Toward Understanding the Errors in Online Air-Ride Suspension ...

An ASABE – CSBE/ASABE Joint Meeting Presentation

Paper Number: 141897468

Toward Understanding the Errors in Online Air-Ride Suspension Based Weight Estimation

Balmos, Andrew D.1; Layton, Alexander W.1; Ault, Aaron1; Krogmeier, James V.1; Buckmaster, Dennis R.2

1. Electrical and Computer Engineering, Purdue University, West Lafayette, IN United States

2. Agricultural and Biological Engineering, Purdue University, West Lafayette, IN United States

Written for presentation at the

2014 ASABE and CSBE/SCGAB Annual International Meeting

Sponsored by ASABE

Montreal, Quebec Canada

July 13 – 16, 2014

Abstract. It has been previously shown that the weight of a vehicle can be accurately estimated from pressure measurements in its air-bag suspension with just limited calibration. However, because the current state-of-the-art does not account for possible suspension dynamics, the vehicle must, in general, be static and on flat level ground. This work presents progress toward overcoming this limitation, thus, enabling activities such as yield mapping silage or stover and on-the-fly in-field calibration of classical yield monitors.

The first part of this work presents an overview of a trailing-arm air-ride suspension assembly and provides data gathered from a semi-tractor-trailer as evidence that the originally proposed algorithm is very capable in static conditions, but has significant error when the vehicle is in motion. Suspension dynamics from road variations cause fluctuations in the air-ride’s air-spring pressure and therefore fluctuations in the weight estimation.

To further understand how the pressure signal is affected, the second part of this work develops a dynamic model for the motion of a trailing-arm air-ride suspension. It also demonstrations a method of randomly generating a road surface for use when simulating the model.

Further work of modeling the source and forms of the pressure noise, and developing a filter to reduce the noise’s effects is still required.

Keywords. Vehicle Weight, Weight Estimation, Weigh-in-Motion, Air-Ride, Air-spring, Dynamic Motion Model.

The authors are solely responsible for the content of this meeting presentation. The presentation does not necessarily reflect the officialposition of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Meeting presentations are not subject to the formal peer review process by ASABEeditorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ASABE meeting paper. EXAMPLE: Author’s Last Name, Initials. 2014. Title of Presentation. ASABE Paper No. ---. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a meeting presentation, please contact ASABE at [email protected] or 269-932-7004 (2950 Niles Road, St. Joseph, MI 49085-9659 USA).

2014 ASABE – CSBE/SCGAB Annual International Meeting Paper Page 1

Introduction Online weight estimation of vehicles, particularly hauling based ones such as a semi-tractor-trailer or a grain cart, enables a farm to gather new types of data and can increase operational efficiency. For example, combine yield sensors need to be re-calibrated whenever plant properties change, such as type, moisture, etc. The re-calibration is generally a time consuming process, because it is typically not easy to weigh the true yield in the field. If the equipment that the combine transfers its harvest to could immediately report the load weight, yield sensor calibration would not only be made easier, it could now be done continuously. Additionally, the weight of all loads off the field, including those that go directly to storage, can now be recorded to improve a farm’s total yield tracking. Another technology that online weight estimation would enable is silage yield mapping. Vehicle weight measurements could be combined with harvester GPS tracks to generate yield maps for crops, in which silage is immediately blown out into a trailing semi or cart. Finally, loading operations are simplified because axle weights and total weight can be monitored during the entire process. Adjustments to the loader can be made in real-time ensuring that the final weight and weight distribution is legal for the roadways.

