Program 60-460—Internal Gear Coordinates Introduction · UTS Integrated Gear Software 8 Example 2...

Program 60-460—Internal Gear Coordinates

Introduction The primary purpose of this model is to provide an accurate set of polar and rectangular coordinates for use in plotting the final form of internal involute spur and helical gears. In addition to a plot of the teeth the model furnishes numerical results for many of the design parameters of interest to the designer. The model can be used for the design of the necessary tooling or as a “final visual” check of the design process. The gear may be shaped or defined by an involute and a circular arc fillet. If the gear is post processed after shaping, provision has been made to accommodate the finishing stock. IT IS ASSUMED THAT NO STEPS WERE CUT IN THE INVOLUTE OR FILLET BY THE FINISH TOOLS. The model will warn you if the finish stock on the side of the tooth is greater than the protuberance but the step produced on the plot of the tooth is not necessarily at the actual location of the step produced by the finish tool. The shaper cutter tooth thickness at the shaper reference pitch diameter, the protuberance and the tip radius are measured in the normal plane. The model checks for trochoidal interference (shaper tooth tip interference with the gear ID) if a shaper cutter is used. Trim interference (as cutter is fed radially into the gear) is also checked. In the case of molded gears a plot of the mold along with coordinate lists for the mold will be created at any shrinkage rate specified (+ or -). For form ground spur gears the wheel cross section shape is plotted and coordinate lists for the wheel are created. The model default will produce coordinates at intervals of 0.050 inch/Operating Normal Pitch on the involute and 1/5 of this in the fillet area. These values may be changed if desired. Caution should be used, as accuracy of the plots is dependent upon the coordinate spacing. This diameter will be calculated and marked on the plot of the tooth in addition to being displayed as an output value in the analysis report.

UTS Integrated Gear Software

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The coordinates for spur gears are the actual coordinates of the gears produced by the specified tool. For a helical gear the coordinates are produced for the virtual spur gear in the normal reference plane. If the gear is helical the model will allow one tooth only to be plotted since the accuracy of the plot depends upon the equivalence of the curvature of the virtual gear pitch diameter and the actual helical gear pitch ellipse in the normal plane. The model contains some warning messages that may stop execution of the program (“Inside Diameter Less Than Base Diameter”, for example). If it is desired to “visually” check the gears (if a gear is possible with the condition) when these messages appear, power users of TK Solver can toggle to the TK Rule Sheet and temporarily cancel the rule or statement producing the message. (The rule or statement producing the message will be marked with > in the status column.) Some messages occurring at the end of model execution will cause TK to indicate that the model is not resolved. This will be the case if the gear has an undesirable condition or a condition making the gear useless. The solution indicator at the right side of the Status Bar, located at the bottom of the screen, will not read “OK”. You will still get a solution, valid data on the report and, usually, a plot of the gear. Other warning messages may appear that only halt execution to notify you of some condition. You need only press the enter key to continue execution. The gear data to audit a design should be available from your production data. The shaper cutter data is available from the tool supplier.

60-460—Internal Gear Coordinates

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Examples The following examples are meant to aid in learning to use this model. Many design factors must be considered to optimize a design. Therefore, these examples are not meant to be optimized designs and should not be used as rigid “patterns” for actual designs. Example 1 This is a 66 tooth internal spur gear shaped with a “standard” finish shaper cutter. Use the data input form and dialog defaults when they appear, and check the two plot checkboxes at the bottom of the form. Figure 1 and Report 1 show the inputs and outputs for the solved model. Fig. 1


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Report 1

Model Title : Program 60-460 Unit System: US Description Value Unit Comment

Number of teeth 66

Shaped or formed shp

NORMAL PLANE

Diametral pitch 10.000000 1/in `

Nominal pressure angle 20.000000 deg

Module 2.540000 mm `

Base pitch 0.2952 in

Finished tooth thickness at Ref PD 0.1543 in

Finished space width at Ref PD 0.1599 in

Total normal circular finish stock on tooth 0.0000 in thickness

Reference diameter (optional) in

Normal tooth thickness of auxiliary in involute (optional) TRANSVERSE PLANE





Tooth thickness at Ref PD 0.1543 in


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Space width at Ref PD 0.1599 in

Helix angle 0.000000 deg

Base helix angle 0.0000 deg

Axial pitch in

Lead in

Net face width 1.1250 in

Inside (minor) diameter 6.4000 in

Roll at ID 14.594 deg

Normal top land width 0.0882 in

Start of tip modification in

Roll at start of tip modification deg

Normal ID tip relief in

Normal circular ID tip relief in

Transverse circular ID tip relief in

Effective inside diameter 6.4000 in

Roll at effective ID 14.594 deg

Normal effective ID tip relief in

Normal tt at eff ID 0.0882 in

Pointed tooth diameter (no tip mod) Below BD in

Reference PD 6.6000 in

Roll at PD 20.854 deg

Involute/Fillet intersection diameter 6.8192 in

Roll at Involute/Fillet intersection 26.190 deg

Normal tt at Involute/Fillet intersection 0.2512 in


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Minimum fillet radius 0.0267 in

