Clean Snowmobile Competition: 4-Stroke Snowmobile System ...



System Modeling

Michael DeMaio

Matthew Allard

William Hotchkiss

Serdar Yorulmaz

University of Maine 2004 SAE CSC System Modeling Team

Department of Mechanical Engineering

ABSTRACT

The purpose of this System Modeling project was to accurately develop a model of a snowmobile’s performance through the use of computer programs and given data related to the snowmobile and its operating environment. Through the development of an accurate model, it has been possible to tune a snowmobile to maximize its performance in the 2004 SAE Clean Snowmobile Challenge without wasting valuable time and money doing so with the physical medium itself.

Furthermore, through the use of the model it was discovered that the tracks moment of inertia had an enormous effect on the snowmobiles performance. In order to further ensure the accuracy of the model, a lab experiment was performed to calculate numerical data pertaining to this aspect of the snowmobile.

APPROACH

It was determined that the best approach would be to produce three separate models; an engine model, a sound model, and a complete model of the snowmobile as a whole. After examining the rules of the 2004 SAE Clean Snowmobile Challenge (the competition that the model would be used to optimize the snowmobiles performance in), it was noted that the majority of the points could be obtained by developing a snowmobile that was quiet, had low emissions, and good fuel economy. It was decided that the fuel economy and sound characteristics of the sled would benefit most from an accurate model, thus this is where the effort was put forth. It was also noted that 1/8th and ¼ mile performance should be modeled as well. While not weighted as much point wise as fuel economy or emissions in the competition, modeling the sleds acceleration was determined to be equally important. It produces useful insight as to what components of the snowmobile have the greatest effect on its performance, and how different modifications geared towards improving the snowmobiles fuel economy, emissions, and sound output will affect it’s performance as well. Lastly, it was noted that an acceleration model would be ideal for testing against the snowmobiles real world acceleration to ensure the model was accurate.

ENGINE MODEL

It is fairly easy to find horsepower and torque data of virtually any mass produced vehicle, however, this data is often times of no value for modeling purposes for several reasons. First and foremost, the horsepower and torque curves are frequently based on dynamometer results obtained at the point of the system that transmits the power to the ground. Therefore, this data is actually a measurement of the engines performance coupled with the various losses throughout the drive train. This means that a low horsepower output could be caused by anything from restricted intake flow into the engine to large inefficiencies in the transmission. One of the primary benefits of an accurate system model is the ability to be able to pinpoint the performance of every individual aspect of the system itself, which is not possible with data obtained in this manner.

Another large problem with using given engine horsepower and torque data in system modeling is that this data not only varies slightly from engine to engine due to tolerances in production, but also varies greatly for many other different variables, such as the type of fuel used and the environmental conditions in which the engine is operating. Furthermore, modeling of the engine and its reaction to different modifications is often desired as well. Due to all of the aforementioned reasons, as well as being the primary source of the criteria being analyzed as a whole, an accurate model of the engine was determined to be essential to the modeling process.

SNOWMOBILE SYSTEM MODEL

A complete model of the snowmobile is crucial. First and foremost, an accurate system model of the sled can calculate how tuning the snowmobile to perform well in one category will affect its performance in other categories. Therefore, through the use of the system model one could determine the configuration that will produce the most net points in the competition. For example, this could be used to calculate the optimal RPM to set the snowmobiles continuously variable transmission to hold as the snowmobile is driven; high enough to allow the snowmobile to run the 1/8th mile drag in the desired time, yet low enough to net optimal fuel efficiency, emissions, and noise.

Furthermore, an accurate system model of the snowmobile could even indicate the optimal way in which to operate the snowmobile that could only be found otherwise through excessive testing, such as the optimal speed to drive the snowmobile at over the 100 mile fuel economy part of the competition to minimize fuel consumption.

NOISE VIBRATION AND HARSHNESS

Having the largest impact on the scoring of the Clean Snowmobile Competition, this portion of the modeling was essential to optimizing further modification of the snowmobile. Sound modeling allowed for pin pointing the individual components on the sled that had the greatest contribution to the principal noise source.

Sound modeling is a common practice in most industrial situations today. An accurate sound model can be worth its weight in gold when designing a piece of equipment that produces noise. The advantage to having an accurate sound model, is that the prototype can be modified “on paper” and the outcome can be obtained with virtually no lost time or money. Without a sound model, the design process would have been trial and error, which leads to unnecessary spending and testing. The disadvantage to testing is that it takes time, and not every piece of machinery can be tested in a lab without the proper equipment. However, the sound model can allow us to test in almost every environment, if adequate conversions are made.

In this case the piece of equipment being tested was an Arctic Cat 660 trail snowmobile. After reading the rules of the 2004 SAE Clean Snowmobile Challenge, it was understood that the snowmobile would be tested at the competition in a certain manner that is unattainable in a lab without a sound model. It would be driven through a sound barrier with a radius of 50 feet, at speeds varying from 35 mph to 55 mph. It was clear that there would be no possible way to drive the snowmobile at these speeds in a laboratory, so it was decided that it would be tested at 1 ft in a stationary position. After the proper calculations were made, an accurate model of the same testing environment as that of the competition was obtained.

