Program 60-1163--Simple Epicyclic Differential Design Introduction
Contents
1. 1206 195 po epu Ee 135 1 185 a EE eee 180 200 Ca aaa he BA 178 225 IC Engine po The table KUL contains K factors and Unit Loads for a number of materials and conditions for steel gears 60 1163 Simple Epicyclic Differential Design Bj INT TABLE KUL Toy x HISPEED 128up HELICAL BAGA a Cat 2 10 1 00 800 LL BON 2090 2E10 100 1 00 MED SPEED Sg D Ajaja eiejiao ojo oe olala NI MED SPEED Q10 11 HELICAL 550 800 170 460 620 190 460 100 ol 4 000 6600 BHN360 1E9 100 4000 260 4900 Q8 SPUR Caro TEB 1 00 4 000 270 5200 BIL co ceo eau BHN380 1E8 100 4 BHN240 1E8 100 4 Jow SPUR Car tea 100 4 BHN380 1E9 100 4 BHN24D 1EB 100 088 1 00 4A 4A e e e e e e I c e DOO e c ce ce HELICAL BIL DO DO DO BHN380 169 1 00 4 000 180 3800 BHN240 1EB 1 00 4 000 80 3000 LOW SPEED 08 7 HELICAL 4000 510 5800 280 Car IER 100 BHN380 1E8 100 LL BON IER 100 ESS c6 mx SPUR ead BHN 360 BHN240 1E8 Bib DO DO DO 8 6 6 BIL ceo ceo eau e M3 N DO 9 g ET E SPUR 5E 1 e ce co NI A oa oa e e oa oa 1 00 1 00 1 00 Cab SPUR 1E92. Number of Planets and solve The effective number of planets may be different from the actual number of planets due to errors preventing the planets from sharing the load equally When one or two members are allowed to float radially the load sharing is better than when all members are constrained by bearings In this case if floating is utilized the effective number of planets is 3 7 The effective number of planets will be the same as the actual number only for 3 planets or less with float If all members are fixed the effective number of planets is 3 The transmitted torque is divided by the effective number of planets to determine the load for an individual planet Enter 3 7 for Effective Planets We will use a sun planet K factor of 700 for this load condition with about a 1 inch face for now We want to solve for gear size and normal pitch To do this will require iteration so we will toggle to the TK Solver Variable Sheet and enter a Guess value of 3 inches for the operating pitch diameter of the sun to give the iterative solver a place to start See the TK Solver User s Manual for more information about Guess values Sheet 1 1 shows this entry If you wish to watch the convergence take place go to Settings under the Options menu and set Display Intermediate Values to Yes The values will display in the Status Bar as the model is solved It will slow the program down somewhat The solution is shown in
3. Normal Pitch 10 000000 1 in Normal Pressure Angle 20 000000 deg Helix Angle 0 000000 deg Transverse Pitch 10 0000 1 in Transverse Press Angle 20 0000 deg Axial Pitch in Normal Module 2 540000 mm Transverse Module 2 5400 mm PLANET SPACING Least mesh angle Planets must be 3 5294 deg NUMBER OF EQUALLY SPACED PLANETS These are the 1st 4 up to 50 that 2 will assemble without interference 3 planets will assemble equally if ring sun planets integer OPERATION AS GEAR UNIT OR DIFFERENTIAL Enable table e enable c clear e Type of unit Planetary Number of planets 4 70 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment ck Chk Spc Effective planets 1 member floating 3 7000 Effective planets All fixed 3 0000 Effective planets 3 7000 Planet Interference OD 3 6199 in Radial Loads On Sun amp Ring Balanced Yes Ring Sun gear ratio 4 1000 Planet Sun Ratio 1 5000 Ring Planet Ratio 2 7333 ROTATION SPEED Sun gear 1200 000 rpm Ring gear 0 000 rpm Carrier 235 294 rpm ROTATION SPEED RELATIVE TO CARRIER Sun gear 964 706 rpm Ring gear 235 294 rpm Planet gear 643 137 rpm Carrier 0 000 rpm DRIVER DRIVEN Sun gear Driver Ring gear Driven Carrier Driven 71 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description SUN PLANET Sun Planet Max Recommended Spacing Tolerance Min Recommended AGMA Q
4. Program 60 1163 Unit System US Description Helix Angle Transverse Pitch Transverse Press Angle Axial Pitch Normal Module Transverse Module PLANET SPACING Least mesh angle Planets must be NUMBER OF EQUALLY SPACED PLANETS These are the ist 4 up to 50 that will assemble without interference planets will assemble equally if ring sun planets integer OPERATION AS GEAR UNIT OR DIFFERENTIAL Enable table e enable c clear Type of unit Number of planets ck Effective planets 1 member floating Effective planets All fixed Effective planets Planet Interference OD Radial Loads On Sun amp Ring Balanced 10 Value Unit Comment 0 000000 deg Tin deg 8 2253 deg Diff 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment Ring Sun gear ratio 4 0735 Planet Sun Ratio 1 5368 Ring Planet Ratio 2 6507 ROTATION SPEED Sun gear 1500 000 rpm Ring gear 225 000 rom Carrier 115 000 rpm ROTATION SPEED RELATIVE TO CARRIER Sun gear 1385 000 rpm Ring gear 340 000 rpm Planet gear 901 244 rpm Carrier 0 000 rpm DRIVER DRIVEN Sun gear Driver Ring gear Driven Carrier Driven TORQUES ON ELEMENTS NO LOSSES Sun gear 5000 00 Ibf in Ring gear 20367 65 Ibf in Carrier 25367 65 Ibf in POWER IN OUT NO LOSSES Sun gear 119 00 HP Ring gear 72 71 HP 11 UTS Integrated Gear Software Model Title Program 60 1163 Unit
5. Description Min Recommended AGMA Quality Class TORQUES ON ELEMENTS NO LOSSES Sun gear Ring gear Carrier POWER IN OUT NO LOSSES Sun gear Ring gear Carrier PER PLANET GEAR Relative power at sun mesh no loss Relative power at ring mesh no loss Tooth tangential load at sun Tooth tangential load at ring Face width sun planet K factor sun planet Unit load sun planet Helical axial contact ratio Face width planet ring K factor planet ring Unit load planet ring Helical axial contact ratio 66 Value Q6 3413 85 13996 80 17410 66 65 00 0 00 65 00 17 4183 17 4183 1094 18 1137 95 2 2500 389 67 4863 04 2 2500 106 91 5057 56 Unit Ibf in Ibf in Ibf in HP HP HP HP HP Ibf Ibf in psi psi in psi psi Comment Model Title Program 60 1163 Unit System US Description Centripetal acceleration on planet OPERATING PITCH DIAMETERS Ring gear Planet with ring gear Planet with sun gear Sun gear ASPECT RATIOS Sun Face PD Planet Face PD Sun Planet Mesh VIBRATION Fundamental meshing frequency Factorized Non factorized Torsional variation frequency Value 4 089 8 2000 3 0000 3 1200 2 0800 1 08 0 72 321 57 0 0000 100 0000 964 71 Figure 2 2 is a plot of the operating pitch diameters 67 60 1163 Simple Epicyclic Differential Design Unit Comment G s in in in in Hz Hz 60 116
6. so Hydraulic Power a na c c LL 150 200 250 300 350 400 450 Hydraulic Power rpm We can see from the plot that power circulates through the differential and back through the hydraulic unit to the motor for fan speeds up to about 290 RPM At higher fan speeds power flows from the motor through the hydraulic unit to the differential The maximum power the hydraulic unit must handle is about 120 HP 58 60 1163 Simple Epicyclic Differential Design If a table is useful it can be quickly made using the TK Solver Table Sheet Go to this sheet and label a table hyd_pow See Sheet 1 7 Sheet 1 7 TRE Ti planets Location Data for Planets inches JSF 1 Suggested Serice Factors SF for Steel Gears XUL SunPlanetUnitLoad amp K Factors for Steel Gears Input iTable Speed RPM PowerHP Torque bfin PLV f min Load lbf K UnitLoad psi units Conversion Ur Conversion Units 1 hyd_pow Hydraulic Power Dive into the table subsheet for hyd_pow using the right mouse button and set up the table Sheet 1 8 Sheet 1 8 TABLE hyd pow Title Hydraulic Power Vertical or Horizontal Vertical The table should look like Sheet 1 9 59 UTS Integrated Gear Software Sheet 1 9 Element Fan RPN Hydraulic P Rm 0883143 2838571 5716286 9778286 1 467857 2 027314 2 6418 3 296914 3 978257 4 671
