A2 Actuator Design
Review of Requirements
| Requirement | Value | Units |
|---|---|---|
| Permissible Mass (Motor + Gearbox) | 1.5 | kg |
| Output Ideal RPM | 3-4 | RPM |
| Output No Load Torque (No SF) | 44 | Nm |
| Output Max Load Torque w/ (No SF) | 95 | Nm |
| Backlash | < 30 | arcmin |
| Budget | ~1000-1200 | USD (See note**) |
*Note: We have currently ~4000 USD budget for entire arm. Motors/gearboxes for Axis 4/5/6 are estimated to be about 1500 USD, and on axis 1 and 3 approximately 400 USD each. We also want to aim to save ~500-750 USD on arm budget for construction materials of custom parts, bearings, fasteners, etc. This leaves us with ~1000-1200 USD leftover
Review of Testing Data
- Testing was not as comprehensive as desired for axis 2 - have ran into challenges with broken components and belt skipping
- Current tests are also done on prototype arm that has a a 1.25m horizontal reach, after reanalyzing our workspace we have decided to change the maximum horizontal reach of our arm to be 1m
- With arm prototype, our measured no load torque (static + estimated dynamic torque values) at full horizontal extension (max loading scenario) was 61 Nm
- Experimental dynamic torque testing at full horizontal extension and no load showed a peak instantaneous torque of 55.5 Nm (very close to expected calculated values)
- First set of testing data was taken without gripper - installed on arm (different mass / lower moment arm) so results aren't seriously considered
- Further testing has temporarily been stopped as the belt wore out due to repeated skipping under 3kg payloads - replacement belt was installed but constant skipping still observed even under no load. To be investigated on weekend of October 1st
- Current Conclusion - Hand calculations with a generous SF (1.5x) are likely sufficient for torque requirements - performance may not be perfect but that may have to be optimized in the future
Initial Design + Component Selection Concept
Objective of Design
The following design is intended to be the rough layout for an actuator design capable of meeting our requirements for Axis 2. DFM, stress analysis, etc. has not been performed on the current concept (see next steps section for more details)
Design Layout
Component Details + Rationale + Design Considerations
Brief Overview
- The gearbox used in this actuator is a strainwave gearbox with a 120:1 ratio and 20mm frame size made by GAM. This was selected over other strainwave gear manufacturers (Harmonic Drive, Nidec Shimpo, etc.) as this specific gearbox is currently in stock and has an available educational discount through our actuator sponsor (electromate)
- Strainwave gearing is selected over other forms of gearing (such as planetary, worm gears, etc) due to mass/backlash requirements for this joint. Strainwave (and other forms of elliptical gearing) are the main styles of gearbox that can achieve high ratio, single stage and low transmission backlash. Planetary gears of equivalent ratios are heavy as they require multiple stages (1kg + from options available on Maxon, TRUE planetary series, etc.) and have higher backlash (~13arcmin-60arcmin depending on the manufacturer)
- Other forms of transmission such as worm gears have high ratios, but are also heavy and it was difficult to find a solution that remained within our mass spec.
Relevant Properties
Efficiency Considerations
- I was not able to find a good efficiency rating for the gearbox on GAM's website
- However, the harmonic drive sells a very similar motor (CSF-20-120) which has similar load ratings: https://www.harmonicdrive.net/products/gear-units/gear-units/csf-2uh/csf-20-120-2uh
- Used harmonic drives comprehensive catalogue to estimate some of the properties for the GAM gearbox (will contact the GAM manufacturer to get answers on these properties directly, but have used HD data in the mean time to supplement)
- Efficiency: Efficiency of these gearboxes are dependent on proper lubricant application. For our applications, the input speed to the gearbox would likely 300-400 rpm (to hit 3-4rpm on output) and ambient temperature will be at least 30 degrees when competing in Utah. A harmonic drive of similar frame size and ratio will have a ratio of ~85%.
Cost Considerations
- Cost of this gearbox after educational discount is ~1345 CAD (~1000 USD)
Alignment Considerations
- For proper torque transmission, the shaft of the motor and input shaft of the gearbox should be properly and precisely aligned. However, there is SOME leeway in our alignment. For the selected gearbox, there are two variants: GSL-CS-020-120A and GSL-CS-020-120B. The "A" gearbox is just a standard gearbox and input shaft, where as the "B" gearbox has the same load ratings, approximate mass, dimensions etc BUT it includes an oldham coupling on the input. Oldham couplings can compensate for axial misalignment as they "shift" to properly align the shafts - see image below
- I recommend we buy the variant with the oldham coupling if available - this will give us some leeway on the custom shaft coupling and manufactured motor housing
Axial Force Considerations
- Detailed information on the GAM strainwave axial force generation is not listed in the gam datasheets.
