By Konrad Schweiger, Dewesoft GmbH, Austria
HEAD Sport GmbH, Austria
A poorly constructed tennis racket experiences uncontrolled vibrations. The player cannot correctly predict and control the strokes. The stability of the racket is essential, especially during hits off the racket center.
Material testing is part of making the optimum product - and the procedures that ensure quality repeatability from batch to batch. Dewesoft solutions help test the strength, rigidity, and inertia, the swing weight, of HEAD tennis rackets.
Tennis racket properties are of interest to sports engineers and designers as it allows them to evaluate performance, review trends and compare designs. Headquartered in Kennebach, Austria, Head Sport Gmbh is a leading global manufacturer of premium sports equipment. The company produces a wide range of products for skiing, snowboarding, swimming, and racket sports, including tennis. Its products are used by many top athletes around the world.
Tennis equipment plays a critical role in player performance. The game has evolved enormously since its creation in the 1870s. The exchanges have gained speed. The demands on the player and his racket have increased considerably. In the service, the ball can reach speeds near 240 km (150 miles) per hour, and the pressure on the racket is up to 50kg.
Changes concerning the play style and speed, and the materials used in the equipment, have all led to increased stress affecting the main accessory, the racket. During a tennis game, a tennis racket is exposed to vibrations. When we hit the tennis ball, the racket is excited and freely vibrates with its inherent frequency.
The whole point of the manufacturer is to combine the requirements of the player and the technical constraints of manufacturing. This requires an iterative calculation/simulation, prototyping, and test campaign. Therefore, tennis racket manufacturers such as HEAD® have to monitor the frequency response of a racket and modify the structure following findings.
The player wants the racket to support a faster swing, as well as maneuverability, strength, and stability. In the racket validation process, the aim is, therefore, to provide lightness of materials, optimized distribution of weight, stress resistance, and reduced vibration.
Racket Manufacturing Process
To build a racket, the same material is used as aeronautics or Formula 1, graphite fibers made of carbon. With their extensive knowledge engineers carefully modify the arrangement of carbon fibers to influence the behavior and properties of play.
Figure 1. The correlation between player and manufacturer requirements.
Graphite is a preferred material for racket frames - it is remarkably strong for its relatively lightweight. It provides power, as well as good control and a feel for the ball. Graphite and carbon fibers enable the design of more aerodynamic shapes which raises the pace at which the racket can move through the air. The usage of these substances in racket manufacture even enables the tennis rackets to be strung at better stringing tensions without weakening the frame.
The manufacturer uses carbon fiber impregnated with resin in rolls which is placed on a steel mold to give the racket its shape. Additional unhardened carbon impregnates are then strategically bonded onto the racket frame to optimize the weight distribution. The frame is pressed while pressurized air is blown into the center of the frame to retain a hollow core that will later be filled with foam.
The racket is hardened by heating, string holes are drilled, and the frame is polished and varnished. Finally, a grip is applied and the racket is strung in a crisscross horizontal-vertical pattern with either two separate strings or a single string.
Measurement and Modal Testing
Modal testing is an indispensable tool to determine the characteristics and properties of structures and materials - their natural frequencies and mode shapes.
Common Techniques for Experimental Modal Testing
- Multiple-input multiple-output (MIMO) measurement
- Single-input multiple-output (SIMO) measurement
- Operational Deflection Shapes (ODS)
- Impact hammer modal testing
In the Dewesoft modal testing and analysis solution, structures can be excited with impact hammers or modal vibration shakers. Responses are easily measured and geometry structures for visualization and animation can be easily imported or drawn.
Achieving the optimum racket requires an iterative approach. To reach the desired results we need to employ a repeated cycle of operations coming closer to the mark as the number of iterations increases.
To optimize the tennis racket strength, rigidity, and inertia, as well as swing weight, the testing process cycle, in this case, includes:
- Calculation / simulation
- Static and dynamic laboratory tests
- Real-use test campaign
- Correlation tests / simulation
Data Acquisition Instrumentation
To acquire the measurements to be used in the analysis, the HEAD® company uses an 8-channel SIRIUS DAQ device. The SIRIUS is equipped with:
- 7 ACC amplifiers for accelerometers and impact hammer connection, and
- one MULTI amplifier acting as a function generator.
They are using DewesoftX software with a Dynamic Signal Analysis (DSA) software package, including Modal test, Order tracking, Torsional vibration, etc., and the Frequency generator (FGEN) option.
The SIRIUS data acquisition system is modular, and secure, and offers virtually unlimited configuration possibilities. SIRIUS slices are available from 1 to 16 analog channel configurations and can be daisy-chained together to extend channel count. An array of different analog amplifiers is allowing connection to virtually any sensor.