Major diameter 6.8575 in

Whole depth of tooth 0.2288 in

Base diameter 6.2020 in

Mark Involute/Fillet intersections? y

Mark Modification/Involute intersections? y

Involute coordinate spacing 0.00500 in

Fillet coordinate spacing 0.00100 in

Number of teeth on plot 1

CL through tooth or space s SHAPER

Number of teeth 40

Outside diameter 4.2500 in

Normal tooth thickness 0.1571 in

Tip radius - normal plane 0.0250 in

Protuberance - normal plane 0.0000 in

Cutting center distance 1.3038 in

Start of active profile diameter 3.8178 in The diameter at the involute/fillet intersection is 6.8192 inches (26.190 deg roll). This should be compared with the required true involute form diameter (TIF) to be sure that this shaper cutter is producing involute high enough on the tooth. Figure 1A is a plot of the involute tooth flank from the inside diameter to the major diameter along with the trochoidal fillet curve. The shaper cutter does not have a full tip radius so the fillet curve ends with the root diameter.


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Fig. 1A

Figure 1B is a plot of the entire space between the tooth center lines. (If you wish you may change the plot range to space center lines.)

Fig. 1B


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Example 2 This is the same 66 tooth gear as in Example 1, as it might be cut for post processing. 0.010 inch of finish stock is left on each tooth flank. (This is probably more finish stock than should or would actually be used on the gear. It is used here for clarity.) The gear is cut with a protuberance type shaper cutter to leave undercut in the fillet area for runout of the finishing tool (shaving cutter or grinding wheel, for example). First we will look at the tooth as it would appear completely finished, by entering the finish stock and changing the shaper cutter. Figure 2-1 and Report 2-1 show the solved model. Fig. 2-1


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Report 2-1


Number of teeth 66


NORMAL PLANE
















10





Axial pitch in

Lead in





















11












Number of teeth 40






Start of active profile diameter 3.8178 in Figure 2-1A is a plot of the ID, finished involute, the trochoidal fillet and the root (major) diameter.


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Fig. 2-1A

Figure 2-1B is the entire tooth with “tic” marks where the involute and fillet meet.

If the involute/fillet intersection diameter is above the required form diameter the gear looks OK. (You can enter the required TIF as the “Reference diameter” if you wish and it will appear on the “Involute, Fillet, Tip Radius, & Modification curve” plot.) However, it is a good idea to look at the tooth before post processing with the finished involute superimposed to look at the finish stock. There are two ways to do this. We can use the auxiliary involute plotted on the plot “invfil”. Or we can save the plot “gear” to “gearsave” and superimpose the rough cut tooth. We will do both for illustration.

Fig. 2-1B


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On the Plot and List Options tab of the data entry form, you will see the group of radio buttons shown at right. Save the “gear” plot for combining by clicking “Save or Combine Plots” and “Clear Saved Plot”, as shown. We will title the combined plot “Combine.” The resulting plot is shown in Figure 2-1C. Enter the shaped tooth thickness (0.1543 inch finished thickness + 0.020 finish stock), change the finish stock to zero and enter the finished thickness for the auxiliary involute. (The auxiliary involute may be placed at any tooth thickness to obtain a reference involute on the plot. In this case we want the finished tooth thickness.) The solved model is shown in Figure 2-2 and Report 2-2.

Fig. 2-1C


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Fig. 2-2

Report 2-2


Number of teeth 66



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Model Title : Program 60-460 Unit System: US Description Value Unit Comment NORMAL PLANE









Normal tooth thickness of auxiliary 0.1543 in involute (optional) TRANSVERSE PLANE









Axial pitch in

Lead in



16



























17






Number of teeth 40






Start of active profile diameter 3.8178 in Figure 2-2A shows the tooth form both shaped and finished. The amount of finish stock diminishes rapidly above a radius of about 3.35 inches. This may cause the finish diameter to be too low due to distortion of the gear before finishing. A special shaper cutter may be required to bring the undercut higher on the tooth if the required true involute form (TIF) radius is much above 3.35 inches. (If you are a power TK Solver user, you may turn on the plot grid and “zoom” in on this area by using the X and Y axis max/min fields on the plot subsheet to find the amount of finish stock in this area.)


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Fig. 2-2A

Figure 2-2B shows the shaped tooth form. The limit of the involute (where we have full finish stock) is shown by the “tic” marks.