7. 100 2 1 00 1 00 1 00 4 000 Final Carb SPUR 2E6 1 00 The table takes into account the class of gearing such as high speed or medium speed The accuracy to which the gears are made is also included along with the type of gear spur helical and the heat treatment used UTS Integrated Gear Software The unit loads have been adjusted for reverse bending of the planet gear teeth by reducing the unit loads usually used to 70 of the normal values The table is interactive and we can change the items marked with an asterisk The number of cycles needed is found by multiplying the speed relative to the carrier by the life required If the sun meshes with more than one planet this must be taken into account You may move the cursor to the appropriate location in the table and change the values for pinion cycles service factor and ratio to suit the application After solving the model the table will be updated to reflect the changed data 60 1163 Simple Epicyclic Differential Design Examples If you are using model 60 1168 for the first time you may wish to run the following examples Some output values shown here have been rounded off Example 1 Suppose we wish to design a spur gear differential planetary set with a sun gear speed of 1500 RPM a ring gear speed of 225 RPM in the opposite direction from the sun and a carrier speed of about 115 RPM in the same direction as the sun The sun gear torque f
8. 20 0000 Axial Pitch Normal Module 2 540000 Transverse Module 2 5400 PLANET SPACING Least mesh angle Planets must be 3 5294 NUMBER OF EQUALLY SPACED PLANETS These are the ist 4 up to 50 that 2 will assemble without interference 3 planets will assemble equally if ring sun planets integer OPERATION AS GEAR UNIT OR DIFFERENTIAL Enable table e enable c clear e Type of unit Planetary Number of planets 3 ck Effective planets 1 member floating 3 0000 Effective planets All fixed 2 4400 Effective planets 3 0000 Planet Interference OD 4 5033 Radial Loads On Sun amp Ring Balanced Yes Ring Sun gear ratio 4 1000 64 Unit in deg in mm mm deg Comment 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment Planet Sun Ratio 1 5000 Ring Planet Ratio 2 7333 ROTATION SPEED Sun gear 1200 000 rpm Ring gear 0 000 rpm Carrier 235 294 rpm ROTATION SPEED RELATIVE TO CARRIER Sun gear 964 706 rpm Ring gear 235 294 rpm Planet gear 643 137 rpm Carrier 0 000 rpm DRIVER DRIVEN Sun gear Driver Ring gear Driven Carrier Driven SUN PLANET Sun Planet 525 32 ft min Max Recommended Spacing Tolerance 0 00146 in Min Recommended AGMA Quality Class Q7 RING PLANET Ring Planet 505 12 ft min Max Recommended Spacing Tolerance 0 00198 in 65 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US
9. ANGLES Operating Center Distance 2 8400 in Mid point Center Distance 2 8000 in Opr Press Angle Sun Planet Mesh 24 5066 deg 32 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment Opr Press Angle Ring Planet Mesh 19 4381 deg NOMINAL PITCH amp PRESSURE ANGLE Normal Pitch 10 000000 1 in Normal Pressure Angle 20 000000 deg Helix Angle 0 000000 deg Transverse Pitch 10 0000 1 in Transverse Press Angle 20 0000 deg Axial Pitch in Normal Module 2 540000 mm Transverse Module 2 5400 mm PLANET SPACING Least mesh angle Planets must be 3 2143 deg NUMBER OF EQUALLY SPACED PLANETS These are the 1st 4 up to 50 that 2 will assemble without interference 4 planets will assemble equally if ring sun planets integer OPERATION AS GEAR UNIT OR DIFFERENTIAL Enable table e enable c clear C Type of unit Diff Number of planets 4 ck Effective planets 1 member floating 3 7000 33 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description Effective planets All fixed Effective planets Planet Interference OD Radial Loads On Sun amp Ring Balanced Ring Sun gear ratio Planet Sun Ratio Ring Planet Ratio ROTATION SPEED Sun gear Ring gear Carrier ROTATION SPEED RELATIVE TO CARRIER Sun gear Ring gear Planet gear Carrier DRIVER DRIVEN Sun gear Ring gear Carrier 34 Value 3 0000
10. Press Angle deg Axial Pitch in Normal Module 2 911493 mm Transverse Module 2 9115 mm PLANET SPACING Least mesh angle Planets must be 3 2143 deg 20 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment NUMBER OF EQUALLY SPACED PLANETS These are the ist 4 up to 50 that 2 will assemble without interference 4 planets will assemble equally if ring sun planets integer OPERATION AS GEAR UNIT OR DIFFERENTIAL Enable table e enable c clear C Type of unit Diff Number of planets 4 ck Effective planets 1 member floating 3 7000 Effective planets All fixed 3 0000 Effective planets 3 7000 Planet Interference OD 4 5389 in Radial Loads On Sun amp Ring Balanced Yes Ring Sun gear ratio 4 0909 Planet Sun Ratio 1 5455 Ring Planet Ratio 2 6471 ROTATION SPEED Sun gear 1500 000 rpm Ring gear 225 000 rpm Carrier 113 839 rpm 21 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description Value Unit Comment ROTATION SPEED RELATIVE TO CARRIER Sun gear 1386 161 rpm Ring gear 338 839 rpm Planet gear 896 928 rpm Carrier 0 000 rpm DRIVER DRIVEN Sun gear Driver Ring gear Driven Carrier Driven SUN PLANET Sun Planet 915 14 ft min Max Recommended Spacing Tolerance 0 00115 in Min Recommended AGMA Quality Class Q8 RING PLANET Ring Planet 915 14 ft min Max Recommended Spacing Tolerance 0 00153 in Min Recommended
11. Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment PER PLANET GEAR Relative power at sun mesh no loss HP Relative power at ring mesh no loss HP Tooth tangential load at sun Ibf Tooth tangential load at ring Ibf Face width sun planet in K factor sun planet psi Unit load sun planet psi Helical axial contact ratio Face width planet ring in K factor planet ring psi Unit load planet ring psi Helical axial contact ratio Centripetal acceleration on planet G s VIBRATION Fundamental meshing frequency 508 26 Hz Factorized Yo Yo Non factorized Yo Torsional variation frequency Hz APPROXIMATE EFFICIENCY Coefficient of Friction 0 0600 Sun Planet Power Loss HP Ring Planet Power Loss HP Total Power Loss Gear Losses Only HP 17 UTS Integrated Gear Software With 22 and 90 teeth the carrier speed is about 114 RPM The sun is a driver and the ring and carrier are driven The torque and power are listed for all elements The sun power is positive indicating power input and the ring and carrier power are negative indicating power out This should guide any studies of approach and recess action done on the teeth It is not always apparent Use the speeds relative to the carrier and relative power for load analysis To size the unit we need to take a guess at the number of planets we will use Let s assume for now that the number of planets is 4 Enter 4 for
