Design, Fabrication, and Characterization of Split Axle Skateboard Trucks
by
Terran L. Winter Fox
Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the Requirements for the Degree of
Bachelor of Science in Mechanical Engineering
at the
Massachusetts Institute of Technology
June 2018
©2018 Terran Lee Winter Fox. All rights reserved.
The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document
in whole or in part in any medium now known or hereafter created.
Signature of Author: _________________________________________________________ Department of Mechanical Engineering
May 11, 2018
Certified by: _______________________________________________________________ Dawn Wendell Senior Lecturer, Department of Mechanical Engineering
Thesis Supervisor
Certified by: _______________________________________________________________ Rohit Karnik Associate Professor of Mechanical Engineering Undergraduate Officer
3
Design, Fabrication, and Characterization of Split Axle Skateboard Trucks
by
Terran L. Winter Fox
Submitted to the Department of Mechanical Engineering on May 11, 2018 in Partial Fulfillment of the
Requirements for the Degree of
Bachelor of Science in Mechanical Engineering
ABSTRACT
A new design for skateboard trucks has been developed and tested in an effort to reduce the uncomfortable vibration experienced when riding a skateboard. The new design interfaces with existing hardware but also features a split axle geometry which allows the left and right wheels to move independently. In order to determine whether the split axle trucks improved rider comfort, the trucks were tested on a skateboard outfitted with sensors that measure acceleration normal to the road surface. Similar measurements were taken with standard skateboard trucks to serve as a control. Multiple trials were run at each of three different test speeds over a set course. Results showed that the majority of the dominant vibration frequencies are in the range of 20-450 Hz for both truck designs. The magnitude of the peak acceleration and the arms were observed to increase
faster with speed for the standard truck design, and at the highest speed of 20 km/h the split axle design was shown (with 95% certainty) to have a peak acceleration which was 96 m/s2 lower than that of the standard truck. Overall the results suggest that the new split axle design primarily improves rider comfort during localized vibration events by reducing the peak acceleration that is experienced. This effect, along with a reduction in the measured arms, become increasingly
apparent at higher speeds.
Thesis Supervisor: Dawn Wendell, PhD
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ACKNOWLEDGMENTS
To Dr. Dawn Wendell: Thank you for your guidance and unyielding enthusiasm on this and a number of other endeavors I’ve undertaken while at MIT. I appreciate you sharing your experience and giving me the freedom to create my own.
To Dr. Barbara Hughey: Thank you for providing the tools and methods through which so many things at MIT get measured. Many of us, myself included, would still be staring at meaningless data if not for you.
To ProjX: Thank you for not only encouraging students to pursue wacky projects of all shapes and sizes, but also providing funding to help make them become a reality. I feel incredibly fortunate to have had my project selected and I can’t wait to see what comes out of ProjX next. To the MIT Edgerton Center: Thank you for providing a space in which I could think, design, and build. I am very grateful to have had access to the world class facilities you all have created.
To Pat McAtamney: Thank you for keeping the machine shop running and sharing all the tricks of the trade. I appreciate you doing so much to help students actually make the crazy things they come up with.
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TABLE OF CONTENTS
Table of Contents 7
List of Figures 8
1 Introduction 9
2 Background and Theory 10
2.1 Skateboard Truck Architecture 10
2.2 Vibration Theory 11
2.3 Previous Work 12
3 Skateboard Truck Design 13
3.1 Design Goals and Functional Requirements 13
3.2 Design Concept 13
3.3 Analysis 15
3.4 Manufacturing 17
4 Measurement and Testing 20
4.1 Equipment and Test Set-up 20
4.2 Test Method 22
5 Results and Discussion 22
6 Conclusions 29
8
LIST OF FIGURES
Figure 1: Skateboard Overview Diagram 9
Figure 2: Skateboard Truck Diagram 11
Figure 3: Split Axle Truck Design CAD Renderings 14
Figure 4: Hanger Finite Element Analysis 16
Figure 5: Hanger Milling Operations 17
Figure 6: Axle Shaft Milling and Turning Operations 18
Figure 7: Fully Assembled Split Axle Skateboard Truck 19
Figure 8: Test Set-up Diagram 21
Figure 9: Annotated Physical Set-up 21
Figure 10: Raw Acceleration Data 22
Figure 11: Acceleration Magnitude Distribution Fits 23
Figure 12: Probability Density Function Comparisons 24
Figure 13: Peak Acceleration Bar Graph 26
Figure 14: Average Normalized Integrated PSD 27
9 1 INTRODUCTION
Skateboards are a fun and unique form of transportation which can be used for both efficient travel as well as recreation. In all use cases though, the skateboard and rider are subjected to vibrations imparted from the surface on which they are rolling. On particularly rough terrain or when riding for extended periods of time this can cause rider discomfort and component wear on the skateboard. In particular, loads are directed through the skateboard trucks which connect the wheels to the skateboard deck as illustrated in Fig. 1.
