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+ | ==== Gears ==== | ||

+ | |||

+ | ==== Face Width, F ==== | ||

+ | * "Face width is the width of the gear parallel to the axis of the gear. It is defined by the designer as one of the required //design decisions//. More is said about face width in Chapter 9, where strength of the teeth is considered. For now, we can state that a nominal value for face width is approximately F ~ 12 / P<sub>d</sub>, but a wide range is permitted." (Machine Elements in Mechanical Design, 5th by Robert L. Mott, p. 282) | ||

+ | |||

+ | ==== Diametral Pitch ==== | ||

+ | * {{engineer-mechanical:inventor-gears:gearsizediametralpitch.png|Figure 1-0 Gear-tooth size as a function of diametral pitch}} | ||

+ | * Barber-Colman Company, Loves Park, IL, referenced from Machine Elements in Mechanical Design, 5th by Robert L. Mott, p. 279. | ||

+ | |||

+ | |||

+ | === Spur Gears - Drafting and Design === | ||

+ | * [[http://www.learnengineering.org/2013/02/spur-gear-design.html|Learn Engineering - Spur Gear Design]] | ||

+ | * [[http://myagma.agma.org/iweb/Purchase/ProductDetail.aspx?Product_code=917-B97|AGMA 917-B97 Design Manual for Parallel Shaft Fine-Pitch Gearing]]. This manual provides guidance for the design of fine-pitch gearing of the following types: Diametral pitch from 20 to 120; Spur and helical (parallel axis); External, internal and rack forms. ([[http://jefferyjjensen.com/secure/pdf/drafting/AmericanGearManufacturersAssociation-AGMA/AGMA917-B97DesignManualForParallelShaftFinePitchGearing.pdf|secure PDF]]) | ||

+ | |||

+ | == Part 1 - Determine the four Gear Circle Diameters (Pitch, Outside/Addendum, Root, and Base) == | ||

+ | * {{engineer-mechanical:inventor-gears:spurgearnomenclature.png|Figure 1-0 Spur Gear Nomenclature}} | ||

+ | * {{engineer-mechanical:inventor-gears:spurgearvocabulary.png|Figure 1-0 Spur Gear Vocabulary Quiz}} | ||

+ | * Step 1 - select size of gear teeth (**Diametral Pitch, //P//**) | ||

+ | * "Diametral Pitch (D.P.). This is certainly by far the most common and the most useful method of notation for small gears and the definition of a small gear in this case is any gear that the model engineer or backyard amateur is likely to handle. The diametral pitch is simply the number of teeth a wheel has per inch of pitch diameter. For example, if a gear has a P.C.D. (Pitch Circle Diameter) of 2in. diameter and has 40 teeth then it is said to be 20 D.P. If the number where to be 40 on a P.C.D. of 1 in. diameter then the D.P. would be 40. **D.P.s are usually whole numbers and, more often than not, even numbers.** It is not usual to encounter an odd D.P. number after 10 D.P. has been reached and gears below 10 D.P. will in the main be larger than the amateur will want to cut. This arrangement makes the setting out of gear train centres easy. For example, should it be decided to product two gears to give a ratio of 3:1 and 20 D.P. was chosen for the tooth size, two gears - one with 20 teeth and one with 60 teeth - would appear to be satisfactory. The P.C.D. of the 20 tooth would be 1 in. whicle the P.C.D. of the 60 tooth would be 3 in. This would mean that the gear centre would be 2in., or half of the addition of the two P.C.Ds. (Gears and Gear Cutting by Law, p.30) | ||

+ | * "Diametral pitch is not a pitch in the same sense as the preceding pitches. It represents the size of the tooth. The larger the numeric value of the diametral pitch, the smaller the size of the gear tooth... Many fine-pitch gears are produced by means of generating tooling. Even gears produced by molding, casting or stamping are intended to have teeth which are the same as if they were generated. Gear generating tools, such as hobs, shaper cutters and racks, have a basic tooth form which, when cutting a gear on a generating machine, produces involute gear teeth. Although a hob, for example, can generate gears having any desired number of teeth, it can only produce a single normal diametral pitch and normal profile angle. Since several tools may be needed to produce a job lot of gears, it is generally desirable to select a diametral pitch for which most gear shops are likely to have tooling. This may avoid the need to purchase special tooling. **Thus the following have become recommended normal diametral pitches, //P<sub>nd</sub>// = 20, 24, 32, 40, 48, 64, 72, 80, 96, 120** ([[http://myagma.agma.org/iweb/Purchase/ProductDetail.aspx?Product_code=917-B97|AGMA 917-B97 Design Manual for Parallel Shaft Fine-Pitch Gearing]], p. 16) ([[http://jefferyjjensen.com/secure/pdf/drafting/AmericanGearManufacturersAssociation-AGMA/AGMA917-B97DesignManualForParallelShaftFinePitchGearing.pdf|secure PDF]]) | ||

+ | * Dudley's Handbook of Practical Gear Design and Manufacture, 2nd ([[http://jefferyjjensen.com/secure/pdf/Drafting/DudleysHandbookOfPracticalGearDesignAndManufacture2nd-Radzevich.pdf|secure PDF]]) gives the following Diametral Pitch, D recommendations | ||

+ | * {{engineer-mechanical:inventor-gears:dudleyshandbookp124.png|Figure 1-0 Recommended Diametral Pitches}} | ||