12. know that 2 planets will assemble 180 degrees apart the 4 planets would be placed at 0 degrees 87 907 degrees 180 degrees and 267 907 degrees The tip clearance should then be checked Since we have two sets of planets 180 degrees apart the theoretical summation of the bearing loads on the sun and ring is still zero The model will calculate the planet interference outside diameter The planet OD must be less than this diameter The planet tooth tip clearance will be the amount the actual planet OD is less than the interference OD The summation of radial loads on the sun and ring will be made to determine whether or not the radial loads on the sun and planet are balanced The result is displayed as a Yes or No under Radial Loads On Sun amp Ring Balanced It is not necessary or even desirable that Ning Noun 22 N saad If this relationship is met and the center distance is standard then the operating pressure angles at the sun planet external mesh and the planet ring internal mesh 9 will be equal to the nominal pressure angle of the system If is made higher than nominal and Pint lower than nominal it will increase the strength of the set and reduce the burst stress on the ring x and can be easily controlled by the number of planet teeth and the operating center distance If the ring gear rim thickness is 2 tooth depths or more a high operating pressure angle will tend to reduce the bending str
13. o 851858 880262 ILL 405 300 0 824 1 NI co 4 NI ce Sun EMEND MEER 1388 16 Driver 82450 MEE Per Planet Solve and you should have Table 1 5 46 60 1163 Simple Epicyclic Differential Design Table 1 5 Bj INT TABLE iTable List 1 2 3 Sun Ring Carrier Planet Speed 2140 81 150 00 300 00 Power 16 61 4 76 11 85 Torque 488 89 2000 00 2488 89 Rel Speed 1840 91 450 00 D 1227 27 Driver Driven Driven Driver Driver PL Velocity 1094 99 1056 57 Per Planet Per Planet Rel Power 3 86 3 86 Tan Load 116 31 120 54 K Factor 68 26 18 57 Unit Load 930 51 964 34 Planet G Load Note that with the change of rotation entered we now have both the ring and the carrier driving and the sun as the driven With the rotation data we originally used we had the sun as the driver and both the ring and carrier were driven The table makes a note of driver and driven and the algebraic signs of the power for each element also indicates the direction of power flow In many situations it can be helpful to investigate the behavior of the elements of a differential over a range of operating conditions For example suppose that we wish to use this differential to control the speed of a fan driven by a constant speed electric motor We will connect the motor to the sun gear and the carrier to the fan shaft The motor will also drive a
14. variable speed hydraulic pump motor combination The hydraulic unit will also be connected to the ring gear This is not meant to imply that this is a good design for this differential unit and is included to illustrate the TK Solver setup for this type of work The motor will run at a speed of 1500 RPM The fan power is known to conform to this equation Horsepower 300 RPM 500 3 The maximum speed for the fan is 500 RPM where the power is 300 HP In terms of the variables used in the model this equation would be written 47 UTS Integrated Gear Software Pe 300 Nc 500 3 where Pc the power removed from the carrier Ne the carrier RPM To set up the model the first step is to enter the equation on the Rule Sheet Go to the bottom of the Rule Sheet and type in the equation Sheet 1 2 Sheet 1 2 if and plot y solved eltG 0 then plt plot plot opr_cd opr_pdr opr_pdpr opr_pdps opr_pds plnt if andfplots n solved eltQ 0 then pltztrans plot opr cd plint ma ni maxOD maxODIplt plnt Bal chk bal plt plnt f given ff D6 call PLf effpl RHPpls RHPplr Ps Pr Pc Pls Plr Pl Eff approx effeciency call factors update K and UL table Pe 300 Nc 500y 3 Next go to the Variable Sheet and enter c for Enable table to avoid waiting for the solution of the table as we proceed To check the equation we entered on the Rule Sheet enter 1500 for sun gear speed electric moto
15. 3 Simple Epicyclic Differential Design A possible solution to the load problem is to go to 4 planets instead of 3 The sum of the teeth in the ring and sun is 102 which is divisible by 3 but not by 4 Therefore 4 planets cannot be assembled with equal spacing However 102 is divisible by 2 so we may be able to use 2 sets of 2 planets spaced 180 at degrees Since at least one element is floating we must make sure that the loads on the sun and ring are balanced We will change to 4 planets and solve the model After solving we note that the effective number of planets with at least one member floating is 3 7 Enter 3 7 for the effective number of planets and solve again This solution is shown in Report 2 2 Report 2 2 Input and output report Model Title Program 60 1163 Unit System US Description Value Unit Comment MESSAGE FIELD ERROR MESSAGE internal mesh none ERROR MESSAGE external mesh none ERROR MESSAGE mesh general Chk Spc Prime factors greater than 100 none NUMBER OF TEETH Ring Gear Teeth 82 Planet Gear Teeth 30 Sun Gear Teeth 20 Plot pitch diameters y CENTER DISTANCE amp PRESSURE ANGLES Operating Center Distance 2 6000 in 69 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description Value Unit Comment Mid point Center Distance 2 5500 in Opr Press Angle Sun Planet Mesh 25 3712 deg Opr Press Angle Ring Planet Mesh 20 0000 deg NOMINAL PITCH amp PRESSURE ANGLE
16. 3 7000 4 0164 Yes 4 0909 1 5000 2 7273 1500 000 225 000 113 839 1386 161 338 839 924 107 0 000 Driver Driven Driven Unit rom rom rpm rpm rpm rpm rpm Comment 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment SUN PLANET Sun Planet 824 50 ft min Max Recommended Spacing Tolerance 0 00120 in Min Recommended AGMA Quality Class Q7 RING PLANET Ring Planet 795 57 ft min Max Recommended Spacing Tolerance 0 00163 in Min Recommended AGMA Quality Class Q7 TORQUES ON ELEMENTS NO LOSSES Sun gear 5000 00 Ibf in Ring gear 20454 55 Ibf in Carrier 25454 55 Ibf in POWER IN OUT NO LOSSES Sun gear 119 00 HP Ring gear 73 02 HP Carrier 45 98 HP PER PLANET GEAR Relative power at sun mesh no loss 29 7214 HP Relative power at ring mesh no loss 29 7214 HP Tooth tangential load at sun 1189 57 Ibf Tooth tangential load at ring 1232 83 Ibf 35 UTS Integrated Gear Software Model Title Unit System US Description Face width sun planet K factor sun planet Unit load sun planet Helical axial contact ratio Face width planet ring K factor planet ring Unit load planet ring Helical axial contact ratio Centripetal acceleration on planet OPERATING PITCH DIAMETERS Ring gear Planet with ring gear Planet with sun gear Sun gear ASPECT RATIOS Sun Face PD Planet Face PD Sun Planet Mesh VIBRATI
17. 429 5 362029 6 035657 6 677914 7 2744 92 967343 102 49508 112 5728 123 21428 Note The relative power in an epicyclic differential is often misunderstood The input and output torques of any gear unit must balance The carrier of an epicyclic differential is rotating Therefore the meshing velocities of the teeth are different than in a non epicyclic gear The power carried by the teeth is a product of load and linear velocity Since the linear velocity is different than rotation speed multiplied by pitch radius the relative power is different than the shaft transmitted power The relative power should be used in load calculations and of course the relative speed must then also be used 60 60 1163 Simple Epicyclic Differential Design Example 2 This example is a planetary gear ring fixed with a ratio of 5 1 to 1 The ring gear has 82 teeth and the sun gear has 20 teeth The planet gear has 30 teeth instead of the standard 31 teeth in order to bring the operating pressure angle of the external mesh up to about 20 degrees This is done to increase the beam strength of the external mesh The operating center distance has been set to standard for the internal mesh This is not a requirement but this brings the external operating pressure angle to about what we want The maximum K factor Fig 2 1B allowed is 320 psi However with th
