Program 60-610—Plastic Gear Geometry and Load Analysis ...Program 60-610—Plastic Gear Geometry and Load Analysis Introduction The primary purpose of this model is to provide an

Program 60-610—Plastic Gear Geometry and Load Analysis

Introduction The primary purpose of this model is to provide an accurate set of coordinates for use in plotting the final form of external 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 a gear set and the necessary tooling or as a “final visual” check of the detailed design processes that were used to produce the design. If load and material data is entered, an analysis of the load capacity will be made. Geometry

The gears may be hobbed with non-topping, semi-topping, tip relief or topping hobs, shaped with pinion type cutters or defined by a basic rack form for molding. (If molded, four different depth racks defined by the AGMA Plastic Gear Committee are built into the model as default values.) If the gears are post processed after hobbing or 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. Only if there is enough natural undercut (small pinions) will a satisfactory gear be produced under these conditions. These conditions must be checked by programs such as UTS Program 500. The hob (or basic rack) flank angle is measured from a normal to the hob (or basic rack) reference line. The shaper cutter tooth thickness is at the shaper reference pitch diameter, the protuberance and the tip radius are measured in the normal plane. The model will produce coordinates at intervals of about 0.050 times the Operating Normal Module (near the fillet/involute intersection the fillet coordinates are about one tenth of this). For example, a gear set with an operating normal module of one the coordinates would be spaced at about 0.050 mm intervals. For an operating normal module of 0.10 the coordinates would be spaced at about 0.005 mm intervals. The intersection between the involute flank and the fillet of the tooth and the intersection of the involute flank and any tip radius or modification will be calculated and marked on the plot of the tooth (if “Mark inv/fil intersections? and/or “Mark mod/inv intersections?” are set to 'y). (These diameters will also be displayed in the output column on the variable sheet.

UTS Integrated Gear Software

2

The coordinates for spur gears are the actual coordinates of the gears produced by the specified tools. For helical gears the coordinates are produced for the virtual spur gears in the operating normal plane. (In some very low tooth number helical pinions the error between the tooth thickness at the effective outside diameter or the involute-fillet tangent point and the virtual spur tooth will affect the accuracy of the plot of the teeth. In this case it is suggested that models 60-411, 60-104 and 60-410 also be used to analyze the geometry of the gear set. The model will notify you of this condition.) The model contains some warning messages that may stop execution of the program. (such as “Root Interference”) If it is desired to “visually” check the gears when these messages appear it is only necessary to 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 set has an undesirable condition or a condition making the set useless. The solution indicator on the Status Bar at the bottom of the screen will not read “OK” if this is the case. You will still get valid data on the variable sheet and, usually, a plot of the teeth. 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.

Load Analysis

Many fine pitch gears in today's market place are made of plastic. Plastics used as gear materials present some design problems not encountered with metal gears. However, plastic has some advantages that cannot be realized with metal gears.

The main disadvantages of plastic as a gear material are:

1. Load capacity due to wear and bending strength is low 2. Load capacity for pitting not well defined 3. Load capacity is reduced with increasing temperatures 4. High accuracy of form hard to achieve with molding 5. Form can change with time 6. Physical properties change appreciably with temperature 7. High thermal coefficients of expansion 8. High moisture coefficients of expansion for some materials 9. High tooling costs if molded 10. Difficult to mold in coarser pitches

Plastic Gear Geometry & Load Analysis 60-610

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The main advantages are: 1. Very low cost when injection molded 2. Low modulus of elasticity allows high aspect ratios 3. Low modulus of elasticity can reduce transmission error 4. Quieter than metal gears for same accuracy 5. Can be run without lubricants (with lower capacity) 6. Complex mechanical features can be molded with gear 7. Can tolerate chemical environments that metal cannot 8. Light weight and low inertia

For many plastic gear applications the following problems are of primary importance:

1. Low load capacity Difficult to design adequate gears in required space 2. Difficulty in obtaining adequate contact ratio Low contact ratio at max effective center distance 3. Oil bath lubrication is unusual in plastic gear applications due to cost constraints, etc 4. Grease on open gears would contaminate environment Food processors, printers, copiers, etc

If the same plastic (or plastics with nearly the same thermal and moisture coefficients of expansion) can be used for the gears and support elements the problem of large differences between maximum and minimum effective center distance due to thermal and moisture changes become much easier to control. The tooth geometry of coarse and fine pitch gears has been standardized by the AGMA and others. For many non-demanding applications the standard tooth proportions work well. However, if large center distance variations, high load capacity or smoother operation are required the standard tooth proportions may not be adequate. "Standard” hobs are, of course, desirable from a lead time and cost standpoint. However, on gear sets that must run with the possibility of large changes in center distance, large temperature ranges or changes in humidity the use of “non-standard” tooth proportions may well be a practical solution to the profile contact ratio problem.


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Strict attention to the tools to be used and a good analysis of the tooth form they are to produce will avoid many of the tooling problems associated with plastic gears. Any geometry problems inherent in the tooling can be found and corrected before the gears are cut. (Of course, if the gears are to be molded, the question of cutting tools would apply only to prototype parts.) In general, gears with high contact ratios will be quieter and smoother and will have higher load capacity. This reference may be helpful in the design and application of plastic gears and the data they furnish are used in this model: Bulletin B.1.1 - Spur Gears and Gearwheels Made From Hostaform® POM, Celanex® PBT and Gur® UHMWPE

Ticona GmbH Postfach 1561 65444 Kelsterbach Germany

U.S.A. Properties and Data from

Ticona 90 Morris Avenue Summit, NJ 07901-3956

Gearing standards: • DIN 3990 Calculation of Load Capacity of Cylindrical Gears December 1987 • ISO 6336 Calculation of Load Capacity of Spur and Helical Gears 1991

Note: Calculation of tooth load intensity is in accordance with ISO 6336 as modified by Ticona Bulletin B.1.1, Ticona and the Universal Technical Systems staff.

