BenchBot V3.1 Motion Calculations

Constraints

·       1 m/s velocity

·       1 m/s² acceleration

·       3 degree incline

·       1,000 lb maximum weight

·       8 – 10-inch wheel diameter

·       Wheel material: polyurethane

·       60A polyurethane hardness

·       Steel rail

·       ½ inch shaft

Assumptions

·       Coefficient of friction = 0.6 (this is the low end for polyurethane on steel)

·       6:1 gear ratio

·       Gear efficiency = 0.9

Significant Values Calculated for 3-degree slope (Worst case)

·       Opposing force: 629.9 N

·       Normal force: 4418.9 N

·       Frictional force: 2651.34 N

·       Maximum friction limited acceleration: 5.8 m/s

·       Linear force needed for 1m/s²: 1084.9 N

·       Torque needed for 1m/s²: 138 Nm

·       Torque needed per wheel: 34.5 Nm

·       Motor torque needed after 6:1 ratio with 90% efficiency: 6.4 Nm