In this article I explain how system modeling was used to validate some of the design decisions of an electronic throttle body (ETC). I go over the context and motive behind designing an ETC. Then the physical design of the ETC is briefly covered.
Context
Before focusing solely on the EV side of my Formula Student Team I wanted to develop one last component specific to IC vehicles. When I assembled my first Formula Student car (circa 2017), I realised one of the most unreliable components was the throttle actuation. Frequently, this actuation mechanism is badly designed leading to, in most cases, to a throttle body closing slower than optimal. The unreliability usually arises from badly chosen springs as well as friction along the throttle cable. The solution that has been devised eliminates these sources of unreliability entirely and is identical to throttles used in all new production vehicles, albeit with different requirements.
Many FS teams have already implemented Electronic Throttle Control (ETC) on their cars but practically all of them use an off the shelf solution, frequently the Bosch ETC. System Complexity & stringent competition rules are the main challenges FS teams face to developing their own ETC. In this project, I attempt to mitigate these two problems by using simulation to verify my design, which also serves as documentation for the competition’s Tech inspection.
Personally, I believed designing an ETC at this moment in time would be a very good opportunity to gain an understanding of Matlab’s Multiphysics environment (Simscape) as I hope to use it frequently in the EV development (more on that later), and there is no better way to learn something than to apply it to a real life situation.
Requirements
- The ETC must be able to use the existing mounting strategy
- The ETC will use the same diameter (∅32mm)
- The ETC must carry a Throttle Position Sensor (TPS) that has 2 outputs with independent power supplies
- The weight of the ETC must be under 350g (previous TB: 200g+ cable & Housing:150g)
- Lag from 0% to 100% Throttle must be less than (<)400ms
Design
The ETC is based on a barrel-type throttle body. Barrel throttle bodies offer an unrestricted pathway, and therefore, the best flow characteristics at wide open throttle (WOT) as compared to a butterfly valve. They are also easily actuated compared to slide throttles that require translation motion compared to just rotational motion. Barrel throttle bodies are not common in OEMs due to their increased cost. To build a barrel throttle body in large numbers you would need a minimum of 3 casted components, which is 3 times more than a traditional butterfly throttle body.
Manufacturing wise the most complex component will be the throttle barrel as it will require machining on a lathe and then on a mill, even then it is not extremely intricate. Whilst the throttle housing may look complex having access to a 5-axis mill reduces the setup stages down to 2. The machining jig used to make the previous cable based throttle body may be used as the mounting holes remain the same.
Igus flange bearings offer very predictable operation and require no maintenance, as well as low weight and low cost. Iglidur J flavour is chosen as it offers reduced wear and low coefficients of friction compared to other polymers.
The Variohm XPD sensor has two Hall analog outputs with their own power supply wiring. This meets the Formula Student rules.
The Gear Side Cover is a 3d printed component in ABS that creates an enclosure around the gearing as well as containing the rotational end stops for the throttle.
The Re-385 is an inexpensive DC brushed motor that meets the set requirements. More on this in the appendix.
The gearing has been chosen given the tight spatial constraints, for an overall gear reduction of 8. This ratio is verified by the simulation below. More details on the durability of these can be found in the appendix.
The Spring choice was carefully chosen and validated using the simulation. It allows for high preload even with a small spring constant, a feature common in springs with a large number of turns.
Simulation
Motor analysis
The RE-385 specs are summarised below:
| Motor Specs | RE-385 |
| Nominal Voltage | 12V |
| No-Load Current | 0.18A |
| No-Load Speed | 11646rpm |
| Stall Torque | 50.4mNm |
| Stall Current | 5.55A |
With this data I was able to plot the motor characteristic curves on Matlab. This graph is used to identify the performance of the motor at the chosen operating points. It helps us to determine if the motor will be running too stressed (failing prematurely) or if it is overpowered for the application. The motor friction can also be identified by extrapolating the Current-Torque line until it crosses the 0A line, this value is important when choosing the spring preload.
Simscape Model
In order to ensure the motor selection and gear reduction was appropriate I built a Simscape model to simulate the end product. Simscape is a multi-physics library inside Simulink where I can model electrical and mechanical systems combined.