18. AGMA Quality Class Q7 TORQUES ON ELEMENTS NO LOSSES Sun gear 5000 00 Ibf in Ring gear 20454 55 Ibf in Carrier 25454 55 Ibf in 22 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment POWER IN OUT NO LOSSES Sun gear 119 00 HP Ring gear 73 02 HP Carrier 45 98 HP PER PLANET GEAR Relative power at sun mesh no loss 29 7214 HP Relative power at ring mesh no loss 29 7214 HP Tooth tangential load at sun 1071 75 Ibf Tooth tangential load at ring 1071 75 Ibf Face width sun planet 1 0000 in K factor sun planet 700 00 psi Unit load sun planet 9350 00 psi Helical axial contact ratio Face width planet ring in K factor planet ring psi Unit load planet ring psi Helical axial contact ratio Centripetal acceleration on planet 1 181 G s OPERATING PITCH DIAMETERS Ring gear 10 3163 in Planet with ring gear 3 8973 in Planet with sun gear 3 8973 in Sun gear 2 5218 in 23 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description Value ASPECT RATIOS Sun Face PD 0 40 Planet Face PD Sun Planet Mesh 0 26 VIBRATION Fundamental meshing frequency 508 26 Factorized Non factorized Torsional variation frequency APPROXIMATE EFFICIENCY Coefficient of Friction 0 0600 Sun Planet Power Loss 1 10 Ring Planet Power Loss 0 55 Total Power Loss Gear Losses Only 1 65 Approx Efficiency 98 6 Unit
19. ARRIER Sun gear 1386 161 rpm Ring gear 338 839 rpm Planet gear 896 928 rpm Carrier 0 000 rpm DRIVER DRIVEN Sun gear Driver Ring gear Driven Carrier Driven SUN PLANET Sun Planet 798 37 ft min Max Recommended Spacing Tolerance 0 00122 in Min Recommended AGMA Quality Class Q7 RING PLANET Ring Planet 798 37 ft min Max Recommended Spacing Tolerance 0 00162 in Min Recommended AGMA Quality Class Q7 TORQUES ON ELEMENTS NO LOSSES Sun gear 5000 00 Ibf in Ring gear 20454 55 Ibf in Carrier 25454 55 Ibf in 28 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment POWER IN OUT NO LOSSES Sun gear 119 00 HP Ring gear 73 02 HP Carrier 45 98 HP PER PLANET GEAR Relative power at sun mesh no loss 29 7214 HP Relative power at ring mesh no loss 29 7214 HP Tooth tangential load at sun 1228 50 Ibf Tooth tangential load at ring 1228 50 Ibf Face width sun planet 1 3139 in K factor sun planet 700 00 psi Unit load sun planet 9350 00 psi Helical axial contact ratio Face width planet ring in K factor planet ring psi Unit load planet ring psi Helical axial contact ratio Centripetal acceleration on planet 1 031 G s OPERATING PITCH DIAMETERS Ring gear 9 0000 in Planet with ring gear 3 4000 in Planet with sun gear 3 4000 in Sun gear 2 2000 in 29 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Desc
20. ARRIER Sun gear 1386 161 rpm Ring gear 338 839 rpm Planet gear 924 107 rpm Carrier 0 000 rpm DRIVER DRIVEN Sun gear Driver Ring gear Driven Carrier Driven SUN PLANET Sun Planet 824 50 ft min Max Recommended Spacing Tolerance 0 00120 in Min Recommended AGMA Quality Class Q7 RING PLANET Ring Planet 795 57 ft min Max Recommended Spacing Tolerance 0 00163 in Min Recommended AGMA Quality Class Q7 TORQUES ON ELEMENTS NO LOSSES Sun gear 5000 00 Ibf in Ring gear 20454 55 Ibf in Carrier 25454 55 Ibf in 40 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment POWER IN OUT NO LOSSES Sun gear 119 00 HP Ring gear 73 02 HP Carrier 45 98 HP PER PLANET GEAR Relative power at sun mesh no loss 29 7214 HP Relative power at ring mesh no loss 29 7214 HP Tooth tangential load at sun 1189 57 Ibf Tooth tangential load at ring 1232 83 Ibf Face width sun planet 1 2500 in K factor sun planet 698 10 psi Unit load sun planet 9516 56 psi Helical axial contact ratio Face width planet ring 1 2500 in K factor planet ring 189 95 psi Unit load planet ring 9862 62 psi Helical axial contact ratio Centripetal acceleration on planet 1 045 G s OPERATING PITCH DIAMETERS Ring gear 8 9684 in Planet with ring gear 3 2884 in Planet with sun gear 3 4080 in Sun gear 2 2720 in 41 UTS Integrated Gear Software Model Title Unit Syste
21. Comment Hz Hz HP HP HP The normal pitch for this condition is about 8 72 Four planets is OK for equally spaced assembly Note that the effective number of planets from a tooth load standpoint is 3 7 With more than 3 planets even with one or two members floating it is very difficult to share the load between planets equally You may of course change the effective number of planets if you desire With a 700 K factor and 1 inch face width the operating pitch diameter of the sun is about 2 5 inches Let s suppose we wish to use a little lighter pitch and a higher face to PD ratio Change the normal pitch to 10 and enter 20 degrees for the normal pressure angle Blank the face width The data entry is shown in Figure 1 3 the solved model in Report 1 4 24 60 1163 Simple Epicyclic Differential Design Fig 1 3 0 000000 540000 0 000000 000000 AA END en NEN NENNEN NEN a a Aa AN Report 1 4 Input and output report Model Title Program 60 1163 Unit System US Description Value Unit Comment MESSAGE FIELD ERROR MESSAGE internal mesh none ERROR MESSAGE external mesh none ERROR MESSAGE mesh general none 25 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description Value Unit Comment Prime factors greater than 100 none NUMBER OF TEETH Ring Gear Teeth 90 Planet Gear Teeth 34 Sun Gear Teeth 22 Plot pitch diameters n CENT
22. ER DISTANCE amp PRESSURE ANGLES Operating Center Distance 2 8000 in Mid point Center Distance 2 8000 in Opr Press Angle Sun Planet Mesh 20 0000 deg Opr Press Angle Ring Planet Mesh 20 0000 deg NOMINAL PITCH amp PRESSURE ANGLE Normal Pitch 10 000000 1 in Normal Pressure Angle 20 000000 deg Helix Angle 0 000000 deg Transverse Pitch 10 0000 1 in Transverse Press Angle 20 0000 deg Axial Pitch in Normal Module 2 540000 mm Transverse Module 2 5400 mm PLANET SPACING Least mesh angle Planets must be 3 2143 deg 26 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment NUMBER OF EQUALLY SPACED PLANETS These are the ist 4 up to 50 that 2 will assemble without interference 4 planets will assemble equally if ring sun planets integer OPERATION AS GEAR UNIT OR DIFFERENTIAL Enable table e enable c clear c Type of unit Diff Number of planets 4 ck Effective planets 1 member floating 3 7000 Effective planets All fixed 3 0000 Effective planets 3 7000 Planet Interference OD 3 9598 in Radial Loads On Sun amp Ring Balanced Yes Ring Sun gear ratio 4 0909 Planet Sun Ratio 1 5455 Ring Planet Ratio 2 6471 ROTATION SPEED Sun gear 1500 000 rpm Ring gear 225 000 rpm Carrier 113 839 rpm 27 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description Value Unit Comment ROTATION SPEED RELATIVE TO C