• AGMA 2001-B88 Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth June 1990


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The following are the Celcon® acetal copolymer equivalents to the Hostaform® acetal copolymer products listed in Ticona Bulletin B.1.1:

HOECHST AG HOECHST CELANESE CORP Hostaform C 9021 Celcon M90™ Hostaform C 2521 Celcon M25 Hostaform C 27021 Celcon M270 Hostaform C 13021 Celcon M140 Hostaform C 9021 K Celcon LW90 Hostaform S 9063 Celcon TX90 Hostaform S 9064 Celcon TX90+

The data provided here is as indicated in Bulletin B.1.1. Some of the data has been updated with input from Ticona as provided by Dr. Zan Smith, Engineering Associate, Ticona. Hostaform Celcon, Celanex and GUR are registered trademarks of Ticona. Data on the following materials has been added based on the available information at this time. The allowable flank and root stresses given are engineering judgments, however, and are not based on actual gear testing.

Celcon GC25A™ Glass Reinforced Acetal Copolymer (4-94) Celanese® Nylon 1000 General Purpose Nylon 6/6 (5-94) Celanese® Nylon 1503 Heat Stabilized, 33% Glass Nylon 6/6 (5-94)

Celanese is a registered trademark of Celanese International


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Data has been included on the following Delrin® acetal resins from DuPont Engineering Polymer:

Delrin® 100P Delrin® 500P Delrin® 500TL Delrin® 500CL Delrin® 500AL

The Delrin® resins are acetal polymers. Delrin® 100P and 500P are both general-purpose and unmodified (no additional lubrication for wear characteristics). The properties of Delrin® 100P are representative of other high-viscosity grades of Delrin®, such as Delrin® 111DP. The properties of Delrin® 500P are representative of other medium-viscosity grades Delrin®, such as 311DP and 511P. The other Delrin® polymers whose properties are included all have their own added lubrication. Delrin® 500TL contains Teflon®, 500CL contains a special chemical lubricant, and 500AL has a package of advanced lubricants. Data on these materials is based on engineering judgments made after a review of test data. Delrin® and Teflon® are registered trademarks of E. I. du Pont de Nemours and Company.


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The engineering properties of plastic materials are quite sensitive to temperature. This is accounted for in the model by calculating the flank temperature of the gear teeth and altering the “room temperature” properties accordingly. The flank temperature of the teeth depends on:

1. Ambient temperature 2. Power transmitted 3. Lubrication (if any) 4. Dynamic coefficient of friction 5. Ratio 6. Number of teeth in pinion and gear 7. Pitch line velocity 8. Face width 9. Heat conduction properties of gear materials 10. Sliding velocity between teeth 11. Heat transfer characteristics of housing or surroundings

The dynamic elastic modulus of the gear material varies with the operating temperature. The dynamic elastic modulus affects the deflection and both the flank stress and the root stress of the gears. Each material in the material data table has an elastic modulus temperature curve, an allowable flank stress temperature curve and an allowable root stress temperature curve. These curves are used to calculate the change in modulus of elasticity, allowable flank stress and allowable root stress with a change in operating temperature. The temperature curve number identifies the proper curve for the material being used. These curves are used to calculate a temperature factor for adjusting the modulus of elasticity, allowable flank stress and allowable root stress for the difference between the reference temperature and the operating temperature. The curves were developed by normalizing data from laboratory tests of the above materials. (The curves for steel are included but consist only of values of one.)


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Fig. L1

Figure L1 is a typical normalized temperature vs. elastic modulus curve for a plastic material.


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Fig. L2

Figure L2 is a typical normalized temperature vs allowable contact stress curve for a dry running plastic material. Note that the value remains at 1 until a temperature of about 60 degrees C is reached. This is because the allowable contact stress is based on wear of 20% of tooth thickness and NOT on pitting failure. This wear rate is fairly constant below 60 degrees C. This allowable contact stress does not, of course, apply to fully or continuously lubricated gears. The pitting contact stress limits for lubricated plastic gears have not been established. Most lubricated plastic gears fail by tooth breakage, not pitting. However, gears with a calculated flank stress safety factor less than one should be tested before assuming that pitting failure is not possible.


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Fig. L3

Figure L3 is a typical normalized temperature vs. bending stress curve for a plastic material. This curve applies to dry running or lubricated gears. Calculation of tooth load contact and bending stress numbers is in accordance with ISO (Draft) 6336 as modified by Hoechst AG. Bulletin B.1.1, the Hoechst Celanese Advanced Materials Group and the Universal Technical Systems staff. Since the gear tests run by Hoechst Aktiengesellschaft were on “standard” proportion gears the model makes adjustments for the actual gear set being analyzed. These include, among others, adjustment of tooth tip deflection by comparison of tooth length and thickness, comparison of area under the specific sliding curves for heat input and adjustment of the stress by the face load factors for contact and bending stress. (The face load factors are based on tooth alignment along the length of the tooth.) The modulus of elasticity, deflection, wear capacity and strength of plastic gears are dependent on the operating temperature of the gear mesh. The model will calculate the tooth flank temperature of a dry running or greased plastic gear using a formula that has been verified by testing. The model will calculate the tooth bending stress with the load applied at the tooth tip or further down on the tooth depending on the valves of the deflection, the base pitch error and the tip relief.


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If the gear is oil lubricated the temperature depends on the oil temperature which must be entered as the ambient temperature for the gears. The model will add 5 degrees C to the ambient temperature for the flank temperature for oil lubricated gears. If you wish, you may enter the flank temperature directly for each gear if it is known.


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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. The gear data to audit a design should be available from your production data. The hob or shaper data is available from the tool supplier. Example 1 Example 1 is a spur gear set with a “high-addendum” 12 tooth steel pinion cut on a 13 tooth blank meshed with a “standard” 36 tooth plastic gear. We will check the gear geometry first and then the load capacity. The pinion is hobbed with a topping “standard” finish hob. The pinion is the driver. We will check for undercut and interference at the first and last points of contact. Since the pinion is the driver the first point of contact will be at the pinion root (gear tip) and the last point of contact will be at the pinion tip (gear root). Open a new analysis in 60-610. For this example, select metric units. Enter the input data as shown in Figure 1A. (You will need to change defaults for standard center distance, driven outside diameter, and finished tooth thickness at reference PD for driver.) Click “Yes” for all dialog boxes except for entering radial tip champfer, tip relief and load data. The inputs and outputs for the solved model are shown in Report 1A.


