Program Gear Yield Stress Steel Gears

Transcription

1 Program Gear Yield Stress Steel Gears Introduction This TK Solver model is written in accordance with the yield stress analysis in American Gear Manufacturers Association Standard 2001-B88. The model covers steel gears which are quenched and tempered, annealed or normalized. The brinell hardness range is 130 HB to 220 HB for annealed or normalized gears and 180 HB to 410 HB for quenched and tempered gears. The actual bending stress number is taken from the right hand side of Eq of the standard: W max K a P d K s K m S y = K v F J K f where: W max K a P d K s K m K v F J K f = maximum peak tangential load = Application factor = Nominal transverse diametral pitch = Size factor = Load distribution factor = Dynamic factor = Net face width of narrowest gear = Geometry factor = Stress correction factor K a, K s, K m, and K v may be obtained from the standard or UTS Program The model will default K s to 1 if not entered. K m and K v will be calculated if not entered and enough other data is entered. P d, J and K f may be obtained from the standard or UTS Program 500. The allowable bending stress number, S ay, is taken from the curves in Fig. 17 of the standard. S ay for quenched and tempered gears is calculated from the equation given on the curve with the inclusion of the yield strength factor, K y : S ay = K y (482 H B 32,800) Say for annealed or normalized gears is calculated from a parabolic curve fit equation from the curve in the figure: S ay = K y ( H B H B ) where: H B = Brinell hardness of the gear

2 UTS Integrated Gear Software A plot of these curves is included in the model. In the Brinell range of 130 to 180 the model will default to annealed or normalized material. In the Brinell range of 220 to 410 the model will default to quenched and tempered material. In the range of 180 to 220 it is necessary to enter 'A for annealed or normalized or 'Q for quenched and tempered because the material could be either in this range. If you enter the Brinell hardness only the model will remind you to enter your choice. It should be noted that the stress numbers we are working with are not the true stress in the material. They are considered safe stress numbers from experience. Any attempt to equate these stress numbers with true stresses, from lab tests for example, will lead to difficulty. 2

3 Gear Yield Stress-Steel Gears Example As an example, we will check the yield stress numbers for a set of gears made of normalized steel at 210 Brinell. Open a new analysis in and enter data in the data input form as shown in Figure 1. Report 1 gives the input and output values for the solved model Fig 1 Report 1 Model Title : Program Unit System: US CAUTION MESSAGE m2 m3 m4 COMMON Normal Diametral Pitch, Nominal Normal Module, Nominal PINION STRESS TOO HIGH /in ` mm ` 3

4 UTS Integrated Gear Software Model Title : Program Unit System: US Transverse Diametral Pitch Transverse Module AGMA Quality Class 12.0 Operating Transverse Pressure Angle Helix Angle, Nominal /in ` mm ` deg deg Profile Contact Ratio (Helicals) Face Width Lead Mismatch Across Face Elastic Coefficient (Def) Tooth Stiffness Constant (Def) LOAD DATA in in 2300 psi^ psi Application Factor Dynamic Factor (Def) Size Factor (Def) Trans Load Distribution Factor (Def) Face Load Distribution Factor Load Distribution Factor Tangential Tooth Load Pitch Line Velocity PINION lbf ft/min Speed of Rotation rpm Pinion Torque lbf-in Operating Pitch Diameter of Pinion in Pinion AGMA J-Factor

5 Gear Yield Stress-Steel Gears Model Title : Program Unit System: US Brinell Hardness (BHN) 210 Stress Correction Factor Yield Strength Factor(Industrial: 0.75, Conservative: 0.5) ('Q)uench/Temper-('A)nneal/Normalize A Allowable Bending Stress Number Actual Bending Stress Number Allowable Unit Load Unit Load psi psi psi psi ALLOWABLE YIELD STRESS/ACTUAL STRESS GEAR Gear AGMA J-Factor Brinell Hardness (BHN) 210 Stress Correction Factor Yield Strength Factor( Industrial: 0.75, Conservative: 0.5 ) ('Q)uench/Temper-('A)nneal/Normalize A Allowable Bending Stress Number Actual Bending Stress Number Allowable Unit Load Unit Load psi psi psi psi ALLOWABLE YIELD STRESS/ACTUAL STRESS The CAUTION MESSAGE tells us that the pinion stress is too high. Under ALLOWABLE YIELD STRESS/ACTUAL STRESS for the pinion we find that the 5

