Space Engagement Theory Research Articles

Kinematic analysis and experimental verification of an oval noncircular bevel gears with rotational and axial translational motions

This paper proposes a new type of gear transmission based on the space engagement theory, which can achieve not only simple motion transmission between intersecting axes, but also the compound motion of the rotation and axial translation between them. An oval noncircular bevel gear engagement coordinate system was first established with parameter equations of the pitch cone described in spherical coordinates. Then, the spherical involute equations and formula for calculating displacement and axial translational velocity of the gears were derived. Experimental tests were carried out to validate the kinematic characteristics of oval noncircular bevel gear transmission calculated from theoretical models. The influences of eccentricity on the indicators, such as axial displacement, rotational angle, angular velocity and acceleration, periodicity of the line of contact and periodicity of each motion characteristic parameter, have been analyzed and discussed in last. Experimental verification and kinematic analysis indicate that the proposed gear design method is appropriate with great potential for industrial applications.

A Novel Optimization Design Method of Form Grinding Wheel for Screw Rotor

The profile accuracy of screw rotors plays a vital role in stabilizing the meshing operation between mated rotors. Such stability can minimize the vibration and noise, as well as improve the sealing performance and wear resistance. This is the main reason why form grinding is extensively applied as a finishing process to maintain high screw rotor profile accuracy. Since the installation parameters for form grinding wheels affect both the grinding wheel profile accuracy and grinding performance, it is essential to obtain reasonable installation parameters to guarantee the high precision and good grinding performance of form grinding wheels. In this paper, a novel optimization design method for form grinding wheels for screw rotors has been proposed. For the first time, the relationship between the grinding wheel installation parameters and profile accuracy is established to evaluate the grinding performance. A parameterized program has been designed based on space engagement theory. The characteristics of the contact line and profile features of form grinding wheels under different installation parameters have been investigated. Then, the proposed method was employed to select the correct range of installation parameters. To validate the proposed method, a set of experiments, including the manufacture and measurement of several screw rotors, was carried out. The results reveal that the precision of the screw profile is significantly improved compared with the empirical method, thus showing the effectiveness of the proposed method.

Surface modelling and design approach research for single cone screw-bush pair with equal volume of chambers

To increase the delivery capacity and flow stability of the screw pump and reduce wear between the stator and the rotor, a surface forming method of single-head cone screw-bush pair with equal cavities and large delivery capacity was investigated based on the conventional single cone screw theory. An equation of the cone screw-bush pair surface was established according to the space engagement theory. A flow equation of single cone screw bush pair was built based on the cone screw-bush pair section equation and the rule of its variation. The calculation method of the screw structure size at a given flow rate was determined as well. A kinematics equation of the single cone screw-bush pair was obtained after a kinematics analysis of the single cone screw-bush pair conducted. The movement formula of a single cone screw-bush pair with equal cavities and large delivery capacity was concluded. Three-dimensional model of a single cone screw and a bush was built and the motion simulation of the pair was conducted based on MATLAB and Pro/Mechanism. The kinematics rules were summarized at the same time. Moreover, a single cone screw and a bush solid model were processed based on the three-dimensional model of the cone screw-bush pair and the three-dimensional printing technology. The correctness of the equation of the single cone screw-bush pair surface was verified.

Numerical Calculation of Tooth Profile of a Non-circular Curved Face Gear

Based on the cylindrical coordinates and the space engagement theory, which utilize a cylindrical coordinate system, an arbitrary curve equation was obtained and a method of curve expansion was established. This allows any order of pitch curve of non-circular curved face gear and normal equidistant curve parameter equations to be derived. The tooth profile points of the non-circular curved face gear can be solved using the numerical calculation method where the tooth profile intersects with the pitch curve and normal equidistant curves of non-circular curved face gear. Finally the numerical method used to solve the tooth profile of the non-circular curved face gear was proved to be accurate and correct from the small error between measured data and the data of theoretical calculation.

Study on Design Method of the Double Arc Gear Hobs

This article find that one of the effecting the double circular arc gear s running performance is the double circular arc gear tooth profile precision, through analysis to the running-in properties of double arc gear. The problems about tooth profile precision of gear hobs caused by the current profiling theory and approximate design method of gear hobs are analyzed. In the design of circular arc gear hob, use the space engagement theory, can eliminating the tooth error. Acquiring the equation of hobs basic of worm tooth surface by analytical and calculation that the establishment of basic gear rack and worm of hob meshing. The hob not only eliminate the tooth profile error in manufacturing, but also improve the running performance of double circular arc gear, and provides the theory evidence for engineering practice.

