Torsion Resonant Frequency (TPMS)
 Mark Dalton
 TwoWaves
 Posts: 102
 Joined: Mon Dec 01, 2014 9:35 pm
 Location: Melbourne
Torsion Resonant Frequency (TPMS)
The customer concern is for the Tyre Pressure Monitoring message appearing in the cluster. The system doesn't provide any actual readings, just an indication that one or more tyres may be under inflated. The TPMS system is an indirect system i.e. there are no intyre sensors, tyre pressure is infered via an algorithm.
My original understanding was that the system infers low tyre pressure because the tyre with lower tyre pressure has a smaller diameter and rotates faster. After a drive at constant speed on the Motorway for as long as I possibly could, I could see no more than 1 Km/Hr difference from all 4 wheels in the scan tool data. After being unable to reproduce the customers concern, I have returned the vehicle to the customer for the time being.
Later I came across a second method for infering tyre pressure from wheel speed sensor data called, Torsion Resonant Frequency. Up to this point the diagram below is the best explanation of this method I have come across without having to pay for an academic paper.
Has anyone had any experience with this method of TPMS and trying to scope the wheel speed sensors and extract the resonant frequency. No doubt there is some next level maths involved.

 Pico Staff Member
 Posts: 1335
 Joined: Sun Aug 25, 2013 7:22 am
Re: Torsion Resonant Frequency (TPMS)
Thank you for this and now you have set wheels in motion as I was not aware of this additional Resonance Frequency method
I did start to have a look yesterday and started to go down numerous rabbit holes
I will devote some time to this in the future and see what we can come up with
Don’t you just love this profession Mark?
Just when you think you know something, reallife pulls you back and lets you know you know very little indeed
Thank you again, take care……Steve
Re: Torsion Resonant Frequency (TPMS)
Due to the elastic properties of a tire, while driving, the rim speed v1 will be different from the speed of the outer part of the tire v2.
The magnitude of the difference is determined (among others) by a torque constant k which is proportional to the tire pressure.While driving, the irregularities on the road surface create a resonance between the speeds of the rim v1 and the tire v2.The resonant frequency is proportional to the elastic constant k and thus to the tire pressure.
Changes in tire pressure can be detected by monitoring the resonant frequency. Wheel speed sensors provide information about this resonant frequency.Systems that use the resonant frequency method also use the relative wheel speed difference method.In practice, for pressures of 1.62.5 bar the resonant frequency will be 4050 Hz.
Best regards

 Pico Staff Member
 Posts: 1335
 Joined: Sun Aug 25, 2013 7:22 am
Re: Torsion Resonant Frequency (TPMS)
This is awesome information and I am intrigued to see how we can measure this resonance captured by the wheel speed sensor
Would you have further literature you can share Victor on this subject?
I would like to carry out a number of tests and experiments that demonstrate the theory in practice
Take care......Steve
Re: Torsion Resonant Frequency (TPMS)
I can't find anything new except an article(saemobilus.sae.org/content/2016010459) from which I can read only the beginning,but for the estimation of resonant frequency,the vibration noise in wheel speed must be analyzed in frequency domain.
update:On Mazda6 2014 I found this system,please see the attached file,on 2018 Mazda 6 use tyre sensors for pressure,temperature.
Best regards
 Attachments

 mazda6 tmps.pdf
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 Mark Dalton
 TwoWaves
 Posts: 102
 Joined: Mon Dec 01, 2014 9:35 pm
 Location: Melbourne
Re: Torsion Resonant Frequency (TPMS)
As you say Steve just when you think you're getting to grips with the complexities of cars, along comes something new to boggle your mind. The things the engineers come up with, blows my mind....
Would be very cool to be able to see that frequency in the wheel speed traces, it would be just one more thing that proves just how powerfull the Pico can be.