Fig. 2-2B


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Using “Save and/or Combine Plots” in the Plot and List Options tab, combine the shaped tooth form with the finished form that we saved previously (see page 15). Click the radio buttons for “Save and/or Combine Plots” and “Combine Gear Tooth Plots”. The result is shown in Figure 2-2C.

Fig. 2-2C


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Example 3

This is a molded plastic gear with a full fillet and 0.013 inch radii at the tooth tips. The tooth tips at the effective inside diameter are relieved 0.002 inch normal to the involute. The relief ends at a diameter of 2.227 inches. The “Normal tip relief exponent” is the default value of 1.5. (An exponent of 1.0 is a linear drop away from the involute, 2.0 is a parabolic drop, etc.) The gear is made of high strength plastic with a shrinkage rate of 0.025 in/in. First, we wish to check the dimensions of the tooth. Then we want to obtain a plot of the mold and coordinates for use in cutting the mold using wire electric discharge machining (Wire EDM).

In filling in the data input form for this model, answer yes for tip radius and tip relief, and no for other dialogs. Note that the tip relief exponent rounds to 2 in the data input form; the actual input is 1.5. Figure 3-1 and Report 3-1 show the solved model.

Fig. 3-1


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Report 3-1


Number of teeth 45

Shaped or formed frm

NORMAL PLANE
















22





Axial pitch in

Lead in





Start of tip modification 2.2270 in

Roll at start of tip modification 18.954 deg

Normal ID tip relief 0.00300 in

Normal circular ID tip relief 0.00305 in

Transverse circular ID tip relief 0.00305 in



Normal effective ID tip relief 0.00201 in









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CL through tooth or space s FORMED GEAR

Normal fillet radius 0.0255 in

Radial tip chamfer (w/o modification) 0.0000 in

Normal tip radius 0.0130 in

Normal tip relief exponent 1.5000

Molding shrinkage rate (spur gear) n in/in

Distance from origin to gear root for form in grinding wheel coordinates It takes a few tries to get 0.002 inch tip relief at the effective inside diameter (where the involute is tangent to the tip radius). Note: If the value of a full fillet radius is not known enter a large number and the model will furnish the full radius value. Figure 3-1A is a plot of the ID, involute, tip relief modification, tip radius and fillet. Note that the actual tip relief is 0.002 inch at the effective ID of 2.1677 inches where the tip radius is tangent to the tip relief.


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Fig. 3-1A

Figure 3-1B is the entire space. The “tic” marks indicate the intersections between the tip radius and relief, relief and involute and involute and fillet.

If the tooth form is satisfactory we may then proceed with the mold coordinates. Enter 'n for no for “Mark.....intersections?” as we certainly do not want the coordinates for the “tic” marks to wind up in our gear mold. (The model will remind you if you forget.) We will space the coordinates for the wire EDM machine at 0.003 inch. Enter the shrinkage rate for the plastic. Change the defaults for involute coordinate spacing and filet coordinate spacing, and click off the checkboxes for plot marks. (The mold shrinkage rate displays as 0 on the data input form; the actual input is .025.) The solved model is shown in Figure 3-2 and Report 3-2.

Fig. 3-1B


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Fig. 3-2

Report 3-2


Number of teeth 45



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Model Title : Program 60-460 Unit System: US Description Value Unit Comment NORMAL PLANE


















Axial pitch in

Lead in



27





Start of tip modification 2.2270 in


Normal ID tip relief 0.00300 in

Normal circular ID tip relief 0.00305 in

Transverse circular ID tip relief 0.00305 in



Normal effective ID tip relief 0.00201 in












Mark Involute/Fillet intersections? n

Mark Modification/Involute intersections? n


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Normal fillet radius 0.0255 in

Radial tip chamfer (w/o modification) 0.0000 in

Normal tip radius 0.0130 in


Molding shrinkage rate (spur gear) 0.0250 in/in

Distance from origin to gear root for form in grinding wheel coordinates Figure 3-2A is a plot of one tooth space and one mold space. The equations for calculating the mold coordinates from the tooth coordinates are in a rule function called “shrink”. You may, of course, change the equations if you want a different type of allowance for mold shrinkage. (You may change “shrink” to a procedure function if necessary.) If the shape of the mold compared to the tooth is satisfactory we now want to create a complete list of mold coordinates for all the teeth. Do another analysis, entering 45 for “Number of teeth on plot”.


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Fig. 3-2A

Figure 3-2B is a plot of the entire gear and mold.


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Fig. 3-2B

Table 3 was made by choosing “ASCII X-4 coordinate List/File for Mold” on the Plot and List Options tab of the data input form (see graphic at right). The table shows the first 20 coordinate pairs.