DESIGN OVERVIEW

ENGINE MODEL

In order to accurately produce horsepower and torque curves of the snowmobile’s engine given various engine specifications and information concerning its operating environment, a Matlab program modeling the four-stroke engine itself was developed. After some basic engine theory research, it was determined that the most accurate way to model the engine analytically would be through brake mean effective pressure calculations. Brake mean effective pressure, commonly referred to as BMEP, is defined as the average pressure which, if imposed on the pistons evenly during each power stroke, would produce the measured power output. The equation used to calculate the BMEP of a four stroke engine is as follows:

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Where r equals the compression ratio, k is the specific heat ratio, and P1 and P3 are the cylinder pressures at state one and three of the idealized air standard Otto Cycle, respectively. A P-v diagram illustrating the idealized Otto Cycle is shown in Figure 1 below:

Figure 1 – Idealized Otto Cycle

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With P1 and P3 being found through cycle analysis of the Otto Cycle, the BMEP of the engine was found. The power produced by the engine is then calculated from the following equation:

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Where Nc is the number of cylinders, S is the engines piston stroke, Ap is the surface area of one of the engines pistons, and N is the engines RPM.

In order for the program to accurately model the engine quickly and efficiently with different given input data (such as various piston strokes and diameters, atmospheric pressures, compression ratios, etc.), it is essential that the Matlab program do the cycle analysis of the engine itself. As such, this was incorporated into the Matlab file such that with the given atmospheric pressure, atmospheric temperature, compression ratio, heating value of the fuel used, piston diameter, piston stroke, and the air fuel ratio of the intake charge, the power and torque of the engine versus its RPM can be determined.

Theoretical engine modeling, in its simplest form, produces constant torque at any given rpm, and a power “curve” that has a steady slope with no peak. This is because the thermodynamic, inertial, and fluid losses that affect the engines power output at different engine speeds are ignored. Accurately calculating these losses requires information that was nearly impossible or simply impractical to determine (such as the drag on the air as it passed through the intake manifold at different engine speeds). However, the snowmobile model is highly dependent upon an accurate power “curve” with a peak. Therefore, the power and torque output of the theoretical engine model was adjusted to mimic the Arctic-Cat 660’s actual power and torque curves obtained from running the snowmobile on a dynamometer. This was done by multiplying the horsepower obtained through the engine model by varying constants that represented the engines efficiency at various RPM’s. These adjusted values are then output into matrices that are used in the complete snowmobile model. An example of the power and torque curves calculated by the engine model is shown in Figure 14 in the results section.

SNOWMOBILE SYSTEM MODEL

For compatibility reasons it was decided that the system model for the snowmobile should be completed in Simulink, as the engine model was. It was decided to initially focus on designing a “drag” model of the snowmobile, and then later make slight alterations such that the model could be used to calculate the sleds fuel economy at various speeds.

Knowing that the power available for acceleration is the engines power output at the track minus the power required to overcome inertial losses, aerodynamic drag, and frictional losses, the first step to creating the model was to derive an equation that would calculate all of the aforementioned properties as a function of the vehicles acceleration and velocity,

In order to calculate the power required for acceleration, a kinetic diagram of the snowmobile was created. The inertial losses of the snowmobile primarily come from its track, and were determined as shown in Figure 2 below;

Figure 2 – Kinetic Track Model

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The two semicircle sides of the track were modeled as one rotating thin walled disc as shown in Figure 3 below:

Figure 3 – Inertia of Rotating Part of Track

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Combining the mass of the sled with the rider (labeled as the variable mB) with the equivalent masses obtained from the kinetic track diagram above into a kinetic energy equation, and taking the derivative of the equation with respect to time yields the power required for acceleration as shown at the top of the following column:

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The equations to determine the power required to overcome ground friction and aerodynamic drag, which are fairly universal and can generally be found in any university physics text book, are shown below:

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Where:

CD = Snowmobiles coefficient of drag

A = Sleds frontal area

ρ = Air density

V = Velocity

CR = Coefficient of Friction

g = Gravity

mB = Mass of the sled and rider minus track

mθ = Mass of the rotating part of track at any given time

mT = Mass of the translational part of the track at any given time.

Therefore, the power available for acceleration as a function of velocity and acceleration is as follows;

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This equation was then rearranged to calculate the acceleration of the sled in terms of all of the above mentioned variables and as a function of velocity. The developed acceleration can then be integrated once and twice to determine the snowmobiles velocity as a function of time, and the snowmobiles position as a function of time (which can be used to determine the snowmobiles ¼ or 1/8 mile elapsed time and trap speed). The rearranged equation is shown on the following page:

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In this equation, Pengine is the power output from the engine model.

The Arctic Cat 660 four-stroke Touring snowmobile is equipped with a continuously variable transmission, commonly referred to as a CVT. As the snowmobile accelerates under a full load, the CVT will maintain the highest numerical gear ratio possible (the snowmobile’s “lowest” gear), until the engine reaches a pre-determined RPM. Once this RPM is met, the CVT will then hold the engine at this RPM, and then the sled will continue to accelerate by changing the gear ratio’s seamlessly and infinitesimally until the engine reaches its lowest gear ratio possible (so long as the snowmobile doesn’t reach it’s top speed before this point due to a lack of available power to overcome aerodynamic drag and frictional losses). At this point, the CVT will hold this gear ratio, and the snowmobile will continue to accelerate through continuing to increase the engine speed.