It is already known in the literature and industry that it is possible to estimate the weight of a vehicle without traditional permanent, or semi-permanent, scales. (Lee, Schueller, & Burks, 2005) used load cells installed between the vehicle’s frame and axles to monitor the weight while in motion for the purpose of generating silage yield maps. They were able to achieve an overall error of less than 5 percent of the total; however, this design requires a relatively invasive installation. (Lingman & Schmidtbauer, 2002) developed a Kalman filter around a motion model that estimates vehicle mass and road slope using speed and acceleration measurements available from the vehicles CAN bus as inputs. (Holm, 2011) expanded upon those ideas by incorporating other CAN bus data such as fuel injection, gear ratio and shift in-progress, and breaking signals. As a result, the weight estimation errors were between 2 and 5 percent as compared to a permanent scale. There are several products on the market, such as (AirWeigh, 2014) and (Farmtronics, 2014) that use air pressure measurements from within an air-ride equipped semi-tractor-trailer suspension to estimate weight. The authors studied the effectiveness of such a scheme in a prior work (Layton, et al., 2013) and found that errors are typically less than 1 percent. However, because the simple design only related pressure measurements to vehicle weight with an affine line there was the potential for significant error when the semi was in motion, on uneven ground, or if the height control valve had not yet leveled the suspension. Most agricultural applications, including the ones previously discussed, require that the weight be measured in at least one of the mentioned environments and therefore a more robust scheme is necessary.

Objectives To help alleviate the operating restrictions of the air pressure weight estimation technique the authors set out to

1. understand how the operating environment affects the pressure within the suspension, 2. develop an estimation algorithm that is successful while the vehicle is both in motion and on uneven

ground, 3. and characterize the expected distribution and magnitude of the remaining error.

The remainder of this work focuses on weight estimation of vehicles equipped with trailing arm air-ride suspensions systems. In particular, we exclusively consider a semi-tractor-trailer, but the results should generalize to other vehicles with similar designs. Additionally, this paper will present example pressure and weight signals collected from a semi during static loading and silage corn harvest and develop a trailing arm air-ride suspension model that will enable further studying of the errors. It is important to note that further work is still necessary to fully complete the goals set forth.

Overview of trailing arm air-spring suspensions Trailing arm assemblies with air-springs are commonly found on so-called air-ride equipped vehicles. An air-ride equipped semi-tractor or trailer will have air-spring suspensions installed on either the tractor drive or trailer tandems, respectively. Unfortunately, tractor steering axles often still have a mechanical spring based suspension, so not all of the vehicle’s weight is carried through an air-ride assembly. The assemblies generally consist of an air-spring, hanger, arm, axle mount, damper, and an optional height control valve. Its main purpose is to distribute the load between the hanger and the air-spring so that the spring can help improve the suspension qualities while still maintaining an overall structure rigidity. Generally there are two assemblies per axle, one on both sides and mounted closely to the respective tires. An example of one such assembly is shown in figure 1.


There are various designs of air-springs; however, most are a cylindrically shaped chamber made from a flat steel plate for the top, a steel piston for the bottom, and high strength rubber-coated fabric for the sides. An example of a rolling lobe style air-spring can be seen in figure 2. The chamber is typically filled with air and pressurized between approximately 276 to 552 kPa (40 to 80 PSIG) under normal loads, but can be operated upwards of 690 kPa (100 PSIG) if need be (Goodyear, 2008). Pneumatic force is used to carry the majority of the air-spring’s load, and because the chamber is a closed system when the height control valve is not active it must compress or expand to appropriately adjust the internal pressure when the applied load changes. The unit is installed by mounting the top plate to the tractor or trailer frame and the piston to the suspension arm. This results in the vehicle weight being partially supported by the top plate, and road and motion forces are transferred through the piston.

The arm is pinned to the hanger and forms a mechanical lever in which the axle, shock, and air-spring are mounted to. Traditionally, the air-spring is mounted at the far other end of the arm and the axle and shock are mounted together somewhere in between; however, there are other configurations in use. The actual distance from the pivot to each component affects the overall response of the suspension, because the lever causes vertical movements at one location to become larger or smaller movements at other locations. For example, in the typical configuration a vertical perturbation in the axle becomes a larger perturbation at the air-spring as the distance between the axle and air-spring increases. As a result, the apparent spring constant of the suspension also increases with the distance. The hanger is rigidly mounted to the same frame as the air-spring's top plate and together they form the points in which all of the vehicle's weight and road and motion forces are transferred.