Figure 1: Side view (top) and underside (bottom) of a typical skateboard with key
components labeled. The skateboard rolls on four wheels which mount on the front and rear trucks. The trucks are bolted to the underside of the skateboard deck which is a solid piece of wood or composite material. The rider stands on the deck and maneuvers by shifting their weight which causes the trucks and wheels to turn.
Skateboard trucks enable turning, but they often experience large and unbalanced loading when bumps and debris are encountered. This can result in unexpected or unpredictable movements which impact the overall behavior and feel of the skateboard during riding. In an effort to improve rider comfort and mitigate the negative effects of riding on rough surfaces, a novel design for a split axle skateboard truck was developed and tested. This design allows the wheels of the skateboard to move more independently and react to bumps as needed without the coupling effects of commercially available solid axle trucks.
In order to both characterize and validate this design, the accelerations induced in the skateboard during riding were measured and compared with similar data taken for standard trucks. An accelerometer mounted to the skateboard deck near the trucks captured the vibration spectrum at riding speeds of 5, 10, and 20 km/h. Vibrations of this nature are commonly modeled as a
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random (stochastic) process owing to the unpredictability of the riding surface [1], [2]. The data was analyzed in both the frequency and time domains in order to extract key parameters and make useful comparisons between the two designs. Ultimately, the behavior of the split axle trucks could be quantified and conclusions could be drawn about the viability of such a design.
2 BACKGROUND AND THEORY
2.1 Skateboard Truck Architecture
Skateboard trucks are the fundamental component which interface directly with the deck on which the rider stands as well as the wheels that allow the skateboard to roll. Fig. 2 provides an overview of a typical truck and its components. The trucks, which mount at the front and rear of the skateboard deck, are normally attached by way of a standardized mounting hole pattern with Unified #10-32 bolts and lock nuts. Countersunk bolts are typically used so that the hardware is flush with the upper surface of the deck giving the rider a uniform surface to stand on. Wheel mounting is achieved through a long central axle that measures 8 mm in diameter and spans the width of the truck. The ends of the axle are threaded to allow the wheels to be held in place with Unified 5/16-24 lock nuts. The left and right wheels each ride on two sealed deep groove ball bearings (typically 608 series).
The trucks must support the full weight of the rider in a number of positions while being able to withstand additional sustained loading from cornering as well as brief impact loading from bumps and debris. As such, the majority of trucks have a metal construction consisting of aluminum alloys for the main structure with steel axles and hardware. Commercial trucks are often cast, however, forged trucks and trucks CNC machined from billet aluminum are also available.
Another critical feature of the trucks is that they allow the skateboard to turn by pivoting as the rider shifts their weight to one side of the skateboard. The pivoting component is referred to as the hanger and it rotates relative to the base which is rigidly bolted to the deck. The wheel axle passes through the hanger, which means that if one wheels moves the other must move the opposite direction as the hanger pivots. This is the origin of the coupling effects which can result in unintentional turning when an obstacle forces one wheel to move. Hangers for commercial trucks typically have a small rounded pivot which serves as the point of rotation and sits in a low friction pivot cup within the base of the truck. Bushings or, less commonly springs, are then used to provide the restoring force that acts on the hanger and returns the skateboard to a neutral state in which it rolls straight. Bushings of various shape and hardness can be selected to fine tune the turning behavior of the trucks.
This style of trucks has been widely adopted by the skateboarding community, and the overall design architecture has become highly standardized even between different manufacturers. Small variations on this design do exist, however, they are relatively uncommon and they often come at much higher cost. For the purposes of this study the truck design described here will be referred to as a standard truck.
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Figure 2: Diagram showing a typical skateboard truck with key components marked. The
truck mounts to the skateboard deck via the mounting holes in the baseplate with standard hardware (not shown). The bearings and wheels mount on the two ends of the solid axle which protrudes form the hanger on both sides. The wheels are secured using a nut that threads directly onto the axle.
2.2 Vibration Theory
Stochastic vibration theories were used to identify the most important features of the measured acceleration spectra for these experiments. Road induced vibration is commonly treated as a purely random process, owing to the random distribution of particles that make up the paved surface [1], [2], [3]. As a result of this, analysis of the measured vibration is often done by obtaining the peak acceleration, power spectral density (PSD), and root mean square acceleration (arms). PSD and arms
are both obtained from frequency domain analysis which allows for close examination of the individual frequency components and how they contribute to the cumulative signal. These parameters can serve as a proxy for the energy of a random vibration event and facilitate comparison of events which otherwise lack features by which to draw comparisons due to their random variation in time. Furthermore, arms has units of m/s2 and can be calculated using Eq. (1).
arms=√ 1 (f2− f1)∫ |a(f)|2df f2 f1 (1)
where a(f) represents the measured acceleration as a function of frequency for a given test and f1
and f2 are the frequencies which define the limits of the test bandwidth. The time domain equivalent
of this expression can be found by substituting the acceleration signal in the time domain, a(t), along with the points in time which define the limits of the test interval, t1 and t2, into Eq. (1) [4].