Fuel economy is determined by modifying the equation such that the inertial losses (the “Paccel” term) are eliminated, and then rearranging it such that the engine power required to maintain a velocity can be calculated, as shown below;

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By comparing the engines power required to maintain various speeds with the engines measured brake specific fuel consumption (the ratio of the mass of fuel consumed per unit of mechanical work output by the engine shaft, commonly referred to as the engine’s BSFC), the optimal speed at which to operate the snowmobile over the 100 mile endurance/fuel economy part of the competition can be determined. Furthermore, it can be determined how great of an extent rider weight, rider position, and the snowmobiles front hood design have on the snowmobiles fuel economy by altering the sled and driver mass and the aerodynamic drag variables.

NOISE VIBRATION AND HARSHNESS

Before any modeling of the sound output from the snowmobile could be completed, basic acoustic concepts had to be researched. The sound meter that was used to measure the noise produced by the snowmobile measured the sound pressure level over a wide range of frequencies. This information was useful but not fully adequate in an accurate sound model of the snowmobile.

Sound Pressure Level (SPL) is the change in pressure of air above and below the average atmospheric pressure. This is measured in PSI by the sensor on the sound meter and automatically converted to SPL. The equation used to make this conversion is:

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The value for (p) is the RMS pressure and the value for (po) is ambient pressure. The reason that these sound levels are converted to a log scale is because the difference in pressure in a standard room measured in the Pascal scale is so large. The log scale makes the data easier to work with.

The common range of frequencies focused on in industrial acoustic design is 20 Hz to 16000 Hz. This span of frequencies must then be broken into octave bands because if the sound energy was analyzed at every frequency there would be an excess of data. An octave band is basically a band of frequencies ranging from one frequency to double that frequency. The “1/3” octave band was determined to be sufficient in examining the sound data obtained from the snowmobile.

The center frequencies for the 1/3 octave band are as follows: 31.5, 40, 50, 63, 80, 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1000 Hz. The center frequencies follow this scheme throughout the frequency range up to 16000 Hz. The frequency range above the center frequency is found by the following equation:

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The frequency range below the center frequency is found by:

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A band is formed between the high and low frequency range around the center frequency. The sound pressure levels between these frequencies are then averaged.

After the sound pressure was converted to the decibel scale it had to then be converted to an “A” weighted scale. The decibel scale does not accurately reproduce what the human ear actually perceives. The human ear is more sensitive to frequencies between 1000 Hz and 5000 Hz and is less sensitive to frequencies above and below this range. Therefore the A-Weighted scale accentuates this range. A set of correction factors is used to convert from the linear decibel scale to the A-Weighted scale. The following is used for this conversion:

dB – (Correction Factor)

A list of the correction factors can be found in the Appendix.

All experimental sound measurements were taken in the laboratory in Crosby Hall. The sensor for the sound meter was positioned approximately 1 meter away from the snowmobile. According to the 2004 Clean Snowmobile Competition rules, the sound meter would be positioned 50 feet from the snowmobile. By creating an accurate sound model, the snowmobile was able to be tested in the laboratory while still obtaining accurate theoretical far field results.

Next the “Far Field” effect of the sound propagation of the snowmobile had to be taken into account. Far Field accounts for any distance greater than or equal to 50 feet. SPL decreases with distance as sound waves propagate through space. The relationship between near field SPL and far field SPL is as follows:

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Where Lp(R2) is the final location SPL measured in dBA. Lp(R1) is the initial location SPL. R1 is the distance from the noise source to the initial location. R2 is the distance from the noise source to the final location.

EXPERIMENTATION

Through the use of the dynamic system model it was discovered that the tracks moment of inertia had an enormous effect on the snowmobiles performance. In order to further ensure the accuracy of the model, a lab experiment was performed to calculate numerical data pertaining to this aspect of the snowmobile.

The snowmobile track is affected by two types of inertia; rotational inertia and translational inertia, as shown previously in Figure 2.

The actual translational inertia of the track can be determined as was done in Figure 2 by simply measuring the mass mT of the translational part of the track at any given time.

As shown earlier in Figure 3, the initial calculations for the rotational portion of the tracks inertia in the model were done by simplifying it to a rotating thin walled disc. This would have worked sufficiently if one could have assumed that the paddles on the outside of the track had negligible effects on the tracks inertia, which is was not a reasonable assumption.

Since the snowmobile tracks paddles do have an effect on the tracks rotational inertia, and because they significantly complicate its geometry, general equations are not available to calculate its inertia based on its physical dimensions and its mass; the rotational inertia of the track had to be found experimentally.

One common way to calculate the inertia of an object about an axis is by hanging the object from a wire and measuring the objects natural frequency (the frequency at which an object tends to vibrate when disturbed) about the wire. The inertia of the object can then be found through the equation on the following page:

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Where ωnr is the natural frequency of the object about the wire, kt is the torsional spring constant of the wire, and Ir is the inertia of the object about the wire. It was decided that this would be the optimal way to calculate the tracks rotational moment of inertia.

However, the snowmobile tracks size and profile (as illustrated in Figure 4) made it virtually impossible to experiment on the track as a whole.

Figure 4 – Whole Snowmobile Track

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Furthermore, only a select portion, not the entire track, is rotating at any given time, and as such, only this select portion has rotational inertial effects on the snowmobile and needs to be considered.