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Table 3

ASCII X,Y Mold Coordinates, inch XYmold 1.09919,.07686 1.09940,.07380 1.09960,.07073 1.09971,.06901 1.10002,.06686 1.10068,.06479 1.10166,.06285 1.10295,.06110 1.10450,.05959 1.10628,.05834 1.10824,.05740 1.10951,.05699 1.11263,.05611 1.11575,.05521 1.11888,.05429 1.12200,.05336 1.12512,.05241 1.12825,.05145 1.13137,.05048 1.13449,.04951


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Example 4 In this example we will obtain the coordinates of the cross section of a form grinding wheel used to finish the teeth on a 4 module, 66 tooth internal spur gear. A fillet radius of 1 mm will be used. Tip relief is to be ground on the teeth. We will space the coordinate points at 0.1 mm although any spacing desired can be used. The grinding wheel coordinates will be from an origin that is 2 mm from the wheel tip. The required true involute form (TIF) diameter will be entered as the “Reference Diameter”. Make certain you change the units to metric. In the dialog boxes that appear during data input, choose yes for finished tooth thickness, tip relief and distance from origin to gear root. Change the defaults for involute coordinate spacing and fillet coordinate spacing. Figure 4-1 and Report 4-1 show the solved model. Fig. 4-1


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Report 4-1

Model Title : Program 60-460 Unit System: Metric Description Value Unit Comment

Number of teeth 66


NORMAL PLANE




Base pitch 11.8085 mm

Finished tooth thickness at Ref PD 6.2800 mm

Finished space width at Ref PD 6.2864 mm

Total normal circular finish stock on tooth 0.0000 mm thickness

Reference diameter (optional) 270.1200 mm

Normal tooth thickness of auxiliary mm involute (optional) TRANSVERSE PLANE




Base pitch 11.8085 mm

Tooth thickness at Ref PD 6.2800 mm


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Space width at Ref PD 6.2864 mm



Axial pitch mm

Lead mm

Net face width 200.0000 mm

Inside (minor) diameter 258.0000 mm


Normal top land width 3.8288 mm

Start of tip modification 262.0000 mm


Normal ID tip relief 0.18000 mm

Normal circular ID tip relief 0.18720 mm

Transverse circular ID tip relief 0.18720 mm

Effective inside diameter 258.0000 mm


Normal effective ID tip relief 0.18000 mm

Normal tt at eff ID 3.8288 mm

Pointed tooth diameter (no tip mod) Below BD mm

Reference PD 264.0000 mm


Involute/Fillet intersection diameter 272.2000 mm


Normal tt at Involute/Fillet intersection 9.8795 mm


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Minimum fillet radius 1.0000 mm

Major diameter 273.3830 mm

Whole depth of tooth 7.6915 mm

Base diameter 248.0789 mm

Mark Involute/Fillet intersections? n

Mark Modification/Involute intersections? n

Involute coordinate spacing 0.10000 mm

Fillet coordinate spacing 0.10000 mm



Normal fillet radius 1.0000 mm

Radial tip chamfer (w/o modification) 0.0000 mm

Normal tip radius 0.0000 mm


Molding shrinkage rate (spur gear) n cm/cm

Distance from origin to gear root for form 2.0000 mm grinding wheel coordinates Figure 4-1A is a plot of the involute, tip relief and fillet curves.


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Fig. 4-1A


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Figure 4-1B is a plot of the whole tooth. Note that we did not place tic marks at the intersections of the fillet and involute and the tip relief and involute. If you wish to mark the intersections, blank the “Distance from origin....” and “Mark.....intersections”. The model will not allow “tic” marks when producing grinding wheel coordinates as the coordinates of the marks would then be in the grinding wheel coordinate list.

Fig. 4-1B


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Figure 4-1C is the shape of the cross section of the grinding wheel required to produce the tooth form. The coordinates extend past the inside diameter of the tooth to allow for reasonable adjustments in the wheel depth while grinding. Fig. 4-1C

List 4 was made using “Send X-Y Coord List/File for Form Wheel” in the Plot and List Options tab of the data entry form (see page 35). The sheet shows the first 20 coordinate pairs.


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List 4

ASCII X,Y Form Griding Wheel Coordinates, mm XYform 2,0 2,.0272 2.0001,.2272 2.0002,.3272 2.0004,.3272 2.0007,.4272 2.0010,.5272 2.0014,.6272 2.0031,.6805 2.0139,.7799 2.0345,.8777 2.0648,.9729 2.1045,1.0647 2.1531,1.1520 2.2102,1.2341 2.2752,1.3100 2.3474,1.3791 2.4262,1.4406 2.5108,1.4939 2.6002,1.5385

Program 60-460—Internal Gear Coordinates Introduction · UTS Integrated Gear Software 8 Example 2...

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Transcript of Program 60-460—Internal Gear Coordinates Introduction · UTS Integrated Gear Software 8 Example 2...