12
This quantity can also be calculated by taking the square root of the area under the PSD curve for acceleration. arms and PSD are used to draw comparisons between trials whose inputs or conditions
differ as well as between tests performed with different set-ups.
The inherent variation between trials which necessitate characterization through parameters such as arms is partially due to the unique properties of stochastic processes. These types of random
phenomena can be described by continuous random variables [2]. This means that the variable (the magnitude of a skateboard’s acceleration in this study) can take on a range of possible values which an observer cannot know with absolute certainty. Random variables describing vibration induced by a paved surface are assumed to be continuous since they could, in theory, take on any value in response to perturbation from an infinitely large number of different surfaces. As a result of this variability, measured data forms a distribution and can be visualized using probability density functions which represent the possible values the variable can assume and the probability of it taking on a given value [2]. The form of the distribution offers insight into the nature of the system response and loading characteristics such as how likely the rider is to experience the most extreme vibration or how widely varied the acceleration amplitudes are.
2.3 Previous Work
The measurements in this study, draw on prevailing historical methods as well as previous experiments in this area. A number of studies which rely on much of the same random vibration theory discussed in section 2.2 have been undertaken in the past to develop models for the system dynamics of human powered vehicles such as bicycles and skateboards. Study of vibration from road surfaces is often aided by or executed primarily through field tests involving rider-vehicle systems which have been fitted with additional instrumentation to measure important dynamic quantities [5], [6], [7]. Data acquisition and sensor systems, such as the one used in this experiment, typically measure acceleration at various positions on the rider or vehicle using accelerometers which measure along one or more axes. For this type of measurement, sampling for 5-20 seconds at a rate of 1000 Hz or above has been shown to provide adequate resolution while avoiding clipping of acceleration peaks [5], [4]. Additionally, (depending on the sample rate) frequency analysis of the time domain acceleration data is often limited to frequencies up to 1000 Hz, since the bulk of the relevant frequency components for the vibration signal fall below this threshold.
Test methodology and data from dynamic studies of bicycles has been well established and documented in the literature [4], [5], [6]. However, similar analysis for skateboards is far less available. The results from one related study which used similar methodology for testing skateboards showed that the acceleration data is distributed according to a t-distribution with a maximum peak magnitude of around 700 m/s2 [7]. These trials also generally exhibit arms values
in the range of 20-70 m/s2 for riding velocities of 5-20 km/h [7]. The dominant vibration frequencies also fell within the range of 50-200 Hz for most trials. The measured acceleration is shown to vary significantly with riding velocity, indicating that this variable must be carefully monitored and controlled [4], [6]. These results offer a valid point of reference, however, it is important to note that the skateboard set-ups being tested here differ from those of past experiments.
13 3 SKATEBOARD TRUCK DESIGN
3.1 Design Goals and Functional Requirements
The primary goal of the skateboard truck design was to improve the comfort of the rider by creating skateboard trucks that could better adapt to discontinuities in the riding surface. One of the dominant contributors to the harsh reaction of the skateboard to bumps was identified to be the coupling effect caused by the use of a single rigid axle which links the left and right wheel. To address this, the trucks were be designed to allow the wheels to move more independently. This necessitated a high level design change and the transition to a split axle system architecture.
Another important design goal was that the truck design should not compromise functionality or performance. Therefore, the trucks needed to match reasonably well with the expected performance of standard trucks while also preserving the qualitative feel of riding. This would help ensure that the trucks could readily interface with existing deck and wheel combinations while also not requiring riders to relearn how to ride the skateboard.
These high level design goals were used to identify the key functional requirements for the system. These requirements would then serve to help guide the design process.
Functional Requirements:
a) Must withstand loading from normal riding conditions b) Wheels must be capable of independent displacement
c) Wheels must remain in contact with ground during normal operation
d) Mounting features must be compatible with existing deck and wheel hardware
3.2 Design Concept
The concept for the truck design achieves the split axle architecture by using two separate hangers which pivot independently about a central shaft. This is illustrated in Fig. 3, where the two hangers can be seen on the left and right of the pivot axis. The hanger pivot shaft is integrated into a baseplate which utilizes the standard skateboard mounting hole pattern. Each hanger has an integrated axle which matches the commercially available 8 mm diameter. To provide the restoring force necessary to return the skateboard to its neutral position, existing skateboard bushings have been modified and placed beneath the hangers.
A key feature of the truck design is that it has a flexible coupling between the two hangers. This allows the wheels to be lightly coupled and transfer steady forces which ensure that they remain in contact with the ground, however, the flexibility of the coupling allows the hangers to displace relative to each other as needed. This ensures that when one wheel hits a bump it can move without necessarily forcing the opposite wheel to move. The flexible coupling is achieved through a separate bushing seated inside one of the hangers which is pressed upon by a lever arm on the second hanger. A full digital model created using computer-aided design (CAD) tools was developed as part of the design process, and selected views are shown in Fig. 3.