It was observed that the snowmobile track could be split into 24 equal sections. Each separate section of the track contains 2 sets of paddles. This can be seen from Figure 5 at the top of the following column:

Figure 5 - Diagram of a Piece of the Track

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Then it was decided that this piece of track could be hung at its center point from a wire which has a known torsional spring constant. An initial “disturbance” would cause the piece of track to vibrate at its natural frequency. By measuring the natural frequency of the vibrating track piece, and with the use of the known spring constant, the track piece’s moment of inertia about its center point could be determined from the aforementioned equation. Then, in order to determine the rotational moment of inertia of this track piece about the drive wheel in which it would actually be rotating, we noted that we could use the parallel axis theorem:

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Where Jradius is the rotational inertia of the track piece about the drive wheel, Jtrack is the rotational inertia of the track piece about the wire as determined through the experiment, mT is the mass of an individual track piece, and r is the radius of the drive wheel.

Once the moment of inertia of an individual track piece is found, the total rotational inertia of the track as a whole can be determined by multiplying the calculated value by the number of track pieces that are rotating at any given time.

EXPERIMENTAL PROCEDURE

The first thing that had to be done was to cut off a representative section of the track (one of the 24 equal pieces sketched in Figure 5) with a ban saw. This is shown below in Figure 6

Figure 6 - Cutting the Track

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Next the piece of track that was cut needed to be massed and the dimensions needed to be found. The piece of track was massed on a digital scale, and its length across the top (labeled as “L” in Figure 5) was measured with a measuring tape accurate to 1/32nd of an inch, which can be seen from Figures 7 and 8 as follows:

Figure 7 - Massing a Piece of the Track

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Figure 8 – Measuring the Length of the Track Piece

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While the purpose of the experiment was to find the moment of inertia for a single piece of track, the spring constant of the wire that it was hanging from had to first be calculated. The torsional spring constant of a wire is determined by the equation:

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Where G is the strings modulus of elasticity, ds is the wires diameter, and Ls is the length of the wire, and kts is the torsional spring constant of the wire. While the wires length could be easily calculated, the wires modulus of elasticity had to be determined experimentally. It was determined that this value should be determined with the diameter of the wire as well, as it was found to be extremely difficult to measure this value without a large percentage of error.

In order to determine the modulus of elasticity and diameter of the wire that the track would be hung from, it was decided we would have to perform the experiment first with a solid bar with a known moment of inertia about its center, measure its natural frequency, and solve the equation below:

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This can then be substituted into to equation for the torsional spring constant of the wire. Because the “spring constant” of the wire may not be linear, it is critical that the solid bar have a similar moment of inertia about its center point as the track; that is, that the mass and length of the bar be similar to that of the track piece being used in the experiment. The bar was massed in the same manner that the piece of track was massed.

Figure 9 illustrates the measurement of the length of the solid steel rod. Note it is about the same length as the track piece shown in Figure 8.

Figure 9 – Measuring the Length of the Solid Rod

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Next, the experiment was setup as shown in the sketch labeled Figure 10 at the top of the following column, with the steel rod hanging from a piece of wire of known length but unknown modulus of elasticity and diameter.

Figure 10 – Sketch of the Apparatus used to calculate the Wires Torsional Spring Constant

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Figure 11 below shows an actual picture of the apparatus sketched above.

Figure 11 – Picture of the Apparatus used to calculate the Wires Torsional Spring Constant

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The experiment was setup in a room that could be made completely dark if so desired, and a strobe light was used to find the natural frequency of the steel rod and wire setup. To initiate the vibration of the rod, it was rotated about the axis perpendicular to its length. After some trial and error, it was determined that in order to obtain a steady oscillation, the bar should be initially rotated approximately 135°. The bar was then allowed to oscillate for a period of approximately three minutes, a time period lengthy enough to reduce sources of error, yet short enough that the track piece does not come to rest before the experiment is stopped.

Before the rod was displaced approximately 135°, the lights in the room were turned off and the strobe light was activated. Once the steel rod is set into motion, the frequency of the strobe light can be adjusted until the steel rod appears motionless. When this phenomenon occurs, the natural frequency of the object can be calculated from the frequency of the strobe light. This procedure was repeated for three trials until an accurate value of the frequency of the strobe light was determined. Figure 12 below illustrates the steel rod vibrating at its natural frequency under the illumination of the strobe light.

Figure 12 – Steel Rod Vibrating at its Natural Frequency in the Dark Room

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Since the natural frequency of the steel rod and wire setup can be found from the experiment, and its moment of inertia about its central axis can be accurately calculated through a known equation based on its dimensions and mass, the modulus of elasticity and diameter of the wire can be found from some the equations listed earlier. These calculations are shown in the data reduction section of the report.

With this information regarding the wire, the moment of inertia of the piece of the track can be found by determining its natural frequency through the same experiment described above. The experiment was again repeated for 3 trials in order to ensure that the data obtained was accurate. Figure 13 at the top of the following column shows the experimental setup for calculating the natural frequency of a piece of the track.