23. Mid point Center Distance Opr Press Angle Sun Planet Mesh Opr Press Angle Ring Planet Mesh NOMINAL PITCH amp PRESSURE ANGLE Normal Pitch Normal Pressure Angle Helix Angle Transverse Pitch Transverse Press Angle Axial Pitch Normal Module Transverse Module PLANET SPACING Least mesh angle 38 Value none 90 33 22 2 8400 2 8000 24 5066 19 4381 10 000000 20 000000 0 000000 10 0000 20 0000 2 540000 2 5400 3 2143 Unit 1 in deg deg 1 in deg mm mm deg Comment 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment NUMBER OF EQUALLY SPACED PLANETS These are the ist 4 up to 50 that 2 will assemble without interference 4 planets will assemble equally if ring sun planets integer OPERATION AS GEAR UNIT OR DIFFERENTIAL Enable table e enable c clear C Type of unit Diff Number of planets 4 ck Effective planets 1 member floating 3 7000 Effective planets All fixed 3 0000 Effective planets 3 7000 Planet Interference OD 4 0164 in Radial Loads On Sun amp Ring Balanced Yes Ring Sun gear ratio 4 0909 Planet Sun Ratio 1 5000 Ring Planet Ratio 2 7273 ROTATION SPEED Sun gear 1500 000 rpm Ring gear 225 000 rpm Carrier 113 839 rpm 39 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description Value Unit Comment ROTATION SPEED RELATIVE TO C
24. ON Fundamental meshing frequency Factorized Non factorized Torsional variation frequency Program 60 1163 Value 1 2466 700 00 9542 40 1 045 8 9684 3 2884 3 4080 2 2720 0 55 0 37 508 26 50 0000 50 0000 2033 04 36 Unit Comment in psi psi psi psi Hz Hz 60 1163 Simple Epicyclic Differential Design We now have A at about 24 5 degrees and at about 19 4 degrees The face width for the sun and planet required to keep the K factor at 700 is 1 247 Let s even the face up to 1 1 4 inch Blank the 700 K factor and input 1 25 for the face width of both meshes We could use different faces if we wish but although the compressive stress is much less at the internal mesh the unit load is about the same and we should probably set the faces about the same The data input is shown in Figure 1 6 and the solved model in Report 1 7 Fig 1 6 Report 1 7 me 23 e 2 Input and output report Model Title Program 60 1163 Unit System US Description Value Unit Comment MESSAGE FIELD ERROR MESSAGE internal mesh none ERROR MESSAGE external mesh none ERROR MESSAGE mesh general none 37 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description Prime factors greater than 100 NUMBER OF TEETH Ring Gear Teeth Planet Gear Teeth Sun Gear Teeth Plot pitch diameters CENTER DISTANCE amp PRESSURE ANGLES Operating Center Distance
25. Program 60 1163 Simple Epicyclic Differential Design Introduction The simple epicyclic gear unit consists of a central external gear sun gear meshed with one or more external gears planet gears The planet gears are then meshed with an internal gear ring gear which encloses the system The planet gears and planet gear support bearings are held in a carrier which rotates about the geometric center of the unit The term epicyclic comes from the path of a point on a planet gear which traces out an epicycloid in space Therefore there are three input output elements in simple epicyclic gear differentials The ring sun ratio range for which these units can be designed with reasonable proportions is about 2 1 to 11 1 Below this range the planet gears become quite small and it becomes difficult to design the gears and planet bearings for reasonable life Above this range the sun gear becomes small and the number of planets that can be used without interference is limited This again makes the design of the bearings difficult The range can be extended using compound epicyclic differentials See UTS TK model 60 1164 Compound Epicyclic Differentials If more than one planet gear is used the number of planets that will assemble between the sun and ring is limited by the numbers of teeth in the sun and ring and by the possibility of interference between the tips of the planet gear teeth For a number of planets to assemble equally spaced
26. Report 1 3 18 60 1163 Simple Epicyclic Differential Design Sheet 1 1 EG Variables Status Input Comment i Face width sun planet K factor sun planet See Table Unit load sun planet See Table Helical axial contact ratio Face width planet ring K factor planet ring See Table Unit load planet ring See Table Helical axial contact ratio Centripetal acceleration on planet OPERATING PITCH DIAMETERS d opr pdr i Ring gear opr pdpr ji Planet with ring gear opr pdps i Planet with sun gear opr pds i Sun gear Report 1 3 we 18 Input and output report Model Title Program 60 1163 Unit System US Description Value Unit Comment MESSAGE FIELD ERROR MESSAGE internal mesh ERROR MESSAGE external mesh ERROR MESSAGE mesh general Prime factors greater than 100 none 19 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description Value Unit Comment NUMBER OF TEETH Ring Gear Teeth 90 Planet Gear Teeth 34 Sun Gear Teeth 22 Plot pitch diameters n CENTER DISTANCE amp PRESSURE ANGLES Operating Center Distance 3 2095 in Mid point Center Distance 3 2095 in Opr Press Angle Sun Planet Mesh deg Opr Press Angle Ring Planet Mesh deg NOMINAL PITCH amp PRESSURE ANGLE Normal Pitch 8 724047 1 in Normal Pressure Angle deg Helix Angle 0 000000 deg Transverse Pitch 8 7240 Vin Transverse
27. System US Description Carrier VIBRATION Fundamental meshing frequency Factorized Non factorized Torsional variation frequency APPROXIMATE EFFICIENCY Coefficient of Friction Sun Planet Power Loss Ring Planet Power Loss Total Power Loss Gear Losses Only Approx Efficiency Value 46 29 507 83 0 0600 Unit Comment HP Hz Hz HP HP HP With 22 teeth in the sun and the required speeds we need about 90 teeth in the ring Enter 90 for the ring gear and blank the carrier speed as shown in Figure 1 2 After solving again you should have the solution shown in Report 1 2 12 60 1163 Simple Epicyclic Differential Design Fig 1 2 Integrated Gear Software 60 1163 I Il 13 UTS Integrated Gear Software Report 1 2 Input and output report Model Title Program 60 1163 Unit System US Description Value Unit Comment MESSAGE FIELD ERROR MESSAGE internal mesh ERROR MESSAGE external mesh ERROR MESSAGE mesh general Prime factors greater than 100 none NUMBER OF TEETH Ring Gear Teeth 90 Planet Gear Teeth 34 Sun Gear Teeth 22 Plot pitch diameters n CENTER DISTANCE amp PRESSURE ANGLES Operating Center Distance in Mid point Center Distance in Opr Press Angle Sun Planet Mesh deg Opr Press Angle Ring Planet Mesh deg NOMINAL PITCH amp PRESSURE ANGLE Normal Pitch 1 in Normal Pressure Angle deg Helix Angle 0 000000 deg 14 Model Title Unit Syste
28. an output list but we are for this example only building a list for Pr Now that we have a list of fan speeds Ne and the corresponding hydraulic power Pr we can quickly have a plot of these values Go to the plot sheet and label a plot hyd_pow Select Line Chart and type in the title Hydraulic Power See Sheet 1 5 Next dive into the plot sub sheet for hyd_pow using the right mouse button Set Display Zero Axes to X axis label the X and Y axes enter Nc as the X Axis List and Pr as the Y Axis list as shown in Sheet 1 6 Plot F7 key and you should have a screen that looks like Figure 1 8 Sheet 1 5 Name Plot Type PD s Line chart Operating Pitch Diameters 0 x j LIST Hc I Comment Format Display Unit Calculation Unit rpm rpm Element Value co DAHONG DNS Ko wk SS x w hyd_pow Line chart Hydraulic Power 56 60 1163 Simple Epicyclic Differential Design Sheet 1 6 L LINE CHART hyd pow Display Scale Yes Display Zero Axes x axis Display Grid No Display Legend No Line Chart Scaling Linear Title Hydraulic Power Subtitle X Axis Label Hydraulic Power Y Axis Label Fan RPM X Axis Minimum Maximum Y Axis Minimum Maximum x Axis List 57 UTS Integrated Gear Software Fig 1 8 5 PLOT hyd pow