6 UTS Integrated Gear Software allowable is only 94.8% of the actual. For the gear the allowable is 101.9% of the actual. Something must be done to bring this ratio over 100% for the pinion. If we make the pinion of harder material it will increase the allowable yield stress number for the pinion. (Some change could be made to reduce the load instead, if desired.) Let's increase the pinion hardness to 250 Brinell by quenching and tempering before machining. Toggle to the Power User form or TK Solver Variable Sheet and change the Brinell hardness of the pinion and solve. (TK is the better choice because you also need to blank the input value 'A for the pinion or you will get an error message.) The data should look like Sheet 1. If desired, you can use the Integrated Gear Software report generator to create a print report of this solution to the model. Sheet (Ver 6.0) GEAR YIELD STRESS ANSI/AGMA 2001-B88 Steel Gears USE 'TOOLS', 'RUN' TO START WIZARD m1 None CAUTION MESSAGE m2 _ m3 _ m4 _ COMMON: 6 Pn 1/in ` Normal Diametral Pitch, Nominal n_mod mm ` Normal Module, Nominal Pd /in ` Transverse Diametral Pitch t_mod mm ` Transverse Module 12 Q AGMA Quality Class opr_tpa deg Operating Transverse Pressure Angle 10.5 ha deg Helix Angle, Nominal mp Profile Contact Ratio (Helicals) 6 F in Face Width.0013 et in Lead Mismatch Across Face Cp 2300 psi^.5 Elastic Coefficient (Def) G 1.79E6 psi Tooth Stiffness Constant (Def) LOAD DATA: 1.1 Ka Application Factor Kv.9 Dynamic Factor (Def) Ks 1 Size Factor (Def) Cmt 1 Trans Load Distribution Factor (Def) Cmf Face Load Distribution Factor Km Load Distribution Factor Wt lbf Tangential Tooth Load vt ft/min Pitch Line Velocity PINION: 4134 rev rpm Speed of Rotation Tp lbf-in Pinion Torque d in Operating Pitch Diameter of Pinion 6

7 Gear Yield Stress-Steel Gears.598 Jp Pinion AGMA J-Factor 250 bhnp Brinell Hardness (BHN) Kfp *Stress Correction Factor.75 Kyp *Yield Strength Factor Industrial: Kyp = 0.75 Conservative: Kyp = 0.5 htp 'Q *('Q)uench/Temper-('A)nneal/Normalize sayp psi Allowable Bending Stress Number syp psi Actual Bending Stress Number ulp psi Allowable Unit Load actulp psi Unit Load pratio ALLOWABLE YIELD STRESS / ACTUAL STRESS GEAR:.617 Jg *Gear AGMA J-Factor 210 bhng *Brinell Hardness (BHN) Kfg *Stress Correction Factor.75 Kyg *Yield Strength Factor Industrial: Kyg = 0.75 Conservative: Kyg = 0.5 'A htg ('Q)uench/Temper-('A)nneal/Normalize sayg psi Allowable Bending Stress Number syg psi Actual Bending Stress Number ulg psi Allowable Unit Load actulg psi Unit Load gratio ALLOWABLE YIELD STRESS / ACTUAL STRESS The change to a harder material for the pinion solved the problem and the allowable stress number exceeds the actual stress number by 48.3%. If you wish to see the rules and formulas used in the model bring the Rule Sheet up on the screen. The rules are annotated to make it easy to follow the flow of the model. Reference: Data was extracted from ANSI/AGMA 2001-B88, Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth with the permission of the publisher, American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, VA