Showing papers on "Pressure angle published in 2017"

Apparent contact angle and contact angle hysteresis on liquid infused surfaces

Abstract: We theoretically investigate the apparent contact angle and contact angle hysteresis of a droplet placed on a liquid infused surface. We show that the apparent contact angle is not uniquely defined by material parameters, but also has a dependence on the relative size between the droplet and its surrounding wetting ridge formed by the infusing liquid. We derive a closed form expression for the contact angle in the limit of vanishing wetting ridge, and compute the correction for small but finite ridge, which corresponds to an effective line tension term. We also predict contact angle hysteresis on liquid infused surfaces generated by the pinning of the contact lines by the surface corrugations. Our analytical expressions for both the apparent contact angle and contact angle hysteresis can be interpreted as ‘weighted sums’ between the contact angles of the infusing liquid relative to the droplet and surrounding gas phases, where the weighting coefficients are given by ratios of the fluid surface tensions.

Role of blade rotational angle on energy performance and pressure fluctuation of a mixed-flow pump

Abstract: The role of blade rotational angle in the energy performance and pressure fluctuation of a mixed-flow pump is investigated through an experimental measurement and numerical simulation. The mixed-fl...

An improved numerical method for the mesh stiffness calculation of spur gears with asymmetric teeth on dynamic load analysis

Abstract: Gears are one of the most crucial parts of power transmission systems in various industrial applications. Recently, there emerged a need to design gear drivers due to the rising performance require...

Study of a harmonic drive with involute profile flexspline by two-dimensional finite element analysis

Abstract: Purpose This paper aims to present simulation results of a harmonic drive (HD) with involute flexspline (FS) profiles based on two-dimensional (2-D) finite element analysis (FEA). Design/methodology/approach First, the mathematical model of the FS with involute tooth profile was developed using a straight-edge rack cutter based on the theory of gearing. Then the engaging circular spline (CS) with conjugate tooth profile of FS was derived based on the enveloping theory and theory of gearing. Additionally, a mesh generation program was developed to discretize the FS based on the mathematical model. An elliptical wave generator (WG) was inserted into the FS, and a torque was applied to drive the FS meshing with the CS. The WG and the CS were both assumed to be rigid in the finite element model. Findings Finally, a 2-D FEA was conducted to explore the stress distribution on the FS, the engagement movement of the FS, the torsional stiffness and the engaged area of teeth of the HD under various conditions. Moreover, this research also studied the effect of changing pressure angle of the involute FS on the performance of the HD. Research limitations/implications The simulation model and methodology presented in this paper paved the way for further investigation and optimization of the HD with involute tooth profile FS and conjugate CS. Originality/value The simulation model of HD is established on conjugate shape based on the theory of gearing and an automatic mesh generation program is developed to generate the finite element model. The characteristics of the HD can thus be simulated according to the developed model.

Low-loss gears precision planetary gearboxes: reduction of the load dependent power losses and efficiency estimation through a hybrid analytical-numerical optimization tool

Abstract: In the field of robotics, extremely accurate gearboxes are mandatory in order to ensure the adequate precision required by the automatic processes. For these applications, planetary gearboxes represent one of the most attractive solutions because they ensure high reduction ratios in a compact solution. However, their compactness and high power density, imply some thermal limitations. In order to overcome this problem, new gear designs have been studied by a hybrid analytical-numerical approach in order to reduce the power dissipation and, consequently, the operating temperatures. The efficiency increase is obtained mainly by a reduction of the module of the gears. This, together with other modifications of the tooth form (pressure angle, profile shift, etc.), allows to reduce the relative sliding between the tooth flanks that causes the power loss maintaining at the same time an adequate load carrying capacity. Low-loss gears have already been studied by other authors on bigger gears. Furthermore, by means of dedicated CFD simulations performed with an especially developed tool based on the open-source code OpenFOAM®, it has been shown that the sliding optimized design has a positive impact also on the churning power losses. The global winning in terms of reduction of the gear meshing power losses can be assessed in about 50%, depending on the reduction ratio. The new design has been validated by means of experimental tests performed in the internal laboratory of the company. The results have fully validated both the numerical approach and the new design.

A mixed finite element and analytical method to predict load, mechanical power loss and improved efficiency in non-standard spur gear drives:

Abstract: A reasonably accurate estimation of gear power loss is desirable to maximize gear performance. The load share by teeth pair, contact stress, sliding speed, elastohydrodynamic film thickness and coefficient of friction are some of the most important contributing factors which determine frictional power losses in gears. This paper presents an improvement concept to minimize the load-related power losses (sliding and rolling power losses), which will lead to an enhancement in gear efficiency by selection of non-standard gears. The tooth thickness at the pitch circle of the pinion and gear is different in non-standard gears (kpπm > 0.5 πm and kgπm < 0.5 πm), whereas it is equal in standard gears (kpπm = kgπm = 0.5 πm). In this work, the load share-based frictional power loss and the respective mechanical efficiency have been determined for comparative performance of standard and non-standard gears. Finally, the influence of various gear and drive parameters such as gear ratio, pressure angle pinion teeth numb...