Figure 3 is a schematic top-view of a complete typical semi-tractor-trailer air-ride suspension system. As shown, not all the air-springs necessarily have independent air supplies; in fact, most air-ride enabled tandems pneumatically join all the air-springs together and feed the set with one height control valve. The height control valve ensures that the vehicles ride height is acceptable at all times. If the height is too low, the valve will open to the supply pressure and allow air to flow into the air-spring's chambers, causing them to expand, and if the height is too high the valve will open to the atmosphere and allow air to flow out of the air-spring’s chambers, causing them to compress. This is usually accomplished by mounting the valve itself on the hanger and using a rod to link the valve's lever to the assembly arm. As the angle of the arm changes, with respect to the horizon, so does the angle of the valve's lever. For example, as weight is added to an air-ride enabled vehicle, the air-springs increase their internal pressure by compressing. This results in the arms pivoting upward and the frame dropping closer to the ground. However, the link between the height control valve and an arm causes the valve

Figure 1: Wide view of suspension assembly showing the air-spring, axle, shock, arm, hanger,

and height control valve.

Figure 2: Close-up view of a rolling lobe air-spring mounted between the trailer and the

assembly arm.

Arm Air-Spring

Axle Shock

Hanger

Height Control Valve


to open to the supply pressure therefore making the air-spring expand. As the air-springs return to their desired height, the arms pivot back into their original position, thus, returning the frame to the correct height and the height control valve closes. A similar reverse process occurs when weight is removed and the frame begins to rise. Most height control valves have built in hysteresis and they will not activate until the valve's lever has rotated through some angle, typically 2 to 5 degrees. This is to reduce the consumption of air when movement is caused by suspension dynamics and not because of load changes. Suspension dynamics will eventually even out and do not require a height adjustment.

Static Analysis In the author’s previous work (Layton, et al., 2013) it was shown that the total weight at the axle can be calculated by knowing the system geometry and the force which the air-spring is producing, assuming everything is stationary. See figure 4 for a generalized drawing of a trailing-arm air-spring assembly geometry. By taking the moment around the pivot point, the total weight can be found to be

(1)

where is the total weight supported by the axle. The actual weight of the axle, tires, and related components need to be added to to find the weight on the ground, that is, the weight a truck scale would measure.

Figure 4: Generalized drawing of a trailing-arm air-ride suspension. Shown are the vehicle frame, hanger, arm, air-spring and piston, shock, and height control valve. Also shown, is the dimension of those components

from the pivot point.

Figure 3: A top schematic view of a semi-tractor-trailer detailing the pneumatic connections of the suspension's air-springs, also known as air-bags, and height control valves. Each air-spring shown in this high level diagram is part of a complete trailing-arm

assembly.


The force produced by the air-spring can be related to its pressure using Pascal’s principle. Thus air-spring force, , is

(2)

where is the gauge pressure of the chamber and is the area of the air-spring. However, because the air-spring is not a perfect cylinder its effective area may not be the actual area of either the top plate or piston and would need to be experimentally determined if needed.

A stationary semi-tractor-trailer’s total weight can be estimated using equations (1) and (2) with the following expression

4 4 (3)

where it is assumed there is one trailer tandem, one tractor tandem, and one non air-ride steering axle. The factor of four accounts for the standard tandem design, which has four assemblies, all pneumatically joined. Finally, is a constant that models any weight that cannot be directly observed with the air-spring pressure, such as the weight of the axle, tire, and other related components or the weight supported by the steering axle. It is assumed that nearly all of the vehicles variable weight is carried by either the drive and trailer axle and therefore the steering axle weight is roughly constant.