 Pico Staff Member
 Posts: 1335
 Joined: Sun Aug 25, 2013 7:22 am
Re: Torsion Resonant Frequency (TPMS)
I have to say, this has sent me on a journey that has then become an obsession as I know we have the measurement capability to prove the concept, I just don’t know how at this stage!
In a nutshell we have a number of TPMSs
• Direct TPMS utilize an absolute pressure sensor located inside the tyre cavity
• Indirect TPMS 1 utilizes the ABS sensor signal to determine a drop in tyre pressure based on a change in tyre radius and therefore circumference (Reduced circumference = increases in wheel speed/frequency)
• Indirect TPMS 2 as per TPMS 1 above but with the addition of tyre resonance frequency detection again utilizing the ABS wheel speed sensor signal!
The following link has a neat, informal summary of the above with all the relevant detail https://unece.org/DAM/trans/doc/2003/wp ... 20ebis.pdf
Please note, with Indirect TPMS 2 there is a lot more to consider than tyre radius and resonate frequency as the interaction with Engine management and VSC also come in to play
One of the draw backs with TPMS 1 is that only a single tyre pressure can be detected relative to the frequency of the remaining tyres. I.e., similar to a relative compression test, if all tyre pressures are equally low, then there will not be a sufficient difference in wheel frequency to determine an offending tyre.
As an enhancement to TPMS 1, TPMS 2 incorporates tyre resonant frequency detection where the inherent properties of the tyre are captured and monitored by the ABS wheel speed sensor
The wheel speed sensor signal is not only monitored using the Time Domain (as we do during diagnosis) but also, using Fast Fourier Transform (FFT) to reveal discrete properties of the speed signal within the Frequency domain (think NVH Frequency view)
More on FFT analysis here https://en.wikipedia.org/wiki/Fast_Fourier_transform
So, what is tyre resonance?
Tyre resonance is the characteristic (vibration) of the tyre in response to applied forces………..
The tyre responds (vibrates) to excitation forces from the road (via the tyre contact patch) and to torsional forces from the drive train/road reaction. Both these excitation forces have a direct effect on the rolling radius of the tyre which in turn have consequences for the speed/frequency of the wheel & tyre assembly.
In the first link provided above, page 7 slide 44, note the graph view (added below) where the speed signal not only delivers a smooth trend of wheel speed but also reveals a sign wave riding on the trend.
The sign wave is generated by the momentary changes in tyre radius as a result of the excitation forces described above and are accepted by the TPMS based on initialization settings and the algorithms within the relevant ECU. i.e., the control unit will expect and tolerate deviations in tyre radius within certain parameters
However, should our tyre become deflated, the entire characteristics of the tyre will change in terms of response to excitation forces. Not only will the tyre radius change but so will the spring rate of the tyre and therefore the frequency of the sign wave riding on the trend
This is where our FFT analysis of the wheel speed signal comes into play as we can detect these frequencies in order to determine tyre deflation
Now, over the last few days I have been experimenting with my own vehicle (BMW 320d F31) which the more I dig and delve has seen me chase my tail to the point where I need help (that has been said before)
Below we have 2 accelerometers fitted to the LH Rear and RH Front caliper bolts capturing vibration at the wheel hub. Channel D is a frequency view of the LH Rear ABS wheel speed signal AC coupled
The focus above is on channel D and typically around the inherent frequency of tyre resonance which falls between 30 and 50 Hz depending on inflation pressure. I think we can agree this is inconclusive at this stage and I need to spend more time using both NVH and PicoScope Spectrum view
I have also tried deliberately lowering the LH Rear tyre pressure by 1 bar in order to locate a possible frequency of interest but no joy as yet. Ironically my car (which utilizes indirect TPMS) displayed a lowpressure warning for the LH Rear tyre! I guess the comfort to take from the vehicle warning is that the system is operating correctly and somehow, the vehicle was able to identity the offending tyre
Rest assured I will liaise with colleagues here at Pico and try to determine how we can capture the required signal
Based on the above disappointment I then looked at the wheel speed signal in the Time Domain using PicoScope in an attempt to detect the change in wheel/tyre frequency for the LH Rear tyre inflated to 3bar and then lowered to 2bar at identical road speeds
Above, we have 2 instances of PicoScope open, on the left we have the wheel frequency and road speed as detected by the LH Rear ABS wheel speed sensor with the tyre at 2 bar, and the same on the right with the tyre at 3 bar
Once again, it’s not conclusive that we have a dramatic change in the frequency of the wheel/tyre at 50 MPH with differing tyre inflation. Ahhrrrrrr.
Before I waffle on, the vehicle speedometer reports 50 mph yet the ABS wheel speed math channel returns approx. 45 mph due to the deliberate error built into the driver’s instrumentation (approx. 10%)
You would have thought it to be very simply to drive down the same road at the same speed (using cruise control) and be able to match road speeds perfect for analysis; as you see above this is not the case!
More information on road speed via ABS speed sensor math channel can be found here viewtopic.php?p=96821#p96821
So, all in all not the best or fruitful diagnostic journey to this point but rest assured I will not give up
Thinking this through, I have a number of variables to consider in order to find the mysterious secrets that lie within the ABS speed sensor signal
• The ABS signal was AC coupled which may well introduce unwanted noise, I will therefore switch to current measurements
• The tyres under test are Run Flats and therefore their radius may not alter sufficiently for detection in the Time Domain. (Deflating the tyre by 1 bar was sufficient for detection by the on board indirect TPMS)
• The FFT settings may well need amendments that I am not currently familiar with at this stage
• The effects of differential action and VSC during cornering
I hope the above is of some use in the interim, take care.....Steve