- However, in the harmonic drive datasheets for similar sized/ratio gearboxes, it notes that an axial force is produced when the wave generator accelerates/decelerates - see image below:
- Will contact GAM to get details on if a similar force is produced in their gearbox, but if we use this information as a reference we can estimate a maximum produced output force of:
Output Considerations
- This gearbox has a crossed roller bearing supporting the output flange. Ratings are listed below
Brief Overview
- This is a pancake style motor from Maxon
- It is currently out of stock (10-14 week lead time). This motor is incredibly light and powerful, so I think it is worth waiting for. While we wait for the motor, we can simply use a lower performance motor of similar frame size, although it will be heavier and less powerful. Backup motor in mind: https://us.nanotec.com/products/2870-db59l024035-a
Relevant Properties
Estimated Cost: 170 CAD after discount
Weight: 360g
Requirement Performance
| Requirement | Value | Units | Motor + Gearbox Expected Value | |
|---|---|---|---|---|
| Permissible Mass (Motor + Gearbox) | 1.5 | kg | ~1.3 kg (pass) | |
| Output Ideal RPM | 3-4 | RPM | Discussed Below** | |
| Output No Load Torque (No SF) | 44 | Nm | Discussed Below** | |
| Output Max Load Torque w/ (No SF) | 95 | Nm | Discussed Below** | |
| Backlash | < 30 | arcmin | 0.5 arcmin (pass) | |
| Budget | ~1000-1200 | USD | ~1200 USD (very conditional pass) |
Arguably, this barely meets our budget requirement. Unfortunately, it eats a ton of our budget but I think it is worth the investment due to performance across loads, mass and backlash.
Output Performance Details
- The max continuous motor torque is ~ 0.534 Nm at standard ambient conditions. With a 120:1 ratio and 85% efficiency, our max continuous output torque is 54 Nm, which exceeds our expected no load torque requirement and is within the continuous permanent torque rating for the strainwave gearbox.
- Keep in mind that the gearbox+motor can provide approximately torque for continuous, non-stop rotation and remain within it's life rating. Our arm will rarely experience these peak loads (as load requirements are for full horizontal extension, an uncommon arm configuration) AND we will never operate continuously as this torque (as torque changes with gearbox angle)
- The maximum permissible torque output of this gearbox and motor combo is 169.1 Nm, which exceeds our expected maximum load torque by a SF of of ~1.75x. However, this torque is listed as the emergency stop torque? What does this mean? Well GAM doesn't have comprehensive information, so once again I have researched equivalent data on similar harmonic drives. Here are my findings:
source: https://www.harmonicdrive.net/_hd/content/documents/csf-csg.pdf - The number of times this maximum torque can be experienced can be very roughly estimated using HD's formula. If we were to operate at this torque, the motor would need to provide a torque of ~1.675 Nm (169.1Nm / 95% / 120) which is ~3.15x the rated torque of the motor.
- Maxons datasheets says that at STP and basic heat dissipation (no additional heat sink components), motors can operate at 2.5x continuous max torque for approximately the thermal winding time constant before thermal damages may occur. If we make some conservative estimates, we can assume that the motor can operate at 3.13x continuous torque (still well underneath motors stall torque of 4.3 Nm) for about half the time of the thermal time constant (~4.5s) (time interval)
- Assuming we are operating at our desired output speed (4 RPM), input speed will be approx (480 RPM) (input speed)
- Using HD's formula, we can apply this load for 138 times before fatigue failure may occur. This gives us a very rough estimate of how many times we can apply this load before potential gearbox failure, although we would likely never operate at this range
- Max acceleration torque is approximately equal to expected 5kg torque (w/o SF).
- Once again, keep in mind that our max loading scenario is rare (as we will not be lifting 5kg often, and if we do it will be in a "folded" arm config w/ a much shorter moment arm)
- Gearbox can sustain loads greater than this requirement, and for infrequent loading we should be ok
- When operating at max rated torque, max rated motor speed is 3240 rpm → 27 rpm on output. Will need to apply some speed control in SW/FW
- We can limit current to avoid exceeding max load ratings on gearbox in SW as well
- I am about 70% confident that we will be able to meet our load requirement without damaging the gearbox (:
- This part would be milled from 1in thick aluminum (7075 or 6061)
- Part needs to sustain radial, axial and moment loads
- Bolted flanges need to sustain moments without bending/failing
- Small cutouts are included to reduce part mass while maintaining strength
- Strainwave gearbox fits within hole (H7 fit) and is directly mounted to bracket via 8 M5 fasteners
- Motor mount plate will also be CNC machined - it needs that flanged shoulder in the middle. It includes mounting holes for the plastic encoder/shaft housing, encoder mounting holes and motor mounting holes (counter sunk
- Aluminum mounting plate is recommended for thermal performance of motor. Maxon specified that including motor housing with excellent heat dissipation (i.e. aluminum) will improve cooling capabilties and increase thermal time constants for motor. The extent of this benefit is currently hard to quantify and low priority, as we need an easily machinable/high precision part anyway.
- There is an internal hole and shoulder for a deep grooved ball bearing.