Experimental modal testing is a method for validating the mathematical model describing the dynamic properties of a structure.
The structure can be excited by different means to make it resonate on its natural frequencies, determining the damping and mode shapes.:
- Via impact hammer,
- shaker, or
- real random excitation.
During measurement, the transfer functions are acquired which are connected to the geometry model.
For the impact hammer testing, the tennis racket is hanging in the air, attached with two thin strings. The triaxial accelerometer is glued on the racket, measuring the vibrations in all three directions. The racket is then sequentially struck along its head with a modal hammer, point by point using the roving hammer method.
Figure 2. Impact hammer testing - excitation and responses.
Alternatively, by using the Dewesoft function generator software option and MULTI amplifier on the SIRIUS measurement instrument, an external shaker can be excited about modal analysis. The advantage of this method is to brings more energy into a specific frequency point.
Dewesoft offers a portfolio of modal and inertial shakers with integrated amplifiers.
Figure 3. Setup for impact hammer modal testing.
Figure 4. Impact hammer modal testing – measurement
The measurement interface allows the creation of simplified geometry of the racket and assigns the measurement points to it. Depending on the need, multiple Cartesian and Cylindric coordinate systems can be merged.
During the guided measurement procedure the current point is highlighted. You can go freely forth and back and repeat user-selectable points. A warning notifies you about unwanted double hits.
Figure 5. Screenshot of experimental results in DewesoftX.
Correlation of Structural Vibrations Vs. Simulation
These results then make it possible to readjust the digital models and refine them for future developments & prototyping.
For the analysis, HEAD® technicians are monitoring the frequency response spectrum (transfer functions) of all the points as well as the MIF (mode indicator function) function.
With the markers included in the Dewesoft software, the engineers can search for maximum peaks, amplitude, and their positions in the frequency domain. With modal circle visual control, the resonant peak can be examined in detail, offering a more exact insight into the frequency and damping factor of the peak with a circle fit procedure.
Figure 6. Screenshot of modal circle visual control
The geometry can be animated at any frequency. Results are compared with one of the most accurate finite element models software suite on the market.
Figure 7. Numerical simulation in third-party Finite element software.
High-Speed Video Synchronized With Analog Data
Another test carried out by HEAD is measurements in game situations. The aim is to record the real stresses of the racket and in synchronization with a fast camera to correlate time signals from the sensors with the images for visualization of player position and racket behavior.
Figure 8. The Photron FASTCAM SA4 can capture images at a maximum frame rate of 500,000fps.
The camera used is a PHOTRON Fastcam SA4, which can capture video up to max. 500 000 frames per second. The DewesoftX Photron plugin provides the acquisition of high-speed video from Phottron cameras with perfect synchronization between analog and video data.
The illustration below shows the working principle. When a predefined trigger occurs on the analog input, the camera is started over Ethernet. When the camera captures the first frame, it puts out the TRG_TTL_OUT signal. This is then feedback to the SIRIUS SuperCounter input, which acquires the TTL signal with 100 MHz precision.
Figure 9. The synchronization principle between Photron and Dewesoft.
The download of the video data can take quite a while. Immediately after the measurement, the engineers can zoom on the video data in the preview mode, and narrow down the download to the section of their interest. This reduces download time dramatically.
Vibration and Video Measurements in a Game Situation
Another test involved a third-party mobile data logger on the tennis player. The technicians then imported the recorded TXT files and analyzed these using DewesoftX software.
Figure 10. Importing the data logger TXT file for further analysis in Dewesoft.
The tests resulted in tennis racket optimization for HEAD®. The use of the Dewesoft data acquisition solutions for the development of the new HEAD® GrapheneXT range made the racket up to 20% lighter and 30% more resistant. The optimal racket weight distribution – and the faster swing – now takes into account the dynamic vibrational behavior. The weight has been shifted to the tip of the head and the handle improves handling and increases the moment of inertia of the racket (more power).
These tests made it possible to optimize the latest Head rackets (GrapheneXT series) and in particular the weight distribution on the racket. Thanks to the weight shifted to the tip of the head and the handle, players generate more kinetic energy when they hit the ball. Less effort, but more power.
By monitoring the frequency response, one of the world’s leading manufacturers of sporting goods can improve the tennis racket and shift the weight to where the user needs it the most for fast and precise hits.
Related Measurements Performed on Rackets Made by Other Companies
Human Body and Hand-Arm Vibration Measurement
Another method to objectify the player's feelings - normative analysis methods from occupational health (OSHA) for the measurement of Human Body / Hand Arm Vibrations.
