A Novel Method of Obtaining Honing Tool Profile for Machining Gears With Profile Modifications

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Michał Batsch
Keyword(s):  
Mathematical Model ◽  
Design Process ◽  
High Precision ◽  
Prediction Error ◽  
Industrial Applications ◽  
Helical Gears ◽  
Profile Deviation ◽  
Tool Profile ◽  
Novel Method ◽  
Two Parameter

Abstract In this study, a mathematical model of the honing process for helical gears with external teeth was developed. The proposed novel method of obtaining the two-parameter envelope of a family of surfaces proved useful in simulated machining by means of a tool with a profile deviation. Based on performed simulations and industrial applications, it was found that this method can be useful in predicting the accuracy of machined gear and therefore can be used in the design process of honing tool for high precision aerospace gears. For the example provided, the average absolute prediction error of machined tooth profile was 0.28 µm.

A parametric analysis of the surface roughness of teeth shaped by a pinion shaper cutter and guidelines for choosing process parameters

2019 ◽  
Vol 233 (21-22) ◽  
pp. 7368-7377
Author(s):  
Mattias Svahn
Keyword(s):  
Mathematical Model ◽  
Surface Roughness ◽  
Parametric Analysis ◽  
Gear Tooth ◽  
Cutting Parameters ◽  
Three Dimensions ◽  
Tooth Surface ◽  
Roughness Parameters ◽  
Helical Gears ◽  
Novel Method

A parametric mathematical model is presented, by which it is possible to determine the machined gear tooth surface topography cut by a pinion shaper cutter. Arbitrary internal or external helical gears designs can be considered, the gear and the shaper cutter must only share a basic rack design. The basic rack has here an elliptical fillet, as it allows fewer tool tooth numbers without the risk of undercut. The machined tooth surface is presented in three dimensions and by surface roughness parameters [Formula: see text], and [Formula: see text]. A novel method to choose cutting parameters and tool design is also presented.

scholarly journals Design, Analysis and Test of a Hyperbolic Magnetic Field Voice Coil Actuator for Magnetic Levitation Fine Positioning Stage

Energies ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 1830
Author(s):  
Yiheng Zhou ◽  
Baoquan Kou ◽  
He Zhang ◽  
Lu Zhang ◽  
Likun Wang
Keyword(s):  
Magnetic Field ◽  
High Precision ◽  
Magnetic Levitation ◽  
Structural Parameters ◽  
Industrial Applications ◽  
Degree Of Freedom ◽  
Force Density ◽  
Precision Positioning ◽  
Element Analysis ◽  
Voice Coil Actuator

The multi-degree-of-freedom high-precision positioning system (MHPS) is one of the key technologies in many advanced industrial applications. In this paper, a novel hyperbolic magnetic field voice coil actuator using a rhombus magnet array (HMF-VCA) for MHPS is proposed. Benefiting from the especially designed rhombus magnet array, the proposed HMF-VCA has the advantage of excellent force uniformity, which makes it suitable for multi-degree-of-freedom high-precision positioning applications. First, the basic structure and operation principles of the HMF-VCA are presented. Second, the six-degree-of-freedom force and torque characteristic of the HMF-VCA is studied by three-dimensional finite element analysis (3-D FEA). Third, the influence of structural parameters on force density and force uniformity is investigated, which is conducive to the design and optimization of the HMF-VCA. Finally, a prototype is constructed, and the comparison between the HMF-VCA and conventional VCAs proves the advantage of the proposed topology.

The Research on Tooth Profile Total Deviation Measuring Method Based on Coordination Measuring Machine

2012 ◽  
Vol 184-185 ◽  
pp. 789-792
Author(s):  
Bing Li ◽  
Yu Lan Wei ◽  
Meng Dan Jin ◽  
Ying Ying Fan
Keyword(s):  
Mathematical Model ◽  
Data Processing ◽  
High Precision ◽  
Gear Tooth ◽  
Measuring Method ◽  
Tooth Profile ◽  
Cylindrical Gears ◽  
Total Deviation ◽  
Measuring Machine

Put forward a method that use scatter points which got in different places to measure the involution cylindrical gears, give a mathematical model that use the discrete points to sure the total deviation of gear tooth profile. The experience results show that this way is of high precision in measurement points, measurement an error data processing less intervention, etc.

Influence of Tooth Errors and Truing Principles of Grinding Wheel Abrasion for Machining Arc Enveloping Worm

2013 ◽  
Vol 652-654 ◽  
pp. 2153-2158
Author(s):  
Wu Ji Jiang ◽  
Jing Wei
Keyword(s):  
Mathematical Model ◽  
Case Studies ◽  
High Precision ◽  
High Performance ◽  
New Method ◽  
Grinding Wheel ◽  
Grinding Process ◽  
The Mathematical Model

Controlling the tooth errors induced by the variation of diameter of grinding wheel is the key problem in the process of ZC1 worm grinding. In this paper, the influence of tooth errors by d1, m and z1 as the grinding wheel diameter changes are analyzed based on the mathematical model of the grinding process. A new mathematical model and truing principle for the grinding wheel of ZC1 worm is presented. The shape grinding wheel truing of ZC1 worm is carried out according to the model. The validity and feasibility of the mathematical model is proved by case studies. The mathematical model presented in this paper provides a new method for reducing the tooth errors of ZC1 worm and it can meet the high-performance and high-precision requirements of ZC1 worm grinding.

scholarly journals On the prediction error for two-parameter stationary random fields

1992 ◽  
Vol 46 (1) ◽  
pp. 167-175
Author(s):  
R. Cheng
Keyword(s):  
Random Fields ◽  
Prediction Error ◽  
Duality Relation ◽  
Stationary Random Fields ◽  
Error Formulas ◽  
Two Parameter ◽  
General Duality

A number of Szegö-type prediction error formulas are given for two-parameter stationary random fields. These give rise to an array of elementary inequalities and illustrate a general duality relation.