Figure 13 – Experimental Apparatus for Calculating the Natural Frequency of the Track Piece

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DATA REDUCTION

DATA OBTAINED FROM EXPERIMENTATION

Mass of Steel Rod = 0.456 kg

Length of wire = 30.480 cm

G*d4 of wire = 172829 kg*m3/s2

Length of Steel Rod =12.700 cm

Diameter of Steel Rod = 2.064 cm

Rod Natural Frequency= 9.530 rad/sec

Mass of Piece of Track = 0.546 kg

Width of track = 12.700 cm

Track Natural Frequency= 9.23 rad/sec

(Refer to Data Reduction MathCAD sheet in Appendix)

After the moment of inertia is found from the method described in the appendix, it must be inserted into the kinetic track diagram as shown in Figure 2. The energy required to move each piece of the track across the top and bottom (the translational inertia) will stay the same. The parts of the diagram that will change are the semi-circles on the left and right side of the track. The calculated rotational moment of inertia will tell us the energy required to rotate each piece of track about the outside of the drive wheel.

RESULTS

ENGINE MODEL

Figure 14 below displays an example of the output obtained from the engine model when its constants are set to the specifications of the 2003 Artic Cat 660 4-stroke snowmobile that the model was based off of.

Figure 14 – Power and Torque Calculated by the Engine Model

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The horsepower and torque curve that was produced by the engine model was compared to the horsepower and torque curves obtained by testing the snowmobiles engine performance on a dynamometer. It should be foremost noted that the results above differ from that of the dynamometer data in that the dynamometer produces a graph that displays power and torque as a function of velocity as opposed to displaying it as a function of RPM, and that the dynamometer determines the snowmobiles power and torque at the track, as opposed to at the engines crank. However, the dynamometer data can still be used as a reference to ensure that the engine model produces results that are similar in magnitude, which it suggests it indeed does.

SYSTEM MODEL - DYNAMIC

A screen shot of the dynamic version of the system model can be found in the appendix section labeled Appendix A.

The snowmobiles dynamometer data is most comparable to the graph produced by the system model that displays engine power as a function of time. This can further be related to a velocity vs. time graph, also produced by the system model, to determine the snowmobiles power vs. velocity.

Because of the way the CVT performs under full acceleration, the engines power is directly dependent upon the vehicles speed. This was incorporated into the system model, and the engines power output (in Watts) as a function of velocity (in meters per second) as the snowmobile accelerates under full load is shown in Figure 15 below:

Figure 15 – Engine Power as a Function of Velocity

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Note that the engine power is constant until a little over 40 m/s, where it becomes discontinuous. This is because the snowmobile doesn’t have enough power to accelerate past the CVT’s top gear ratio; its maximum speed (slightly over 40 m/s) is limited by power, not by gearing.

It should also be noted that the snowmobile starts changing gear ratios at around 15m/s. This was exactly when the Arctic-Cat 660 four-stoke started changing gears as well, meaning the initial gear ratio was properly assumed.

In order to calculate the snowmobiles elapsed time to reach various positions under full acceleration from rest, the system model calculates the snowmobiles position versus time. An example of a graph obtained is shown in Figure 16 below:

Figure 16 – Position as a Function of Time

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Note that the position versus time is initially exponential, but becomes linear as the sled achieves its maximum velocity and ceases to accelerate.

To verify the data produced by the model was correct, the Arctic Cat 660 was run for an approximate 1/8th mile. It was found that it took the snowmobile just under 12 seconds to do so. Noting that an 1/8th mile is about 200 meters, it can be seen that the model states the snowmobile of the same physical properties should run the 1/8th in approximately 11.7 seconds, further justifying the accuracy of the model,

At the top of the following column is Figure 17; a graph produced by the dynamic system model that demonstrates the force on a snowmobile due to aerodynamic drag as a function of time as it accelerates under full throttle, starting from rest.

Figure 17 – Aerodynamic Drag on the Snowmobile as a Function of Time

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Initially, the drag grows exponentially with time. However, as the snowmobile begins to reach its top speed it can be seen that the drag force on the snowmobile flattens out. This again is because the snowmobile’s top speed is actually limited by the drag and frictional losses on the snowmobile, not the CVT’s gear ratios.

SYSTEM MODEL – STEADY STATE

A screen shot of the steady state version of the system model, labeled Appendix B, can be found in the appendix section.

The system model can be run in steady state mode for the purpose of determining the power required to maintain various velocities due to either frictional rolling/sliding resistance, aerodynamic drag, or a combination of both. Figure 18 on the following page displays this data.

Figure 18 – Power Consumption as a Function of Velocity

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It can be noted from the graph that the power required to overcome the snowmobiles frictional rolling/sliding resistance is larger than the power required to overcome aerodynamic drag at lower velocities. However, as expected, at higher velocities the aerodynamic drag on the snowmobile dominates power consumption.

Since fuel economy is directly related to a vehicle’s power requirements, this model can be used to determine whether one should put their efforts forth to minimize the snowmobiles aerodynamic drag or rolling/sliding resistance to most effectively improve the snowmobiles fuel economy at any particular velocity.

Furthermore, if one had data pertaining to the snowmobiles brake specific fuel consumption, this model could be used to calculate the snowmobiles actual fuel economy at various velocities.

TRACK INERTIA

Through the lab experiment it was found that the rotational inertia of the 1/24th representative piece of the track around its center point was .000744kg*m2. Through the parallel axis theorem, it was then found that this track piece had a rotational moment of inertia of .023288kg*m2 about the center of the drive wheel which it rotates.