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Fig. 1A


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Report 1A

Model Title : Program 60-610 Unit System: Metric Description Value Unit Comment

DRIVER, number of teeth 12

Hobbed ('hob), Shaped ('shp), Formed hob ('frm)

DRIVEN, number of teeth 36

Hobbed ('hob), Shaped ('shp), Formed frm ('frm)

NORMAL PLANE

Module 2.000000 mm `

Diametral Pitch 12.700000 1/in `

Nominal pressure angle 20.000000 deg

Base pitch 5.904 mm

NORMAL PLANE DRIVER

Finished tooth thickness at Ref PD 3.870 mm

Total normal circular finish stock on tooth 0.000 mm thickness

NORMAL PLANE DRIVEN


Total normal circular finish stock on tooth 0.000 mm Thickness


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Model Title : Program 60-610 Unit System: Metric Description Value Unit Comment TRANSVERSE PLANE


Diametral_Pitch 12.700000 1/in `

Nominal_pressure angle 20.0000 deg

Base_pitch 5.904 mm

Tooth_thickness, Driver 3.870 mm

Tooth_thickness, Driven 3.112 mm

COMMON

Helix angle 0.000000 deg

Base_helix angle 0.0000 deg

Axial pitch mm

Operating_center distance 49.000 mm

Standard_center distance 48.0000 mm

Net face width 26.000 mm

Aspect ratio 1.061

COMMON DRIVER

Outside Diameter 30.002 mm

Normal_top land width 0.569 mm

Start_Tip Modification mm

Roll_at_start of tip modification deg

Normal_OD tip relief mm

Normal_circular OD tip relief mm


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Transverse_circular_OD tip relief mm


Effective_outside diameter 30.002 mm

Normal_effective OD tip relief mm

Normal_tooth_thickness_at_Eff OD 0.569 mm

Load_angle with tooth CL at eff OD 49.82 deg

Pointed tooth diameter (No tip mod) 30.642 mm

Reference PD 24.000 mm

Inv/fillet intersection dia (TIF) 22.621 mm

Roll_at_inv/fill intersection dia 4.453 deg

Normal_TT_at_inv/fill intersection d 3.981 mm

Minimum_fillet radius 0.663 mm

Root diameter 21.002 mm

LA 4.500 mm

Base_diameter 22.553 mm

Lead mm

Area of space (Normal section) 16.336 mm^2

Area of tooth (Normal section) 13.708 mm^2

COMMON DRIVEN








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Whole depth of tooth (from Eff OD) 4.700 mm


Lead mm



OPERATING DATA

Change in Operating CD from "Std" CD 1.000 mm

Working depth of active flanks 3.933 mm

Total_working depth 4.001 mm

Normal_circular_backlash 0.084 mm

Transverse_circular backlash 0.084 mm


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Normal_module 2.041667 mm `

Transverse_module 2.041667 mm `

Normal_pressure angle 22.998 deg

Transverse_pressure angle 22.998 deg

Helix_angle 0.000 deg

OPERATING DATA DRIVER

Pitch_diameter 24.500 mm

Normal_tooth thickness 3.751 mm

Transverse_tooth thickness 3.751 mm

Start of active profile (SAP) 22.900 mm

Root_clearance 0.499 mm

Max_specific sliding ratio 1.879

OPERATING DATA DRIVEN







PLOT CONFIGURATION

Mark inv/fil intersections? y

Mark mod/inv intersections? y

Number of teeth on plot 1


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Driver_contact roll angle of deg

Driver tooth number 1

DRIVER ROLL ANGLES

Start_of_active profile-No Undercut 10.093 deg

Actual_start of active profile 10.093 deg

Lowest_single contact-LCR Spur 20.269 deg

Lowest_double contact-HCR Spur deg

Operating pitch point 24.319 deg

Highest_single contact-LCR Spur 40.093 deg

Highest_double contact-HCR Spur deg

Actual_end of active profile 50.269 deg

Effective outside diameter 50.269 deg

DRIVEN ROLL ANGLES











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CONTACT DATA

Total_arc of contact, driver 40.176 deg

Arc_of_approach 14.225 deg

Arc_of_recess 25.951 deg

Approach action 35.41 %

Recess action 64.59 %

Profile contact ratio (SAP > TIF) 1.339

Actual profile contact ratio 1.339

Contact below finished involute? No

Helical contact ratio 0.000

Total_contact ratio 1.339

Unmodified (light load) profile CR

Profile_contact ratio

Helical contact ratio

Total_contact ratio

FORMED DRIVEN

Flank angle 20.0000 deg

Tip to reference line 2.660 mm

Tooth thickness at reference line 3.142 mm

Tip_radius 0.860 mm

Radial_tip chamfer (w/o mod) 0.000 mm

Normal_tip radius 0.125 mm

Normal_tip_relief exponent


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DRIVER HOB

Hob type t


Tip to Reference Line 2.500 mm

Tooth thickness at Reference Line 3.142 mm

Tip_radius 0.600 mm

Protuberance 0.000 mm

Protuberance_angle from flank deg

Protuberance_pressure angle deg

Tip_to_flank/prot intersection mm

Reference_Line_to Start Mod Ramp mm

Pressure Angle of Mod Ramp deg

Reference_Line_To Hob Tooth Root 2.000 mm

Radius in Hob Tooth Root 0.628 mm

Ref_Line to Hob SAP 0.979 mm

Normal_Space Width at Hob SAP 2.429 mm Contact should start on the pinion at 10.094 degrees roll angle if there is no contact below the finished involute profile. (There isn't; “Contact below finished involute?” is “No” on the report.). We will plot 3 teeth on each gear with tooth #1 on the driver at the start of contact. On the Plot Configuration tab of the input form (Figure 1B), click the radio button for SAP with a roll angle of 10.094 degrees. Enter 3 teeth to be plotted and tooth #1 at the driver SAP. The plot should look like Figure 1C. The small “tic” marks indicate the intersection of the involute and fillet and involute and tip radius.


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Fig. 1B

Fig. 1C

Note that contact is just taking place at the root of the driver (pinion) and the start of the tip radius of the driven (gear). One base pitch away down the line of action a second tooth is also in contact.


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We wish to visually check the driver tooth at the first point of contact for undercut and interference. To do this, toggle to TK Solver and go to the plot subsheet for “mesh”. Put the cursor anywhere on the plot and click the right mouse button. Enter yes for “Display Scale:” and “Display Grid:”, as shown in Figure 1D: Fig. 1D


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The plot should then look like Figure 1E. Fig. 1E

From the plot grid we see that the area we are interested in is bounded by -4, -2 on the X-Axis and 0, 2 on the Y-Axis. Enter these values on the subsheet, as shown in Figure 1F. The plot is shown in Figure 1G.