+ | * "Pitch Diameters Obtained with Diametral Pitch System.-The diametral pitch system is arranged to provide a series of standard tooth sizes, the principle being similar to the standardization of screw thread pitches. Inasmuch as **there must be a whole number of teeth on each gear**, the increase in pitch diameter per tooth varies according to the pitch. For example, the pitch diameter of a gear having, say, 20 teeth of 4 diametral pitch, will be 5 inches; 21 teeth, 5 1/4 inches; and so on, the increase in diameter for each additional tooth being equal to 1/4 inch for 4 diametral pitch. Similarly, for 2 diametral pitch the variations for successive numbers of teeth would equal 1/2 inch, and for 10 diametral pitch the variations would equal 1/10 inch, etc." (Machinery's Handbook, 27th Edition by Industrial Press, p. 2034-5 [[http://jefferyjjensen.com/secure/pdf/drafting/machineryshandbook/MachinerysHandbook27th-IndustrialPress.pdf|secure PDF]]) | ||

+ | * select a Diametral Pitch, //P//. Must be a whole number like 1, 2, 3, 4,.... | ||

+ | * "Since diametral pitch is used only with U.S. units, it is expressed as teeth per inch." (Shigley's Mechanical Engineering Design, 8th, p. 656) | ||

+ | * Figure showing comparative sizes and shape of gear teeth. The higher the //P// the smaller the teeth | ||

+ | * "Spur gear design normally begins with selecting pitch diameters to suit the required speed ratio, center distance, and space limitations. The size of the teeth (the diametral pitch) depends on the gear speeds, gear materials, horsepower to be transmitted, and the selected tooth form." (Technical Drawing with Engineering Graphics, 14th Ed by Giesecke, Mitchell, Spencer, Hill, Dygdon, Novak, & Lockhart, p. 653) | ||

+ | * {{engineer-mechanical:inventor-gears:machhand27th-gears-p2033.png|Figure 1-0 Comparative Sizes and Shape of Gear Teeth}} | ||

+ | * {{engineer-mechanical:inventor-gears:comparegearteeth.jpg|Figure 1-0 Comparative Sizes of Gear Teeth - Involute}} | ||

+ | * [[http://books.google.com/books?id=Ko9KAAAAMAAJ&pg=PA10&img=1&zoom=3&hl=en&sig=ACfU3U0BL0pwC-PI-oO5q_SFCWTwaFMswA&ci=82%2C139%2C859%2C1327&edge=0|Reference - Comparative Sizes of Gear Teeth - Involute]] | ||

+ | * [[http://books.google.com/books?id=Ko9KAAAAMAAJ&pg=PP1#v=onepage&q&f=false|Formulas in Gearing by Charles C. Stutz, p. 10]] | ||

+ | * "Diametral pitch is the ratio of the number of teeth to the number of inches in the pitch diameter in the plane of rotation, or the number of gear teeth to each inch of pitch diameter. Normal diametral pitch is the diametral pitch as calculated in the normal plane, or the diametral pitch divided by the cosine of the helix angle." (Machinery's Handbook, 27th Edition by Industrial Press, p. 2030 [[http://jefferyjjensen.com/secure/pdf/drafting/machineryshandbook/MachinerysHandbook27th-IndustrialPress.pdf|secure PDF]]) | ||

+ | * "Diametral and Circular Pitch Systems.-Gear tooth system standards are established by specifying the tooth proportions of the basic rack. The diametral pitch system is applied to most of the gearing produced in the United States. If gear teeth are larger than about one diametral pitch, it is common practice to use the circular pitch system. The circular pitch system is also applied to cast gearing and it is commonly used in connection with the design and manufacture of worm gearing." (Machinery's Handbook, 27th Edition by Industrial Press, p. 2034 [[http://jefferyjjensen.com/secure/pdf/drafting/machineryshandbook/MachinerysHandbook27th-IndustrialPress.pdf|secure PDF]]) | ||

+ | * Step 2 - select **Number of Teeth, N** | ||

+ | * Number of teeth must be a multiple of diametral pitch, //P// | ||

+ | * Number of teeth of large gear/wheel, N<sub>G</sub>. Say //P// = 4, then N<sub>G</sub> must be a multiple of 4 (i.e. 4, 8, 12, 16, 20,...). Lets use N<sub>G</sub> = 44. | ||

+ | * Number of teeth of small gear/pinion, N<sub>P</sub>. Also, N<sub>P</sub> must be a multiple of 4. Lets use N<sub>P</sub> = 24 | ||

+ | * "The minimum number of teeth N<sub>min</sub> of standard proportion that may be cut without undercut is: | ||

+ | * N<sub>min</sub> = 2P csc<sup>2</sup><html>φ</html>[a<sub>H</sub>- r<sub>t</sub>(1 - sin<html>φ</html>)] | ||

+ | * where a<sub>H</sub> = cutter addendum; r<sub>t</sub> = radius at cutter tip or corners | ||

+ | * <html>φ</html> = cutter pressure angle; and P = diametral pitch. | ||

+ | * (Machinery's Handbook, 27th Edition by Industrial Press, p. 2058 [[http://jefferyjjensen.com/secure/pdf/drafting/machineryshandbook/MachinerysHandbook27th-IndustrialPress.pdf|secure PDF]]) | ||

+ | * Step 3 - calculate **gear ratio, m<sub>G</sub>** | ||

+ | * "The teeth on mating gears must be of equal width and spacing, so the number of teeth on each gear, N, is directly proportional to its pitch diameter, or m<sub>G</sub> = N<sub>G</sub> / N<sub>P</sub>" (Technical Drawing with Engineering Graphics, 14th Ed by Giesecke, Mitchell, Spencer, Hill, Dygdon, Novak, & Lockhart, p. 648) | ||

+ | * Example m<sub>G</sub> = 44/24 = 11/6 or 11:6 (read as 11 to 6) | ||

+ | * Step 4 - select a common **Pressure Angle, f** (14.5°, 20° or 25°) between the larger gear/wheel and the small gear/pinion | ||