Geometry design, three-dimensional modeling and kinematic analysis of orthogonal fluctuating gear ratio face gear drive

As the current research of face gear drive cannot realize fluctuating gear ratio, a design method of orthogonal fluctuating gear ratio face gear drive is proposed. The mathematical model of orthogonal fluctuating gear ratio face gear drive is found based on the space engagement theory. The equation of the pitch curve, addendum curve and dedendum curve of face gear are derived. The design method of tooth surface of the face gear is available based on the envelope method. The conversion relationship of enveloping coordinate systems is obtained during the enveloping process of orthogonal fluctuating gear ratio face gear drive after the establishment of enveloping coordinate systems. Then combining with equation of generating surface, the tooth surface equation of the face gear is obtained. The three-dimensional model of orthogonal fluctuating gear ratio face gear is acquired on the basis of a modeling program, which is developed under the environment of VB and Solidworks (API). Furthermore, localization of the bearing contact is achieved by the manufacturing method and it is justified by the finite element method analysis result. Finally, the kinematics of the orthogonal fluctuating gear ratio face gear drive is analyzed, and the change laws of transmission ratio, angular displacement and angular acceleration of the face gear are acquired.

The Design and Experiment of Oval Bevel Gear

Aiming at the complex design and analysis methods of noncircular bevel gear, combining the gear space engagement theory and the generating method of tooth profile, the profile generating process was seen as the pure rolling between the pitch line of virtual processing tool and pitch curve of oval bevel gear based on the virtual generating method. The blank parameters and relation equation between tool parameters and procedure parameters of generating method were deduced. General parametric solid models of oval bevel gear were founded. Based on experimental result of oval bevel gear transmission, the design profile of oval bevel gear which was obtained according to generating method was verified.

Research on High Efficient Virtual Measuring Method for Globoidal Cam Machining Error

Current methods for measuring Globoidal cam exist these problems: difficulty of measurement of profile machining error, heavy dependency on expensive measuring equipment and low measuring efficiency. In order to solve them, this paper established a high efficient virtual measuring method for globoidal cam machining errors. Based on virtual measuring theory and globoidal cam space engagement theory, and by taking the three-dimensional machining simulation models of the globoidal cam profile as the measured object, the virtual gauge head can do measurement along the planned measuring path. The machining error calculation method was determined according to the degree of geometric interference between virtual gauge head and the surface of machined models. And a virtual measuring system on UG platform for globoidal cam profile machining errors was built by use of Visual C++ 6.0 and UG/Open API secondary development tools. Finally, a virtual measuring experiment was performed for the two kind of machining simulation models generated by generating method and one-side machining method. The experimental results show that the high efficient virtual measuring method for globoidal cam machining error is correct and the virtual measuring system is reliable. On the one hand, an effective method is provided to achieve an efficient, low-cost measurement for globoidal cam profile machining errors in this paper. On the other hand, it has great engineering guiding significance for the actual production and processing of globoidal cam.

Research on Tool Post Angle of Standard Hob Cutting Modified Gear

In view of the adjustment of tool post angle during hobbing modified spur gear, the basic worm helicoids of hob is generated according to national standards. The model of the hobbing is established according to space engagement theory and actual processing conditions. The formulae for the transversal shape of workpiece gear and its tooth-profile and tooth-thickness deviations are derived. Several calculating examples are given. The results show that there are different zero (tooth-profile and tooth-thickness) deviation tool post angle for different modification coefficient. Finally, the approximate formulae for zero deviation tool post angles are given to be easy to use in engineering. The tool post angle adjusted according to the method can ensure precision of workpiece gear.

Meshing theory and simulation of noninvolute beveloid gears

Based on the space engagement theory, a special type of noninvolute beveloid gears meshing with line contact between intersecting axes has been studied in this paper for the first time. The engagement equation and tooth profile equation have been presented by applying the theory of gearing. Meanwhile the tooth profile errors and axial errors have been calculated by means of numerical analysis in this paper. As a numerical example, the three-dimensional simulation of beveloid gears between intersecting axes has been finished by means of the CAD system, Pro/Engineer.