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Fig. 1F

From the plot, Figure 1G, we see that there is no undercut on the driver and the driven tooth tip is contacting on the involute profile. Now we will take a quick look at the start of active profile on the driven gear, although, with “standard” proportions we expect no difficulty here. The lowest point of single tooth contact on the pinion for driver tooth #1 will place driver tooth #2 in contact at the tooth tip. This is also the start of active profile on the driven. Make this selection from the Plot Configuration tab (Figure 1B).

Fig. 1G


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Enter 2 teeth to be plotted and set the driver tooth number to 1. (The same thing could be accomplished by choosing the driver roll angle to 50.269 degrees (outside diameter) and the driver tooth number to 2.) You will also need to toggle to TK Solver and bring up the subsheet for the plot “mesh”. Set “Display Scale” to “No” and blank the X and Y axis minimum-maximum on the plot subsheet. The plot is shown in Figure 1H. Fig 1H

As a matter of interest we will confirm that at the operating pitch point, 24.319 degrees, we only have one tooth in contact. (The zone of single tooth contact, of course, extends from 20.269 to 40.093 degrees.) Solve the model again, then choose this option on the Plot Configuration tab. (See Figure 1B.) Figure 1I shows the teeth in contact at the operating pitch point.


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Fig. 1I

Now we are ready to check the load capacity of the gears. The load and material specification is as follows:

Power = 500 W Pinion Speed = 3600 RPM Housing shaft alignment: Parallel = 0.0010 mm/mm Plane = 0.0010 mm/mm Pinion is steel made to AGMA Quality Class Q9. The pinion shaft is solid. Gear is Celanese Celcon M90 Acetal made to AGMA Quality Class Q7 Gears are greased. The gear rim diameter is 52 mm. Ambient temperature = 40 deg C

If you have saved the earlier analysis, open it now; otherwise start a new analysis and enter the inputs in Figure 1J. When the dialog asks “Do you want to enter load data?” click yes this time. Choose “power,” not “torque,” then enter the power and pinion speed as given above. The housing shaft alignment figures are both defaults. Enter the ambient temperature and pick “grease” from the pick list. Choose “no” for entering the driver bore/diameter data, but “yes” for driven, and enter 52. Neither gear is an idler.


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The completed input form is shown in Figure 1J and the input and output values for the solved model in Report 1B. Fig. 1J


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Report 1B



Hobbed ('hob), Shaped ('shp), Formed hob ('frm)



NORMAL PLANE




Base pitch 5.904 mm

NORMAL PLANE DRIVER



NORMAL PLANE DRIVEN




30





Base_pitch 5.904 mm



COMMON



Axial pitch mm




Aspect ratio 1.061

COMMON DRIVER








31














LA 4.500 mm


Lead mm



COMMON DRIVEN








32
















Lead mm



OPERATING DATA







33





















PLOT CONFIGURATION





34


Driver_contact roll angle of 10.094 deg


DRIVER ROLL ANGLES










DRIVEN ROLL ANGLES











35


CONTACT DATA












Profile_contact ratio 1.344



FORMED DRIVEN




Tip_radius 0.860 mm





36


DRIVER HOB

Hob type t


Tip to Reference Line 2.500 mm

Tooth thickness at Reference Line 3.142 mm

Tip_radius 0.600 mm

Protuberance 0.000 mm

Protuberance_angle from flank deg

Protuberance_pressure angle deg

Tip_to_flank/prot intersection mm

Reference_Line_to Start Mod Ramp mm

Pressure Angle of Mod Ramp deg

Reference_Line_To Hob Tooth Root 2.000 mm

Radius in Hob Tooth Root 0.628 mm

Ref_Line to Hob SAP 0.979 mm

Normal_Space Width at Hob SAP 2.429 mm

LOAD

Power 0.50000 kW

Driver Speed 3600.0 rpm

Driver Torque 1.326 N-m

Driven Speed 1200.0 rpm

Driven Torque 3.928 N-m

Tangential Load 108.269 N


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Unit_Tangential Load 4164.180 N/m

Efficiency 98.7 %

COMMON

Peripheral Speed 4.618 m/sec

Shafts Maximum Out of Parallel 0.001 mm/mm

Shafts Maximum Out of Plane 0.001 mm/mm

Root_Mean Square Face Mismatch 0.035 mm

Running-In Factor 0.55

Eff RMS Face Mismatch (Run-In) 0.019 mm

Transverse Tooth Tip Deflection 0.024 mm

Root_Mean_Square Base Pitch Error 0.043 mm

Mesh Linear Stiffness (AGMA 2001) 8406921 N/m

Line of Action Deflection 0.014 mm

Relative Wear for Mat`l Combination

Ambient Temperature 40 C

Lubrication ('dry, 'grease, 'oil) grease

Coefficient of Friction 0.05

Material_Combination Factor 1.0000

Lube/Housing/Air Circulation Factor 0

Surface Area of Gear Housing mm^2

TOOTH FLANK (CONTACT) STRESS

Shape Factor 1.63

Material_Factor 42.97


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Contact_Ratio Factor 0.941

Face Load Factor 1.742

Flank_Contact Stress 41503331.71 Pa

K factor 226622.017 Pa

Unit Load 2082089.784 Pa

TOOTH ROOT (BENDING) STRESS

Helix_Angle Factor 1.00


TOOTH ROOT (BENDING) STRESS DRIVER

Load Applied at Tooth Tip? Yes

Tooth_Shape Factor

Fillet Radius @ Critical Section mm

YF Valid? (Fil Rad >.25*module)

Stress correction factor

Bore/Rim Diameter UNKNOWN mm

Rim Thickness Factor 1.000

Backup Ratio UNKNOWN

Root_Bending Stress Pa

TOOTH ROOT (BENDING) STRESS DRIVEN

Load Applied at Tooth Tip? Yes

Tooth_Shape Factor 2.57

Fillet Radius @ Critical Section 1.201 mm

YF Valid? (Fil Rad >.25*module) Yes


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Stress correction factor 1.00