The actual transformation of pressure to weight can be found for a specific vehicle without having to actually know , , , or . A collection of pressure and actual weight measurement pairs could be used to fit either a two-dimensional (equation 4a) or one-dimensional (equation 4b) model of equation (3).

≅ (4a)

≅ (4b)

Equation 4b is merely a simplification of 4a, where it is assumed that the assemblies are identical, and so and are equal to each other. The reduction in dimensionality means fewer calibration points are necessary; however, the model may not be as accurate.

Air-Spring Pressure Logging To further understand how motion and suspension dynamics affect the overall weight estimation error, custom weight sensors were developed and deployed. One of those sensors is shown installed on a semi-tractor in figure 5. The device consists of discrete pressure, accelerometer, and temperature sensors that are all sampled, buffered, and forwarded via Bluetooth to a nearby Android device. Running on the Android device is a custom built app, previewed in figure 6, which logs and processes the received measurement stream in real time. The measurement log is persisted to the tablet's disk making it accessible for future offline processing. The app also manages the active calibration scheme and displays the current weight estimate to the user.

Experiment Setup

To gather example pressure signals in various environments, two of the weight sensors were installed on a semi-tractor-trailer. One of the sensors monitored the tractor tandem and the other monitored the trailer tandem. Both the tractor’s and trailer’s air-ride suspensions are well modeled by the generalized geometry given in figure 4. Figure 1 and figure 2 are pictures of one of the actual trailer assemblies used.

The sensors were left on the vehicle for several months, and calibration points and measurements streams were collected opportunistically during the vehicles normal farm operation. Figure 7 plots the least squares best fit of the one-dimensional model to the collected calibration data. There appears to be a good agreement.


Figure 5: Custom weight sensor installed on a semi-tractor. The sensor records pressure, temperature, and accelerometer

measurements and forwards them over Bluetooth to an Android app for further processing.

Figure 6: Custom Android app that receives measurements from a weight sensor via Bluetooth. The app manages the

current calibration pairs, calculates the model’s best-fit, and displays the current weight estimation. The app is also capable

of logging the received measurement streams to the disk for later processing.

Figure 7: The red circles are calibration points obtained with the custom Android app and a permanent full vehicle scale. The blue line is a one-dimensional model fit to the calibration data. There appears to be good

agreement.

Figure 8 is an example of the pressure signals from the semi-tractor-trailer during a stationary loading process. The trailer was filled from front to back (tractor to end of trailer), explaining the gap in time between the pressure signals. The signals themselves have little noise other than a few small bursts which is related to suspension movement such as height control valve activating, changes in rate of loading, or some external force. Figure 9 shows the resulting weight estimates for both the one- and two-dimensional models. The two algorithms are in very close agreement, because the air-ride assemblies for both the tractor and the trailer were of the same design, meaning the model coefficients are roughly equal to each other.


Figure 8: Pressure signal, in analog to digital converter (ADC) values, of both the tractor (font) and trailer (rear) tandems

during a stationary loading process. The front of the trailer was loaded before the rear. The signal does not appear to have any

significant noise other than what was caused by a few small perturbations in the suspension.

Figure 9: The result of the vehicle weight estimation using both the one- and two-dimensional estimators and pressure signals

from figure 8. The signal does not appear to have any significant error other than what was caused by a few small

perturbations in the suspension.

Increased Errors In Motion

The pressure signals and weight estimation are significantly noisier when a vehicle is loaded while in motion. Figure 10 is an example of pressure signals collected from a semi being loaded by a combine in the field. More precisely, the truck is being filed roughly from front to back (tractor to end of trailer) while traveling alongside the combine as it harvests. The desired pressure signal is evident; however, it has clearly been disturbed by some suspension dynamics as the vehicle moved over the rough field. The pressure signal noise translated into a significant weight estimation error, as can be observed in figure 11. The large noise bursts are caused by the vehicle traveling at a higher speed across the field in-between loading operations.