29. around the center the sum of the tooth numbers in the ring and sun divided by the number of planets used must be an integer Nang Nun integer where N ng Number of teeth in ring gear sun Number of teeth in sun gear n Number of planet gears P The distance between the planet gear centers in the carrier must of course be greater than the outside diameter of the planet gears or tooth tip interference will result assuming the planet gears are in the same plane It is not necessary that the planets be equally spaced However to make assembly possible they must be spaced at multiples of the Least mesh angle UTS Integrated Gear Software e B integer B 360 Nying tN sun where e Angle between adjacent planet gears deg B Least mesh angle deg For example suppose we have an epicyclic set with Ning 68 teeth and Nun 18 teeth and we wish to use 4 planets arranged 90 degrees apart Nying Noun 4 21 5 which is not an integer so we cannot arrange 4 planets 90 degrees apart UN ing Nun 2 48 which is an integer so we can arrange 2 planets 180 degrees apart The least mesh angle 8 360 NoingtN sun 4 186 degrees When we attempt to place a planet 90 degrees from the first planet we find that we are at 90 B 21 5 least mesh angles and cannot assemble We can however place the planet at 21 or 22 least mesh angles This would put the planet gear at 1 2 D or 2 093 degrees from 90 degrees Then since we
30. ess If the ring gear rim thickness is 1 5 tooth depths or less a low operating pressure angle will tend to reduce the bending stress 60 1163 Simple Epicyclic Differential Design The pitch line velocity is calculated and the minimum recommended AGMA quality class is determined is accordance with the ANSI AGMA 6023 A88 Design Manual for Enclosed Epicyclic Gear Drives The percent factorization is also calculated in accordance with ANSI AGMA 6023 A88 See the standard for more information on factorized tooth numbers The fundamental meshing frequency is displayed along with the expected primary torsional variation frequency The model contains a table of K factors and Unit Loads for use in estimating the size of the gears required to carry the necessary load The K factor is a function of the compressive stress carried on the teeth and is proportional to the square of the stress The Unit Load is a function of the bending stress in the root area of the gears and is directly proportional to the stress Both factors are directly proportional to the load Different gear materials are of course capable of carrying different K and Unit Load factors for a given number of cycles These factors are approximate because they do not contain many of the elements affecting the stresses on the gears They are close enough however to allow us to get a starting place for our design with only the information at hand It is essential of course to chec
31. ish to investigate other solutions This model contains a table with which the relationship among speed torque and power can be quickly explored The table uses the geometric data from the model but is independent of the speed torque and power data To use this table first check off the Enable table checkbox and press Enter Put the same data as before in the table just to compare results Your screen should look like Table 1 2 44 60 1163 Simple Epicyclic Differential Design Table 1 2 INT TABLE iTable CO E Sun Ring Carrier Planet 500 00 22500 lolol KENNEN Solve and you should have Table 1 3 Table 1 3 INT TABLE iTable mb xi Sun Ring Carrier Planet 180000 22500 11384 11900 7302 4598 800000 2045455 2545455 1386 16 338 84 0 82411 Driven Driven Driven 82450 79557 Jooo o Per Planet PerPlanet 4 2972 2874 2872 118257 128289 698 10 18895 Il 9518 50 9868262 o 105 45 UTS Integrated Gear Software Now let s change the speed and torque in the table Change your table to match Table 1 4 Table 1 4 EB INT TABLE iTable Sun Ring Carrier 15000 NEE EN 2000 00 1386 18 33884 0 Drive 82450 795 57 o fh O PerPlanet Per Planet 2972 2972 118987 123283 89810 18895
32. k our preliminary design with equations containing all the factors known to affect the operation and life of the gear set The selection of the K factor and Unit Load is of course based on the material used for the gears and our best estimate of the load the gears will carry The number of cycles the gears are required to run will also be part of the selection process The first thing we need to determine is a service factor which adjusts the load to account for the extra load imposed on the gears from non uniform torques produced by the driver and driven machines A few selected service factors are contained in the table SF The number of cycles we must run will be dealt with separately from the service factor and the service factors listed do not include adjustments for duration of service Further information on service factors can be found in various AGMA standards pertaining to specific industries and applications The service factors usually applied sometimes are not sufficient for critical drives running at high power and or speed and must be used with caution AGMA Standard 427 AGMA Information Sheet Systems Considerations for Critical Service Gear Drives is an excellent source for information concerning the rating of these drives UTS Integrated Gear Software H INT TABLE SF Inixi Uniform Mod Shock Heavy Shock En S Hydraulic Motor Multi Cylinder IC Engine Weess 11 Single Cylinder Po
33. m Description ASPECT RATIOS Sun Face PD Planet Face PD Sun Planet Mesh VIBRATION Fundamental meshing frequency Factorized Non factorized Torsional variation frequency You can plot operating pitch diameters and solve Figure 1 7 is the plot Program 60 1163 Value 0 55 0 37 508 26 50 0000 50 0000 2033 04 Unit Comment Hz Hz check the Plot pitch diameters checkbox 42 60 1163 Simple Epicyclic Differential Design Fig 1 7 E PLOT PD s ioj x Operating Pitch Diameters The planets table in the TK Solver model gives the location of the planet bearings Open it by selecting it in the Table Sheet or in the drop down list on the Toolbar Table 1 1 is the table 43 UTS Integrated Gear Software Table 1 1 B INT TABLE planets iof xj Element Angle deg X coord Chord 0 2 8400 0 440164 90 0000 0 2 8400 4 0164 180 0000 2 8400 4 0164 270 0000 0 4 0164 1 2 B 4 5 B 7 8 9 0 2 8400 This completes the solution and all design data for the geometry of the epicyclic gear set is solved for in the model Note that there are no error or caution messages in the error message block Of course this is not the only solution to this design problem The model was solved progressively to obtain this solution With the multiple directional solving capability of TK you may w
34. m Description Transverse Pitch Transverse Press Angle Axial Pitch Normal Module Transverse Module PLANET SPACING 60 1163 Simple Epicyclic Differential Design Program 60 1163 US Value Unit Comment 1 in deg Least mesh angle Planets must be 3 2143 deg NUMBER OF EQUALLY SPACED PLANETS These are the 1st 4 up to 50 that will assemble without interference planets will assemble equally if ring sun planets integer OPERATION AS GEAR UNIT OR DIFFERENTIAL Enable table e enable c clear C Type of unit Number of planets ck Diff Effective planets 1 member floating Effective planets All fixed Effective planets Planet Interference OD Radial Loads On Sun amp Ring Balanced Ring Sun gear ratio 4 0909 15 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description Value Planet Sun Ratio 1 5455 Ring Planet Ratio 2 6471 ROTATION SPEED Sun gear 1500 000 Ring gear 225 000 Carrier 113 839 ROTATION SPEED RELATIVE TO CARRIER Sun gear 1386 161 Ring gear 338 839 Planet gear 896 928 Carrier 0 000 DRIVER DRIVEN Sun gear Driver Ring gear Driven Carrier Driven TORQUES ON ELEMENTS NO LOSSES Sun gear 5000 00 Ring gear 20454 55 Carrier 25454 55 POWER IN OUT NO LOSSES Sun gear 119 00 Ring gear 73 02 Carrier 45 98 16 Unit rom rom rpm rpm rpm rpm rpm Ibf in Ibf in Ibf in HP HP HP Comment 60 1163
