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Stress Analysis - CALCULATIONS AND ANALYSIS See Stress...

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CALCULATIONS AND ANALYSIS See Stress Calculation Spreadsheet for sources of equations, sources of constants and material properties, and additional calculations Impact Analysis Direct wheel impact at max speed By using the deflection equation, EI Fl s 192 3 = (based upon two fully constrained rod ends), solving for F, and using a basic kinematic equation ( ) ( 2 2 2 s a v v o f = = ) to solve for s in terms of F, the force of impact can be determined (227505 N) Utilizing shaft stress equations shown below the stress can be determined (400 MPa) When comparing this to the shaft’s yield strength, a factor of safety of 1.33 is calculated
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Direct pulley impact at max speed Utilizing this same force and finding the stress on the shaft due to bending. I Mc = σ =8510 MPa This means the shaft will permanently bend due to the moment applied on it The way to avoid this catastrophic failure is to ensure the chassis protects these open gears by extending past its edges or enclosing it completely. While this may not completely ensure the module’s safety, it will fix nearly every probable scenario. Shaft Stress Calculations Shaft 1 (Diameter=3/8”) Material: 1045 Steel, Yield Strength (S y )= 530 MPa, Ultimate Strength= 625MPa Max Stress o The shaft is keyed for a 3/32” key, thus a close approximation for the actual yield strength is ¾ the materials yield strength (Keyed Yield Strength=398 MPa) o Loading is comprised of three components Moment-Based on cantilevered distance from bearing and radial load exerted on shaft from the miter gear (2.1 N-m) Force- Based on axial load exerted on shaft from miter gear (156.12 N) Torque- Exerted by the stall torque of the motor, through a gear ratio of 2:1 (9.64 N-m) o Stress Calculation- 2 / 1 2 2 max ] 48 ) 8 [( 4 T Fd M d + + Π = σ =102 MPa 2 / 1 2 2 3 max ] 64 ) 8 [( 2 T Fd M d + + Π = τ = 58.4 MPa o Factors of Safety- max σ y S n = = 3.9 max 2 τ y S n = = 3.4 Fatigue Life o Infinite Life- 2000RPM (Average operating speed)=33.3 cycles/second 5 year life @ 1 hour operating time (2 hr per week)-approximately 1,908,000 seconds of use 33.3*1,908,000= 6.4E7 cycles to failure for infinite life o The endurance strength can be calculated using the stress concentration factors from the keyway (197 MPa) o σ F =S ut +345MPa= 970 MPa
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o ) 2 log( ) / ' log( e e F N S b σ - = =-0.109915548 o b ut F S f ) 10 2 ( ' 3 = σ =.673 o e ut S S f a 2 ) ( = =900 MPa o Loads are based on typical operating conditions, not max conditions Moment-Based on cantilevered distance from bearing and radial load exerted on shaft from the miter gear (2.1 N-m) Force- Based on axial load exerted on shaft from miter gear (156.12 N) Torque- Exerted by the operating torque of the motor, through a gear ratio of 2:1 (2.82 N-m) o 2 / 1 2 2 3 ] 48 ) 8 [( 4 T Fd M d a + + Π = σ = 39.4 MPa o b a a N 1 = σ = 2.25E12 cycles to failure Shaft 2 (Diameter=1/2”) Material: 1045 Steel, Yield Strength= 530 MPa, Ultimate Strength= 625MPa Max Stress o The shaft is keyed for a 1/8” key, thus the actual yield strength can be equated to ¾ the materials yield strength (Keyed Yield Strength=398 MPa) o
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