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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: 1elhajjar@uwm.edu (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.