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Figure 3: CAD renderings of the split axle truck design. The truck mounting holes are
visible in the front view (top) along with the two hangers positioned such that their central pivots are aligned. The back view (bottom) shows the flexible coupling lever arm on one hanger and the corresponding bushing seat on the other hanger. The baseplate support structure and one of the axles are also indicated in the back view (bottom). The bushings used in the trucks are not shown in these images.
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3.3 Analysis
To confirm that the design would meet the survivability requirement, structural analysis was performed through both hand calculations as well as Finite Element Analysis (FEA). This was particularly important given that the design utilized a completely new architecture with geometries and load paths that were not similar to standard trucks.
The central pivot shaft was modeled as a fixed-fixed beam in bending with a uniformly distributed load applied by the hangers [8]. Eq. (2) can be used to calculate the maximum moment experienced by the shaft, while Eq. (3) provides the corresponding maximum bending stress.
Mmax=P ∙ L 12 (2) σmax=Mmax∙ ( 𝐷 2) Is (3)
Where P is the load applied to the shaft, L is the length of the shaft section between the supports, D is the diameter of the shaft, and Is is the area moment of inertia for the shaft cross section. This
could then be used to help size the shaft and select materials. Because this analysis represents an approximation of the actual load cases, a large safety margin was chosen to ensure the parts could survive during testing despite any inaccuracies in the model. The predicted maximum stress in the pivot shaft was found to be 31% of the yield stress for the 12L14 Carbon Steel being used to make the shaft. This means that the part can tolerate loads which are three times larger than expected if necessary. Eq. (4) could also be used to estimate the maximum deflection of the beam to ensure that it would not cause unintentional contact between components.
δmax= PL
3
384 ∙ EsIs (4)
Where the new parameter, Es, is the Young’s Modulus of the shaft material. The expected
deflection at the unsupported center of the pivot shaft is 0.02 mm. This is two orders of magnitude smaller than any of the clearances in the assembly and it does not change the geometry of the truck enough to affect performance so, for the purposes of this study, it can be ignored.
Similarly, the axles were analyzed as cantilevered beams in bending with a fixed base [8]. Eq. (3) can still be used, however, Eq. (2) and Eq. (4) must be replaced by Eq. (5) and Eq. (6) respectively.
Mmax=P(𝑏1+ 𝑏2) (5)
δmax= P 6 ∙ EsIs
(𝑏12(3𝐿 − 𝑏1) + 𝑏22(3𝐿 − 𝑏2)) (6)
Where b1 and b2 represent the distances from the base of the axle to the points at which the wheel bearings make contact. This model assumes the loads transferred from the bearings can be approximated as radial point loads applied at the center plane of each bearing. The size of the axles was predetermined by the requirement that they must interface with existing wheel components, however, this analysis was still useful for material selection. The maximum predicted stress in the axles was 63% of the yield stress for the 12L14 Carbon Steel being used to make the parts. The axles had a lower safety margin than the pivot shaft, however, the geometry of the axle shafts was
16
extremely similar to those commonly used on standard trucks so this was acceptable. As with the pivot shaft, the predicted deflection of 0.08 mm at the free end of the axle was small enough that it would not affect the performance of the trucks and could be ignored.
The geometry of the hangers did not lend itself to simple calculations so FEA models were developed to simulate the loading they would experience. Analysis which simulated the application of simultaneous vertical and lateral loading was performed on each unique hanger geometry. This load case represented the worst case loading the trucks were likely to experience in the scenario where a bump was encountered while cornering. The simulations were able to output 3D stress and deformation distributions, some of which is shown in Fig. 4. The maximum von Mises stresses predicted by the simulation were 71% of the yield stress for the 6061-T6511 aluminum alloy selected for these parts. It is important to note that stresses this high were only found in localized zones near stress concentrations. This information was used to iteratively refine the component geometry through the addition of smooth transitions to help alleviate stress concentrations as well as weight saving pockets to reduce the overall mass of the trucks. The final hanger designs were shown to be capable of surviving the expected loading with a reasonable safety margin throughout the part. Additionally, the maximum deflection of the hangers under load was 0.2 mm at the extreme edges which is still not enough to be perceived by the rider or affect the overall performance.
Figure 4: Stress distributions from FEA simulations that were run for each of the two
hanger designs. The complex geometries of these components could not easily be analyzed through hand calculations so simulations were used to refine the design and ensure they would not fail under load.
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3.4 Manufacturing
Once the design of the trucks had been solidified the individual components were machined and assembled. The baseplate and hangers were manufactured from rectangular 6061-T6511 Aluminum stock, while the axles and pivot shaft were made from cylindrical 12L14 Carbon Steel stock (in the annealed state). The strengths of these materials were shown to be sufficient through the analysis discussed in section 3.4 and they were easy to procure and machine.