Brushed dc motor position control is not very well documented and practically no creations exist so the model built is quite novel in this enviroment. Simscape is mostly used with the more modern brushless motors and all documentation for dc motors use speed based control.
Implementing position control is not complicated as the only big difference with a speed control model is that the feedback loop contains the angle rather than the angular velocity. The PID block has been setup as time-discrete instead of time-continuous in order to make it realistic. It has also been setup to saturate the signal between -5 & +5 volts in order to prevent discontinuities in the model.
The motor is driven through an H-bridge block that is controlled by a PWM signal. Additionally the reverse functionality of the h-bridge is triggered when the signal on the REV terminal exceeds +2.5 volts. The motor is run in reverse when the output of the PID block is negative.
The DC motor model in Simscape allows the user to use different parameter sets to model the motor not just the traditional motor constants. A user can model the motor just by knowing the stall torque, No-load Speed and No-load current, this makes the block very accessible and easy to setup. It also leads to a model that is fairly complex but not robust, this is why a current limiter is placed before the DC motor, preventing it from exceeding its stall current.
This model is a systematic version of what has been modelled on cad. It includes most of the constant losses and the parasitic losses, it should allow a good representation of how the throttle will function in real life.
Motor Friction is included and its value was identified from the motor characteristics plot. Both gearbox blocks represent the meshing of gears, their ratios are 40/14 and 14/5, both have been given a conservative efficiency of 90% of the torque input. The friction due to the bearings is also included and has been calculated using the friction coefficient provided by Igus (0.19) X the weight of the barrel + 80T gear.
The Clock Spring is modelled with its decided pre-load and supplier provided spring rate. The Rotational Hard Stop prevent the Throttle from rotating below the 0% and 100% set angles. The Clock Spring, Igus Bearing Friction and Rotational Hard Stop are all parallel as they act on the same shaft.
The Hall Sensor allows us to retrieve the throttle angle.
This model also allows us to confirm that the pre-load torque of the motor is sufficient to restore the throttle to 0% in the case of loss of power. Under 500ms (as defined by T11.8.12 of 2022 FS rule book).
Results
I first simulated the the operation at 100% throttle:
100% throttle corresponds to 90deg of displacement or WOT. The operation at this position will represent the largest continuous current and therefore largest continuous motor stress. Current spikes during acceleration to 90deg are realistic as the PID attempts to accelerate & decelerate the system as fast as possible. The stability of the PID can be seen as the current flattens out. We can see how the preload works as the Spring Torque does not begin at 0 but at 72mNm.
We can identify another discrepancy in the Simscape motor model by comparing the resultant motor current and motor torque to the values on the motor characteristics plot. We see that the simulated current is around 240mA lower on the characteristic plot.
Regardless, we can identify from the resultant torque on the characteristic plot that this operating point is valid as it sits inside the line.
A 10% Throttle opening or 9deg is also simulated to verify the operation at a value close to throttle idle. Given that there is no idle screw on the throttle, the motor will be in charge of keeping it open during idling. This operating point is where the throttle will be at most of the time and therefore necessary to be analysed.
The PID controller is also proven to be stable at this point as the current flattens. Likewise we once again see the discrepancy between the characteristic plot and the results in the motor current.
As expected the motor torque is within the achievable values.
In order to meet one of my requirements I had to make sure that the throttle responded fast enough to throttle input.
The response of the 0º to 90º throttle opening is plotted and we see that the throttle is extremely fast. Even with the manually tuned PID constants the throttle is able to achieve a 2% settling time of 56.7ms.
Conclusion
Plotting the Characteristic Curves with the motor operating points gives us a good image of the motor reliability and efficiency.
The motor current at 100% throttle is ~28% of the stall current, this is lower than the 40% max recommended by motor manufacturers in order to prevent noticeable pre-mature failure. At its most prevalent operating point (10% opening) the motor current is only 21% of the stall current further more promoting reduced wear.
Whilst thermal effects are not considered in the simulation, plotting the above graph allows us to see that at these operating points the motors are unlikely to experience overheating given the low motor stress. Furthermore, the housing is bolted to an aluminium surface.
Seeing that the operating points sit between the max power and max efficiency points allowing us to confirm that the motor choice is indeed appropriate and not overkill. Using a smaller motor for the same system would lead to a big decrease in power, delivering a slower response and a larger motor stress.