Bore/Rim Diameter 52.000 mm


Backup Ratio 1.576

Root_Bending Stress 8283628.86 Pa

MATERIALS/QUALITY CLASS DRIVER

Material # 1

AGMA Quality Class 9

Tooth_Alignment (Lead) Error 0.010 mm

Tooth_Flank Temperature C

Material_Heat Index

Dynamic Elastic Modulus 207000000000 Pa

Temperature Curve # 1.0000

Temperature_Factor

Poisson`s Ratio 0.3000

Sliding Velocity at Tooth Tip 2.567 m/sec

Allowable_Flank Stress (10^7 cy) Pa

Temperature Curve #

Temperature_Factor

FLANK SAFETY FACTOR

Allowable_Root Stress (10^7 cy) Pa

Idler? 'y/'n

Same Flank Contacts/Rev

Temperature Curve #


40


Temperature_Factor

ROOT SAFETY FACTOR

MATERIALS/QUALITY CLASS DRIVEN

Material # 2


Tooth_Alignment (Lead) Error 0.015 mm

Tooth_Flank Temperature 42.35 C

Material_Heat Index 0.4000

Dynamic Elastic Modulus 2578139103 Pa


Temperature_Factor 0.87


Sliding Velocity at Tooth Tip 1.407 m/sec

Allowable_Flank Stress (10^7 cy) 19000000.0 Pa



FLANK SAFETY FACTOR 0.46

Allowable_Root Stress (10^7 cy) 34632832.3 Pa

Idler? 'y/'n n

Same Flank Contacts/Rev 1.0000



ROOT SAFETY FACTOR 4.18


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With this load applied the tooth tip deflection is 0.024 mm. The RMS base pitch error with the pinion made to AGMA Q9 and the gear made to AGMA Q7 is 0.0431 mm. Since the base pitch error is larger than the tooth tip deflection (and there is no tip relief) the tooth shape factor for bending, 2.57, is calculated with all load applied at the tip of the gear tooth. This results in a root bending stress of 8.28 N/mm2. The contact stress is 41.5 N/mm2. Note that the rim thickness factor for the gear is one. This indicates that the thickness of the rim below the root of the teeth is sufficient (1.2 times the tooth depth) to avoid an increase in root stress due to a thin rim. Since the pinion is made of steel, which has a high thermal conductivity, and the coefficient of friction is low, 0.05, because of the lubrication, the flank temperature of the gear is only 42.35 C. The temperature factor for the gear modulus of elasticity is 0.87. See Figure 1K. Fig. 1K

The temperature factor for the gear allowable flank contact stress is 1.00. See Figure 1L.


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Fig. 1L

The temperature factor for the gear allowable root bending stress is 0.81. See Figure 1M. Fig. 1M


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The values from the table for Celcon M90 (Material #2) are:

Modulus of Elasticity = 2950 N/mm2 Allowable Flank Stress = 19 N/mm2 Allowable Root Stress = 43 N/mm2

After applying the temperature factors the values are:

Modulus of Elasticity = 2578 N/mm2 Allowable Flank Stress = 19 N/mm2 Allowable Root Stress = 34.6 N/mm2

This results in a root safety factor of 4.18 and a flank safety factor of 0.46. The root bending safety factor is more than ample but the flank stress safety factor is less than one.

The allowable flank stress, however, is based on wear of dry running plastic gears and does not apply to continuously lubricated gears. This design is probably sufficient since most lubricated plastic gears fail in root bending, not pitting. (Gear load data for lubricated pitting failure is not yet available.) It is essential that a set of test gears be made and tested to insure that pitting will not occur with a flank safety factor less than one.


44

Example 2 Example 2 is a 25/45 tooth, 16 pitch, 20 degree pressure angle, high addendum spur gear set running on 0.0225 inch “spread” centers. The gears will be extra depth and will have full trochoidal fillets using a basic rack form to preclude tip-root interference. The rack form will be the AGMA Plastic Rack XPT-3. (The practice of using circular arcs for the fillets on external involute gears will lead to interference between the fillet and the tooth tip of the mating gear in many cases. The is especially true when meshing with master gears at minimum tooth thickness conditions.) We wish to use full radius fillets to keep the root bending stress to a minimum. The gears will have a radius at the tooth tips of 0.004 inch. In addition, tip relief is required to hold noise to a minimum. We will first design the gears and check the load capacity without the tip relief. Then, after the tooth tip deflections have been found, we will apply the tip relief. The gears must carry 1.25 HP at a driver speed of 3600 RPM. The shafts can be 0.001 in/in out of parallel and out of plane. The gears will run dry in an ambient temperature of 105 deg F. The housing is partially open with good air circulation. The exposed area of the housing is about 120 in2. The pinion material will be Celanese Celcon M25 made to AGMA Quality Class Q7. The pinion bore is 0.5 inch. The gear material will be Celanese Celcon TX90 made to AGMA Quality Class Q7. The gear rim diameter is 2.0 inches. Change the units in the model to “US”. Enter the input data shown in Figure 2A.


45

Fig. 2A

When solving, we got a message that the tooth tip deflection (0.0049 inch) was greater than the backlash (0.0030 inch). We must increase the backlash or the teeth will contact on the back (non-driving) side. This could cause wear, noise and jamming. We will increase the backlash by changing the tooth thickness of the driver and driven to 0.1065 inch and 0.1020 inch.


46

The tooth tip deflection is about 0.0049 inch which is well below the allowable limit for smooth operation of 0.1/NDP - 0.0062 inch. We will apply tip relief of about 0.003 inch to both gears to further ease contact at the start and end of the mesh cycle. The tip relief will start at a diameter of 1.665 inches on the driver and 2.913 inches on the driven to keep a profile contact ratio of about 1.05 when the set is lightly loaded and the modified portions of the teeth are not in contact (use the cursor to enter the tip relief data). (See UTS Model 60-1111 for further data on tip relief.)

We will plot two teeth in mesh at the first point of contact on the driver. (Use the selection in the Plot Configuration tab of the input form.)

Figure 2B is the input form with the new inputs. The solved model is shown in Report 2B.