The hangers and baseplate were machined using both manual and CNC milling as shown in Fig. 5. The outer profile and weight saving pockets were roughed out in one operation, after which the part was flipped and clamped in soft jaws for machining of the second side. Finally, the part was stood on end for finishing of the pivot features and drilling operations for the axles. The holes for the axles were stepped blind holes that required drilling of an undersized hole, reaming the upper section to a precise diameter, and then tapping the lower section of the hole by hand. The pivot shaft holes were also drilled and reamed in preparation for installation of the bushings. Oil-embedded bronze sleeve bushings were selected so that the rotational interface remained lubricated during operation. The bushings were pressed into the hangers using a standard arbor press.
Figure 5: Machining setups for both sides of a single hanger. The outer profile and front
side features were CNC machined from rectangular aluminum stock (left). The part was then clamped in soft jaws for machining of the backside features (right).
Machining of the baseplate required similar set-ups, except with custom made angle blocks for clamping the angled sections of the part. This part also required a fair amount of 3D machining with a ball endmill in order to achieve the desired smooth transitions on certain sections of the part. The pivot shaft hole was drilled and tapped using the same sequence described above. The final step for the baseplate was drilling the standard mounting hole pattern in the base.
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The axles and pivot shaft were all turned manually on a lathe. The outer diameter of the components was tightly controlled and the fit within the completed hangers and baseplate were verified during machining. The appropriate threads were cut in these components using a threading operation on the lathe followed by manual chasing of the threads with a standard die. Separate milling operations were then carried out to put torque features into these components. The pivot shaft had a groove machined in the top face in order to accommodate a standard screwdriver. The axles were installed in a hex collet and then milled flat in each of the six different orientations to create a hexagonal feature that could be turned with a wrench. The machining operations for these components on both the lathe and the mill are shown in Fig. 6.
Figure 6: Machining setups for the steel axles on both the manual lathe (left) and mill
(right). Turning and threading of the axle shafts (left) was carried out first to achieve a precise fit within the hangers which had already been completed. Milling operations were then carried out to create the hexagonal torque feature which can be turned with a standard wrench during installation.
A range of standard polyurethane skateboard bushing made by Venom Skate Products were purchased so that they could be easily swapped to help tune the feel of the trucks. One of the softest 81a bushings was cut down and fitted inside the flexible coupling of the hangers. A second set of 85a bushings was then shortened to fit beneath the hangers and attached to the base plate using epoxy in such a way that they could be removed if another set needed to be substituted.
After completion, the components were assembled into the final truck shown in Fig. 7. The hangers, along with oil-embedded bronze thrust bushings that sit between each contact surface, were first fitted loosely into the baseplate. The pivot shaft was then installed and threaded into place in order to retain the other components while still allowing them to pivot. This entire assembly could then be outfitted with wheels and mounted on a skateboard deck.
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Figure 7: Fully assembled split axle skateboard truck. The axles and polyurethane
bushings had to be installed prior to final assembly. The completed hangers could then be fitted in the baseplate and secured with the pivot shaft. This completed truck could then be installed on the skateboard and outfitted with wheels.
20 4 MEASUREMENT AND TESTING
After manufacturing and assembly were completed for the split axle truck, testing was conducted on an instrumented skateboard to characterize the system response. Similar testing was also done with the standard truck on the same skateboard as a control. An accelerometer mounted on the skateboard deck was used to measure the acceleration normal to the road surface while the skateboard was ridden over a short section of paved road. Data was logged with a portable data acquisition unit held by the rider during testing. Multiple trials were run for each style of truck at three different test speeds.
4.1 Equipment and Test Set-up
For testing of both truck designs, the same deck and wheels were used for all trials so that the only component being swapped out was the front truck. The skateboard deck used for testing was a Landyachtz Bamboo Wedge Flex which measures 101x24.8 cm and has a wheelbase of 80 cm. The wheels were ABEC11 ZigZags made from 80a durometer polyurethane measuring 70 mm in diameter. These wheels rode on generic sealed 608 skateboard bearings.
The specifications for both trucks used in this experiment are detailed in Table 1. The commercial trucks used for testing were Randal RII series trucks fitted with Venom 90a supercarve bushings. These trucks are quite common, and they are used by skateboarders of all abilities.
Table 1: Characteristic dimensions and overall system mass for the two truck designs being tested.
The skateboard was also outfitted with an instrumentation package consisting of a single-axis accelerometer and a portable data acquisition unit. An Analog Devices ±70G accelerometer was selected along with a Vernier LabQuest2 standalone data acquisition (DAQ) device that sampled at a rate of 1000 Hz during each trial. The accelerometer was attached directly to the skateboard deck immediately behind the front truck using 3M Scotch Outdoor Mounting Tape with the cable routed to the rider as indicated on the diagram in Fig. 8. A close-up of the physical set-up is also shown in Fig. 9. This sensor measured movements normal to the road surface and output a raw voltage signal which could then be converted to acceleration using the sensitivity of 24.2 mV/g (where g represents acceleration due to gravity on earth of 9.81 m/s2). A cellular phone connected to GPS and running the mobile application Speedometer GPS was also carried by the rider to independently verify the average riding speed during testing.