35. mber floating Effective planets All fixed Effective planets Planet Interference OD Radial Loads On Sun amp Ring Balanced Program 60 1163 50 Value 10 0000 20 0000 2 540000 2 5400 3 2143 dk dE Bd N Diff 3 7000 3 0000 3 7000 4 0164 Yes Unit in deg in mm mm deg Comment 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment Ring Sun gear ratio 4 0909 Planet Sun Ratio 1 5000 Ring Planet Ratio 2 7273 ROTATION SPEED Sun gear 1500 000 rpm Ring gear 255 556 rpm Carrier 500 000 rpm ROTATION SPEED RELATIVE TO CARRIER Sun gear 1000 000 rpm Ring gear 244 444 rpm Planet gear 666 667 rpm Carrier 0 000 rpm DRIVER DRIVEN Sun gear Driver Ring gear Driven Carrier Driven SUN PLANET Sun Planet 594 81 ft min Max Recommended Spacing Tolerance 0 00138 in Min Recommended AGMA Quality Class Q7 RING PLANET Ring Planet 573 94 ft min 51 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description Value Unit Comment Max Recommended Spacing Tolerance 0 00187 in Min Recommended AGMA Quality Class Q6 TORQUES ON ELEMENTS NO LOSSES Sun gear 7427 95 Ibf in Ring gear 30387 05 Ibf in Carrier 37815 00 Ibf in POWER IN OUT NO LOSSES Sun gear 176 79 HP Ring gear 123 21 HP Carrier 300 00 HP PER PLANET GEAR Relative power at sun mesh no loss 31 8533 HP Relati
36. odel Report 1 5 Input and output report Model Title Program 60 1163 Unit System US Description Value Unit Comment MESSAGE FIELD ERROR MESSAGE internal mesh none ERROR MESSAGE external mesh none ERROR MESSAGE mesh general none Prime factors greater than 100 none NUMBER OF TEETH Ring Gear Teeth 90 Planet Gear Teeth 33 Sun Gear Teeth 22 Plot pitch diameters n CENTER DISTANCE amp PRESSURE ANGLES Operating Center Distance 2 8000 in Mid point Center Distance 2 8000 in Opr Press Angle Sun Planet Mesh 22 6444 deg Opr Press Angle Ring Planet Mesh 16 9670 deg 31 UTS Integrated Gear Software This brings up to about 22 6 Fig 1 5 iu e to about 17 Center Distance And Pressure Angles egrees A small change in aaa 28400 a operating center distance should finish the job Enter 2 84 for the operating center distance and solve once again Figure 1 5 and Report 1 6 Mid point center distance in Opr press angle Sun Planet mesh deg Opr press angle Ring Planet mesh deg Report 1 6 Input and output report mob Model Title Program 60 1163 Unit System US Description Value Unit Comment MESSAGE FIELD ERROR MESSAGE internal mesh none ERROR MESSAGE external mesh none ERROR MESSAGE mesh general none Prime factors greater than 100 none NUMBER OF TEETH Ring Gear Teeth 90 Planet Gear Teeth 33 Sun Gear Teeth 22 Plot pitch diameters n CENTER DISTANCE 8 PRESSURE
37. or this condition is 5000 Ib in Also the smallest number of teeth we wish to use is about 22 The number of teeth would be selected based upon material and duty cycle see UTS model 60 180 Figure 1 1 shows a portion of the 60 1163 wizard form with the initial conditions entered If the sun and carrier speeds are input as positive the ring must be input as negative to indicate opposite rotation Check and uncheck the Enable table checkbox in the lower right of the form and press Enter to clear the interactive table Report 1 1 shows the solved model UTS Integrated Gear Software Fig 1 1 Integrated Gear Software 60 1163 LI LI En a _ a NN eweg a Ga Wm a EM 1500 000 Report 1 1 Model Title Unit System US Description MESSAGE FIELD ERROR MESSAGE internal mesh ERROR MESSAGE external mesh ERROR MESSAGE mesh general Prime factors greater than 100 NUMBER OF TEETH Ring Gear Teeth Planet Gear Teeth Sun Gear Teeth Plot pitch diameters 60 1163 Simple Epicyclic Differential Design Input and output report Program 60 1163 Unit Comment Value unknown 90 34 22 CENTER DISTANCE 8 PRESSURE ANGLES Operating Center Distance Mid point Center Distance Opr Press Angle Sun Planet Mesh Opr Press Angle Ring Planet Mesh NOMINAL PITCH amp PRESSURE ANGLE Normal Pitch Normal Pressure Angle 1 in deg UTS Integrated Gear Software Model Title
38. ower equation after solving you should have 300 for the carrier horsepower Let s check the horsepower carried by the hydraulic system as the fan is operated over a speed range of 0 to 500 RPM We could check anything we wish but for this example we will check only the hydraulic power against fan speed We will use TK Solver s list solving ability to obtain the information we want The fan speed which is the same as the carrier speed varies from 0 to 500 RPM In the TK Solver Variable Sheet place the cursor in the status column for carrier speed Nc and type L or double click on the cell and pick List from the drop down list that appears This will establish Nc as a list We also need to label the ring gear power Pr as a list The ring gear power is the same as the hydraulic power as the hydraulic unit is connected to the ring gear Your screen should be like Sheet 1 3 54 60 1163 Simple Epicyclic Differential Design Sheet 1 3 Variables Status Input Output Comment Rotation Speed 1500 000 Sun gear 255 556 Ring gear 500 000 Carrier Rotation speed relative to carrier 1000 000 Sun gear 244 444 Ring gear 566 667 Planet gear 0 Carrier Driver Driven Driver Sun gear Driven Ring gear Driven Carrier Sun Planet 594 81 Sun Planet 00138 i Max Recommended Spacing Tolerance Q7 Min Recommended AGMA Quality Class Ring Planet Ring Planet Max Recommended Spacing Tolerance Q6 Min Recommended AGMA Q
39. r and 500 for carrier speed max fan speed Blank the 5000 for the sun gear torque The solved model is shown in Report 1 8 48 60 1163 Simple Epicyclic Differential Design Report 1 8 Ki Input and output report La amp Model Title Program 60 1163 Unit System US Description Value Unit Comment MESSAGE FIELD ERROR MESSAGE internal mesh none ERROR MESSAGE external mesh none ERROR MESSAGE mesh general none Prime factors greater than 100 none NUMBER OF TEETH Ring Gear Teeth 90 Planet Gear Teeth 33 Sun Gear Teeth 22 Plot pitch diameters n CENTER DISTANCE amp PRESSURE ANGLES Operating Center Distance 2 8400 in Mid point Center Distance 2 8000 in Opr Press Angle Sun Planet Mesh 24 5066 deg Opr Press Angle Ring Planet Mesh 19 4381 deg NOMINAL PITCH amp PRESSURE ANGLE Normal Pitch 10 000000 1 in Normal Pressure Angle 20 000000 deg Helix Angle 0 000000 deg 49 UTS Integrated Gear Software Model Title Unit System US Description Transverse Pitch Transverse Press Angle Axial Pitch Normal Module Transverse Module PLANET SPACING Least mesh angle Planets must be NUMBER OF EQUALLY SPACED PLANETS These are the 1st 4 up to 50 that will assemble without interference planets will assemble equally if ring sun planets integer OPERATION AS GEAR UNIT OR DIFFERENTIAL Enable table e enable c clear Type of unit Number of planets ck Effective planets 1 me