47

Fig. 2B


48

Report 2B

Model Title : Program 60-610 Unit System: US Description Value Unit Comment





NORMAL PLANE




Base pitch 0.1845 in

NORMAL PLANE DRIVER

Finished tooth thickness at Ref PD 0.1065 in

Total normal circular finish stock on tooth 0.0000 in thickness

NORMAL PLANE DRIVEN

Finished tooth thickness at Ref PD 0.1020 in

Total normal circular finish stock on tooth 0.0000 in Thickness


49

Model Title : Program 60-610 Unit System: US Description Value Unit Comment TRANSVERSE PLANE




Base_pitch 0.1845 in

Tooth_thickness, Driver 0.1065 in

Tooth_thickness, Driven 0.1020 in

COMMON



Axial pitch in

Operating_center distance 2.210 in

Standard_center distance 2.1875 in

Net face width 1.6250 in

Aspect ratio 1.029

COMMON DRIVER

Outside Diameter 1.7477 in

Normal_top land width 0.0076 in

Start_Tip Modification 1.6650 in

Roll_at_start of tip modification 30.637 deg

Normal_OD tip relief 0.003 in

Normal_circular OD tip relief 0.004 in

Transverse_circular_OD tip relief 0.004 in


50


Effective_outside diameter 1.7445 in

Normal_effective OD tip relief 0.003 in

Normal_tooth_thickness_at_Eff OD 0.0140 in


Pointed tooth diameter (No tip mod) 1.7762 in

Reference PD 1.5625 in

Inv/fillet intersection dia (TIF) 1.4714 in


Normal_TT_at_inv/fill intersection d 0.1221 in

Minimum_fillet radius 0.0242 in

Root diameter 1.3880 in

LA 0.1798 in

Base_diameter 1.4683 in

Lead in

Area of space (Normal section) 0.0185 in^2

Area of tooth (Normal section) 0.0169 in^2

COMMON DRIVEN

Outside Diameter 2.9848 in

Normal_top land width 0.0177 in

Start_Tip Modification 2.9130 in

Roll_at_start of tip modification 26.558 deg

Normal_OD tip relief 0.003 in

Normal_circular OD tip relief 0.003 in


51


Transverse_circular_OD tip relief 0.003 in

Effective_outside diameter 2.9812 in

Normal_effective OD tip relief 0.003 in

Normal_tooth_thickness_at_Eff OD 0.0244 in


Pointed tooth diameter (No tip mod) 3.0380 in

Reference PD 2.8125 in

Inv/fillet intersection dia (TIF) 2.6875 in


Normal_TT_at_inv/fill intersection d 0.1320 in

Minimum_fillet radius 0.0225 in

Root diameter 2.6257 in

Whole depth of tooth (from Eff OD) 0.1796 in

Base_diameter 2.6429 in

Lead in

Area of space (Normal section) 0.0175 in^2

Area of tooth (Normal section) 0.0176 in^2

OPERATING DATA

Change in Operating CD from "Std" CD 0.0225 in

Working depth of active flanks 0.1529 in

Total_working depth 0.1563 in

Normal_circular_backlash 0.0049 in

Transverse_circular backlash 0.0049 in


52








Pitch_diameter 1.5786 in

Normal_tooth thickness 0.1015 in

Transverse_tooth thickness 0.1015 in

Start of active profile (SAP) 1.4884 in

Root_clearance 0.0236 in



Pitch_diameter 2.8414 in

Normal_tooth thickness 0.0920 in

Transverse_tooth thickness 0.0920 in

Start of active profile (SAP) 2.7292 in

Root_clearance 0.0233 in


PLOT CONFIGURATION





53


Driver_contact roll angle of 9.574 deg


DRIVER ROLL ANGLES










DRIVEN ROLL ANGLES











54


CONTACT DATA











Unmodified (light load) profile CR 1.049

Profile_contact ratio 1.914



FORMED DRIVER


Tip to reference line 0.0987 in

Tooth thickness at reference line 0.0982 in

Tip_radius 0.0187 in

Radial_tip chamfer (w/o mod) 0.0000 in

Normal_tip radius 0.0040 in

Normal_tip_relief exponent 1.5000


55


FORMED DRIVEN


Tip to reference line 0.0987 in

Tooth thickness at reference line 0.0982 in

Tip_radius 0.0187 in

Radial_tip chamfer (w/o mod) 0.0000 in

Normal_tip radius 0.0040 in

Normal_tip_relief exponent 1.5000

LOAD

Power 1.25000 HP

Driver Speed 3600.0 rpm

Driver Torque 21.8838 lbf-in

Driven Speed 2000.0 rpm

Driven Torque 36.9832 lbf-in

Tangential Load 27.7261 lbf

Unit_Tangential Load 17.0622 lbf/in

Efficiency 93.9 %

COMMON

Peripheral Speed 1487.7685 ft/min

Shafts Maximum Out of Parallel 0.001 in/in

Shafts Maximum Out of Plane 0.001 in/in

Root_Mean Square Face Mismatch 0.002 in

Running-In Factor 0.25


56


Eff RMS Face Mismatch (Run-In) 0.001 in

Transverse Tooth Tip Deflection 0.005 in

Root_Mean_Square Base Pitch Error 0.002 in

Mesh Linear Stiffness (AGMA 2001) 14876 lbf/in

Line of Action Deflection 0.002 in

Relative Wear for Mat`l Combination GOOD