High-precision small modulus gear vision measurement method

Abstract: A high-precision small modulus gear vision measurement method is disclosed. The method is characterized by after a CCD camera is calibrated, carrying out small modulus gear coordinate conversion, outputting an actual physical coordinate of a small modulus gear and calculating a correlation parameter coordinate scale factor, a rotation matrix and a translation matrix; reflecting a space position relation between a gear to be measured and a measurement system in the measurement system; carrying out image processing, wherein a processed object is a small modulus gear edge contour image acquired from a CCD camera 3; and carrying out denoising; then using and carrying out 1/8 sub-pixel edge extraction, extracting an edge point coordinate, carrying out center fitting and acquiring a center coordinate of the image; according to an edge point, acquiring a basic gear parameter, wherein the basic parameter is a tooth number, a mode number, a reference circle diameter and a pressure angle; fitting a standard gear contour curve; and comparing an actually-acquired edge contour curve with a theoretical contour curve so as to acquire a pitch deviation and a tooth profile deviation. The basic gear parameter and quality can be comprehensively analyzed and evaluated.

Transmission Index of Lower-Mobility Parallel Mechanism: Case Study on 3-PRS Mechanism

Abstract: An extended definition of the transmission index based on the pressure angle was proposed. In order to enable evaluation of motion/force transmissibility and constrainability of parallel mechanism including lower-mobility/hybrid parallel mechanisms, pressure angle of a kinematic structure obtained by blocking all the actuated joints of the original mechanism was defined. In addition to this, an equivalent kinematic model of the original mechanism was introduced, in which the output link is supported by pure forces with the directions determined by the kinematic configuration of the mechanism. With these new ideas, a novel transmission index was proposed, and an illustrative example of 3-PRS mechanism was shown.Copyright © 2017 by ASME

Investigation on the flank surface durability of gears with increased pressure angle

Abstract: Within a funded research project (reference number 0325244C, BMWi – Federal Ministry for Economic Affairs and Energy of Germany), the load-carrying capacity of alternative involute gears was investigated. To find qualified variations for use in gear drives, increased pressure angles (αn > 20°) and/or asymmetric tooth shapes (αn 20°) have been examined experimentally. Optimization goals were the power to weight ratio of the transmission and the power density in the drive train. In this report gears with reference tooth shape (αn = 20°) as well as gears with modified tooth shape (αn = 28°) are discussed with focus on the load carrying capacity of the tooth flank with special regard to the damage mechanisms pitting, micro-pitting and scuffing. The results of experimental and test accompanying studies are shown. They allow a direct comparison between standard and special gears as well as a classification in context of the actual state of knowledge.

Novel plunger pump

Abstract: The invention relates to a novel plunger pump. The novel plunger pump comprises a driving device and pump bodies and further comprises power actuation assemblies and a power transfer assembly, wherein each power actuation assembly comprises a guide rod which reciprocates in the corresponding pump body, and a chute and a swinging disc; the chutes are fixedly mounted at the ends, extending out of the corresponding pump bodies, of the corresponding guide rods; two mutually parallel and opposite working planes are formed on the inner side of each chute and are perpendicular to the corresponding guide rod; the power transfer assembly comprises a driving non-circular gear and driven non-circular gears, which mesh with each other; the driven non-circular gears are in transmission connection with the corresponding swinging discs; and the driving non-circular gear is connected with the driving device and driven by the driving device to rotate. According to the novel plunger pump, sine mechanism transmission can be realized, the chutes and the swinging discs rotate to enable the pressure angle to be zero degree, and the non-circular gears realize stable movement speed of the guide rods. Equipment is transmitted by the non-circular gears, so that many shortcomings of a cam mechanism can be greatly overcome, the service life is long, and the probability of abrasion is low.

Effects of Geometry Design Parameters on the Static Strength and Dynamics for Spiral Bevel Gear

Abstract: Considering the geometry design parameters, a quasi-static mesh model of spiral bevel gears was established and the mesh characteristics were computed. Considering the time-varying effects of mesh points, mesh force, line-of-action vector, mesh stiffness, transmission error, friction force direction, and friction coefficient, a nonlinear lumped parameter dynamic model was developed for the spiral bevel gear pair. Based on the mesh model and the nonlinear dynamic model, the effects of main geometry parameters on the contact and bending strength were analyzed. Also, the effects on the dynamic mesh force and dynamic transmission error were investigated. Results show that higher value for the pressure angle, root fillet radius, and the ratio of tooth thickness tend to improve the contact and bending strength and to reduce the risk of tooth fracture. Improved gears have a better vibration performance in the targeted frequency range. Finally, bench tests for both types of spiral bevel gears were performed. Results show that the main failure mode is the tooth fracture and the life was increased a lot for the spiral bevel gears with improved geometry parameters compared to the original design.