Ideally current consumption at the idle point would be extremely close to the no-load current, however, this is dependent mainly on the spring chosen and springs available that fit to the spatial and operational requirements are limited.
Overall it can be confirmed that the choice of motor and gearing is appropriate for this application given the requirements. The small settling time is very small and will strongly depend on the PID controller implemented in the ECU, therefore it is likely to increase in reality.
Comparing to the most common ETC solution for FS teams. The developed throttle is 60% lighter than the Bosch 32mm ETC (277g vs 900g). The throttle response is 78% faster (56.7ms vs 265ms)
The size of the Custom throttle is much smaller, this is due to the Bosch ETC using standardised components from its whole line up.
Next stages for this throttle are to receive approval for manufacture by the appropriate sub-team leaders. Once assembled the throttle will be tested to compare with the simulated results.
After having done this project I have a much better understanding of how Simscape works. The next project I will attempt to model on Simscape is an EV battery pack to some scale. I plan to include the thermal domain, which will be necessary for future modeling of the battery pack cooling system.
Appendix
Resources:
Gears
The driving/motor metal gear is pressed on to the motor shaft. The driven & layshaft gears will be made of laser cut Acetal/Delrin. This thermoplastic has good structural properties and superior bearing & wear properties (especially important in gears). Additionally, Acetal is much more dimensionally stable than Nylon making it a better candidate for laser cutting.
Below I carry out some calculations to validate these gears:
| Fatigue Strength for 106 cycles (σ1) | 36MPa |
| Service lifetime correction factor (Cn) | 0.22 |
| Number of cycles in million (n) | 10(recommended) |
To calculate the nominal allowable fatigue stress we use the formula below:
\sigma_n=\sigma_1[1-C_n*log(n)] \space \space (\textrm{MPa})To get σn=28.1MPa. To calculate the application specific allowable fatigue stress we must consider the velocity factor, Shock-load factor and the temperature factor using the formula below:
\sigma_{\textrm{app}}=\sigma_n*(1-0.6\frac{T-20}{80})*\frac{1}{1+\frac{\pi d\omega}{60000}}*c_{\textrm{sl}}In this case the Shock load factor (csl) is 1 as there are no shock loads expected in this application. T is temperature which we will assume to be 25ºC as it far away from heat sources. d is the pitch diameter of the driven gear, which are 40mm respectively. ω is the rotational velocity at which the gear operates at, as seen from the graphs above it is on average (from the 0➙100% operation) ~400rpm.
Calculating the above we find the σapp=14.7MPa. This is representative of both gears as they are in the same system. The bending stress of the gear in our system can be found using the formula below:
\sigma_b=\frac{F}{yMf}Where F is the max tangential force, which is equal to 11.8N. y is the tooth form factor, which in the case of the driven gear is 0.629 and 0.485 for the layshaft gear. M is the module, in this case 0.5 and f is the tooth width equal to 4mm. We find that the layshaft gear has a σbS=12.2MPa & the driven gear a σbB=9.38MPa.
We see that the bending stresses (σb) in our system are lower than the application specific fatigue stress (σapp), meaning that our gears are not expected to fail in their lifetime and so suitable for this application.
Motor Choice
The choice of a brushed dc motor seems appropriate in this application even though accurate position control is required. Compared to a stepper motor a dc motor offers much greater power density, which is something necessary to open the throttle fast whilst reducing weight. A brushless dc motor was not suitable as it would require an additional system outside the ECU to power and control the brushless motor, increasing overall complexity. Single phase brushless dc motors that can be driven off a standard h-bridge only exist in small continuous operation applications, like cooling fans.
When looking for a motor I created the following requirements:
- The length of the body of the motor must be less than 40mm
- Must be designed to run nominally at 12V
- The extrapolated stall current must not exceed 6A, this is a requirement from the ECU.
The above really narrowed down the choice of motors available. I came across the RE-385 dc motor, which met all of the requirements. Other options were also identified but these were smaller motors with lower stall currents, where the safety factor of burning them out was lower. Established manufacturers, like Maxon, also made motors meeting my requirements, however these were a factor of 100 more expensive than the chosen motor.
The RE-385 is a very common motor and is used on a variety of appliances and industrial actuation systems. It has a very low cost at £3.69 on RS components.