Ambient Temperature 105 F

Lubrication ('dry, 'grease, 'oil) dry

Coefficient of Friction 0.33

Material_Combination Factor 2.5000

Lube/Housing/Air Circulation Factor .04

Surface Area of Gear Housing 120.0000 in^2

TOOTH FLANK (CONTACT) STRESS

Shape Factor 1.69

Material_Factor 19.34

Contact_Ratio Factor 0.834


Flank_Contact Stress 1444.03 psi

K factor 16.8134 psi

Unit Load 272.9954 psi

TOOTH ROOT (BENDING) STRESS

Helix_Angle Factor 1.00



57


TOOTH ROOT (BENDING) STRESS DRIVER

Load Applied at Tooth Tip? No


Fillet Radius @ Critical Section 0.0349 in



Bore/Rim Diameter 0.5000 in


Backup Ratio 2.491

Root_Bending Stress 484.66 psi

TOOTH ROOT (BENDING) STRESS DRIVEN

Load Applied at Tooth Tip? No


Fillet Radius @ Critical Section 0.0337 in



Bore/Rim Diameter 2.0000 in


Backup Ratio 1.760

Root_Bending Stress 463.48 psi

MATERIALS/QUALITY CLASS DRIVER

Material # 4



58


Tooth_Alignment (Lead) Error 0.001 in

Tooth_Flank Temperature 201.65 F


Dynamic Elastic Modulus 142874 psi




Sliding Velocity at Tooth Tip 531.3442 ft/min

Allowable_Flank Stress (10^7 cy) 1742.0 psi




Allowable_Root Stress (10^7 cy) 2347.6 psi

Idler? 'y/'n n




ROOT SAFETY FACTOR 4.84

MATERIALS/QUALITY CLASS DRIVEN

Material # 7


Tooth_Alignment (Lead) Error 0.001 in

Tooth_Flank Temperature 166.24 F


59



Dynamic Elastic Modulus 157039 psi




Sliding Velocity at Tooth Tip 492.4290 ft/min

Allowable_Flank Stress (10^7 cy) 2814.0 psi




Allowable_Root Stress (10^7 cy) 2447.7 psi

Idler? 'y/'n n




ROOT SAFETY FACTOR 5.28 Figure 2C is the plot of the teeth. (Use the Plot Configuration tab of the data input form to obtain the mesh plot, as described in Example 1.) Plots should be made at various stages of mesh to insure that no fillet interference exists. (The root clearance should be large enough to avoid jamming if small amounts of debris collect in the root area of the gears.)


60

Fig. 2C

The lowest flank stress safety factor is 1.21 for the driver and limits the power capacity of the set. The lowest root stress safety factor is 4.84, also for the driver. This is mostly due to the higher flank temperature for the driver. In any event, the gear rating is much higher in root bending than in flank wear. This is to be expected since the limiting condition for dry running plastic gears is usually the contact stress.


61

Example 3 Example 3 is a 16/64 spur gear set, with a module of 1 mm, molded from thermoplastic materials. The housing is made from unfilled polycarbonate and the gears are molded from unfilled acetal (Celanese Celcon M90). The range of operating temperatures ranges from -34 degrees C to +60 degrees C. The gears will be greased. The relative humidity will range from dry to 100% for long periods. The design must be capable of operation at minimum effective center distance without running out of backlash and without root-tip interference. The design must also retain a contact ratio over 1.3 at the maximum effective center distance. The load is 50 watts at 3600 RPM of the pinion. Assume that the out-of-parallel and out of plane for the shafts are both 0.001 mm/mm. The gears are to be made to AGMA quality class 7. The first step is to find the maximum and minimum effective center distances under the ambient conditions. For design purposes the gear dimensions are subjected to tolerance variations at an assembly temperature of 20 degrees C but not to dimensional changes due to temperature changes and moisture absorption. All such changes are accounted for in the “effective” center distance. The maximum and minimum “effective” center distances will not actually occur but are used to check the gear set for interference and contact ratio under conditions which would have the same effect as the actual operating conditions. The nominal (and “standard”) center distance for this gear set is 40 mm. For the above ambient conditions the maximum effective center distance is found to occur at cold and dry conditions. The maximum effective center distance is 40.391 mm. The minimum effective center distance, under hot and humid conditions, is 40.027 mm. (See Reports 3 MAX and 3 MIN from UTS Model 60-146.)