+ | * "The angle f is called the pressure angle, and it usually has values of 20° or 25°, though 14.5° was once used." (Shigley's Mechanical Engineering Design, 8th, p. 659) | ||

+ | * "The involute tooth form depends on the pressure angle, which was ordinarily 14.5° and is now typically 20° or 25°. This pressure angle determines the size of the base circle; from this the involute curve is generated." (Technical Drawing with Engineering Graphics, 14th Ed by Giesecke, Mitchell, Spencer, Hill, Dygdon, Novak, & Lockhart, p. 650) | ||

+ | * "The dimensions relating to tooth height are for full-depth 14.5° (which are becoming outmoded) or with 20° or 25° involute teeth. Of course, meshing gears must have the same pressure angle." (Technical Drawing with Engineering Graphics, 14th Ed by Giesecke, Mitchell, Spencer, Hill, Dygdon, Novak, & Lockhart, p. 648) | ||

+ | * Step 5 - calculate **Pitch Diameter (D, D<sub>G</sub>, D<sub>P</sub>)** (circle 1 of 4) | ||

+ | * Is the diameter of the pitch circle of the gear or pinion | ||

+ | * Pitch Diameter, D = Number of Teeth, N / Diametral Pitch, P | ||

+ | * D<sub>G</sub> = N<sub>G</sub> / P = 44/4 = 11" | ||

+ | * D<sub>P</sub> = N<sub>P</sub> / P = 24/4 = 6" | ||

+ | * Center Distance, C = (D<sub>G</sub> + D<sub>P</sub>)/2 = R + r = (11" + 6")/2 = 8.5" | ||

+ | * {{engineer-mechanical:inventor-gears:machhand27th-pitchdia-p2033.png|Figure 2-0 Pitch Circles}} | ||

+ | * Step 6 - calculate **outside diameter, D<sub>O</sub> (Addendum Circle)** (circle 2 of 4) | ||

+ | * D<sub>O</sub> = D + 2a where a = Addendum | ||

+ | * Diameter of addendum circle, equal to pitch diameter plus twice the addendum. | ||

+ | * a = 1///P//, example a = 1/4 | ||

+ | * D<sub>OG</sub> = D<sub>G</sub> + 2a = 11" + 2(1/4)" = 11.5" for the larger gear/wheel | ||

+ | * D<sub>OP</sub> = D<sub>P</sub> + 2a = 6" + 2(1/4)" = 6.5" for the smaller gear/pinion | ||

+ | * "Outside diameter is the diameter of the circle that contains the tops of the teeth of external gears." (Machinery's Handbook, 27th Edition by Industrial Press, p. 2031 [[http://jefferyjjensen.com/secure/pdf/drafting/machineryshandbook/MachinerysHandbook27th-IndustrialPress.pdf|secure PDF]]) | ||

+ | * Step 7 - calculate the **Root Diameter, D<sub>R</sub>** (circle 3 of 4) | ||

+ | * D<sub>R</sub> = D - 2b where b = Dedendum | ||

+ | * b = 1.25///P// when f = 20° or 25°, example b = 1.25/4 = 0.3125 | ||

+ | * b = 1.157///P// when f = 14.5° | ||

+ | * D<sub>RG</sub> = D<sub>G</sub> - 2b = 11" - 2(0.3125") = 10.375" | ||

+ | * D<sub>RP</sub> = D<sub>P</sub> - 2b = 6" - 2(0.3125") = 5.375" | ||

+ | * Step 8 - calculate the **base circle diameter, D<sub>B</sub>** (circle 4 of 4) | ||

+ | * "The involute is generated from the base circle the diameter" (Handbook of Gear Design, 2nd by Gitin M. Maitra, Appendix A - Construction of Involute Gear Tooth) | ||

+ | * D<sub>B</sub> = D cos f | ||

+ | * D<sub>BG</sub> = D<sub>G</sub> cos 20° = 11" cos 20° = 10.3366" | ||

+ | * D<sub>BP</sub> = D<sub>P</sub> cos 20° = 6" cos 20° = 5.6382" | ||

+ | |||

+ | == Part 2 - Drafting the four Gear Circles == | ||

+ | * Step 9 - Drafting Gear Teeth | ||

+ | * {{engineer-mechanical:inventor-gears:mechdraw10th-p406.png|Figure 2-0 Involute Circle}} | ||

+ | * "Involute gears are interchangeable when they have set conditions that allow them to mesh properly. The four conditions for interchanging involute gears are the following: the same diametral pitch, the same pressure angle, the same addendum, and the same dedendum." (Mechanical Drawing, 10th Ed by French, Svensen, Helsel, & Urbanick, p. 407) | ||

+ | * [[http://forums.autodesk.com/autodesk/attachments/autodesk/78/338824/1/Spur%20Gear%20Tutorial.pdf|13 Easy Step by Step Tutorial to Model Involute Spur Gear in IV 9]] | ||

+ | * [[http://www.sdp-si.com/|SDP/SI Gear Catalog]] | ||

+ | * [[http://gearhead22.netau.net|True Involute Gear Services]] | ||

+ | * Autodesk Community - Inventor General [[http://forums.autodesk.com/t5/Inventor-General/True-involute-gear-generation/td-p/2469035|True involute gear generation]] | ||

+ | * Background | ||

+ | * "The gear ratio is also the pitch diameter of the gear divided by the pitch diameter of the pinion. For example, if the gear has a pitch diameter of 4 and the pinion has a pitch diameter of 1, then the gear ratio is 4:1, and the pinion ratio is 1:4." (Technical Graphics Communication, 4th by Bertoline, Wiebe, Hartman, and Ross, p. 1112) | ||

