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A Proportional Integral Derivative (PID) Force Control System Design for a Fatigue Testing Machine For New Bicycle Fork Standards
Paul Sisneros, Advisor: Professor Rani F. El-Hajjar1
Engineering Mechanics and Composites Laboratory College of Engineering and Applied Science University of Wisconsin-Milwaukee Milwaukee, WI, 53211 USA Corresponding information: [email protected] (R. F. El-Hajjar)
Tel: 1-414-229-3647, Fax: 1-414-229-6958
Abstract
This paper summarizes the efforts to build a fatigue-testing machine for testing of bicycle forks to support
academic participation in standard developments in the ASTM F08.10 Committee. The motivation behind the
work in this committee is to develop new standards for bicycles considering the new materials such as
composites that are being used in production. The goal of this effort is to involve the University of Wisconsin-
Milwaukee in the effort to advance the knowledge of failure processes in carbon fiber bicycle parts and to
advance the state of ASTM test standards currently under development. It is intended that the results from
these test efforts will be available to assist the engineering community in developing better test standards for
bicycle components made from composites by examining the results of testing carbon fiber composite forks
under existing testing standards. This paper summarizes the efforts to develop a fatigue test machine with load
control that is integrated with a Matlab [1] based test environment for test control and data acquisition. This
machine was successfully built and will be used to test parts donated by the industry partners.
1. Introduction
The continuing effort to reduce the weight of bicycles has led to the increased development
and use of polymer resin based carbon fiber components. Laminated carbon fiber
components are significantly different in their properties and behavior from metals, which are
homogeneous. Laminated carbon fiber can offer several advantages over metals. The
direction and number of layers can be varied to achieve greater strength or stiffness in various
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directions based on the stresses to be experienced by the design. However, the manufacturing
process can produce anomalies that are not necessarily accounted for in testing standards that
were originally developed for metallic forks and other metallic bicycle components. Some of
these failure modes include fiber breakage, delaminations in addition to other patterns of
crack growth not seen in metallic forks.
Carbon fiber based composites also
vary from metals in that they lack the
ductility and toughness that make metals
such an advantageous and versatile class of
materials. Due to metal’s ductility and
isotropic structure, when a part yields in
one-location forces are readily
redistributed to other areas due to the
isotropic nature of the materials.
Composite materials by contrast must be
designed and laid with an understanding of
the way forces are likely to redistribute
through the structure should local failures occur. The tests run using the proposed equipment
are designed to be identical to standards originally designed for metallic forks, so that the
carbon/epoxy composite forks can be assessed using this setup. The method describes the
procedures used to develop a fatigue testing capability using servo-pneumatic actuator in
force control. A proportional–integral–derivative controller (PID controller) is used to obtain
the load control capability necessary for this project. The PID controller is a control loop
feedback mechanism widely used in industrial control systems and machinery. A PID
controller calculates an error value as the difference between a measured force and the
desired set point. The controller then attempts to minimize the error by adjusting the process
control inputs. For motion control alone PI controllers are usually adequate, but since this
system is required to control force without excessive overshoot the derivative aspect is also
useful. A PID system is characterized by its control parameters, they set the proportion of the
adjustment the controller will make in its output based on its calculation of the position,
integral and derivative of the input signal. Denoting the proportional control parameter as !!,
the integral control parameter as !!, and the derivative control parameter as !!, with input
! ! and output ! ! , the transfer function !! ! for this PID system is:
Figure 1 Fatigue testing machine assembled at the
University of Wisconsin -Milwaukee
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!! ! = !(!)!(!)
= !! + !!!+ !!! [2]
Typically the parameters are adjusted to obtain the desired system behavior, and the values
required for a given response depend on the dynamics of the system. Because the system
dynamics are likely to change over the span of the test due to strain hardening and fatigue, the
Matlab program was designed to monitor the overshoot of the system and adjust the k
parameters of the PID actively. Every 10 cycles the Matlab program calculates the average
overshoot and makes adjustments to !! and !!. Testing has shown that this allows the
machine to test forks with a wide variety of strain hardening characteristics without the error
in maximum force per cycle exceeding the 5% specified in the standard.
2. Experimental Method
2.1 Testing and Mechanical Hardware
The mechanical components of the system were required to withstand the repeated stress of
the forces they would apply in carrying out fatigue testing without losing accuracy. In
addition, it was important to consider the cost issues in selection of the most cost-effective
yet reliable system. After building a prototype with an electrical solenoid driven actuator it
was determined that an electrical actuator would not withstand repeated application of forces
up to the 700 N range at high speed for long periods of time. A pneumatic actuator was
selected for their ability to run continuously under the required forces without overheating or
wearing out its mechanisms. An Enfield Technologies servo pneumatic proportional control
system was selected as this system is capable of high precision position and proportional
control and can withstand high cycle fatigue testing. The system uses a LS-V05s Proportional
Pneumatic Control Valve [3] to control airflow and is based around an Enfield LS-C41
Hybrid PID Controller/Driver [4] see figure 1. To interface the PID controller with a
command signal from the computer a LabJack LJ-U3 HV USB data acquisition and control
module [4] was installed. In order to accomplish force control an accurate readout of the
force applied to the part by the pneumatic actuator was required. Several types of load cells
were used in prototyping the system but loss of accuracy at high strain rates and distortion of
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the load cell itself due to impact forces became issues. It was determined that a load cell
rated for fatigue was required. A Fatigue Rated Load Cell Model F370 [5] from SensorData
was selected because it has a fatigue rating to !"! cycles. The system was tested with these
components and an op-amp amplifier with a gain of 201 was installed with the load cell input
line to bring the load cell output range closer to the full range of the LabJack in order to
improve accuracy. Additionally a universal joint rated for 9 kN was added between the end of
the pneumatic actuator and the coupling with the end of the test piece in order to allow the
fork to swing through an arc without experiencing axial forces. See Figure 1 for a layout of
the system. Structurally, the entire testing system was mounted to a table made of a
reinforced 1/4” steel grate. The fork was secured in a custom made clamp designed to
emulate the locking used in the head tube of a bicycle to better simulate real world use
conditions. The clamp holds the actual spacers and bearing that go with the fork. The clamp
had to be designed such that it allows the rotation of the fork during the testing along the axis
of the steering tube.