62

Report 3 MAX


External or Internal Set e

ASSEMBLY CONDITIONS

Normal_Diametral Pitch 25.400000 1/in `

Normal_Module 1.000000 mm `

Helix Angle 0.000000 deg

Operating Transverse Pressure Angle 20.000000 deg

Temperature 20 C

Relative Humidity 50.00 %

HOUSING

Material_Number-See Material Table 12

Material_Code PCUF

Thermal Coefficient of expansion 0.00 1/degC

Moisture Coefficient of expansion 0.00 cm/cm

Basic or nominal center distance 40.0000 mm

Minimum center distance tolerance -0.0500 mm

Maximum center distance tolerance 0.0500 mm

Pinion total composite tolerance 0.08636 mm

Gear total composite tolerance 0.09906 mm

Pinion_bearing runout (TIR) 0.0300 mm


63


Gear_bearing runout (TIR) 0.0300 mm

Pinion_bearing_radial play, max 0.1200 mm

Pinion_bearing_radial play, min 0.0900 mm

Gear_bearing_radial play, max 0.1200 mm

Gear_bearing_radial play, min 0.0950 mm

Minimum_assembled CD, absolute 40.0125 mm

Maximum_assembled CD, absolute 40.3854 mm

Minimum_assembled CD, statistical 40.0886 mm

Maximum_assembled CD, statistical 40.3093 mm

PINION


Material_Code Acetal UF

Number of teeth 16




Nominal_operating pitch diameter 16.0000 mm

GEAR



Number of teeth 64




64




OPERATING CONDITIONS

Housing_temperature -34 C

Pinion_temperature -34 C

Gear_temperature -34 C

Relative_humidity 0.00 %

Change_in relative humidity -50.00 %

EFFECTIVE CENTER DISTANCE

Change in CD (Thermal, Moisture) 0.0813 mm

Approximate change in backlash 0.0597 mm

EFFECTIVE CD, ABSOLUTE

Minimum_effective center distance 40.0938 mm

Maximum_effective center distance 40.4667 mm

Mean effective center distance 40.2802 mm

CD Range 0.37292 mm

EFFECTIVE CD, STATISTICAL

Standard deviations, +/- 3.0000

Range of deviations 6.0000

Amount of assemblies included in the 99.7300 % range

Number_of assemblies included in range 370 per assembly outside range


65





CD Range 0.22076 mm Report 3 MIN


External or Internal Set e

ASSEMBLY CONDITIONS

Normal_Diametral Pitch 25.400000 1/in `

Normal_Module 1.000000 mm `

Helix Angle 0.000000 deg

Operating Transverse Pressure Angle 20.000000 deg

Temperature 20 C

Relative Humidity 50.00 %

HOUSING


Material_Code PCUF



66



Basic or nominal center distance 40.0000 mm

Minimum center distance tolerance -0.0500 mm

Maximum center distance tolerance 0.0500 mm

Pinion total composite tolerance 0.08636 mm

Gear total composite tolerance 0.09906 mm

Pinion_bearing runout (TIR) 0.0300 mm

Gear_bearing runout (TIR) 0.0300 mm

Pinion_bearing_radial play, max 0.1200 mm

Pinion_bearing_radial play, min 0.0900 mm

Gear_bearing_radial play, max 0.1200 mm

Gear_bearing_radial play, min 0.0950 mm

Minimum_assembled CD, absolute 40.0125 mm

Maximum_assembled CD, absolute 40.3854 mm

Minimum_assembled CD, statistical 40.0886 mm

Maximum_assembled CD, statistical 40.3093 mm

PINION



Number of teeth 16





67



GEAR



Number of teeth 64





OPERATING CONDITIONS

Housing_temperature 60 C

Pinion_temperature 60 C

Gear_temperature 60 C

Relative_humidity 100.00 %

Change_in relative humidity 50.00 %

EFFECTIVE CENTER DISTANCE

Change in CD (Thermal, Moisture) -0.0611 mm

Approximate change in backlash -0.0442 mm

EFFECTIVE CD, ABSOLUTE





68


CD Range 0.37292 mm

EFFECTIVE CD, STATISTICAL

Standard deviations, +/- 3.0000

Range of deviations 6.0000

Amount of assemblies included in the 99.7300 % range

Number_of assemblies included in range 370 per assembly outside range




CD Range 0.22076 mm

We will design the gear set at minimum effective center distance and tooth tip radius along with maximum tooth thickness and outside diameters. The backlash will be set to 0.030 mm, as this is the tightest mesh condition. (We can not set the backlash too low, because if the backlash is less than the tooth tip deflection the teeth will contact on the nondriving side.) These conditions will produce the greatest chance of interference. Because we will lose contact ratio when we go to maximum effective center distance, we will use the nominal default outside diameters as maximum for the design and use a negative tolerance to obtain the minimum ODs.

The tooth tip radius will be 0.10 mm to 0.15 mm. At minimum effective center distance we need to use a tip radius of 0.10 mm to get the largest effective outside diameters.

Open an analysis in 60-610 and enter the data in the input form, shown in Figure 3A. Override the defaults when necessary. We will use the AGMA XPT4 plastic rack form to keep the profile contact ratio as high as possible with the large difference in effective center distance necessary with these design requirements. The inputs and outputs for the solved model are shown in Report 3A. Figures 3A1 and 3A2 are plots of the pinion and gear tooth.


69

Fig. 3A


70

Report 3A






NORMAL PLANE




Base pitch 2.952 mm

NORMAL PLANE DRIVER



NORMAL PLANE DRIVEN




71





Base_pitch 2.952 mm



COMMON



Axial pitch mm




Aspect ratio 0.937

COMMON DRIVER









72













LA 3.039 mm


Lead mm



COMMON DRIVEN








73
















Lead mm



OPERATING DATA







74





















PLOT CONFIGURATION





75




DRIVER ROLL ANGLES










DRIVEN ROLL ANGLES











76


CONTACT DATA








Contact below finished involute? Yes






Total_contact ratio

FORMED DRIVER




Tip_radius 0.248 mm





77


FORMED DRIVEN




Tip_radius 0.248 mm



Normal_tip_relief exponent Fig 3A1


78

Fig 3A2

Note that the 16 tooth pinion is intentionally undercut. The tip of the gear will project into the undercut in the pinion root area when the gears are at low center distance and will not interfere with the pinion root fillet. The contact ratio is controlled, under these conditions, by the OD of the pinion and the involute/fillet intersection diameter on the pinion. (The profile contact ratio may be calculated by subtracting the roll angle at the inv/fil intersection from the roll angle at the pinion OD and dividing by the angle between pinion teeth.) The actual contact ratio is 1.634. This condition will cause no harm if the fillet profile was generated by a basic rack form. However, if the fillet profile is a circular arc starting at the involute-fillet intersection point or a straight radial line starting at the base diameter (if contact extends down to the base diameter), interference is inevitable and the gear set is not usable. Interference must be checked, in any event, by plotting the tooth forms in the proper relation to each other and checking for contact between the tooth tips and fillets.


79

To help equalize the bending strength between the pinion and gear, we will increase the pinion tooth thickness by 0.25 mm and reduce the gear tooth thickness by 0.25 mm. This should make the tooth thickness at the involute/fillet intersections about the same. ((2.211-1.712)/2 = .25) We must also decrease the basic rack tooth thickness of the pinion and increase the rack tooth thickness of the gear by the same amount to keep the root diameters where they are. Enter a large number for the tip radii of the racks and the model will give you the rack maximum tip radii so we will have full fillet radii in the gears. Figure 3B and Report 3B are the model after making these changes. Fig. 3B


80

Report 3B






NORMAL PLANE




Base pitch 2.952 mm

NORMAL PLANE DRIVER



NORMAL PLANE DRIVEN




81





Base_pitch 2.952 mm



COMMON



Axial pitch mm




Aspect ratio 0.937

COMMON DRIVER









82













LA 3.039 mm


Lead mm



COMMON DRIVEN








83
















Lead mm



OPERATING DATA







84





















PLOT CONFIGURATION





85




DRIVER ROLL ANGLES










DRIVEN ROLL ANGLES











86


CONTACT DATA








Contact below finished involute? Yes






Total_contact ratio

FORMED DRIVER




Tip_radius 0.070 mm





87


FORMED DRIVEN




Tip_radius 0.427 mm



Normal_tip_relief exponent Figures 3B1 and 3B2 are plots of the pinion and gear teeth. Figure 3B1


88

Fig 3B2

Figures 3B3 and 3B4 are plots of the pinion and gear in mesh at the first point of contact at the pinion root and gear tip and at the last point of contact at the pinion tip and gear root.


89

Fig 3B3

Fig 3B4


90

No interference is occurring at these points. However, plots of the gears in mesh should be made at enough contact points along the line of action to be sure than no interference exists at any position. (Save the max temperature, min eff CD Variable Sheet to a file for use in checking the load data later without typing the data into the model again.) The set must also be checked at maximum effective center distance and tip radius along with minimum ODs and tooth thickness. This condition will produce the lowest contact ratio and the maximum backlash. By further optimization we reduce the thickness of the driver and driven teeth, increase the backlash by .076 mm, and reduce the outside diameters by .140 mm each. Figure 3C shows the inputs and Report 3C the results at the maximum effective center distance and maximum temperature.


91

Fig. 3C


92

Report 3C






NORMAL PLANE



No

Documents

Program 60-610—Plastic Gear Geometry and Load Analysis ...Program 60-610—Plastic Gear Geometry and Load Analysis Introduction The primary purpose of this model is to provide an