Hanger Width [mm] Baseplate Angle [deg] Ride Height [mm] Mass [g] Standard Trucks 180 50 63 403 Split Axle Trucks 180 50 65 626
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Figure 8: Diagram of the data acquisition system used for data collection with two
different skateboard set-ups. The accelerometer mounted behind the front truck measures acceleration normal to the road surface. This sensor is connected to a portable data acquisition unit which is attached to the rider during trial runs.
Figure 9: Image showing the underside of the skateboard outfitted for testing. The
accelerometer sensor was mounted close to the front truck with the cable routed along the underside of the deck with restraints and strain relief at several points.
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4.2 Test Method
Once all of the instrumentation had been properly mounted the skateboard was checked for loose hardware and other abnormalities which might otherwise compromise the repeatability of the results. Typical riding trials were then carried out on a relatively flat section of paved road with varying levels of surface roughness. The selected surface did not have regularly spaced cracks or markings typically found on sidewalk paths, but it did include sections of both new and worn asphalt which were representative of typical surfaces riders commonly encounter. The average grain size of the riding surface ranged from approximately 3-20 mm in diameter. Before each individual run along the course the rider had to stop and manually reset the data acquisition unit to collect a new sample. As a result, each run was started from rest. To account for this, the first 5 seconds of data gathered for each run was removed as part of the analysis. Each test had a duration of 20 seconds which resulted in 15 seconds of usable data. Speed was monitored and maintained using the real-time readout on the mobile app, and then verified and examined for deviation using the recorded velocity time history stored in the app once each set of trials was complete. Three average test speeds of 5, 10, and 20 km/h were selected for this experiment. The selected course was ridden five consecutive times at each speed to ensure a sizeable data set was acquired. This helped identify possible outlier values and reduce uncertainty on extracted parameters.
5 RESULTS AND DISCUSSION
Data gathered during testing captured the vibration response of both the standard and split axle truck designs. As expected, the data exhibited stochastic variation for the duration of each trial, as illustrated in Fig. 10. Even without further processing of the data, it can be observed that the overall acceleration magnitude increases with speed for both truck designs. This trend is both fairly intuitive and well documented in similar studies [4].
Figure 10: Raw acceleration data measured in the direction normal to the road surface for
each of two skateboard truck designs. The data shown represents a single trial run at 10 km/h for the split axle truck (left), along with similar data for a single run at the same speed for the standard truck (right). As expected, the signals exhibit random variation in time with large local spikes caused by the irregular riding surface.
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The acceleration amplitude can be looked at in more detail through probability density functions. A single dataset for the split axle truck design has been isolated to show the observed trends in distribution fitting in Fig. 11. The fit curves in Fig. 11 illustrate the fact that the distribution of the acceleration magnitudes is most accurately described by a t-distribution. This type of distribution has more pronounced tails, which indicates that a there is an increased probability that larger (harsher) accelerations will be experienced than if the values were normally distributed. This result may be influenced by the fact that even though the grains which make up the riding surface are likely to be normally distributed, the measurement of the response is being made after the vibration has been transmitted to the skateboard. The skateboard and rider system is rather complex and cannot reasonably be expected to have perfect vibration transmissibility. This means that parts of the response may be attenuated or amplified according to the dynamics of the skateboard and, as a result, an ideal normal distribution cannot necessarily be expected. It is clear that the normal distribution fails to capture the peak near the mean of zero as well as the exaggerated tails simultaneously. The data collected for both truck designs followed a t-distribution at all speeds, meaning that no distinct differences in the form of the t-distribution of magnitudes could be identified between the standard and split axle trucks.
Figure 11: Probability density function for acceleration data collected with the split axle
truck design showing fit curves for different distributions. The normal distribution fails to simultaneously capture all of the key features of the observed distribution. A t-distribution is better suited to follow the exaggerated tails of the distribution and it provides a more accurate fit. This trend continues, and the t-distribution fit appears to be more appropriate for both truck designs at all speeds.
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Figure 12: Probability density function comparisons for the split axle and standard truck
designs at 5, 10, and 20 km/h. The spread of the distributions increases with speed, indicating that there is an increased probability of larger and more extreme vibrations occurring. The distributions tend to match fairly closely except in the case of the 5 km/h test where the split axle truck distribution exhibited slightly more spread.
25
Fig. 12 shows the acceleration magnitude distributions compared for both truck designs at each of the three test speeds. The spread of the data can be seen to increase with speed, however, all of the distributions are roughly symmetric with a mean near zero. Increased spread (width of the distribution) indicates that accelerations with larger magnitudes occur more often. Therefore, this suggests that, on average, the rider is more likely to experience increasingly harsh and uncomfortable vibrations. Overall, the distributions for the two truck designs match reasonably well at each speed, except for the 5 km/h trials. At the lowest test speed, the acceleration magnitudes for the split axle truck exhibit slightly more spread and a probability peak near zero which is 0.9% lower than the standard truck. A lower peak and increased spread both indicate an increased likelihood of harsher vibration for the split axle truck. This type of average difference may become perceptible if the skateboard is ridden at this speed for an extended period of time. This is due to the fact that the rider may fatigue more quickly under these conditions. At higher speeds, however, the spread of the corresponding distributions as well as the likelihood of experiencing a given acceleration magnitude are fairly similar. One potential reason for this could be the prevalence of discontinuities and bumps which affect both wheels simultaneously, thereby reducing the possibility that the split axle will help the system react in a more favorable way.
