As outlined in our original parameters, the final design must be
inexpensive and have simple drive architecture. Stepper motors satisfy
both of these requirements. However, minimizing this machine’s overall
volume is also important, so a stepper isn’t recommended: The 17.64-W
minimum power requirement at the load (not including system losses and
instantaneous peak power) would necessitate a large stepper. A brushless
motor solves the problem of design footprint, but adds cost and
complicates the drive architecture.

The third option — a dc-brush gearmotor with an in-line planetary gearhead — provides a small footprint, simplified drive, and relatively low cost. Adding a leadscrew for rotary-to-linear conversion keeps gear reduction stepper motor

output speed at around 1,000 rpm, which reduces generated heat at the leadscrew and nut-thread interface.

Step one: Calculate the peak linear velocity of the application with its

Step two: Calculate the minimum pitch needed to keep the leadscrew speed at about 1,000 rpm:

where

For one typical linear stepping motor, the closest pitch in an 8-mm screw diameter is 20.32 mm.

Step three: Calculate the peak shaft speed of the leadscrew (in rad/sec) for a linear velocity of 0.3 m/sec:

The leadscrew we select is TFE coated, 275-mm long, 8 mm in diameter with a 20.32-mm pitch, and paired with a freewheeling nut. Assume the leadscrew efficiency, ηs, is 86% and its inertia,

Step four: Determine the total reflected inertia, JT, back from the load to the leadscrew shaft:

where

Step five: Determine the shaft torque needed to accelerate the load inertia T

where

m/sec

WHERE TO GET 3 AXIS CNC CONTROLLER

The third option — a dc-brush gearmotor with an in-line planetary gearhead — provides a small footprint, simplified drive, and relatively low cost. Adding a leadscrew for rotary-to-linear conversion keeps gear reduction stepper motor

output speed at around 1,000 rpm, which reduces generated heat at the leadscrew and nut-thread interface.

### Gearmotor output

3. What’s the velocity, reflected inertia, and reflected load at the gearmotor output shaft (acting as the leadscrew input)?Step one: Calculate the peak linear velocity of the application with its

^{1}/_{3}-^{1}/_{3}-^{1}/_{3}motion profile:Step two: Calculate the minimum pitch needed to keep the leadscrew speed at about 1,000 rpm:

where

*p*= minimum leadscrew pitch, m._{min }For one typical linear stepping motor, the closest pitch in an 8-mm screw diameter is 20.32 mm.

Step three: Calculate the peak shaft speed of the leadscrew (in rad/sec) for a linear velocity of 0.3 m/sec:

The leadscrew we select is TFE coated, 275-mm long, 8 mm in diameter with a 20.32-mm pitch, and paired with a freewheeling nut. Assume the leadscrew efficiency, ηs, is 86% and its inertia,

*J*_{s}, is 38.8 × 10-7 kg-m^{2}.Step four: Determine the total reflected inertia, JT, back from the load to the leadscrew shaft:

where

*J*= reflected load inertia, kg-m_{L}^{2};*m*= mass, kg; and*p*= leadscrew pitch, m.Step five: Determine the shaft torque needed to accelerate the load inertia T

_{a}:where

*T*= torque required to overcome load inertia, Nm;_{J}*T*= torque required to overcome friction, Nm;_{f}*T*= torque required to overcome gravity, Nm; a = linear acceleration,_{g}m/sec

^{2}; Θ = load orientation, with horizontal = 0° and vertical = 90°; m = mass, kg;*g*= gravitational constant = 9.8 m/sec2;*p*= leadscrew pitch, m;*v*= final linear velocity, m/sec;_{f }*v*= initial linear velocity, m/sec;_{i }*t*= final time, sec;_{f}*t*_{i}= initial time, sec; and α = angular acceleration, rad/sec2.WHERE TO GET 3 AXIS CNC CONTROLLER

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