Clearly the pressure signals need to be conditioned prior to the weight estimation to improve the measurement quality. However, to select the correct filter, more must be understood about the pressure signals and noise.

Figure 10: Pressure signal, in analog to digital converter (ADC) values, of both the tractor (front) and trailer (rear) tandems

during a non-stationary loading process. The front of the trailer was loaded before the rear. There appears to be significant

noise caused by the vehicle motion. The two large noise bursts were caused by the vehicle traveling at a higher speed.

Figure 11: The result of the vehicle weight estimation using both the one- and two-dimensional estimators and pressure

signals from figure 10. The signal appears to have significant error caused by the vehicle’s motion.


Trailing Arm Air-Spring Dynamic Motion Model To better understand how the suspension dynamics affect the air-spring pressure, we began developing a dynamic motion model for the assembly. Others have demonstrated similar models, but mainly focus on the air-spring itself and not the rest of the assembly. (Hao & Jaecheon, 2011) developed an analytical model for an air-spring, including the effects of a height control valve, assuming it is an isothermal polytropic process. (Lee S. J., 2010) did similar work; however, it also accounted for heat flow into and out of the system. (Feihong, Xiaoping, & Wei, 2001) used a dynamic air-spring and height control valve model to study the affect air flow disturbance has on vibration isolation, and (Zhong, Yang, & Bao, 2011) focused on understanding the primary resonances that the nonlinear air-spring produces under harmonic motion. Finally, (Trangsrud, Law, & Janajreh, 2004) took a bigger picture view of a semi-tractor-trailer and modeled the vehicle’s total motion with a 14 degrees of freedom. In particular, they used the model to consider how the ride dynamics and pavement loading were affected when various parameters of the vehicle’s suspension were adjusted. Unfortunately, the air-ride suspension assemblies were not carefully modeled, but rather they were assumed to be a parallel linear spring and damper.

Figure 12: The air-ride suspension generalized mechanical drawing with an ideal damper modeling the shock and an ideal spring and damper modeling the tires. (arm angle from horizon), (position of trailer), (air-spring

pressure), and (mass of air in air-spring) are the state variables of the dynamic model and (road surface) is an input. (trailer mass), (load mass), and (arm mass) are all the masses of the system. (position of axle) and (position of spring) are shown for understanding. They can always be calculated from system constants

and state variables so they are not included in the final model.

Figure 12 is based on figure 4 with various components replaced by ideal linear models of their original behavior. The air-spring itself is left as is and will be modeled in more detail in the following derivation. The tires have been replaced with a parallel spring ( ) and damper ( ) system and the shock modeled as a single damper ( ). We will take the arm as a rectangular prism with height , length , and mass . The state variable represents the angle formed between the arm’s center axis and the horizon. It is assumed that the height control valve has been installed in such a way that also represents the angle of the valve’s lever. and are state variables for the pressure and mass of the air in the air-spring chamber, respectively. The portion of the mass that the frame supports, and is also carried by the suspension assembly, is assumed to be

, where is a piece of the total trailer mass and is a piece of the total load mass. The change in the horizontal position of the frame is represented by the state variable . and track the change in the horizontal position of the points where the axle and air-spring respectively mount to the arm. They are included only for clarity and can always be determined from the state variable and various system constants from figure 4 using equations 5a and 5b. Finally, , the road elevation being traveled over, is the sole input of the system.

(5a)

(5b)


Modeling

Newton’s second law of motion is used to develop a differential model for the motion of

where is the gravitational constant of earth, is the reaction force at the hanger pin, is the force produced by the air-spring, and is the typical ideal damper force. The reaction force at the hanger can be written as a function of the air-spring and damper forces by taking the moment around the axle. By combing the above results, equation 6, the final model for the motion of is determined.