+ | |||

+ | == Approximate Involute Curve Method Spur Gears in Technical Drawing == | ||

+ | * How to draw a spur gear tooth from Technical Drawing, 4th by Goetsch and Chalk, p. 596 ([[http://jefferyjjensen.com/secure/pdf/drafting/TechnicalDrawing4th-Goetsch/TechDraw4thCh16-Gears.pdf|secure PDF]]) | ||

+ | * <HTML><iframe width="560" height="315" src="https://www.youtube.com/embed/BiK2Em8seTw" frameborder="0" allowfullscreen></iframe></HTML> | ||

+ | * [[http://jefferyjjensen.com/wikidata/inventor/videos/SpurGear-ApproxInvoluteCurve/SpurGear-ApproxInvoluteCurve/SpurGear-ApproxInvoluteCurve.mp4|SpurGear-ApproxInvoluteCurve.mp4]] | ||

+ | * Step 0: Draw the following Spur Gear | ||

+ | * {{engineer-mechanical:inventor-gears:gearapproxinvolutestep00.png|Figure 3-0 Drafting a Spur Gear - Finished Product}} | ||

+ | * Step 1: Spur gear specifications | ||

+ | * Diametral Pitch (tooth size), P = 4 | ||

+ | * Pitch Diameter, D<sub>P</sub> = 6.0" | ||

+ | * Number of Teeth, N = 24 | ||

+ | * Pressure angle, f = 20° | ||

+ | * Step 2: Calculate Base Circle | ||

+ | * Base Circle Diameter, D<sub>b</sub> = D<sub>P</sub> cos f | ||

+ | * D<sub>b</sub> = 6.0" cos 20° = **5.638"** (R<sub>b</sub> = 5.638" / 2 = 2.819") | ||

+ | * Draw the Base Circle in Inventor (use color Blue) | ||

+ | * Step 3: Calculate approximate involute profile curve radius (R<sub>approx involute curve</sub>) | ||

+ | * R<sub>approx involute curve</sub> = Pitch Diameter / 8 = D / 8 = 6.0" / 8 = 0.75" | ||

+ | * Draw two circles with (R<sub>approx curve</sub> = 0.75") anywhere outside the Base Circle (use color Green) | ||

+ | * {{engineer-mechanical:inventor-gears:gearapproxinvolutestep03.png|Figure 1-0 Drafting a Spur Gear - Base and Approximate Involute Circles}} | ||

+ | * Step 4: Apply coincident constraints between edge of Base Circle and center of green circle (approximate involute curve) | ||

+ | * apply a coincident constraint between the center of the 0.75" radius circle and anywhere along the base circle | ||

+ | * Step 5: Draw Pitch Circle, D<sub>P</sub> = 6.0" (use color Pink) | ||

+ | * Step 6: Draw the radial lines for the circular pitch arc | ||

+ | * draw two lines from the center of the pitch circle to the edge of the pitch circle (pink circle) | ||

+ | * assign a dimension to the tooth width angle = 360° / (N * 2) = 360° / (24 * 2) = 7.5° | ||

+ | * {{engineer-mechanical:inventor-gears:gearapproxinvolutestep06.png|Figure 2-0 Drafting a Spur Gear - Pitch Circle and Tooth Angle}} | ||

+ | * Alternative - Calculate Circular Pitch, p distance (not chord distance) | ||

+ | * Circular Pitch, //p// = p / Diametral Pitch ? //P// = 3.14159 / 4 = 0.785" | ||

+ | * tooth thickness = p / 2 = 0.785" / 2 = 0.392" | ||

+ | * "Circular pitch is the distance on the circumference of the pitch circle, in the plane of rotation, between corresponding points of adjacent teeth. The length of the arc of the pitch circle between the centers or other corresponding points of adjacent teeth." (Machinery's Handbook, 27th Edition, Industrial Press, p. 2030) | ||

+ | * Step 7: add two points at the intersection of the radial lines with the Pitch Circle (use black color) | ||

+ | * Step 8: apply another coincident constraint between these two points and the approximate involute circles with r<sub>approx. involute</sub> = 0.75" | ||

+ | * {{engineer-mechanical:inventor-gears:gearapproxinvolutestep08.png|Figure 3-0 Drafting a Spur Gear - Coincident Constraint}} | ||

+ | * Step 9: delete the radial lines (pink) | ||

+ | * Step 10: create two new radial lines (color blue) from the center of the base circle (blue circle) and the intersection with the approximate involute circles (green circles). | ||

+ | * {{engineer-mechanical:inventor-gears:gearapproxinvolutestep10.png|Figure 3-0 Drafting a Spur Gear - Coincident Constraint}} | ||

+ | * Step 11: calculate the tooth dedendum, b height | ||

+ | * b = 1.250 / P = 1.250 / 4 = 0.3125" | ||

+ | * Step 12: calculate the root circle diameter | ||

+ | * D<sub>R</sub> = D - 2b = 6" - 2 * 0.3125" = 5.375" | ||

+ | * Step 13: draw the root circle (color red) | ||

+ | * Step 14: trim the approximate involute circle (green circle) between the base circle (blue circle) and the root circle (red circle) | ||

+ | * {{engineer-mechanical:inventor-gears:gearapproxinvolutestep14.png|Figure 3-0 Drafting a Spur Gear - Root Circle and Trim}} | ||

+ | * Step 15: draw the outer circle (color orange) | ||

+ | * D<sub>O</sub> = (N + 2) / P = (24 + 2) / 4 = 6.5" | ||

+ | * Step 16: trim top of gear tooth | ||

+ | * delete outer circle (orange color) | ||

+ | * delete approximate involute circle (green circle) | ||

+ | * delete pitch circle (pink color) | ||

+ | * delete work points (black color) | ||

+ | * delete base circle (blue color) | ||

+ | * {{engineer-mechanical:inventor-gears:gearapproxinvolutestep16.png|Figure 3-0 Drafting a Spur Gear - Root Circle and Trim}} | ||