Since the primary reason for finding an actual measured value of the tracks inertia was to allow the input of the accurate value into the dynamic system model, this inertia value was then converted into a form which would make it easy to do so. As noted earlier in the section of this report that discusses the Design Overview of the System Model, the dynamic system model calculates the snowmobiles acceleration based on the principle that the power available for acceleration is the engines power output at the track, minus the power required to overcome inertial losses, aerodynamic drag, and frictional losses.

Through the initial calculations illustrated in Figures 2 and 3, it was found that the power required to accelerate the snowmobiles track was as follows:

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Where V is the vehicles current velocity, Pat is the power required to accelerate the track, and dv/dt is the vehicles instantaneous acceleration.

Through the lab experiment, it was found that the actual power required to accelerate the track was given by the following equation:

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While at first glance one might observe the similarity between the equation above and the one before it and believe that the initial procedure, used in Figures 2 and 3 to theoretically estimate the power required to accelerate the track, was adequate. However, it should be noted that the magnitude of the theoretically calculated value differs from the experimentally determined value by approximately 24.2%. This difference in magnitude has a significant affect on the performance of the dynamic system model, and as such, it can be reasonably assumed that the use of the experimentally obtained track inertial data in the model improves the models accuracy considerably.

NOISE VIBRATION AND HARSHNESS

The final result obtained from the sound model is the far field (50 ft) SPL measured in dBA over a 1/3 octave band frequency range. Figure 19 on the following page represents this:

Figure 19 – Far Field (50 ft) SPL Measured in dBA over a 1/3 Octave Band Frequency Range

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It can be seen from the figure that the greatest sound pressure level measurements are located at the 1600 Hz center frequency. Other deliverables such as the near field SPL measured in dBA, and the far field SPL measured in dB, are included in the appendix to show the various steps taken to arrive at the final product. For future reference, these other plots will be used to pinpoint any stray noise sources not included in the A-Weighted decibel scale.

Initially, the snowmobile was tested in the same environment as the competition so that the accuracy of the sound model could be tested. It turns out the trend when tested at 1 ft in the laboratory is almost exactly the same as the test with the microphone at 50 ft. The dB level was approximately .7 dB less throughout the trend for the 1 ft test. This proves that the sound model was worth completing.

FUTURE WORK

Based on the rules published prior to the 2004 SAE CSC competition, our sound model seemed to be extremely successful at replicating the noise test of the competition in a laboratory setting. As such, the snowmobile was tuned with the use of the model, and should have done extremely well in this part of the challenge. Unfortunately, this was not the case, and it has been determined (albeit at this point in time inconclusively) that the snowmobile was tested in a different manner than indicated in the original rules. As such, future sound modeling efforts should be put forth into obtaining more data as to how the snowmobile will be tested in next year’s competition. An accurate sound model that could be used to replicate this testing procedure in the laboratory would allow the future University of Maine Clean Snowmobile Team to do extremely well in this portion of the contest.

Further increasing the usefulness of any sound model would be the construction of a dampened sound room somewhere on campus. This has been used by companies such as Arctic Cat, and as demonstrated by their snowmobiles which consistently become quieter and quieter with each consecutive model year, has been extremely successful. While admittedly a large and expensive project, it would be one that would prove to be extremely valuable and would certainly give future University of Maine CSC teams a big advantage over their competition.

When making a simulated model of a system, the detail and accuracy of the model is essentially limited by the amount of time that is available to be spent researching each individual component of the system. The primary focus this year was to develop models that could be used, to some extent, to determine where the biggest improvements could be made to the teams Arctic Cat 660 snowmobile before the 2003 SAE CSC competition. Being that this is the first year of development for these system and engine models, many assumptions and estimations had to be made for the sake of having a running model completed in time.

As illustrated by the comparison between the theoretically estimated and later experimentally determined values for the track inertia, considerable gains in the models’ accuracy can be had if time is spent experimentally determining many of the snowmobiles estimated constants. Future work could be put forth into determining the actual coefficient of drag on the snowmobile (currently it is estimated to be that of a full faring motorcycle), the actual thermodynamic and fluid power losses on the engine, and how different snow properties effect the rolling and sliding resistance of the track.

Further improvements to the model may be had by making the model itself more complex, yet more accurate and useful. For example, the dynamic system model could be altered in such a way that it takes into account the slipping of the track under various levels of acceleration. Being that emissions bears so much weight in the competition, it would be worthwhile to focus on improving the detail of the engine model so the team could determine how different factors such as the engines displacement, fuel choice, and air fuel ratio effects its various emissions. Additionally, the team could make a model that would determine the snowmobiles braking distance dependent on rider mass, snowmobile and snowmobile track mass, snow conditions, rider position, and the snowmobiles braking design.

As noted earlier, one of the models greatest features is that it has the ability to determine the CVT clutching RPM that will produce the most net points in the competition. For example, this could be used to calculate the optimal RPM to set the snowmobiles continuously variable transmission to hold as the snowmobile is driven; high enough to allow the snowmobile to run the 1/8th mile drag in the desired time, yet low enough to net optimal fuel efficiency, emissions, and noise.

In order to make this feature valuable in competition, however, one must actually be able to re-clutch the snowmobile as they wish. Having this feature incorporated into the snowmobile and using it in conjunction with the dynamic and steady state models would most certainly prove to be a powerful tool; one could strategically determine how to obtain the most points in the competition without having to dramatically alter the snowmobile. Furthermore, if done correctly, this would have little or no negative effect on the snowmobiles reliability, and would keep the team’s costs down to a minimum.