(6)

Modeling

The rotational equivalent to Newton’s second law of motion is used to develop a differential model for the rotation of the arm, or

where and are the same as defined above, is the sum of the tire spring and damper force. The 1/cos scaling accounts for the fact that only the forces perpendicular to the arm contribute to torque at the arm’s pivot point. is the arm’s moment of inertia and it can be shown to be equal to

124

for a rectangular prism with height a, length b, and mass that is pinned on one side. By combining the above results in equation 7, the complete model for is

12

4 (7)

Modeling the gas state of the air-spring’s chamber

In order to model the pressure of the air-spring’s chamber the entire gas state needs to be modeled. The ideal gas law, , suggests that at least three of the four parameters, , , , and , need to be known in order to fully do so. The volume of the air-spring chamber, , can be deduced from the system geometry and the state variables and and therefore by picking and as the final two state variables the gas state is completely known.

In order to incorporate the height control valve the gas state model must also allow the air mass in the system to change. Thus, we turn to the thermodynamic energy balance equation

where is the change in heat, is the change in work, is the change in mass, and is the change in the gas’ internal energy all with respect to time.

The literature suggests that air-springs are well-modeled by adiabatic processes (Feihong, Xiaoping, & Wei, 2001) and so it is assumed that 0, meaning there is no heat transfer between the air-spring and the outside. Continuing with the assumption that the air-spring operates similar to a piston, we have . Energy associated with the a gas’ mass is proportional to its enthalpy, , where is the specific heat of the gas under a constant pressure (Green & Perry, 2007). It is assumed that the temperature of the mass flowing in is constant and the same as the air supply. Additionally, it is also assumed the temperature of the mass flowing out is the current temperature of the air-spring chamber and therefore it can be calculated from state variables and the ideal gas law. Finally, (Green & Perry, 2007) derive the internal energy of an ideal gas to be , where is the specific heat of that gas under constant volume.

Gauge Pressure Model

By combining the above results with the ideal gas law, , and its derivative, a final

model for the gas pressure can be found. However, because the process is widely known in the literature to be a polytropic process it would be beneficial to write the model in terms of the polytropic index, , and thus


removing the dependences on the specific heat of constant pressure ( ) and constant volume ( ). Thus, the

following two identities, and 1 are also used to arrive at equation 8, the final model for the air-

spring’s chamber gauge pressure.

(8)

where is given to be between 1.3 and 1.38 depending on the environment (Hao & Jaecheon, 2011) . The air-spring’s chamber volume can be calculated using , where is the chambers initial volume and is the cross-sectional area of the chamber, if the chamber has a constant cross-sectional area. Trivially,

.

It is worth noting that the air-spring is not a linear device and therefore has a variable spring constant. This is because the air-spring’s force, , is a function of the current pressure and the current pressure is a nonlinear function of the volume, rate of change of the volume, and the mass flow.

Mass Flow Model

Lastly, the mass flow model is simply

(9)

where and are dependent on the specific height control valve in use. During normal operation, the mass flow through the valve can often be considered choked, and taken as a constant as long as the supply pressure is also assumed to be a constant (Green & Perry, 2007). However, most height control valves have a variable orifice area that is a function of how open the valve is, and as a result the mass flow rate is also variable. In order to complete the model, two functions and for the specific height control valve in use are required. Typically, these are simple clamped ramp-like shaped curves that are completely off between 0 and 2 to 5 degrees of rotation, and then grow from no flow to the maximum flow in roughly the next 10 degrees of rotation. For any further rotation, the mass flow stays constant at its maximum value (Hendrickson, 2013).

Complete Model

Equation 6, 7, 8, and 9, reiterated below, form a system of nonlinear differential equations that model the complete motion of a trailing-arm air-ride suspension. The model can easily be re-written in state-space form and simulated using standard ordinary differential equation solvers.

(repeat 6)

12

4 (repeat 7)

(repeat 8)

(repeat 9)

However, in order to simulate the model to study the pressure signal and noise, an elevation trace of a road is needed as the input.