40. re This brings the K factor for the sun and planet mesh down to about 316 psi which is less than the maximum of 320 psi The loads on the sun and ring are balanced with this arrangement The TK Solver table planets will give us the proper location for the planets to make assembly possible and insure that the sun and ring loads are balanced See Sheet 2 Sheet 2 B INT TABLE planets Element Pint Ange deg Xcoord Ycoord Chord Ba o 2 6000 3 6199 88 2353 0 0801 2 5988 3 7331 180 0000 2 6000 3 6199 268 2353 0 0801 3 7331 2 6000 Figure 2 3 is a plot of the operating pitch diameters Note that the planets are in pairs 180 degrees apart but the pairs are not at 90 degrees 74
41. ree planets the K Center Distance And Pressure Angles factor is about 390 psi which Operating center distance 2 6000 in is too high The sun gear Mid point center distance in aspect ae SS a s ane Opr press angle Sun Planet mesh deg one and we do not wish to e increase ito reduce the K Opr press angle Ring Planet mesh deg factor Figures 2 1A and 2 1B show the data inputs in the wizard form Report 2 1 shows the solved model 61 UTS Integrated Gear Software Fig 2 1A 0 000000 540000 0 000000 000000 62 60 1163 Simple Epicyclic Differential Design Report 2 1 Input and output report Model Title Program 60 1163 Unit System US Description Value Unit Comment MESSAGE FIELD ERROR MESSAGE internal mesh none ERROR MESSAGE external mesh none ERROR MESSAGE mesh general none Prime factors greater than 100 none NUMBER OF TEETH Ring Gear Teeth 82 Planet Gear Teeth 30 Sun Gear Teeth 20 Plot pitch diameters n CENTER DISTANCE 8 PRESSURE ANGLES Operating Center Distance 2 6000 in Mid point Center Distance 2 5500 in Opr Press Angle Sun Planet Mesh 25 3712 deg Opr Press Angle Ring Planet Mesh 20 0000 deg NOMINAL PITCH amp PRESSURE ANGLE Normal Pitch 10 000000 1 in Normal Pressure Angle 20 000000 deg Helix Angle 0 000000 deg 63 UTS Integrated Gear Software Model Title Program 60 1163 Unit System US Description Value Transverse Pitch 10 0000 Transverse Press Angle
42. ription ASPECT RATIOS Sun Face PD Planet Face PD Sun Planet Mesh VIBRATION Fundamental meshing frequency Factorized Non factorized Torsional variation frequency APPROXIMATE EFFICIENCY Coefficient of Friction Sun Planet Power Loss Ring Planet Power Loss Total Power Loss Gear Losses Only Approx Efficiency With a 34 tooth planet gear and a center distance of 2 8 Pot and 0 are both standard at 20 degrees The Operating Center Distance is defaulted to the Mid Point Center Distance if the operating center distance is not entered If the sun and ring are both odd or both even the mid point distance will be standard We can assemble 2 or 4 planet gears with equal spacing Value 0 60 0 39 508 26 50 0000 50 0000 1016 52 0 0600 1 10 0 55 1 65 98 6 Fig 1 4 Unit Comment Hz Hz HP HP HP ntegrated Gear Software 60 1163 Number Of Teeth Ring gear teeth Planet gear teeth Sun gear teeth a0 33 22 30 60 1163 Simple Epicyclic Differential Design We want 9 to be about 25 degrees so we need to change the number of planet teeth In this case the condition Nang NT 2 N janet is met Enter 33 for the number of planet teeth Changing the planet gear to an odd number of teeth will also double the torsional variation freguency and reduce the amplitude to about half Figure 1 4 shows the data entry Report 1 5 is the solved m
43. uality Class RING PLANET Ring Planet Max Recommended Spacing Tolerance Min Recommended AGMA Quality Class TORQUES ON ELEMENTS NO LOSSES Sun gear Ring gear Carrier POWER IN OUT NO LOSSES Sun gear Ring gear Carrier PER PLANET GEAR Relative power at sun mesh no loss Relative power at ring mesh no loss Tooth tangential load at sun Tooth tangential load at ring 72 Value 525 32 0 00146 Q7 505 12 0 00198 Q6 3413 85 13996 80 17410 66 65 00 0 00 65 00 14 1229 14 1229 887 18 922 66 Unit ft min in ft min Ibf in Ibf in Ibf in HP HP HP HP HP Ibf Ibf Comment 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment Face width sun planet 2 2500 in K factor sun planet 315 95 psi Unit load sun planet 3943 01 psi Helical axial contact ratio Face width planet ring 2 2500 in K factor planet ring 86 68 psi Unit load planet ring 4100 73 psi Helical axial contact ratio Centripetal acceleration on planet 4 089 G s OPERATING PITCH DIAMETERS Ring gear 8 2000 in Planet with ring gear 3 0000 in Planet with sun gear 3 1200 in Sun gear 2 0800 in ASPECT RATIOS Sun Face PD 1 08 Planet Face PD Sun Planet Mesh 0 72 VIBRATION Fundamental meshing frequency 321 57 Hz Yo Factorized Yo Yo Non factorized Yo Torsional variation frequency Hz 73 UTS Integrated Gear Softwa
44. uality Class Torques on elements no losses 7427 95 Sun gear 30387 05 Ring gear 37815 Carrier Power in out no losses 176 79 Sun gear 123 21 Ring gear 300 Carrier Both lists have been established but of course neither contains any data We wish Ne the carrier or fan speed to be an input list If there is an entry in the input column then Nc will be an input list The value on the Variable Sheet will not be used in list solving unless it is also in the list but only instructs TK that Nc is an input list The other list Pr the hydraulic power will be an output list as there is no entry in the input column The next job is to enter the values we desire in the list for Nc Go to the list subsheet for Nc See the TK Solver documentation if necessary Instead of typing in the RPM values we need we will use the automatic list fill feature Select Add Step enter 0 for the first value 10 for the step size and 500 for the last value The list will fill with values from 0 to 500 by a step of 10 The screen should look like Sheet 1 4 55 UTS Integrated Gear Software Sheet 1 4 Return to the variable sheet and list solve The values from the list Ne will be used one by one for input The model will solve and the solution for Pr will be placed in the list for Pr We could specify any variables we wish as
45. ve power at ring mesh no loss 31 8533 HP Tooth tangential load at sun 1767 21 Ibf Tooth tangential load at ring 1831 47 Ibf Face width sun planet 1 2500 in K factor sun planet 1037 10 psi Unit load sun planet 14137 70 psi Helical axial contact ratio Face width planet ring 1 2500 in K factor planet ring 282 19 psi Unit load planet ring 14651 80 psi 52 60 1163 Simple Epicyclic Differential Design Model Title Program 60 1163 Unit System US Description Value Unit Comment Helical axial contact ratio Centripetal acceleration on planet 20 166 G s OPERATING PITCH DIAMETERS Ring gear 8 9684 in Planet with ring gear 3 2884 in Planet with sun gear 3 4080 in Sun gear 2 2720 in ASPECT RATIOS Sun Face PD 0 55 Planet Face PD Sun Planet Mesh 0 37 VIBRATION Fundamental meshing frequency 366 67 Hz Factorized 50 0000 Non factorized 50 0000 Torsional variation frequency 1466 67 Hz APPROXIMATE EFFICIENCY Coefficient of Friction 0 0600 Sun Planet Power Loss 1 18 HP Ring Planet Power Loss 0 59 HP Total Power Loss Gear Losses Only 1 77 HP Approx Efficiency 99 4 53 UTS Integrated Gear Software The centripetal acceleration on the planets is quite high at 20 G s The model warns you of this TK Solver EN A CAUTION Centripital Acceleration on Planet Gear gt 10 G s i Cancel The planet bearings would have to be capable of running under these conditions According to the fan speed p
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