Study on precision forming and lift-out process of small cone angle spiral bevel gear by finite element analysis

Abstract: Meshing tooth surface of a small cone angle spiral bevel gear appears as the spiral structures. And the cone angle pitch is small, while helix angle is large. It is very difficult for materials to precisely flow into the cavity in precision-forming process. It is also difficult to ensure that no damage is introduced in the forging rotated from the gear cavity. Deform-3D analysis shows that material deformation primarily occurs on the tooth part in the forging process. On the tooth profile, the flow of material is primarily radial direction. In the gear root area, the flow of material is the radial direction and axial compression. In the center of the tooth profile, the flow of material is primarily vertical. ADMS analysis of liftout process indicates that the spiral bevel gear can be put out of the cavity smoothly. With an increase of the pressure angle, the liftout force decreases. With an increase of the spiral angle and tooth width, the liftout force increases. Finally, spiral bevel gear Pb sample is obtained by precision plastic forming technology. It is proved that the spiral bevel gear can be manufactured by precision plastic forming technology and the numerical result is reliable.

Dynamic analysis of a geared rotor-bearing system with translational motion due to shaft deformation under residual shaft bow effect

Abstract: In this paper, the dynamic response of a spur geared rotor-bearing system has been studied when the gear set has translational motion due to shaft deformation and residual shaft bow effect. A new dynamic model for the geared rotor-bearing system, considering translational motion and residual shaft bow effect, is proposed, in which the distance between the centers of two gears varies with time. Therefore, the proposed model regards gear pressure angle and contact ratio as time-varying variables, while the previous model regards them as constant. A finite element model of the geared rotor-bearing system developed, the equations of motion are obtained by applying Lagrange’s equation. After deriving nonlinear equations of motion for the geared rotor-bearing system, the dynamic responses are computed by applying the fourth-order Runge-Kutta numerical method. The dynamic response including lateral response of two gears, gear pressure angle and contact ratio with different phase angle between two residual shafts are investigated. The results show that the magnitude of the residual shaft bow, the phase angle between two residual shafts will significantly affect gear pressure angle and contact ratio. This new model produces more accurate dynamic responses in comparison to those of the previous model.

Analysis of composite motion law and force of high speed curve-face gear

Abstract: A new type of curve-face gear pair high speed curve-face gear pair is proposed. It combines the high speed cam motion law and the curve-face gear transmission, and can transmit rotation/axial motion and power between intersecting axis. The meshing coordinate system of the gear transmission is established and the basic principle of engagement is expounded. The composite motion law and force of high speed curve-face gear drive are analyzed, and influences of the basic structural parameters on the pressure angle and the force are analyzed in detail. The comparison between the experimental results and the theoretical results shows that the basic principle and design of the gear transmission are verified.

Optimisation of effective design parameters for an automotive transmission gearbox to reduce tooth bending stress

Abstract: Optimisation of effective design parameters to reduce tooth bending stress for an automotive transmission gearbox is presented. A systematic investigation of effective design parameters for optimum design of a five-speed gearbox is studied. For this aim contact ratio effect on tooth bending stress by the changing of contact ratio with respect to pressure angle is analysed. Additionally, profile modification effects on tooth bending stress are presented. During the optimisation, the tooth bending stress is considered as the objective function, and all the geometric design parameters such as module, teeth number etc. are optimised under two different constraints, including tooth contact stress and constant gear centre distance. It can be concluded that higher the contact ratio results in a reduced tooth bending stress, while higher the pressure angle caused an increase in tooth bending stress and contact stress, since decreases in the contact ratio. In addition, application of positive profile modification on tooth reduces tooth bending stress. All of the obtained optimum solutions satisfy all constraints.

