ME 475- FALL 2022
HOMEWORK 1 Due September 28th Midnight
In this homework, you will pick out components for a linear motion system that consists of a lead or
ball-screw drive and a stepper motor. This system should be capable of horizontally moving a 40 kg
object 45 cm in 3 seconds with an acceleration and deceleration time of 0.05 s. See the plot below for
the required velocity profile:
Read the ReadingAssignment.pdf file that is posted on the blackboard and keep it handy. You are very
much encouraged to use Matlab or Excel to automate the calculations such that you can iterate the
process given below multiple times easily. Follow these steps:
1. Determine Vmax using the above plot and the total distance. Also determine the acceleration a,
assuming constant acceleration.
2. Determine the motion stage. It is wise to pick a system that packages every component except
the motor (bearings, conversion and coupler) which are commercially available. However, you
are welcome to pick individual components one-by-one. DO NOT propose a stage that includes a
motor as it should be selected separately. Here are a few links to that might be helpful:
https://www.automationdirect.com/adc/Shopping/Catalog/Power_Transmission_(Mechanical)/
Linear_Motion_Slides_and_Actuators#Driver_Type_s=(%22Ball%20Screw%22%20%22Lead%20S
crew%22)&start=0&Travel_Length_s=%2224%20in%22
https://us.misumi-ec.com/vona2/mech/M0100000000/M0118000000/
https://www.thomsonlinear.com/en/products/linear-motion-systems-products
Note that you are not restricted to these sites. When you are selecting the stage, check two
things: (1) if the max speed rating of the stage is compatible with Vmax and (2) the max load it
can handle perpendicular to the motion direction is more than the weight of the object.
3. Using the pitch or lead of the stage, calculate the max rotational speed and the rotational
acceleration of the motor if this stage is used. If both pitch and lead are given as different
numbers, use the lead in your calculations. Be careful with the units of the pitch or lead, it
needs to be rev/distance for the given formulas. Some manufacturers give it in distance units.
In that case you need to take the reciprocal of the given number.
4. Now, select a stepper motor. Most motion stages that includes the coupling will tell you what
“motor frame” they are compatible with (e.g. NEMA 17, NEMA 23 etc.). Pick a motor with a
compatible frame with your stage. The websites given in Link 2 above also offer several motors.
Make sure the max speed and acceleration of the motor is more than the values determined in
Step 3.
5. Now calculate the total effective inertia of the system with the picked components as
discussed in the lectures and the reading assignment. Here some important tips about this:
1. If the moment of inertia of the stage is not provided in its specs, estimate it by the
moment of inertia of the cylinder with a height and diameter equal to the length and
diameter of the screw in your system, respectively.
2. If the efficiency of the motion stage you picked is not given, use the table in reading
assignment to determine it.
3. If an inertia factor is given for the motion stage, use that while calculating the
corresponding reflected inertia as discussed in the lecture.
6. Now calculate the reflected, acceleration and deceleration torques for your system. Here are
some important tips:
1. For friction force calculation, if no friction coefficient is given for the stage, use the table
in the reading assignment for the bearing your stage features.
2. Assume that no preload torque is used.
3. Bearing torque is also negligible.
7. Now go to torque vs. speed curves for the motor you selected to see if it can handle the max
torque you calculated at the given rotational speed. If yes, you are done. If not, pick a different
motor and repeat the calculations.
8. Now answer these questions :
1. Would the system you put together work if the motion was vertical (against gravity)?
How would your calculations change? If your system ends up not working in the vertical
case, you don’t need to pick a new system.
2. Determine the maximum additional force opposing the motion your system can handle.
3. If you picked a lead screw stage, find one similar ball screw stage. If you picked a ball
screw stage, find one similar lead screw one. Compare the two in terms of their specs
and cost. What are your observations?