Additional insight can be gained by looking more locally at the peak acceleration values that were experienced during each trial. Particularly large discontinuities or debris in and on the riding surface can lead to brief acceleration events which register magnitudes far above what is normally experienced. These events are particularly jarring for the rider as well as the skateboard components. This type of event will cause severe discomfort for a brief time but can usually be overcome, however, in extreme cases it could lead to a crash or fall. The average peak acceleration for each test speed is shown in Fig. 13. As before, the acceleration magnitude can generally be seen to increase with speed. Specifically, the peak acceleration magnitude for the standard truck increases by 335% between the lowest and highest speeds. The magnitude for the split axle design, however, only increases by 129% for the same change in speed. The peak values for each truck design were also compared for each different speed. To within 95% certainty, the peak acceleration experienced by the split axle truck design was larger than that of the standard truck design by 6.6 m/s2 at 5 km/h. This difference corresponds well with the observed differences in the magnitude distribution for this speed. The opposite was found to be true at 20 km/h where (with 95% certainty) the standard truck’s peak acceleration was higher by 96 m/s2. No statistically significant
difference was found at 10 km/h. Because the benefit of reduced peak acceleration is more apparent for the split axle design at higher speeds, a possible extension of this work would be to increase the range of speeds over which the trucks are tested in order to see if this behavior continues in a predictable manner or if limits are reached at higher speeds.
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Figure 13: Average peak acceleration magnitude for vibration experienced on each of two
different styles of skateboard trucks at three different test speeds. Error bars indicating the 95% confidence interval for each value are shown at the top of each bar. The peak acceleration value, which captures the intensity of the most extreme vibration events, is found to increase with speed for both truck designs. Statistically significant differences of 6.6 m/s2 and 96 m/s2 were found for the 5 km/h and 20 km/h trials respectively.
In order to better understand the subtle differences and behavioral trends of the two truck designs, the acceleration spectra were analyzed in the frequency domain. The dominant vibration frequencies and their relative power contributions are captured in the PSD of each acceleration signal. The average normalized integrated PSD shown in Fig. 14 illustrates the frequency response of both designs for the full range of test speeds. The majority of the dominant frequencies fall in the range of 20-450 Hz for both trucks (for reference, passing trains and subways can cause ground vibration on the order of 5-20 Hz while motors, pumps, and handheld power tools can vibrate at 60 Hz and above). The total power contributions from higher frequencies are also larger at higher speeds for both truck designs. The 95% power thresholds range from 210-288 Hz when riding at 5 km/h, 290-335 Hz at 10 km/h, and 410-435 Hz at 20 km/h. All of the observed vibration frequencies can be detected by and cause discomfort for humans, however, skateboarders experience vibration constantly and are able to tolerate it during riding [9], [10]. The extent of this tolerance could be studied to determine the duration and frequency ranges which cause the most or least discomfort, but as of now this is not well understood in the context of skateboarding.
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Figure 14: Average normalized integrated PSD of acceleration data for skateboard truck
testing on a paved road. The dominant frequencies which contribute the most power are in the range of 20-450 Hz for both truck designs. Frequency spikes can be observed as sharp increases in slope. The split axle truck design exhibits two separate frequency spikes while the standard design has a more continuous rise in power with a single dominant peak. The contributions from higher frequencies increase with speed for both set-ups.
The PSD for the split axle truck design generally exhibits two peaks with a sharp drop off at mid-range frequencies. This can be seen in Fig. 14 with the multiple changes in slope for each curve. The standard truck typically exhibits a single peak, illustrated by the sharp increase in the slope of the curve followed by a steady rise until it eventually tapers off. This behavior, where mid-range frequencies contribute significantly less power to the split axle truck’s vibration signal, can be observed at all test speeds. This difference may stem from the fact that the two truck designs being tested utilize slightly different durometer bushings which may impact the frequency response properties of each truck. Bushings are available in a range of durometers and they are typically made to be highly modular and swappable. Future testing could focus on modeling and evaluating how bushing characteristics influence the trucks response to help identify the cause of the attenuation observed in this experiment. Development of a predictive model which describes the system response to step and sinusoidal inputs could also help explain how key system parameters such as bushing durometer and hanger mass contribute to other observed behaviors like lower peak acceleration and arms. Additionally, rigorous modeling would enable fine tuning
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of the acceleration response characteristics without requiring a large number of tests to try different bushing configurations or hanger geometries.