As mentioned earlier, brake specific fuel consumption data pertaining to the modeled snowmobile is needed in order to use the steady state model to obtain fuel economy results for the snowmobile at various velocities. The best way to obtain brake specific fuel consumption results is to run the snowmobile at a steady state on a track dynamometer (such that the dynamometer records a constant horsepower output from the snowmobile) for an extended period of time, and then to record how much fuel the snowmobile consumed in this time period. Knowing how long the snowmobile was run for, the steady power it was producing, and the amount of fuel it consumed, one can easily calculate the ratio of the mass of fuel consumed per unit of mechanical work output by the engine shaft, which is its BSFC.

While the University of Maine does have a snowmobile track dynamometer available, it is an inertial dynamometer and can not be used for steady state testing. With the simple addition of a resistance unit for the dynamometer, steady state results could be obtained, which would allow the model to determine the snowmobiles fuel economy at various velocities. Even more importantly, this could be used to test the snowmobiles fuel economy over a 100 mile distance, as is done in the competition, quickly and easily without having to find the space, snow, or time to do so with the actual sled itself.

Both the laboratory and dynamic system model revealed that the track significantly affected the snowmobiles performance due to its high moment of inertia. As such, the reasonable solution would be to reengineer the snowmobile track. This would consist of a multi-year development program for new track designs.

However, it should be noted that the rules for the 2004 SAE Clean Snowmobile Challenge clearly state that the snowmobile to be tested must have a stock track that is mass produced and may be acquired by any team. With the University of Maine’s present and future success in the competition, the school hopes to put its own advisor on the rules board to argue that any team may modify their snowmobile track to any extent they desire (within certain safety limits, of course), as its been found that the track is easily one of the biggest sources of loss in a snowmobiles drive train. Due to this discovery, it is desired that the competition move its focus away from engine modification, and put more emphasis on drive train modification, as increasing the drive train efficiency will make the snowmobiles more economical while increasing their performance as a whole; something many teams seemed to struggle with at the 2004 SAE CSC competition.

FUTURE TRACK DESIGN

The process of redesigning the track would be a multi-year program that has not been included as a project for the current University of Maine Clean Snowmobile Teams due to the present rules for the competition. Yet if the rules were changed, the first step would be to reduce the weight and vibration of the track while maintaining its fracture toughness and flexibility properties. The obvious step would be to design a composite track, as opposed to the solid rubber track found on most snowmobiles today.

ENGINEERING MATERIAL SELECTION

There are a few properties of the track that must be taken into consideration for the track to remain functional. One of these characteristics is fracture toughness. Fracture toughness is a measure of the resistance of the material to propagation of a crack. This is important because the snowmobile track needs to be durable to withstand any obstacles encountered on a trail, such as rocks or logs, or even from the steady impact of hard packed snow. By looking at materials selection charts, one can obtain the material with the most desired properties. It is important to keep in mind that mass is related to density, therefore, the denser the material the heavier it will be. The material with the most attractive fracture toughness/density ratio falls in the engineering composites group. These include Carbon Fiber Reinforced Plastics, Graphite Fiber Reinforced Plastics, and Laminates (Refer to Materials Selection Chart Fracture Toughness vs. Density in the Appendix.)

The Young’s Modulus of a material refers to the materials ability to withstand a constant tension or compression. This is a very important factor in snowmobile material track selection because most of the time it is in tension due to the force of the engine. Again, the materials that fall into the engineering composites group stand out as the optimal choice, as they have the highest Young’s Modulus to density ratio. (Refer to Materials Selection Chart Young’s Modulus vs. Density in the Appendix.)

The final characteristic studied to determine material selection is Strength. Strength is defined as the ability of a material to yield without failing. There are various choices that could be made for material selection in this category. Two obvious choices would be the engineering composites again, or engineering alloys. It might prove valuable to integrate an engineering alloy, in composite form, such as Titanium, into the track to provide it with the ability to withstand impacts. Then again, cost must be taken into account, and this might be a little overboard for this application when looking at the relatively low power and torque output of the 2003 Artic Cat 660’s Power Plant. (Refer to Materials Selection Chart Strength vs. Density in the Appendix.)

Finally, there must be some aspect of the track design or material to dampen vibrations, as these vibrations certainly add to the NVH of the snowmobile and are thought to induce high drive train losses. Again studying the Materials Selection Chart, the most obvious choice for this application would be an engineering polymer.

If the rules do indeed change such that significant track modification is permitted, all of the features should be taken into account for the purpose of designing a track that greatly increases the performance and economy of the snowmobile while remaining durable and cost effective. Even if the rules weren’t changed, if the school was able to accomplish this feat, take the snowmobile to the competition with the modified track, and prove to the judges that track design is where the real strides in snowmobile technology and performance are to be had, the judges would be hard pressed to deny changing the rules for the following years competition.

CONCLUSION

Even though this is first project of its kind to be attempted for the use of tuning a snowmobile for the SAE Clean Snowmobile Competition, and the first project of its kind at the University of Maine, much headway has been made. The engine and system models, which can be used to determine various aspects of the snowmobiles performance computationally with little or no use of the actual snowmobile itself, have proven their accuracy, and their value in determining where future efforts should be put fourth.

