Analysis And Experimental Study On Mechanical Characteristics Of Tennis Racket

The basic property of the tennis racket is the foundational research of tennis,which affects the coefficient of restitution of tennis ball,the deformation of the string bed and the storage of energy.In tennis,a tennis racket is an extension of an arm,and when the racket is hit by an impact force,it is transmitted to an arm to produce tennis injury.In recent years,research has advanced our understanding of the basic property of racket and tennis injury,but the existing research has shortcomings,mainly in these areas:(1)The research on the stiffness of a string bed is mainly aimed at the specific string bed,so the methods are not universally applicable and convenient through the experiments or mechanical analysis method of string intersection;(2)There are few researches on the dynamic characteristics of racket string bed.In the research,a string bed is simplified as a spring damping system.At the same time,the function of the equipment is single;(3)Research on arm injuries is focused on biology and medicine,which are difficult to quantify the exercise damage.Aiming at the application of tennis racket,the basic mechanical properties of tennis racket are analyzied deeply in this thesis,and the stiffness and dynamic characteristics of tennis string bed are studied by combining theoretical deduction,experimental verification and numerical analysis.On this basis,the property of tennis racket was further extended to the relation betweent arm and racket,and the motion characteristics of holding a racket are studied.The main contents are as follows:1.Through mathematical abstraction of the mechanical properties of the racket,the racket frame was modeled as a beam on the basic of Euler Bernoulli beam theory.Then a free vibration equation about the model of a racket was solved by a harmonic function product method,and the first mode shape of racket was getten from the equation,which provided a theoretical basis for racket-holding model.The string bed was modeled as a thin membrane on the basic of elastic thin membrane theory.Then Laplasse equation of tennis racket deformation was solved,and the relationship between the shape function and forece applied on the string bed was discussed,which provided a theoretical basis for the stiffness model,the dynamic model and the first mode shape of a string bed.2.An analytical model of the string bed was contributed that employed improved nonlinear membrane theory to estimate static stiffness.The shape of a deformed string bed due to an elliptical disc was a logarithmic shape function for the string bed deflection,and a two dimensional step function was used to express the shape function.The partial differential equation governing string bed deformation was discretized using a one-term Galerkin approximation.The resulting force-displacement relation at the center of the string bed yielded the string bed stiffness as a function of the major design parameters,including the shape and size of the frame,string tension used during stringing,and string spacing,diameter,and elastic modulus.An experiment on the string bed stiffness was designed to measure the stiffness of a string bed with a clamped racquet frame.The apparatus applied a measured force to a string bed from an elliptical disc whose lateral displacement was tracked simultaneously.Companion experiments yield the force-displacement characteristics of the string bed over a range of string tensions,disc sizes and string bed sizes.The predicted force-displacement relation remained in agreement with that measured from experiments on a string bed instrumented,so the nonlinear membrance model yielded a practical way to estimate different string bed stiffness.3.A dynamic geometric nonlinear model of the string bed was contributed that employed improved nonlinear membrane theory.The partial differential equation was discretized using a one-term Galerkin approximation to get the centre displacement response of a string bed by the impact force applied on a string bed.A nonlinear relationship of the centre maximum displacement of string bed,tennis ball speed,contact area between tennis ball and string bed,string tension used during stringing and string elastic modulus were discussed.sAiming at the shortcomings of the current tennis dynamic experiment,an equipment of tennis serve and test was developed according to a relation between gas pressure and a tennis ball speed,which solved the problem of adjustable tennis ball speed,and a center maximum displacement of string bed was measured when a tennis ball impacted on a string bed.By using this experimental system,the displacement response to different tennis ball speed and string tension used during stringing was investigated.The accuracy of the dynamic model of string bed was assessed by the dynamic experimnet,and the relationship between tennis ball speed and dynamic characteristics was discussed.4.The basic property of the tennis racket is related to the athlete's hitting action,then affects the pattern of tennis injures.An impact force applied on a string bed was extended to an arm,and a dynamic model of basic actions was proposed in tennis involving the shoulder,wrist,racket and string bed by employing Lagrange's equation.The parameters of the dynamic model about racket-holding condition were obtained to estimate motions in the shoulder and wrist while playing.An equation governing four motions was computed using the Runge–Kutta methods.To assess the accuracy of the model,the predicted motions in the shoulder and handle of the racket were compared with those obtained from experiments using IMUs(inertial measurement units).In the dynamic model,the impact force and location of holding the racket were dicussed to affect the tennis injury by method of parameter analysis.The basic property of the tennis racket is very important for the tennis.In the thesis,the stiffness and dynamic characteristics of a string bed depending on numerous factors are studied,and the mechanism of each factor in tennis is discussed.The work has applications for athletes' racket choice,which may have different head geometries and string type.This is of benefit to potentially manufacturers of racquets and string and the research community for tennis injury.