Graph 2
3.18 Bearing Load Calculation
Fig. 3.33 shows the bearing load setting screen; Fig. 3.34 shows the result of the bearing load calculation.
Fig. 3.33 Bearing Load Calculation      Fig. 3.34 Bearing Load Settings                            Calculation Result
3.19 Tooth Contact Analysis
An example of analysis on the tooth flanks of the worm and worm wheel is shown below. The setting screen in Fig. 3.35 provides various settings for tooth contact analysis. In this example, analysis will be made on the tooth contact of the worm and wheel specified in Fig. 3.3. Here, the number of rotation position partitions is set to "4" although it accepts values in a range of 3 to 20. Fig. 3.36 shows a tooth contact state between the worm and the wheel and Figs. 3.37 to 3.40 show their tooth contact states by 1/4 pitch. This example, however, does not take the deflection of the teeth and the pitch error into account.
It is noticeable that tooth contact pattern in Fig. 3.36 slightly differs from the tooth profile rendering image shown in Fig. 3.8. The reason for this is that the analysis in this example was made at a fineness that is two times (up to five times allowed) greater than that of the number of tooth profile
partitions setting used for the tooth profile rendering image of the wheel.
Fig. 3.35 Tooth Contact Analysis Settings
Fig. 3.36 Tooth Contact State (Worm and Wheel)
Fig. 3.37 Tooth Contact State 1 Fig. 3.38 Tooth Contact State 2
Fig. 3.39 Tooth Contact State 3  Fig. 3.40 Tooth Contact State 4
In addition to viewing the tooth contact state as a color pattern as shown in Fig. 3.36, to examine it in more detail, the user may click the [Tooth contact value] button in Fig. 3.35 to display the contact clearance values in Fig. 3.41. The slider control bar at the bottom of the screen can be used to change the target rotation position (1 to 4 in this example).
Fig. 3.41 Contact Clearance Values
3.20 Example of Hob Tooth Profile Analysis Simulation 1)3.20.1 Introduction
The tooth contact state between the worm and the worm wheel in mesh will be influenced by the hob used to cut them. The contact point will be deviated to a great extent particularly if the lead angle of the worm is large or if there is a significant difference between the diameters of the worm and the hob. Since this is caused by the lead difference between the worm and the hob, to obtain a proper tooth contact, it is necessary to modify the tooth profile of the hob. The following is the result of examination on the tooth contact and backlash of the worm gear using the involute Σ Worm Gear Design System .
3.20.2 Examined Gear Set
The specifications of the examined gear set are shown in Table 3.2. Compared with the worm's pitch diameter of 12 mm, the pitch diameter of the hob used to cut the worm wheel (shown in Fig. 3.42) is 36 mm. This requires the hob to be installed at a setting angle of 14.5916 (degrees) to match the axial pitch.
Fig. 3.42 Hob Dimensions
radius软件
Table 3.2 Worm Gear Specifications
3.20.3 Tooth Profile Rendering
Fig. 3.43 and Fig. 3.44 show the tooth profile rendering images of the Type 1 worm and worm wheel. It can be seen that, while there are three occurrences of major interference on the worm and wheel cut using the non-modified hob, the modified hob has no interference and the worm and wheel mesh without interference around the center of the tooth flank.
Fig. 3.43 Tooth Profile Rendering  Fig. 3.44 Tooth Profile Rendering (Non-Modified Hob) (Modified Hob)
3.20.4 Relationship between Hob Diameter and Backlash
Fig. 3.45 shows the change in the backlash amount when the diameter of the non-modified hob is increased from 12 to 100 mm. The graph shows that the backlash becomes the maximum at a hob diameter of 18 mm and decreases as the hob diameter increases. With the modified hob (shown in Fig. 3.47), the amount of change in backlash improves significantly and the backlash becomes approximately constant as shown in Fig. 3.26.
Fig. 3.45 Hob Diameter versus  Fig. 3.46 Hob Diameter versus  Backlash Graph 1 Backlash Graph 2
Fig. 3.47 Tooth Profile of Modified Hob
1) MPT2001-Fukuoka, Excerpt from Amtec Catalog, 2001

版权声明：本站内容均来自互联网，仅供演示用，请勿用于商业和其他非法用途。如果侵犯了您的权益请与我们联系QQ:729038198，我们将在24小时内删除。