+ | * Step 17: draw radial lines (red color) | ||

+ | * Step 18: apply dimension, interior angle of 360° / Number of Teeth, N | ||

+ | * interior tooth angle = 360° / 24 = 15° | ||

+ | * {{engineer-mechanical:inventor-gears:gearapproxinvolutestep18.png|Figure 3-0 Drafting a Spur Gear - Root Circle and Trim}} | ||

+ | * Step 19: trim blue radial lines and root circle (red). Basically trim everything until left with a single tooth and blank sides | ||

+ | * Step 20: apply root fillet, r<sub>f</sub> | ||

+ | * r<sub>f</sub> = 0.3 / P = 0.3 / 4 = 0.075" | ||

+ | * {{engineer-mechanical:inventor-gears:gearapproxinvolutestep20.png|Figure 3-0 Drafting a Spur Gear - Root Circle and Trim}} | ||

+ | * Step 21: finish sketch | ||

+ | * Step 22: extrude tooth wedge say 1" | ||

+ | * "Face width-to-diameter ratio. To achieve more uniform tooth contact along the face, the ratio of face width to diameter should usually be held to below 2.0." (AGMA 917-B97, p. 29) | ||

+ | * Face Width, F = 2 * Pitch Diameter, D | ||

+ | * "Usually the face width of one of the gears is made wider to allow for axial misalignment and still maintain full face contact. The increase in face width is usually made to the pinion because it requires less additional material." (AGMA 917-B97, p. 29) | ||

+ | * Advantages of helical gears: "Generally quieter than spur gears if the active face width is greater than one axial pitch." (AGMA 917-B97, p. 25) | ||

+ | * {{engineer-mechanical:inventor-gears:gearapproxinvolutestep22.png|Figure 3-0 Drafting a Spur Gear - Root Circle and Trim}} | ||

+ | * Step 24: use circular pattern for the number of teeth, N = 24 | ||

+ | * {{engineer-mechanical:inventor-gears:gearapproxinvolutestep24.png|Figure 3-0 Drafting a Spur Gear - Root Circle and Trim}} | ||

+ | * Reference | ||

+ | * Technical Drawing, 4th Edition by Goesck ([[http://jefferyjjensen.com/secure/pdf/drafting/TechnicalDrawing4thworkbook-Chalk/TechDrawCh16.pdf|secure PDF]]) | ||

+ | |||

+ | == Spur Gear and Inventor Design Accelerator == | ||

+ | * Autodesk Inventor 2014 Help - [[http://help.autodesk.com/view/INVNTOR/2014/ENU/?guid=GUID-CAB3855A-B6B6-44AA-978F-D086217CF2B3|Spur Gears Component Generator]] | ||

+ | * "**Module**. Older text books quote the module as being the reciprocal of the D.P. (Diametral Pitch) but more recently it has become the 'metric' way of quoting the size of the teeth. The module can be said to be the pitch diameter in millimetres divided by the number of teeth, or to put it the other way round, the P.C.D. (Pitch Circle Diameter) in millimetres is the module number multiplied by the number of teeth in the gear. As there are 25.4 millimetres to one inch then a number 1 module is equal to 25.4 D.P., a number 2 module would be 12.7 D.P. whilst a .5 module would be 50.4 D.P." [[http://books.google.com/books/about/Gears_and_Gear_Cutting.html?id=5opONwAACAAJ|Gears and Gear Cutting, Workshop Practice Series 17 by Ivan Law, 1990]] by Argus Books ([[http://jefferyjjensen.com/secure/pdf/drafting/GearsAndGearCutting-Law.pdf|secure PDF]]) | ||

+ | * Create the spur gear (pinion and gear/wheel) in Figure 1-0 using the Inventor Design Accelerator. | ||

+ | * Problem is from [[https://shar.es/1ZlrMH|Fundamentals of Modern Drafting, 1st by Wallach, 2003]] | ||

+ | * {{engineer-mechanical:inventor-gears:funddraftp386.png|Figure 1-0 Fundamentals of Modern Drafting - Figure 20-54 Draw the pinion and spur gear}} | ||

+ | * {{engineer-mechanical:inventor-gears:dudleyshandbookp117a.png|Figure 2-0 Basic Tooth Proportions of Spur Gears, AGMA and ASA Standard System}} | ||

+ | * Formulas needed to calculate inputs for the Inventor Design Accelerator | ||

+ | * {{engineer-mechanical:inventor-gears:machhandp2033and5.png|Figure 2-0 Machinery's Handbook, 27th Edition page 2033 and 2035}} | ||

+ | * {{engineer-mechanical:inventor-gears:machhand27th-p2035.png|Figure 2-0 Machinery's Handbook, 27th Edition page 2035 and 2036}} | ||

+ | * Step 0. Assume pressure angle, f = 20° | ||

+ | * Step 1. Calculate the Gear Ratio, m<sub>G</sub> | ||

+ | * m<sub>G</sub> = D<sub>G</sub>/D<sub>P</sub> = 5.25"/3.75" = 1.4 | ||

+ | * Step 2. Calculate the Center distance, C | ||

+ | * C = (D<sub>G</sub> + D<sub>P</sub>)/2 | ||

+ | * D<sub>G</sub> = 5.25" | ||

+ | * D<sub>P</sub> = 3.75" | ||

+ | * C = (5.25" + 3.75")/2 = 4.5" | ||

+ | * Step 3. Given the Outside/Addendum Diameter, D<sub>O</sub> | ||

+ | * D<sub>OG</sub> = Outside Diameter of large gear/wheel/spur = 6" | ||

+ | * D<sub>OP</sub> = Outside Diameter of small pinion gear = 4.5" | ||

+ | * Step 4. Calculate Addendum, a | ||

+ | * D<sub>O</sub> = D + 2a ? a = ( D<sub>O</sub> - D ) / 2 | ||

+ | * a<sub>G</sub> = ( D<sub>OG</sub> - D<sub>G</sub> ) / 2 = ( 6" - 5.25" ) / 2 = 0.375" | ||