A Gear Mesh Dynamic Model for Analyzing the Nonlinear Vibrations of Spur Gears Supported by Compliant Shafts

Abstract: A gear mesh dynamic model of spur gears is presented in this paper. Initially, the influence of variation in center distance due to geometric eccentricity, assembly error and bending deformation of shaft on gear mesh parameters such as pressure angle, backlash and time-varying mesh stiffness were determined. Then, the gear mesh dynamic model was formulated by replacing the constant backlash and time-varying mesh stiffness under quasi-static conditions of the previous model with continuously calculated time-varying backlash and time-varying mesh stiffness under dynamic conditions. A six-degree-of-freedom lateral-torsional coupled nonlinear dynamic model was established with the gear mesh dynamic model. A gear pair was analyzed to demonstrate and qualify the impact of shaft stiffness and operating conditions on the differences between the dynamic responses predicted by the nonlinear dynamic model established in this study and the previous nonlinear dynamic model. The results showed clear differences between the dynamic responses predicted by different models, especially for the gear rotor bearing system with high compliant shafts. A strong coupling effect between dynamic response and gear mesh parameters was found. The comparison between the gear mesh forces within a wide range of torque and speed also revealed differences, especially in the vicinity of the primary resonance speed and 1/3 of this speed. With increasing torque, the differences increased and the range of speeds corresponding to same difference also increased. The differences reached to a minimum near half of the resonance speed under different input torques.

Effect of Adjacent Teeth Load on Bending Strength of High Contact Ratio Asymmetrical Spur Gear Drive

Abstract: This paper describes methodology for predicting the bending stress of the spur gear accurately by including the load on the adjacent teeth for high contact ratio asymmetric spur gear drive. Higher contact ratio is obtained by enlarging the addendum from the standard addendum value where as the asymmetric is achieved by keeping various pressure angles (170, 200 and 220) at non drive side while the drive side pressure angle was kept as 200. The bending stress developed for the given load according to the load sharing calculated by using stiffness based method along with the effect of adjacent teeth loads are explored in this work. Computer aided design tool is used for generating the gear tooth profile and ANSYS is used to carry out the finite element analysis. The result shows that the maximum bending stress level in a mesh cycle is increased when the load on adjacent teeth are taken into account. The higher pressure angle at the non-drive side yields lesser stress at the fillet region when compared to the lower pressure angle.

Optical fiber pressure sensor of inaction contact angle measurement error

Abstract: The invention provides an optical fiber pressure sensor of an inaction contact angle measurement error. The sensor adopts a high-sensitivity optical fiber F-P chamber to combine a spherical pressure conduction sealing structure so as to realize accurate pressure measurement of a non-contact angle measurement error. Measurement precision is not influenced by a sensing head contact angle change. Extraneous pressure is acted on a pressure sensitive terminal of the optical fiber F-P chamber through the spherical pressure conduction structure so that a chamber length is changed and an interference signal spectrum characteristic is changed. Through optical fiber F-P chamber reflection interference spectrum characteristic data analysis, pressure is accurately measured. Simultaneously, a temperature compensating fiber bragg grating is made on a reflected spectrum signal output optical fiber, cross sensitivity of the temperature and the pressure is eliminated and high precision measurement of a non-contact pressure angle error is realized. The apparatus of the invention possesses characteristics that high sensitivity is possessed; anti-electromagnetic interference is achieved; and there is no temperature crosstalk and the like and especially the pressure measurement precision is not influenced by the sensing head contact angle change.

Face milling for hypoid internal bevel gear using new type of tilt milling machine

Abstract: To improve the machining efficiency, a new model is set up in this paper, which could machine hypoid internal bevel gears by using the tilt cutting method. An algorithm is developed to calculate the processing parameters. Unlike the traditional tilt structure machines, the tilt drum of the new model can only be adjusted in a vertical plane. Firstly, according to its special structure, the machine tool mathematical model is built. Then, the tilt angle is calculated and converted into a machine root angle and machine tilt angle equivalently. Based on the principle that the unit normal vector of the internal bevel gear tooth surface should be equal to that of hypoid gear at the reference point, the pressure angle and spiral angle of the internal bevel gear are calculated. Moreover, by adjusting the cutter position and machine root angle, the pressure angle of the shape gear is revised, which greatly extended the universality of the cutter. Finally, the cutter position affected by tilt angle is compensated. To demonstrate the performance of the proposed method, cutting simulation is carried out and the processing experiment is conducted. The results indicate that the simulation model and the actual model are basically in line with the theoretical model, which verifies the feasibility of the proposed processing method.

Application of a Cam Workbench for Education in Mechanical Engineering

Abstract: The paper shows the conception of a cam workbench for educational purposes. The cam workbench aims at sustaining the learned design process and visualizing learned effects. Therefore different cams with typical transfer functions are selectable for both follower types, translating and oscillating. The properties of these cams can be analyzed by students. Besides, kinematical length of the mechanism like eccentricity and the central distance can be varied. So the students can experience the influence of the pressure angle on the complete mechanisms. In addition, the students can calculate and design their own cam. Therefore, they can practice the learned theory in exercises. The designed cams can be manufactured by 3D-printing and plugged on to the different cam shafts.