Program Center Distance Change

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1 Introduction Program Center Distance Change When the coefficient of thermal expansion of the material used for gears is different from the coefficient for the mountg or housg material, it is necessary to allow for the size changes caused by this condition. For example, if the housg is made of alumum and the gears of steel, an adjustment must be made the tooth thickness of the gears if a mimum backlash is to be present when the gear unit is below the assembly temperature. As the temperature is lowered, the housg will contract more than the gears and the amount of backlash will become less. If the drive is then put to operation the gears may warm up faster than the housg, and the backlash will be even less than at the equal temperature condition. When both the gears and housg are above the assembly temperature the backlash will usually be creased because of the larger expansion of the center distance the housg compared to the gears. (This is, of course, not the case with plastic gears metal housgs.) UTS Gear Model can be used to calculate the amount of these changes and allowance can be made the manufactured tooth thickness of the gears. In addition to thermal effects the center distance tolerance, gear total composite tolerance, bearg runout, bearg radial play, and moisture absorption of plastic gears is taken to account. The model can be used for parallel or crossed axis helical gear sets. Note: Bearg radial play will crease the maximum assembled center distance and the mimum assembled center distance because the gear mesh separatg force will push the gears apart. (The opposite is true for ternal gears.) However, if loads external to the gear mesh push the gears together, the bearg radial play may be entered as a negative value to reflect this condition. The maximum and mimum effective center distance is calculated both on an absolute basis and on a statistical basis. The percentage of assemblies cluded the chosen statistical range is also calculated. The statistical maximum and mimum ECD are based on a normal distribution of part size with the part tolerance. If the part size does not follow a normal distribution, caution should be exercised use of the max and m ECD based on this calculation.

UTS Integrated Gear Software The number of standard deviations will determe the percentage of assemblies that will be the range of the statistical maximum and mimum effective center distance based on

2 UTS Integrated Gear Software The number of standard deviations will determe the percentage of assemblies that will be the range of the statistical maximum and mimum effective center distance based on a normal distribution of part size with the part tolerance. The value that is usually used engeerg applications is 3 and the default value for the number of standard deviations (+ and -) is set to this value. With a +/- 3 standard deviation range there will be about 1 out of 370 assemblies that will be outside the statistical range. The actual center distance will not reach the maximum or mimum values (absolute or statistical) as the changes the gears are cluded the effective center distance calculations. The effect of runng the gears at the effective center distance on the relative position of the gears will be the same as the actual operatg conditions. The TK Solver model for this module contas a table of the thermal coefficients of expansion (and moisture absorption coefficients) for various materials. The table is shown Figure 1D. The values the model are average handbook values for the materials listed. The thermal coefficient values are per deg F units and should be entered per deg F. They are converted to per deg C if metric units are selected. It is recommended that these values be replaced by (or checked agast) values for the specific materials you are usg. Add or delete materials directly usg the Materials Update tab of the data put form, shown below. To add a new material, click the Add button, make entries each of the fields, then click Save. The Material # and Material Code fields are identifiers required by the TK Solver model. See Figure 1D for examples. Use this procedure also to enter materials already listed the table, but whose values are different from those already given. (Only user-entered materials can be edited and deleted with this procedure.) 2

3 Center Distance Change Examples Example 1 We will fd the required manufactured tooth thickness to sure a mimum backlash of about ch under the expected operatg temperatures for a 14/55 tooth external parallel axis gear pair. The gears are to be made to the followg specifications: Housg Material Magnesium Gear Material Nickel Steel Spur Gears Pion Teeth 14 Gear Teeth 55 Normal DP 10 Operatg PA 21.7 deg Nomal Gear Tooth Thickness Center Distance / Mimum Operatg Backlash Inspection and Assembly Temp +68 deg F AGMA Quality Class, Pion 12 AGMA Quality Class, Gear 12 Pion Bearg Runout Gear Bearg Runout Pion bearg radial play.0005/.0010 Gear bearg radial play.0005/.0010 It is estimated that the gears may run 50 degrees F hotter than the housg most of the time. A condition exists when the unit will be quickly exposed to warm air after beg at a low temperature and the housg may be 50 degrees F warmer than the gears. Operatg Temp Conditions: Housg Gears -65 F -15 F Cold Start +100 F +50 F Cold to Hot Transient +160 F +210 F Maximum Operatg Temp Open a new analysis and enter the data for the cold start condition. The completed data put form for this condition is shown Figure 1A. 3

