Worm Gear Drives with Improved Kinematic Accuracy

This paper presents the fundamentals of the design and applications of new worm gear drive solutions, which enable the minimisation of backlash and are characterised by higher kinematic accuracy. Different types of worm surfaces are briefly outlined. Technological problems concerning the principles of achieving a high degree of precision in machining are also described. Special attention is paid to the shaping of conical helical surfaces. Increasing the manufacturing precision of drive components allows one to achieve both lower backlash values and lower levels of its dispersion. However, this does not ensure that backlash can be eliminated, with its value being kept low during longer periods of operation. This is important in positioning systems and during recurrent operations. Various design solutions for drives in which it is possible to reduce backlash are presented. Results of experiments of a worm gear drive with a worm axially adaptive only locally, in its central section, are presented. In this solution, it is possible to reduce backlash by introducing adjustment settings without disassembling the drive. An important scientific problem concerned defining the principles of achieving a compromise between the effectiveness of reducing backlash and the required load capacity of the drive. In this paper it has been shown that in worm gear drives with a locally axially adaptive worm, as well as with a worm wheel with a deformable rim, it is possible to achieve significant reduction of backlash. In high precision drives—for example, those with an average backlash value of <15 micrometers—this can enable more than a two-fold reduction of the average backlash value and more than a three-fold decrease of the standard deviation of local backlash values.

Sensitivity Analysis of Reliability of Low-Mobility Parallel Mechanisms Based on a Response Surface Method

Kinematic accuracy is a crucial indicator for evaluating the performance of mechanisms. Low-mobility parallel mechanisms are examples of parallel robots that have been successfully employed in many industrial fields. Previous studies analyzing the kinematic accuracy analysis of parallel mechanisms typically ignore the randomness of each component of input error, leading to imprecise conclusions. In this paper, we use homogeneous transforms to develop the inverse kinematics models of an improved Delta parallel mechanism. Based on the inverse kinematics and the first-order Taylor approximation, a model is presented considering errors from the kinematic parameters describing the mechanism’s geometry, clearance errors associated with revolute joints and driving errors associated with actuators. The response surface method is employed to build an explicit limit state function for describing position errors of the end-effector in the combined direction. As a result, a mathematical model of kinematic reliability of the improved Delta mechanism is derived considering the randomness of every input error component. And then, reliability sensitivity of the improved Delta parallel mechanism is analyzed, and the influences of the randomness of each input error component on the kinematic reliability of the mechanism are quantitatively calculated. The kinematic reliability and proposed sensitivity analysis provide a theoretical reference for the synthesis and optimum design of parallel mechanisms for kinematic accuracy.

Copula method of the kinematic accuracy of cylindrical roller bearing

The kinematic accuracy of cylindrical rollers bearing isn’t only influenced by the dimensional and form precision of its parts, but also more influenced by the cooperation among them. For cylindrical rollers bearing, the main indices of the kinematic accuracy are the ending beat and the radial run out of bearings. There must be dependent relationship between the cooperative action among the parts of bearings and the ending beat or the radial run out of bearings. This relationship is hardly expressed by mathematical formula. However, because the parts dimension deviation and the run out of bearings follow statistic law and have their distribution characteristics, while the copula joint distribution function can connect the run out of bearings with multiple parts dimension accuracy, the copula function is introduced to analyze the dependent relationship between bearing parts cooperative action and its kinematic accuracy. Based on the copula function of statistic theory, the kinematic accuracy of bearings can be forecast by parts geometric accuracy.

Research and improvement of methods of testing machines for geometric and kinematic accuracy

Purpose. To analyze and check for adequacy the known calculation formulas in determining the geometric and kinematic accuracy, statistical and dynamic rigidity and testing the machine for technological reliability. To carry out comparative calculations to simplify the methodology of complex tests of metal-cutting machines of the universal group. To select and improve the measuring equipment during the complex tests of the milling machine. Methodology. The research is based on the use of analytical methods for calculating the static rigidity coefficient, additional calculation of the measuring instrument design due to the gear ratio, the angle of rotation of the lever and the theoretical error of the displacement mechanism based on the known probability distribution theorem. Findings. The formulas of researches of the coefficient of static rigidity, the mechanism of the measuring device, the angle of rotation of the lever, the theoretical error of the mechanism of movement and the density of probability of distribution of the angle of the lever mechanism of the indicator of tangent type has been obtained. Originality. The research has been carried out and the parametric relationship between the static rigidity coefficient in the design of the spindle assembly of the vertical milling machine with the error of the calculations of the design, the departure of the spindle cone and the location between the supports has been established. The values and functional dependences of the amplitude of oscillations on the maximum allowable spindle speeds and feed rates at which the surface roughness of the workpiece reaches the specified geometric limits has been obtained. It is experimentally confirmed that the parameters of the system of pre-planned repairs are directly related to the reliability of the machine. The resource on the accuracy of the machine determines the need for overhaul, and the repair period depends on the service life of parts and elements of the machine. The actual service life should be a multiple of the repair period, as the restoration of the part is planned during the current repair. Practical value. The practical achievement of the obtained results is to confirm the adequacy of the known calculation formulas in determining the geometric and kinematic accuracy, statistical and dynamic rigidity and testing the machine for technological reliability. On the basis of the received analytical and settlement data was made the simplified complex technique of test of the metal-cutting machine during the: testing the machine at idle; testing of the machine when working under load; testing of the machine for geometric and kinematic accuracy; determination of statistical and dynamic rigidity; research of vibration-resistant vertical milling machine; testing of the machine for technological reliability.