Friction and Tribological Considerations for Nanometer Range Machining

2001 ◽  
Author(s):  
Som Chattopadhyay
Keyword(s):  
Mathematical Model ◽  
High Precision ◽  
Local Deformation ◽  
Experimental Results ◽  
Precision Machining ◽  
Complex Motion ◽  
Positioning Accuracy ◽  
Nanometer Range ◽  
Motion Characteristic ◽  
Low Speeds

Abstract Positioning accuracy within the range of nanometers is required for high precision machining applications. The implementation of such a range is difficult through the slides because of (a) irregular nature of friction at the slider-guideway interface, and (b) complex motion characteristic at very low speeds. The complexity arises due to the local deformation at the interface prior to breakaway, which is known as microdynamics. In this work prior experimental results exhibiting microdynamics have been appraised, and mathematical model developed to understand this behavior.

scholarly journals Localization of a Power-Modulated Jammer

Sensors ◽  
2022 ◽  
Vol 22 (2) ◽  
pp. 646
Author(s):  
Pietro Tedeschi ◽  
Gabriele Oligeri ◽  
Roberto Di Pietro
Keyword(s):  
Mathematical Model ◽  
High Precision ◽  
Radio Channel ◽  
Localization Error ◽  
Constant Power ◽  
Shadowing Effect ◽  
Weak Shadowing ◽  
The Way

Jamming is a malicious radio activity that represents a dreadful threat when employed in critical scenarios. Several techniques have been proposed to detect, locate, and mitigate jamming. Similarly, counter-counter-jamming techniques have been devised. This paper belongs to the latter thread. In particular, we propose a new jammer model: a power-modulated jammer that defies standard localization techniques. We provide several contributions: we first define a new mathematical model for the power-modulated jammer and then propose a throughout analysis of the localization error associated with the proposed power-modulated jammer, and we compare it with a standard power-constant jammer. Our results show that a power-modulated jammer can make the localization process completely ineffective—even under conservative assumptions of the shadowing process associated with the radio channel. Indeed, we prove that a constant-power jammer can be localized with high precision, even when coupled with a strong shadowing effect (σ ≈ 6 dBm). On the contrary, our power-modulated jammer, even in the presence of a very weak shadowing effect (σ < 2 dBm), presents a much wider localization error with respect to the constant-power jammer. In addition to being interesting on its own, we believe that our contribution also paves the way for further research in this area.

scholarly journals A novel method for high precision aortic constriction that allows for generation of specific cardiac phenotypes in mice

2018 ◽  
Vol 114 (12) ◽  
pp. 1680-1690 ◽  
Author(s):  
Arne O Melleby ◽  
Andreas Romaine ◽  
Jan Magnus Aronsen ◽  
Ioanni Veras ◽  
Lili Zhang ◽  
...  
Keyword(s):  
High Precision ◽  
Aortic Constriction ◽  
Novel Method

Numerical Simulation of Boiling Flows Using an Eulerian Multi-Fluid Model

2005 ◽  
Author(s):  
J. Han ◽  
D.-M. Wang ◽  
D. Filipi
Keyword(s):  
Mathematical Model ◽  
Fluid Model ◽  
Bubble Diameter ◽  
Interfacial Area ◽  
Nucleate Boiling ◽  
Industrial Applications ◽  
Turbulent Dispersion ◽  
Steady State Mode ◽  
Simple Method ◽  
Bubble Number

A mathematical model to simulate boiling flows in industrial applications is presented. Following the Eulerian multifluid framework, separate sets of mass, momentum, and energy conservation equations are solved for liquid and vapor phases, respectively. The interactions between the phases are accounted for by including relevant mass, momentum, heat exchanges and turbulent dispersion effects. Velocity-pressure coupling is achieved through a multiphase version of the SIMPLE method and the standard k-ε turbulence model is employed. In order to validate and assess the accuracy of the boiling model, subcooled nucleate boiling flows in a vertical annular pipe are simulated in the steady-state mode. The computed axial velocities, volume fractions, temperature profiles are compared with available experimental data (Roy et al., ASME J. of Heat Transfer, Vol. 119, 1997). The result obtained by assuming a constant value for the bubble diameter shows a reasonable agreement, but several limitations are observed in the details. A more advanced mathematical model incorporating separate transport equations for the bubble number density and the interfacial area is suggested.

Similarity Solution for the Curved Two-Dimensional Jet

1972 ◽  
Vol 39 (4) ◽  
pp. 879-882
Author(s):  
G. K. Fleming ◽  
S. A. Alpay
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Nonlinear Equation ◽  
Similarity Solution ◽  
Separation Bubble ◽  
The Other ◽  
Wall Jet ◽  
Two Dimensional ◽  
Two Parameter ◽  
Outer Half

A similarity solution has been obtained for a fluid jet bounded on one side by a separation bubble and on the other by an unbounded region containing the same fluid. The inner boundary has been approximated by a porous pseudowall. The resulting mathematical model reduces to other cases such as the plane wall jet and the free curved jet. A two-parameter family of solutions to the resulting nonlinear equation for the outer half of the jet correlates well with experimental data.

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