4 UTS Integrated Gear Software Fig. 1A Figure 1B is the completed data entry form for the second temperature condition (cold to hot transient). 4

5 Center Distance Change Fig. 1B 5

6 UTS Integrated Gear Software Figure 1C is the completed data put form for the third condition (maximum operatg temperatures.) Fig. 1C 6

7 Center Distance Change Report 1A is a combed report of the solved models for all three operatg conditions. Such a report is created by savg each analysis, openg a new analysis, selectg the saved analyses you want to clude, then clickg the button labeled Compare. See the Introduction for more formation. Report 1A Model: Program Unit System: US Description Ex 1A Ex 1B Ex 1C Unit No Group External or Internal Set e e e ASSEMBLY CONDITIONS Normal_Diametral Pitch / ` Normal_Module mm ` Helix Angle deg Operatg Transverse Pressure Angle deg Temperature F Relative Humidity % HOUSING Material_Number-See Material Table Material_Code Magnesium Magnesium Magnesium Thermal Coefficient of expansion /degF Moisture Coefficient of expansion / Basic or nomal center distance Mimum center distance tolerance Maximum center distance tolerance Pion total composite tolerance Gear total composite tolerance Pion_bearg runout (TIR) Gear_bearg runout (TIR)

8 UTS Integrated Gear Software Model: Program Unit System: US Description Ex 1A Ex 1B Ex 1C Unit Pion_bearg_radial play, max Pion_bearg_radial play, m Gear_bearg_radial play, max Gear_bearg_radial play, m Mimum_assembled CD, absolute Maximum_assembled CD, absolute Mimum_assembled CD, statistical Maximum_assembled CD, statistical PINION Material_Number-See Material Table Material_Code Nickel St Nickel St Nickel St Number of teeth AGMA Quality Class Thermal Coefficient of expansion /degF Moisture Coefficient of expansion / Nomal_operatg pitch diameter GEAR Material_Number-See Material Table Material_Code Nickel St Nickel St Nickel St Number of teeth AGMA Quality Class Thermal Coefficient of expansion /degF Moisture Coefficient of expansion / Nomal_operatg pitch diameter OPERATING CONDITIONS Housg_temperature F Pion_temperature F Gear_temperature F Relative_humidity % Change_ relative humidity % 8

9 Center Distance Change Model: Program Unit System: US Description Ex 1A Ex 1B Ex 1C Unit EFFECTIVE CENTER DISTANCE Change CD (Thermal, Moisture) Approximate change backlash EFFECTIVE CD, ABSOLUTE Mimum_effective center distance Maximum_effective center distance Mean effective center distance CD Range EFFECTIVE CD, STATISTICAL Standard deviations, +/ Range of deviations Amount of assemblies cluded the range % Number_of assemblies cluded range per assembly outside range Mimum_effective center distance Maximum_effective center distance Mean effective center distance CD Range For the cold start condition the change effective center distance is ch and the approximate change backlash is ch. (The change backlash is approximate because the operatg pressure angle is averaged for the assembly and effective center distance. It is, however, quite accurate.) For the cold-to-hot transient condition he change effective center distance is ch and the approximate change backlash is ch. At the maximum operatg condition the change effective center distance is ch and the approximate change backlash is ch. The maximum backlash will then occur durg the transient condition and not at maximum operatg condition. 9

UTS Integrated Gear Software Fig. 1D The TK Solver model s table of thermal and moisture coefficients, discussed the Introduction, is shown above.