+ | * a<sub>P</sub> = ( D<sub>OP</sub> - D<sub>P</sub> ) / 2 = ( 4.5" - 3.75" ) / 2 = 0.375" | ||

+ | * for gears to mesh, must have the same gear tooth profile, that is Addendum heights are equal, a<sub>G</sub> = a<sub>P</sub> | ||

+ | * Step 5. Calculate Diametral Pitch, P | ||

+ | * a = 1 / P ? P = 1 / a | ||

+ | * P = 1 / 0.375 = 2.67 | ||

+ | * Given P = 21/32 = 0.65625 | ||

+ | * so, why aren't these values the same? | ||

+ | * Step 6. Inventor Assembly ? Design ? Spur Gear | ||

+ | * Design guide: Module and Number of Teeth | ||

+ | * Pressure Angle: 20° | ||

+ | * Desired Gear Ratio: 1.4 | ||

+ | * Center Distance: 4.5" | ||

+ | * {{engineer-mechanical:inventor-gears:funddraftp386-errortable.png|Figure 1-0 Inventor Spur Gear Design Accelerator}} | ||

+ | * {{engineer-mechanical:inventor-gears:funddraftp386-errorfig.png|Figure 2-0 Inventor Spur Gear showing Conflicts}} | ||

+ | * {{engineer-mechanical:inventor-gears:spurgeardesignaccpreview.png|Figure 1-0 Inventor Spur Gear Design Accelerator Preview}} | ||

+ | |||

+ | == Spur Gear Calculations == | ||

+ | * Background | ||

+ | * Angular coordinate is expressed in radians (rad) or occasionally in degrees (°) or revolutions (rev) | ||

+ | * 1 rev = 2p rad = 360° (Vector Mechanics for Engineers Statics and Dynamics 9th by Beer, p. 919) | ||

+ | * {{engineer-mechanical:inventor-gears:understandgears.png|Figure 1-0 Understanding Gears for Calculations}} | ||

+ | * Example: D<sub>G</sub> = 27" and D<sub>P</sub> = 9", what is the gear ratio, m<sub>G</sub> | ||

+ | * Answer: m<sub>G</sub> = D<sub>G</sub> / D<sub>P</sub> = 27" / 9" = 3:1 | ||

+ | * (see Technical Drawing with Engineering Graphics 14th Edition by Giesecke, p. 648) | ||

+ | * Discussion of angular momentum, see [[http://www.dsusd.k12.ca.us/users/phealy/physics/Ebook/htm/_cp9e.htm|Conceptual Physics, 9th by Hewitt]] | ||

+ | * Example: D<sub>G</sub> = 27" and D<sub>P</sub> = 9" and n<sub>P</sub> = ?<sub>P</sub> = 1725 rpm, what is the angular velocity of the large gear/wheel (n<sub>G</sub>) | ||

+ | * Answer: n<sub>G</sub> = n<sub>P</sub> (D<sub>P</sub> / D<sub>G</sub>) = 1725 rpm (9" / 27") = 575 rpm | ||

+ | * (see Technical Drawing with Engineering Graphics 14th Edition by Giesecke, p. 648) | ||

+ | * {{engineer-mechanical:inventor-gears:markscalcsp425.png|Figure 1-0 Spur Gear Calculations}} | ||

+ | * {{engineer-mechanical:inventor-gears:markscalcsp426a.png|Figure 2-0 Spur Gear Calculations}} | ||

+ | * {{engineer-mechanical:inventor-gears:markscalcsp426b.png|Figure 3-0 Spur Gear Calculations}} | ||

+ | * {{engineer-mechanical:inventor-gears:markscalcsp427a.png|Figure 4-0 Spur Gear Calculations}} | ||

+ | * {{engineer-mechanical:inventor-gears:markscalcsp427b.png|Figure 5-0 Spur Gear Calculations}} | ||

+ | * {{engineer-mechanical:inventor-gears:machhand27th-p2540.png|Figure 6-0 Greek letters}} | ||

+ | |||

+ | == Gear Manufactures and Reference == | ||

+ | * Manufactures | ||

+ | * [[http://www.wmberg.com|WM Berg]] Robert Marszalkowski - Application Engineering, 414-747-5808, wmbergtechsupport@wmberg.com, 5138 S. International Dr, Cudahy WI 53110 | ||

+ | * [[http://www.winzelergear.com|Winzeler Gear]] producer of stamped metal gears for radio, appliance and toy industries. email: jwinzelergear.com, phone: 708-867-7971, 355 W Wilson Ave, Harwood Heights, IL 60706 | ||

+ | * [[http://www.sdp-si.com|Stock Drive Products and Sterling Instrument (SDP/SI)]] | ||

+ | * [[https://sdp-si.com/eStore/Catalog/PartNumber/A%201M%202-Y24056|A 1M 2-Y24056 Plastic Spur Gear]] Diametral Pitch, D=24 (24 and 32 are very common for SDP/SI) | ||

+ | * Shipping and handling cost was $11.41 for just two plastic gears | ||

+ | * [[http://www.khkgears.co.jp/en|Kohara Fear Industry Co., Ltd]] and [[http://www.khkgears.co.jp/en/gear_technology/pdf/gear_guide_060817.pdf|Introduction to Gears]] | ||

+ | * [[http://moorecustomgear.com/|Moore Machine and Gear, Inc]] Alan Moore, email: moorecustomgear@gmail.com or mooregear@insightbb.com recommends Stock Drive Products / Sterling Instrument 800-645-1144 for low quantities of gears | ||