Simulation of Roads and Fields The International Organization for Standardization (ISO) standard 8606 models and classifies the roads by the power spectral density (PSD) of their surface elevation, or vertical road profile displacement (ISO 8606, 1995). More accurately, the roads are modeled as a Gaussian random process with a PSD of the following form

where is a spatial frequency parameter (cycles/meter), is a reference spatial frequency given as 0.1 cycles/meter by the standard, is a constant that determines the classification of the road, and, finally, is a parameter that controls the waviness of the road and always equals two for the standard model.

The various road classifications and the corresponding cutoff values, , are given in table 1. The


classification cutoff is also given by the formula, 2 10 m3, where is an integer that starts at 5 and increases by two for each new level of road roughness. Most agricultural applications in the field, such as silage corn harvest, will occur on surfaces of either pasture (E, k=13) or plowed field (F, k=15) and therefore those are of greatest interest.

Table 1: ISO 8606 road classifications and PSD constant cutoff. k is the parameter used to determine the classification cutoff.

Road Type Road Classification k Smooth runway A 5 2 10 m Smooth highway B 7 2 10 m3

Highway with gravel C 9 2 10 m3 Rough runway D 11 2 10 m3

Pasture E 13 2 10 m3 Plowed field F 15 2 10 m3

Potentially unsafe roadway G 17 2 10 m3

Using a technique described by (Shinozuka & Deodatis, 1991) to generate sample functions of a stationary random process with a specific PSD, roads following the specification of ISO 8606 can be randomly generated. Figure 13 is an estimate of the PSD made from a sample function generated to the class A (k=5) specifications. Also shown, are the various classification cutoffs. Figure 14 is the elevation plot of the actual sample function. It appears the technique is quite capable of randomly generating useable roads.

Figure 13: Estimate of PSD from a randomly generated class A (k=5) road. The red lines are the PSD curves at the cutoff of

each classification.

Figure 14: Elevation trace for a randomly generated class A (k=5) road. The PSD of the given road is shown in figure 13.

To better appreciate how the road elevations change with classification, figure 15 shows one example sample function from each process, or classification type. From this view, it is clear that class A roads are extremely smooth and would cause little suspension dynamics to occur as the vehicle drives on it. However, classes E and F are significantly rougher and contain large bumps that would cause severe perturbations of the air-spring.


Figure 15: One example sample function from each ISO 8606 classification to demonstrate how the road roughness varies.

Incorporating into Dynamic Motion Model

The dynamic motion model previously derived requires the road elevation input to be in the time domain and not the spatial domain. Therefore, the generated signal needs to be transformed using the relationship

where is the desired time variable, the simulated spatial variable, and is the velocity of the vehicle, often taken as a constant for simplicity. The motion model also requires the time derivative of the road elevation ( ; however, because the simulated road profile is not a continuous function, it must be numerically estimated. As a result, close attention should be paid to the sample rate to ensure the motion model’s simulation can be trusted.

Conclusions and Future Work This paper presented a stationary weight estimation model of the trailing-arm air-ride suspension and demonstrated with data gathered from a semi-tractor-trailer that the estimation error was low when the suspension was stationary, but has significant issues when in motion. As a result, the paper developed a dynamic motion model for the trailing-arm air-ride suspension to enable further studying of the source and type of errors. Also shown, was a method of randomly generating specific classifications of roads for use when simulating the suspension dynamics.

Further work is still needed to fully complete the initial goals. The work list includes:

further verification of the proposed model, characterizing the source and type of the pressure signal noise, and the development of a filter that can reduce said noise and improve the weight estimate.


Acknowledgements The authors would like to thank Ault Farms for allowing us to make modifications to their equipment and spending time with us rather than farming.

Partial funding for this effort was provided by USDA National Institute of Food and Agriculture under grant 2012-67021-19404

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