10 UTS Integrated Gear Software Fig. 1D The TK Solver model s table of thermal and moisture coefficients, discussed the Introduction, is shown above. For this analysis, the mimum effective center distance (usg absolute values) is ches and occurs durg the cold start condition. If the mimum operatg backlash is to be ch the tooth thickness of the gears will have to be calculated at this center distance. Figure 1D 10

11 Center Distance Change is the solved model from UTS Model with the cold start and cold to hot transition conditions entered. (Note that only enough of the model has been solved to obta the tooth thickness.) Report 1B Model: Program Unit System: US Description Ex 1E Ex 1F Unit CAUTION MESSAGE CAUTION MESSAGE m2 m3 m4 DRIVER, number of teeth DRIVEN, number of teeth Gear ratio Gears shaved or ground? ('s,'g,'no) no no NORMAL PLANE Normal pitch / ` Normal pressure angle deg Normal module mm` Normal base pitch TRANSVERSE PLANE Transverse pitch / ` Transverse pressure angle deg Transverse module mm` Transverse base pitch COMMON 11

12 UTS Integrated Gear Software Helix angle deg Model: Program Unit System: US Description Ex 1E Ex 1F Unit Base helix angle deg Axial pitch I n Operatg center distance Standard center distance Face width TOOTH THICKNESS DRIVER AT REF PD Normal tooth thickness Transverse tooth thickness TOOTH THICKNESS DRIVER AT OD Normal tooth thickness Transverse tooth thickness TOOTH THICKNESS DRIVEN AT REF PD Normal tooth thickness Transverse tooth thickness TOOTH THICKNESS DRIVEN AT OD Normal tooth thickness Transverse tooth thickness CLEARANCE (FOR UNDERCUT CHECK) Root clearance, Driver (approx) Root clearance, Driven (approx) DIAMETERS DRIVER Outside diameter Roll angle at OD deg Reference pitch diameter Poted tooth diameter Base dia

13 Center Distance Change Model: Program Unit System: US Description Ex 1E Ex 1F Unit DIAMETERS DRIVEN Outside diameter Roll angle at OD deg Reference pitch diameter Poted tooth diameter Base dia OPERATING DATA Workg depth Basic transverse backlash Change Opr CD from "Std" CD Normal backlash Transverse backlash Transverse pressure angle deg Helix angle deg Roll angle at pitch pot deg Circular Pitch OPERATING DATA DRIVER Pitch diameter Transverse tooth thickness Start of active profile Roll angle at SAP deg Normal tooth thickness at SAP Transverse tooth thickness at SAP Mid-pot, length of contact Roll angle at mid-pot deg OPERATING DATA DRIVEN Pitch diameter Transverse tooth thickness

14 UTS Integrated Gear Software In the cold start scenario, if the maximum tooth thickness of the gear is held to ch then the maximum tooth thickness of the pion must be ch. This will result a backlash of ch under these conditions. In the cold to hot transient scenario, if the tooth thickness tolerance is ch then the maximum backlash is ch. The tooth thickness values we have been usg are the effective tooth thickness values. Because of allowable tooth element errors that may not be measured by the measurg system beg used the manufactured size may need adjustment. The amount of adjustment depends on the measurg system. (See UTS Gear Model ) Example 2 Figure 2 and Report 2 model an ternal gear set at normal operatg temperature runng an area with high humidity. The housg is alumum, the pion is nylon 6/6 unfilled and the ternal gear is unfilled acetal. The expansion due to moisture absorption is important here especially for the nylon pion. The large change effective center distance is typical for designs usg plastic gears. The design of plastic gearg, even with small temperature differences, is difficult because of large coefficients of thermal expansion and the expansion due to moisture absorption. We will assume that the parts are measured and assembled at 50% relative humidity and will then operate at 100% humidity. 14

15 Center Distance Change Fig. 2 15

16 UTS Integrated Gear Software Report 2 Model Title : Program Unit System: US External or Internal Set i ASSEMBLY CONDITIONS Normal_Diametral Pitch / ` Normal_Module mm ` Helix Angle deg Operatg Transverse Pressure Angle deg Temperature 68 F Relative Humidity % HOUSING Material_Number-See Material Table 6 Material_Code Alumum Thermal Coefficient of expansion /degF Moisture Coefficient of expansion 0.00 / Basic or nomal center distance Mimum center distance tolerance Maximum center distance tolerance Pion total composite tolerance Gear total composite tolerance Pion_bearg runout (TIR) Gear_bearg runout (TIR) Pion_bearg_radial play, max Pion_bearg_radial play, m