Standard indicates orientation and installation of sensors on the hand and also the necessary signal processing - via weighting filters - to adapt the response of an accelerometer to the feeling of the hand - the hand sensitive to frequencies between 8 and 16 Hz.
Using the Dewesoft Human vibration software module and measurement setup hand-arm vibration can be calculated according to the international standard, ISO 5349.
Stiffness and Durability Measurements
With the flexibility of Dewesoft, the test capabilities can be also extended by doing material tests to determine the material characteristics. For this example, a small load frame out of anodized extruded aluminum to house a linear actuator and servo motor was designed and built.
Analog Output Device
Any SIRIUS DAQ system with Analog Output option (AO) and the function generator software upgrade can send the control signal to the servo motor.
In this case, we used a SIRIUS modular data acquisition system with custom DualCoreADC amplifiers setup:
- Three SIRIUS HV amplifiers for high-voltage inputs
- Three ACC amplifiers or voltage/IEPE input
- One SuperCounter input
- One MULTI amplifier with analog out
- One STG amplifier
For this test, we used the analog output available on the SIRIUS MULTI amplifier. The STG channel was used to sample the information from the load cell sensor.
The SIRIUS Watchdog could also be used as a safety precaution. With the SIRIUS Analog Output, the user can look for a heartbeat from Dewesoft throughout the test. If the heartbeat is missing, the SIRIUS Watchdog can be programmed to send a digital signal to the motor stopping or coasting to stop motion.
Typical instrumentation of a compression bench: servo-motor & displacement cylinder, effort sensor, data logger with function generator outputs to control the cylinder (watchdog unit required for safety).
The analog input channels need to be configured based on the sensors used for the test.
The DewesoftX function generator is an additional software option in which the user can define the analog output signal. Using your analog channel as “Signal Output” and creating either a Sine, Triangle, or Arbitrary waveform will be the most practical.
The following image shows a user-defined arbitrary waveform to program the actuator to perform a specific task. In the arbitrary waveform setting, old data could also be copied to simulate data that has already been collected.
Figure 11. The Dewesoft module Function Generator offers rich functionality.
Once the hardware and software have been programmed, entering measurement mode allows running an automated test. If the function generator is configured to start “manually”, the user will have to go to the control tab and select “Start Output”. From this point forward, the test will be conducted just as the user has programmed. Once the test is initialized, the user can watch the test perform while data is being collected from the same measurement PC.
Figure 12. How to manually start the function generator for analog output.
Previously users had to use multiple systems to perform the forcing function and the data acquisition. Otherwise, they had to choose between stability and flexibility: A PLC with limited options in terms of data acquisition and post-processing or a DAQ and post-processing with the susceptibility from the control aspect.
However, now the combination of DewesoftX software along with an analog output device allows the user to easily control the forcing function of the test fixture while simultaneously measuring signals and inputs from the instrumented part.
Figure 13. Determination of the breaking point - adding pressure going beyond the tennis racket material limits.
Press test - stress/displacement/deformation - is used to determine the racket’s breaking point. The testing - a tensile test - is conducted in test machines, applying a controlled and uniformly increasing tension force to the specimen.
- Maximum service forces near 50kg → determine the breaking strength of the racket frame.
- Using a press, apply a force beyond the elastic limit of the material until it breaks.
- The larger the sections of the racket frame, the greater the rigidity but resistance vs weight of the racket is compromised (generally between 200 and 370g).
Figure 14. The stress-strain diagram expresses the relationship between the load applied to a material and the deformation of the material it causes.
Figure 15. Setup of the racket stress test.
Other types of static tests are performed on specific benches: the frame stiffness index and the inertia measurement.
The stiffness or rigidity of the racket is characterized by the deformation of the frame during striking. The measurement is made by holding the racket by the handle and pulling on the top of the frame while remaining in the elastic range. Is measured in Rahmen and depends on the material of the racket. And directly affects the accuracy/stability at impact and power.
Frame stiffness index
- Unit: ra (Rahmen)
- Factor dependent on the racket material
- Influence on stability / comfort on impact, power
- Soft racket (55 to 60 ra), rigid (if> 67 ra)
Figure 16. Determining the stiffness index.
The racket inertia is an expression of the energy spent to move the racket. It is a phenomenon that occurs when holding the handle of the racket and tilting it from right to left like a pendulum. The inertia characterizes the racket's ability to cross the air easily following the player's gesture. The greater the inertia, the more powerful the racket - but then, on the other hand, it will not be very handy.
The inertia is adjustable by adding or reducing the masses on the frame (intended for experienced players).
- Unit: kg / cm²
- Describes the moment of inertia, "swing weight"
- Influence on handling
- The higher it is, the more powerful the racket will be but not very handy.
Figure 17. The inertia determines the handling characteristics.