2.2 Software and Data Acquisition
Matlab was used as the programming language to develop the software side of the fatigue
testing machine. Matlab was selected because it is efficient at handling data, its code is
extremely portable and it is capable of interfacing with the LabJack USB interface device. At
first the force control system was programmed to attempt to attain the requested force for
each cycle as fast as possible, but this method had a tendency to overshoot by up to 20%
while the maximum allowed in the ASTM standard being followed was 5% [6][7].
To remedy these problems the Matlab program has been rewritten with a new signal
generation algorithm that is time based and approaches the peaks as a sinusoid. Since the
integral, derivative and second derivative of a sine function are all continuous, very little
shock or impact is experienced this way. And since the code is now time based the frequency
is selectable by the user. With the sinusoidal control implemented the system maintains
overshoot less than 3%. For data acquisition an option was added to select the sampling
frequency. The maximum sampling frequency of the system is currently 160 samples per
second; the limiting factor is the communication rate of the lab jack device in use. In practice
a sample rate as 30 Hz is sufficient with a cycle rate of 1 Hz, and the option to select lower
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sample rates than 160 was desired to reduce data file sizes and ease data processing and
analysis.
3. Discussion and Test Results
At the date of this report the fatigue testing machine has been tested capable of repeatable
application of force for cycle counts on the order
of 10! and logging the data at 500 samples per
second. The most recent tests, performed on an
aluminum bicycle fork over thirty thousand cycles
show very little force variation between cycles, the
intended load was 650 N and the maximum
variation was less than 13 N, well within the 5%
margin specified in the test standard [6][7]. The
charts for force and displacement in this test are
shown below in Figures 2 and 3 respectively.
Signal inline filtering and additional grounding
were used to reduce the noise in the
measurements.
Once the system was confirmed to be
stable and capable of logging enough data to
perform the full test, comparison tests were started
to confirm its accuracy. To this point the tests
have been consistent in fatigue life and
displacement with the tests performed at the
Cycling Sports Group test facilities, with similar
behavior being shown on aluminum forks from the
same batch tested to 200,000 cycles. Further
testing will be required to ensure that the failure modes and total cycles to failure are
consistent.
Figure 2 Plot of displacement of bicycle fork end in centimeters during testing
Figure 3 Plot of force in Newtons applied to end of bicycle fork during testing
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4. Conclusions
This paper summarizes the design procedure used to develop a servo-pneumatic fatigue-
testing machine to test bicycle forks in support of ASTM standard development. The servo-
pneumatic fatigue-testing machine has been shown to perform adequately in reliability and
repeatability. Cross-laboratory participation is necessary to show the testing machine is
operating within tolerances for force, displacement and frequency consistency. Current
testing has shown no deviation from expected results between the facilities. Future efforts
will be to develop an impact testing capability after high cycle fatigue testing which the
ASTM F08.10 committee is currently considering.
5. Acknowledgements
Special thanks to Dana Parnello, Product Research and Testing Manager of REI
(Recreational Equipment Inc.) and Bud (Gilbert) Kisamore, Testing Manager at the Cycling
Sports Group. Their donation of test articles and their expert advice and guidance through
this project is greatly appreciated. Thanks to Dr. Rani El-Hajjar for his assistance and
guidance in mechanics, material science, and methods of academic research. These were
essential to the completion of the project.
6. References
[1] Software was developed using MATLAB (2007a, The MathWorks, Natick, MA) Web. 24 Jun. 2010.
<http://www.mathworks.com>.
[2] Franklin, Gene F., J. David Powell, and Abbas Emami-Naeini. Feedback Control of Dynamic Systems.
Upper Saddle River, NJ: Pearson Prentice Hall, 2006. Print.
[3] "LS-V05s Proportional Pneumatic Control Valve Data Sheet." Enfield Technologies Inc. 22 Nov. 2004.
Web. 24 Sept. 2010. http://www.enfieldtech.com/
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[4] "U3 | LabJack." LabJack | Measurement & Automation Simplified. Web. 25 Jun. 2010.
<http://labjack.com/u3>.
[5] "Fatigue Rated Load Cell Model F370 Data Sheet." Sensor Data Technologies Inc., 15 Nov. 2004. Web. 24
Sept. 2010. http://www.sensordata.com
[6] ASTM Standard F2273, 2003, "Test Methods for Bicycle Forks," ASTM International, West Conshohocken,
PA, 2003, DOI: 10.1520/F2273-03, www.astm.org.
[7] ASTM Standard F2274, 2003, "Standard Specification for Condition 3 Bicycle Forks," ASTM International,
West Conshohocken, PA, 2003, DOI: 10.1520/F2274-03, www.astm.org.