Another particularly useful parameter that can be extracted from the frequency domain data is the arms of the signal. The arms value is computed for each run independently and then averaged
across trials for a given riding speed, as illustrated in Fig. 15. As with peak acceleration, the arms
for the standard truck exhibited a larger percentage increase between each speed. The standard truck exhibited an increase in arms of 48% between 5 and 10 km/h as well as an increase of 74%
between 10 and 20 km/h. The split axle design’s arms only increased by 25% between 5 and 10
km/h and by 33% between 10 and 20 km/h. In checking for differences it was found with 95% certainty that the only statistically significant difference in the arms occurred at 20 km/h where the
standard truck had an arms which was 2.8 m/s2 higher than that of the split axle truck. This suggests
that the amount of energy inherent in the vibration of the standard truck was slightly higher.
Figure 15: Average arms for vibration experienced on each of two different styles of
skateboard trucks at three different test speeds. Error bars indicating the 95% confidence interval for each value are shown at the top of each bar. arms describes the amount of energy
inherent in the vibration experienced during the trial in addition to how harsh it is for the rider. The standard truck’s arms increased by 158% between the lowest and highest test
speeds while the split axle design only increased by 66%. The only statistically significant difference observed in the data was at 20 km/h where the arms of the standard truck was 2.8
29 6 CONCLUSIONS
The split axle truck design was successful in reducing the intensity of localized vibration events while also maintaining the appropriate qualitative feel of the skateboard. Most notably the peak acceleration experienced with the split axle design was 96 m/s2 lower than the standard design. Additionally, as riding speed is increased from 5 to 20 km/h, the increase in peak acceleration and arms of the standard truck was more than double the increase observed for the split
axle truck over the same range of speeds. This indicates that as riding speed is pushed higher the split axle design will be increasingly effective at reducing the intensity of the vibration transmitted to the rider.
The measured acceleration spectra clearly exhibit stochastic behavior, however, they do not fit exactly with standard normally distributed vibration. The tendency of the data to have more pronounced tails and follow a t-distribution matches well with certain previous studies done on skateboards [7]. However, while this may offer insight into more generalizable behavior and the dynamics of skateboards, it will require more comprehensive testing before the distribution form can be fully understood. In the context of this study, the overall consistency of the distributions across speeds suggests that, on average, the behavior of the two styles of trucks are very similar and that the differences manifest themselves in very localized ways. The observed similarity also suggests that the response may be dominated by acceleration events which affect both wheels simultaneously.
The frequency makeup of the vibration signals was also reasonably consistent with the bulk of the dominant frequencies in the range of 20-450 Hz for both truck designs. This agrees well with test results for vibration testing of similar systems [7], [5]. The curves for the two different designs also tracked each other fairly well for each test speed, however, the standard design experienced larger contributions from mid-range frequencies.
As riding speed increases, the peak acceleration experienced on a skateboard with the split axle truck design was seen to increase slower than the standard truck design. An increase of 335% was observed in the standard truck as compared to 129% in the split axle truck for the same change in speed from 5 to 20 km/h. Additionally, a statistically significant difference of 96 m/s2 was observed with 95% confidence between the peak acceleration of the split axle design at 20 km/h and the even higher peak acceleration of the standard design at the same speed. This difference is 11% of the maximum peak magnitude, which is a significant portion. At 5 km/h it was observed that the peak acceleration of the split axle design was larger by just 3% of the maximum peak magnitude. This is not nearly as significant of a difference as the one observed at high speeds. As a result, it can be concluded that the split axle design has the potential to reduce the maximum acceleration that is imparted to the skateboard at high speeds.
Similarly to peak acceleration, it can be concluded with 95% certainty that the arms of the split
axle design is lower by 2.8 m/s2 at 20 km/h. This difference is only 5% of the maximum measured arms, but it is also the only statistically significant difference that was found for any speed. This
suggests that the split axle design aids in reducing the amount of energy that is transferred through vibration to the skateboard and rider. The difference in the increase of arms between speeds is also
indicative that at higher speeds the split axle design may prove to be less harsh. The standard truck’s arms increased by 158% between the lowest and highest test speeds while the split axle
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Overall it appears as though the split axle design was successful in reducing the intensity of the measured acceleration. It is important to note that improvements are not as apparent when the data is looked at in an averaged sense. The benefits are most clearly seen at higher speeds, and the trends suggest that the relative benefit would continue to grow as speeds are pushed higher. The most significant gain is in reduction of the peak acceleration magnitudes which originates from very localized events. The new design reduces the intensity of extreme vibration events, but the overall comfort of the rider remains largely unchanged.
Finally, it is worth noting that the design of skateboard components is heavily influenced by the rider experience and the qualitative feel of the skateboard. Even if a split axle design has the potential to reduce the intensity of vibration locally, it may not be adopted if riders feel it drastically changes the riding experience. Further work would need to be done in order better tune the ride characteristics of the spit axle truck if it were to be competitive with standard designs. The added complexity of this design also presents a number of challenges for implementation. The split axle truck’s demonstrated potential to improve the riding experience and decrease the jarring effects of bumps certainly warrants further exploration of this new design.
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