Techno Linear Motion Catalog33Technical Informationwhere:w = weight (lb)p= pitch (threads per inch)I(eq)= equivalent polar inertia (lb •in2)to calculate lead screw inertia (steel screw)I(screw)= D4x length x .028Example:Weight = 1000 lbsVelocity = 0.15 feet per secondTime to Reach Velocity = 0.1 secondsBall Screw Diameter = 1.5"Ball Screw Length = 48"Ball Screw Pitch = 5 threads per inchMotor Rotor Inertia = 2.5 lb • in2Friction Force to Slide Weight = 6 oz1I(eq)= wx –– x .025 = 1000 x ––– x .025 = 1.0 lb • in2I(screw)= D4x length x .028 = 5.06 x 48 x .028 = 6.8 lb •in2I(rotor)= 2.5 lb •in2–––––––––––––––––––––––––––––––––––––––––I(total)= 10.3 lb •in2Velocity is 0.15 feet per second, which is equal to 1800 steps per second (motor steps in 1.8° increments).Torque to accelerate system:w 'px 1.81800 3.1416 x 1.8T= 2 x IOx ––– x –––––––– x ––– = 2 x 10.3 x ––––– x –––––––––––– x ––– = 484 oz •int180180 24Torque to overcome friction:F= .393 x Tx px eff.––––FT= ––––––––––––– = ––––––––––––– = 0.22 oz•in.393 x p x eff.where:F= frictional force (lb)T= torque (oz•in)p= lead screw pitch (threads per inch)Total torque required = 0.22 oz • in + 484.00 oz •in = 484.22 oz •inAfter determining the required motor size, it is recommended to add a 20% factor of safety so that unexpecteddynamic loads are easily handled by the motor.Sizing Servo Motors:Two separate torque figures are needed when selecting a DC motor — a peaktorque, being the sum of acceleration and friction torques, and a continuous torque, which is the frictioncomponent only. The torque produced by the motor is given by:T= KtI+=p2251+16611240.1.393 x 5 x 0.90