- The purpose of this is to reduce axial forces on the motor shaft. As discussed previously, the wave generate can produce a max axial force onto the shaft of 170 N. The max permissible axial force on the shaft is 12 N. This deep grooved ball bearing is used to retain the shaft coupling, and take the brunt of any produced axial forces as the motor plate is directly mounted to the strainwave gearbox.
- Bearing is from SKF and should be free within our sponsorship.
- Deep groove ball bearings are not rated for axial loads, but on SKF website: https://www.skf.com/ca/en/products/rolling-bearings/ball-bearings/deep-groove-ball-bearings/loads
- Static axial load rating of selected bearing is 2850N, so even if we only get 10% of that rating we are still fully supporting the max axial force from the strainwave gear. Need to look into if 10% is realistic, and what factors affect this load rating
- Deep groove ball bearings are not rated for axial loads, but on SKF website: https://www.skf.com/ca/en/products/rolling-bearings/ball-bearings/deep-groove-ball-bearings/loads
- This is a custom shaft coupling used to connect the motors shaft (8mm round) to the gearbox input (8mm with 3mm keyway)
- There is also a thick section on the motor that is 20mm
- Currently, I have some setscrew holes on this shaft to couple it to the motor (see questions section to get my thoughts on this)
- Shaft will be made from either 7075 aluminum or steel. Need to do some stress analysis to see what is permissible.
- Smaller flange is matched OD of bearing:
Spacing Washer
- When mating the shaft to the gearbox, I also included a spacing washer. This washer will likely rotate with the shaft (not slide) and is used to provide more contact area between the shaft and input on the gearbox. The idea is that this will allow us to preload the gearbox and shaft assembly to maintain proper alignment and reduce chances for axial shifting and whatnot
- We can also put a greater fillet on the stepdown section of the shaft to reduce stress concentrations and prevent torsional failures (as spacing washer will provide a flat contact surface)
- Currently, I hope to use a plastic housing to mount the motor flanged plate to the gearbox and to protect the shaft/encoder
- I think plastic will be a suitable material choice here, as if shaft is aligned properly low radial forces and moments will be applied to this piece. It will mostly be axial loading, and 3D printed parts are strong in compression
- Need to make sure that 3D print is accurate enough to prevent shaft misalignments
- Weird circle thingy on the end will be used for cable routing. I definitely want to improve my implementation and explore some of the cable options presented by Ethan Cronier but general idea is to route the encoder and motor wires through this ring, and then to tie a cable conduit around it to protect and properly route the cables.
- Cable routing is a rough idea for now.
Questions/Thoughts/General Inquiries on Current Design
- The entire actuator assembly is ~1.8kg (motor, gearbox, housing, custom parts, etc.). This beats the prototype by about 100 grams, and also has significantly less parts
- What are the key factors that I have missed, or elements of the design I should focus on to ensure integration is properly carried out?
- Is the washer space on the shaft necessary? I feel like it is a good idea, maybe not though
- What is the best way to couple the motor shaft to the adapter? Maxons have round shaft profile. I am thinking we either:
- grind a flat for setscrews (risky as we can brick a motor, but you can decouple motor shaft from gearbox in the future)
- shrink fit the coupling, and it is permanently connected (reliable connection, but we need to be carefully when axially loading the motor shaft)
- bond the motor shaft, and it is permanently connected (bonding may deteriorate over time, although it should be ok if done properly with a stronger epoxy)
- The crossed roller bearing on the output of the gearbox is rated for a maximum moment of ~90 Nm. The moment direction of the gearbox is actually perpendicular to our main loading condition. We would see maximum loads on this bearing when the arm is articulated 90 degrees as shown in the very rough sketch below:
- The rest of the arm will be roughly in line with this gearbox, but hypothetically lets just say that the rest of the arm's center of mass is also 0.25m from the output of A2. The arm past axis 2 weighs ~ 10kg, so this would result in a moment on this bearing of ~37 Nm. These are very rough napkin numbers, but my plan is to just make the actuator, test things out and if need be we can easily support the end of the gearbox with the following config:
(adding external plate and bushing on gearbox output link to support moment loa)
- The rest of the arm will be roughly in line with this gearbox, but hypothetically lets just say that the rest of the arm's center of mass is also 0.25m from the output of A2. The arm past axis 2 weighs ~ 10kg, so this would result in a moment on this bearing of ~37 Nm. These are very rough napkin numbers, but my plan is to just make the actuator, test things out and if need be we can easily support the end of the gearbox with the following config:
- Are there any next steps I am missing? (see below)
Next Steps
- Get design feedback, implement changes as necessary or re-evaluate design if necessary
- Contact GAM for manufacturer specific data on load ratings etc.
- Get ordering approval from leads, and order components
- Review/quantify all loads on custom parts and gearbox output, validate numbers and adjust designs to avoid failure while remaining light as possible
- Improve cable routing solution