17 Center Distance Change Model Title : Program Unit System: US Gear_bearg_radial play, max Gear_bearg_radial play, m Mimum_assembled CD, absolute Maximum_assembled CD, absolute Mimum_assembled CD, statistical Maximum_assembled CD, statistical PINION Material_Number-See Material Table 10 Material_Code Nyl 6/6UF Number of teeth 17 AGMA Quality Class 7 Thermal Coefficient of expansion /degF Moisture Coefficient of expansion 0.00 / Nomal_operatg pitch diameter GEAR Material_Number-See Material Table 9 Material_Code Acetal UF Number of teeth 125 AGMA Quality Class 6 Thermal Coefficient of expansion /degF Moisture Coefficient of expansion 0.00 / Nomal_operatg pitch diameter OPERATING CONDITIONS Housg_temperature 90 F Pion_temperature 110 F Gear_temperature 100 F 17

18 UTS Integrated Gear Software Model Title : Program Unit System: US Relative_humidity % Change_ relative humidity % EFFECTIVE CENTER DISTANCE Change CD (Thermal, Moisture) Approximate change backlash EFFECTIVE CD, ABSOLUTE Mimum_effective center distance Maximum_effective center distance Mean effective center distance CD Range EFFECTIVE CD, STATISTICAL Standard deviations, +/ Range of deviations Amount of assemblies cluded the % range Number_of assemblies cluded range 370 per assembly outside range Mimum_effective center distance Maximum_effective center distance Mean effective center distance CD Range The absolute values of the tolerances and changes produced by the temperature and humidity conditions produces a center distance range of ch. This is a considerable amount of change and when combed with the variation produced at possible cold and dry conditions design of an acceptable gear set may be very difficult. It is very unlikely that any gear set would be at these extremes sce all dimensions would have to be at the max tolerance limit and such a direction as to all add up the same way. Because of this, many designs use a statistical center distance variation. In this case a range of +/- 3 sigma produced a center distance range of 18

19 Center Distance Change ch. This reduction may make design much easier. The number of units that could be expected to be outside this range is about NOTE: In this example we only looked at one condition of humidity and temperature. In actual design work it is necessary to run the model under the followg conditions: 1. Max Temp & Max Humidity 2. Max Temp & M Humidity 3. M Temp & Max Humidity 4. M Temp & M Humidity The maximum and mimum values of the effective center distances from all 4 conditions are then used for design purposes. (The effect of different humidity levels can be modeled by changg the operatg relative humidity.) Application Note: All versions of this model prior to Version 4.1 adjusted the maximum and mimum effective center distance effect of the total composite tolerance as follows: Maximum center distance with master gear = tight mesh CD with gear at maximum tooth thickness + 1/2 of total composite tolerance Mimum center distance with master gear = tight mesh CD with gear at mimum tooth thickness - 1/2 of total composite tolerance Ver 4.1 (and later) adjusts the maximum and mimum effective center distance effect of the total composite tolerance as follows: Maximum center distance with master gear = tight mesh CD with gear at maximum tooth thickness Mimum center distance with master gear = tight mesh CD with gear at mimum tooth thickness - total composite tolerance This method is accordance with ANSI/AGMA 2002 B88. Reference: Paul M. Dean, Center Distance Gear Handbook, Chapter 6 Darle W. Dudley, Editor McGraw-Hill Book Company, New York, NY (1st Edition 1962) 19

Program Internal Gear Set Profile Shift Coefficients With Zero Backlash Introduction

Program Internal Gear Set Profile Shift Coefficients With Zero Backlash Introduction Program 60-107 Internal Gear Set Profile Shift Coefficients With Zero Backlash Introduction The purpose of this model is to provide data for a gear set when the tooth thickness and/or the center distance