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-Hajjar 1 Engineering Mechanics and Composites Laboratory College of Engineering and Applied Science University of Wisconsin-Milwaukee Milwaukee, WI, 53211 USA Corresponding information: 1 elhajjar@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 1
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 Figure 1 Fatigue testing machine assembled at the University of Wisconsin -Milwaukee 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: 2
!!! =!(!)!(!) =!! +!!! +!!! [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 3
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 4
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 5
4. Conclusions This paper summarizes the design procedure used to develop a servo-pneumatic fatiguetesting machine to test bicycle forks in support of ASTM standard development. The servopneumatic 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/ 6
[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. 7