+ | * [[http://omnigearandmachine.com/|Omni Gear & Machine Corp]] email: info@omnigear.us, John Hall (jhall@omnigear.us) | ||

+ | * [[http://www.precipart.com|Precipart]] email: gearedsolutions@precipart.com <strike>info@precipart.com</strike> | ||

+ | * [[http://rapidgear.com|Rapid Gear]] email: dave.scapinello@rapidgear.com in Canada | ||

+ | * [[http://qtcgears.com|Quality Transmission Components]] email: qtcsupport@qtcgears.com | ||

+ | * [[http://www.ugaco.com|United Gear and Assembly]] email: <strike>customerservice@ugaco.com</strike> | ||

+ | * [[http://wgear.com|Worcester Gears & Racks]] email: <strike>mail@wgear.com</strike> | ||

+ | * [[http://www.americangear.net|American Gear]] | ||

+ | * [[http://www.gearmfg.com|Gear Manufacturing]] | ||

+ | * [[http://www.akrongear.com|Akron Gear]] | ||

+ | * [[http://www.geartec.com|Gear Tech]] | ||

+ | * [[http://www.rpmachine.com|RP Machine]] | ||

+ | * [[http://www.ashgear.com|Ash Gear]] | ||

+ | * [[http://www.emergencygears.com|Emergency Gears]] | ||

+ | |||

+ | * References | ||

+ | * [[http://www.crcpress.com/product/isbn/9781439866016|Dudley's Handbook of Practical Gear Design and Manufacture, 2nd Edition]] by Stephen P. Radzevich ([[http://jefferyjjensen.com/secure/pdf/Drafting/DudleysHandbookOfPracticalGearDesignAndManufacture2nd-Radzevich.pdf|secure PDF]]) | ||

+ | * [[http://mhprofessional.com/product.php?isbn=0071433287|CAM Design Handbook by Harold A. Rothbart]], Publisher McGraw-Hill 2004, ISBN 0-07-143328-7 ([[http://jefferyjjensen.com/secure/pdf/drafting/CAMDesignHandbook-Rothbart.pdf|secure PDF]]), no discussion on spur gears. | ||

+ | * Excellent Resource - [[http://books.google.com/books/about/Gears_and_Gear_Cutting.html?id=5opONwAACAAJ|Gears and Gear Cutting, Workshop Practice Series 17 by Ivan Law, 1990]] by Argus Books ([[http://jefferyjjensen.com/secure/pdf/drafting/GearsAndGearCutting-Law.pdf|secure PDF]]) | ||

+ | * [[http://www.bh.com|Geometric And Engineering Drawing 2nd by K. Morling]] ([[http://jefferyjjensen.com/secure/pdf/drafting/GeometricAndEngineeringDrawing2nd-Morling.pdf|secure PDF]]) no discussion on spur gears. | ||

+ | * [[http://mhprofessional.com/product.php?isbn=0071436871|Machine Devices and Components Illustrated Sourcebook by Robert O. Parmley]] ([[http://jefferyjjensen.com/secure/pdf/drafting/MachineDevicesAndComponents-Parmley.pdf|secure PDF]]) | ||

+ | * [[http://mhprofessional.com/product.php?isbn=0071436898|Marks Calculations for Machine Design by Thomas H. Brown, Jr.]] ([[http://jefferyjjensen.com/secure/pdf/drafting/MarksCalculationsForMachineDesign-Brown.pdf|secure PDF]]) | ||

+ | * [[http://shop.mcgraw-hill.com/mhshop/productDetails?isbn=0070255954|Schaum's Outlines Machine Design by Allen S. Hall, Alfred R. Holowenko, and Herman G. Laughlin]] ([[http://jefferyjjensen.com/secure/pdf/drafting/SchaumsOutlinesMachineDesign-Hall.pdf|secure PDF]]) | ||

+ | * [[http://highered.mcgraw-hill.com/classware/ala.do?isbn=0073121932&alaid=ala_797360|Shigley's Mechanical Engineering Design 8th Ed by Richard G. Budynas and J. Keith Nisbett]] ([[http://jefferyjjensen.com/secure/pdf/drafting/ShigleyMechanicalEngineeringDesign-Budynas.pdf|secure PDF]]) | ||

+ | * [[http://www.geartechnology.com|Gear Technology]] | ||

+ | * [[http://www.powertransmission.com|Power Transmission]] | ||

+ | * American Gear Manufacturers Association (AGMA) | ||

+ | * AGMA 207.05 20-Degree Involute Fine-Pitch System for Spur and Helical Gears | ||

+ | * AGMA 201.02 and 201.02A Tooth proportions for Coarse-Pitch Involute Spur Gears | ||

+ | * [[http://learning.agma.org/store/seminar/seminar.php?seminar=6101|Fundamentals of Gearing]], AGMA 933-B03 Basic Gear Geometry | ||

+ | * AGMA 917-B97 Design Manual for Parallel Shaft Fine Pitch Gearing ([[http://jefferyjjensen.com/secure/pdf/Standards/AGMA917-B97DesignManualForParallelShaftFinePitchGearing.pdf|secure PDF]] | ||

+ | * AGMA 6022-C93 Design Manual for Cylindrical Wormgearing ([[http://jefferyjjensen.com/secure/pdf/Standards/AGMA6022-C93DesignManualCylindricalWormgearing.pdf|secure PDF]] | ||

+ | * [[http://books.google.com/books?id=3SsxAQAAMAAJ&printsec=frontcover#v=onepage&q&f=false|Involute Spur Gears by Earle Buckingham]] | ||