Furthermore, a lab experiment was performed that has successively determined the snowmobile tracks moment of inertia. Due to the significant effect the track inertia has on the snowmobiles performance, this has already taken the first important step towards making the models more accurate by experimentally determining values used in the model – values that had to be previously estimated to meet deadlines.

Based on the rules published prior to the 2004 SAE CSC competition, the sound model created seemed to be extremely successful at replicating the noise test of the competition in a laboratory setting. While the snowmobiles was not as successful in the sound portion of the competition as expected (presumably because the snowmobile was tested differently in the competition than was stated it would be in the rules), the sound model can still be used as a reference to illustrate how one should go about producing such a model.

APPENDIX

A. Dynamic System Model

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B. Steady State System Model

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C. MathCAD Track Inertia Calculations

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D. Material Selection Chart (Fracture Toughness vs. Density)

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E. Materials Selection Chart (Youngs Modulus vs. Density)

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F. Materials Selection Chart (Strength vs. Density)

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G. Materials Selection Chart (Youngs Modulus vs. Relative Cost)

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H. Materials Selection Chart (Strength vs. Relative Cost)

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I. References Section

Aerodynamics of Road Vehicles, 4th Edition, by Wolf-Heinrich Hucho 1998, SAE

 An evaluation of the concepts of rolling resistance, Journal of Terramechanics, Volume 36 1999 pages 156-166 G.Komandhi 

Development of an all terrain vehicle suspension with an efficient over track, Journal of Terramechanics, Volume 35, 1998 P.209-223 J.Batelam 

A design oriented simulation program for off-road track vehicle, Journal of Terramechanics, Volume 31, 1994 P.329-352 D.Rubisntein and N.Galili 

Prediction of sinkage and rolling resistance for off-road vehicles considering penetration velocity, Journal of Terramechanics, Volume 25, 1991 P.339-347. M.Grahn 

Effects of vibration on rolling resistance, Journal of Terramechanics, Volume 25, 1998, P.231-237 A.Orlandi and M.Matassa 

The bekker theory of rolling resistance amended to take account of skid ad deep sinkage, Journal of Terramechanics, Volume 15, 1978, P.107-110 

The effect of wheel speed on rolling resistance, Journal of Terramechanics, Volume 8, 1971, P.5 R.G.Pope 

Analysis of the rolling resistance losses of wheels operating deformable terrain. Journal of Terramechanics, Volume 6, 1969 P.68 O.Onafeko and J.Agric 

Prediction of the performance of four wheel drive passenger vehicles, Journal of Terramechanics, Volume 30, 1993, P.35-46 H.R.Kemp. 

Environmental Noise Control, Atco Noise Management, 2004 

Industrial Noise Control, N. Paul Jensen Charles R. Jokel, Laymon N. Miller, Bolt Beranek and Newman, Inc. Cabridge. Massachusetts 02138 

Engineering Mechanics: Dynamics, Hibbeler, 9th Edition 2001

Numerical Analysis to Predict Tuning Characteristics of Rigid Suspension Tracked Vehicles, Journal of Terramechanics, Volume 36, Issue 4, P.183-196

Modeling and Simulation of an Agricultural Tracked Vehicle, Journal of Terramechanics, Gianni Ferretti and Roberto Girelli, Volume 36, Issue 3, P.139-158

Predicting the Ride Vibration of an Agricultural Tractor, Journal of Terramechanics, Volume 34, Issue 1, P.1-11

High Speed, Half Tracked Truck with Metal Coreless Rubber Track, Journal of Terramechanics, Volume 33, Issue 2, Great Britain, 1996, P.113-123

The Effect of Engine Variables on Hydrocarbon Emissions – An Investigation with Statistical Experiment, Design and Fast Response F.I.D. Measurements, SAE ARTICLE DN: 961951

J. Required Files for Engine Model

• constants.m : MatLab file (contains all constants that the system models call for)

• runengine.m : MatLab file (executes constants, and other files below)

o Apiston.m: (area of the piston)

o state1.m: (calculates Volume at State 1)

o state2.m: (calculates Volume, Temperature, and Pressure at State 2)

o state3.m: (calculates Volume, Temperature, and Pressure at State 3)

o state4.m: (calculates Volume, Temperature, and Pressure at State 4)

o BMEPcalc.m: (calculates Break Mean Effective Pressure)

o Powercalc.m: (calculates Power in Watts)

o Powerloss.m: (calculates Power with losses in Watts)

o Torquecalc.m: (calculates Torque of engine)

o plotPT.m: (plots Power and Torque of engine)

K. Code for engine model

a. “Constants.m” file

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b. runengine.m : MatLab file (executes constants, and other files below)

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c. Apiston.m: (area of the piston)

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d. state1.m: (calculates Volume at State 1)

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e. state2.m: (calculates Volume, Temperature, and Pressure at State 2)

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f. state3.m: (calculates Volume, Temperature, and Pressure at State 3)

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g. state4.m: (calculates Volume, Temperature, and Pressure at State 4)

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h. BMEPcalc.m: (calculates Break Mean Effective Pressure)

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i. Powercalc.m: (calculates Power in Watts)

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j. Powerloss.m: (calculates Power with losses in Watts)

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k. Torquecalc.m: (calculates Torque of engine)

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l. plotPT.m: (plots Power and Torque of engine)

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Steel Rod

Wire of known length, unknown G and d

Strobe Light

L

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