Weekly Brainware
Week 2: Deterministic Design
Part 1: Design Updates
Over the past week, I made the following changes to the Functional Requirements of my Rising Desk.
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Can lift 30kg load (table top included). Previously, I had set the requirement to 100kg. After reconsidering the size of the desk I want to build and minimizing the need to buy a new motor, I lowered the payload requirement.
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Actuator must self lock. I included this as I felt it was necessary to minimize power consumption of the table.
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Actuation speed of 10mm/s. Previously, I wanted an actuation speed of 1.5inches/s. In order to achieve this, I would need to quadruple my motor power power.
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Total travel of 1.5ft. This was based off of measurements I took. The minimum height of my table would be 2.5ft.
Design Parameters:
I next investigated several concepts that might be feasible. including:
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Linear Actuators
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Lead Screw with two guides
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Lead Screw with one guide
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Scissor Jack mechanism
Analysis:
In order to validate these concepts, I performed some simple first analysis to estimate the specifications of key components.
Lead Screw Designs:
I first analysed the lead screw designs with the objective of identifying the required screw lead as well as estimating the speed of actuation. My estimates suggest that I will require a lead of about 3mm/rev. Account for a safety factor of 1.5, a 2mm/rev lead screw would be a feasible option.
With the current NEMA 17 motor, I would achieve an actuation speed of 13mm/s for a load of 300N. This is close my desired speed. Thus, the lead screw system is a feasible option. The drawback of the system is the visibility of the guide rails as well a the lead screw.
Linear Actuator Design:
The linear actuator design is the most simplistic and is the best looking. Many commercial products use this mechanism. However, they are very expensive. Hence I ruled them out of consideration. Moreover, I would not have the chance to design the mechanism.
Scissor Linkage Design:
Using conservation of energy principles, I attempted to verify the feasibility of the scissor jack mechanism. My objective was to determine the force required to achieve the desired change in height and as well as evaluated the lead of the lead screw needed for the motion. In my calculations, I considered a single lead screw and motor. For this condition, I would require a 1.35mm/rev lead screw. By using two motors, I could use 2 leadscrews of 2mm/rev with some safety factor for the design to work. I am not eliminating this mechanism yet. I plan on carry out detailed analysis using the provided Lazy Tongs Spreadsheet.
Part 2: Precision Linear Motion Axis
Objective: Use deterministic design principles to design a precision linear motion axis.
Using Professor Slocum's Error Apportionment Spreadsheet, I was able to determine the maximum allowable error for the bearings in my single axis system. For a total error of 2mm, the Average of linear and RSS errors for the bearings is 0.861mm.
Using the information, I attempted to find the length of the bearing/slider for the vertical travel. I was able to do by by computing the Abbe Error. For my table of total width 760mm, I would require a bearing of length of 44cm. From Saint Venant's Principle, I deduced my width to be one third of the length, so around 15cm.
Given that length of the slider is fairly large I then explored the possibility of using two rods as guide rails with 4 linear bearings spaced at calculated distances. The linear bearing and the nut will be press-fitted to the carriage. I am aware that the stiffness of the bearing system will be different and I plan to develop a model to analyse such a system.
However since we are meant to build and test the precision linear motion system, I will focus on the single rail system as it is more economical to prototype.
In summary, I narrowed my concepts down to 3 different mechanism but am currently leaning towards the Single Guide mechanism given the simplicity in design and cost. But all three designs will be analysed in greater detail, in the coming weeks.
For the lead screw designs, I expect to use an Oldham style coupling to couple the shaft to the motor. I also plan on using a thrust bearing and a self-aligning bearing to support the shaft at the two respective ends as shown in the sketch.
Part 3: Three Groove Kinematic Coupling
Design Spreadsheet:
From my design spreadsheet, the expected vector displacement error was estimated to be 0.045microns. I did not have any measurement tools capable of measuring at this resolution. Nonetheless, I performed a repeatability test which can be reviewed in the Week 2 Hardware section.
Objective: Design a three grove kinematic coupling to couple anything. (using the Kinematic Coupling Spreadsheet)
To completely constrain a rigid body to another, 6 points of contact are needed.
Before starting on my deterministic design, I surveyed the available materials at my disposal. I found some scrap MDF of 3/4" thickness. I also scrounged a few 3/8" steel roller balls and 3/8" x 1" dowel pins. I sketched out various concepts for the system. I then evaluated them based on ease of machining and accuracy. I was decided to go ahead with dowel pins pressed into pockets as this would require the least machining. It was also the best choice I had as I was not able to find a 45deg end mill to machine V grooves.
On the downside, with dowel pins, I would have a finite groove radius which would mean that I needed more preloading than in the case of V grooves with infinite groove radius. Since MDF is rather dense, I was not too worried by this. I next calculated the spacing between the dowel pins which would result in a 45deg contact angle betwee nthe roller ball and the groove created by the pins.