+ | * Mechanical Drawing, 10th Edition by French, Svensen, Helsel, & Urbanick, [[http://jefferyjjensen.com/secure/pdf/drafting/mechanicaldrawing10th-french/MechDraw10ed-Ch19.pdf|Chapter 19 Cams and Gears]] secure PDF]]) | ||

+ | * Technical Drawing, 4th Edition by Goetsch & Chalk, [[http://jefferyjjensen.com/secure/pdf/drafting/technicaldrawing4th-goetsch/techdraw4thch16-gears.pdf|Chapter 16 Gears]] secure PDF]] | ||

+ | * Technical Drawing, 4th Edition Workbook by Chalk, [[http://jefferyjjensen.com/secure/pdf/drafting/technicaldrawing4thworkbook-chalk/techdrawch16.pdf|Chapter 16 Workbook on Gears]] secure PDF]] | ||

+ | |||

+ | * Technical Graphics Communication, 4th Edition by Bertoline, Wiebe, Hartman, & Ross, ([[http://jefferyjjensen.com/secure/pdf/drafting/TechnicalGraphicsCommunication4th-Bertoline/TechGraph4thCh22.pdf|Chapter 22 Mechanisms: Gears, Cams, Bearing, and Linkages]] secure pdf) | ||

+ | |||

+ | * Youtube.com video [[http://www.youtube.com/watch?v=XZgsV0AZJJ0|Gears - How its Made]] | ||

+ | * Youtube.com video [[http://www.youtube.com/watch?v=qSxSJoBQht4|Gear Train Calculations]] | ||

+ | * {{engineer-mechanical:inventor-gears:mechdraw10thp405.png|Figure 1-0 Gear Tooth Interaction}} | ||

+ | * Gears can be animated using the Motion Constraint or the Contact Solver. The Motion Constraint just animates a rotation of the gear and requires the input of a correct gear ratio. The Contact Solver is a more realistic animation of the gears because the second gear will only move when there is contact with the first gear. In the case of the Motion Constraint, there is no contact and the gears just rotate. | ||

+ | * Step 1. Create //Base Plate.ipt// (5"x5" square with extruded thickness of 3/8"=0.375") | ||

+ | * Step 2. Create //Bearing Housing.ipt// | ||

+ | * {{engineer-mechanical:inventor-gears:bearinghousingdrawing.png|Figure 1-0 Bearing Housing Drawing}} | ||

+ | * Balloon Note 1 is for a chamfer of 0.062" | ||

+ | * {{engineer-mechanical:inventor-gears:bearinghousinghole.png|Figure 1-0 Hole in the Bearing Housing}} | ||

+ | * Step 3. Add the above parts to an Inventor Assembly and fully constraint the parts | ||

+ | * Add two instances of //Bearing Housing.ipt// | ||

+ | * Apply a mate-mate constraint between the top face of //Base Plate.ipt// and the bottom face of //Bearing Housing.ipt// | ||

+ | * Base Plate should be grounded | ||

+ | * Bearing Housing 1 is mate constraint 1.5" from the centerline of the housing to the edge of the base plate. Do this on two sides. | ||

+ | * Bearing Housing 2 is only mate constraint 1.5" from one edge of the base plate. Then apply a 3" mate constraint between the two bearing housing. | ||

+ | * {{engineer-mechanical:inventor-gears:bearinghousing.png|Figure 1-0 Bearing Housing and Base Plate}} | ||

+ | * Assemble ? Productivity - Degree of Freedom Analysis to confirm the assembly is fully constrained | ||

+ | * {{engineer-mechanical:inventor-gears:prepdesignaccelerator.gif|Figure 1-0 Animation to Constrain Base Plate to Bearing Housing}} | ||

+ | * Step 4. Add Bolted Connection | ||

+ | * **Design ? Bolted Connection** | ||

+ | * Design Tab: Type through all | ||

+ | * Design Tab: Placement - On Point | ||

+ | * Design Tab: Start Plane - select the top plane of the Bearing Housing (where the bolts will go) | ||

+ | * Design Tab: Termination - select the bottom of the Base Plate | ||

+ | * Design Tab: Thread - ANSI Unified Screw Threads - 0.164 #8 inch | ||

+ | * Design Tab: ANSI Oval Head Machine Screw applied to the Bearing Housing | ||

+ | * Design Tab: select to add a fastener, select ANSI Cross Recessed Oval Countersunk Head Machine Screw - Type I - inch | ||

+ | * Design Tab: //Click to add a fastener//, Regular helical Spring Lock Washer (Inch) | ||

+ | * Design Tab: //Click to add a fastener// - Hex machine screw nut - inch | ||

+ | * Design Tab: save as Templates Library by clicking the Add button, Bolted Connection name | ||

+ | * Step 5. Spur Gear Design Accelerator | ||

+ | * {{engineer-mechanical:inventor-gears:spurgeardesignaccel.gif|Figure 1-0 Animation showing the Spur Gear Design Accelerator}} | ||

+ | * Gear References | ||

+ | * Liansuo Xie, Ph.D. is the Global CAD Manager (lian.xie@marel.com 515-263-3331) at [[http://www.marel.com|Marel Meat Processing Inc]] and has written an Inventor add-in that creates the actual involute curve for the gear tooth. | ||

+ | * [[http://archive.org/details/0542_Around_the_Corner_05_54_57_29|Differential Gears]] by A Jam Handy Productions | ||

+ | * [[https://archive.org/details/0792_Horsepower_M00251_03_31_16_00|Horsepower (1937)]] by A Jam Handy Productions | ||

+ | * A Jam Handy - Jamison Handy - pioneer in the field in video education. | ||

+ | |||

+ | [[Category:Main]] | ||

+ | [[Category:Autodesk|Inventor]] | ||

+ | [[Category:Cams]] | ||