A Mathematical-Numerical Model to Calculate Load Distribution, Contact Stiffness and Transmission Error in Involute Spur Gears

2009 ◽  
Author(s):  
Mehdi Mohammadpour ◽  
Iraj Mirzaee ◽  
Shahram Khalilarya
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Load Distribution ◽  
Contact Stiffness ◽  
Transmission Error ◽  
Spur Gear ◽  
Spur Gears ◽  
Meshing Stiffness ◽  
Definition Of ◽  
The Mathematical Model

This paper firstly presents a mathematical model in order to calculate the load distribution, single contact stiffness and meshing stiffness as well as transmission error. in this way, there is no need to use finite element like methods and also the calculation time is dramatically reduced. Presented method is based on definition of a statically undetermined problem that is formulated using energy method. Some assumptions considered to convert this problem to a statically determined problem and get the mathematical models. Then a numerical method is employed in order to solve the mathematical model using a double iteration flowchart to close the problem. This model is flexible to adapt for any modification in spur gear profile geometry. Finally, this model is verified using previous works that have been utilized finite element and experimental model.

scholarly journals Mathematical model of energy efficiency in internal spur gears

2019 ◽  
Vol 23 (Suppl. 5) ◽  
pp. 1801-1813
Author(s):  
Predrag Dobratic ◽  
Mileta Ristivojevic ◽  
Bozidar Rosic ◽  
Radivoje Mitrovic ◽  
Dragan Trifkovic
Keyword(s):  
Mathematical Model ◽  
Load Distribution ◽  
Energy Losses ◽  
Spur Gears ◽  
Contact Ratio ◽  
Cylindrical Gear ◽  
Heating Effects ◽  
Effective Efficiency ◽  
The Impact ◽  
The Mathematical Model

The impact of geometric parameters of teeth and lubricating oils to the efficiency of involute internal spur gears, when the transverse contact ratio is 2 < ?? ?3, has been analyzed in this paper. The mathematical model and computer program for determining the current and the effective value of the efficiency have been developed. The influence of the character of load distribution and energy losses due to heating effects during the meshing period is included in the factor of load distribution. The results of computer simulation are given in the form of a diagram of the current values of the efficiency during the meshing period. Also, the values of effective efficiency for the considered cylindrical gear pairs have been calculated.

The Compliance of Solid, Wide-Faced Spur Gears

1990 ◽  
Vol 112 (4) ◽  
pp. 590-595 ◽  
Author(s):  
J. H. Steward
Keyword(s):  
Experimental Data ◽  
Contact Line ◽  
Load Distribution ◽  
3D Model ◽  
Spur Gear ◽  
Point Load ◽  
Spur Gears ◽  
Line Load ◽  
Gear Teeth ◽  
Theoretical Results

In this paper, the requirements for an accurate 3D model of the tooth contact-line load distribution in real spur gears are summarized. The theoretical results (obtained by F.E.M.) for the point load compliance of wide-faced spur gear teeth are set out. These values compare well with experimental data obtained from tests on a large spur gear (18 mm module, 18 teeth).

Low excitation spur gears with variable tip diameter

2021 ◽  
Vol 263 (5) ◽  
pp. 1275-1285
Author(s):  
Joshua Götz ◽  
Sebastian Sepp ◽  
Michael Otto ◽  
Karsten Stahl
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Low Noise ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Axial Forces ◽  
Tooth Width ◽  
Drive Trains ◽  
Static Transmission Error

One important source of noise in drive trains are transmissions. In numerous applications, it is necessary to use helical instead of spur gear stages due to increased noise requirements. Besides a superior excitation behaviour, helical gears also show additional disadvantageous effects (e.g. axial forces and tilting moments), which have to be taken into account in the design process. Thus, a low noise spur gear stage could simplify design and meet the requirements of modern mechanical drive trains. The authors explore the possibility of combining the low noise properties of helical gears with the advantageous mechanical properties of spur gears by using spur gears with variable tip diameter along the tooth width. This allows the adjustment of the total length of active lines of action at the beginning and end of contact and acts as a mesh stiffness modification. For this reason, several spur gear designs are experimentally investigated and compared with regard to their excitation behaviour. The experiments are performed on a back-to-back test rig and include quasi-static transmission error measurements under load as well as dynamic torsional vibration measurements. The results show a significant improvement of the excitation behaviour for spur gears with variable tip diameter.

scholarly journals Research on the Design and Modification of Asymmetric Spur Gear

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaohe Deng ◽  
Lin Hua ◽  
Xinghui Han
Keyword(s):  
Computer Aided Design ◽  
Design Method ◽  
Geometric Model ◽  
Simulation Method ◽  
Transmission Error ◽  
Spur Gear ◽  
Geometric Shape ◽  
Spur Gears ◽  
Gear Design ◽  
Aided Design

A design method for the geometric shape and modification of asymmetric spur gear was proposed, in which the geometric shape and modification of the gear can be obtained directly according to the rack-cutter profile. In the geometric design process of the gear, a rack-cutter with different pressure angles and fillet radius in the driving side and coast side was selected, and the generated asymmetric spur gear profiles also had different pressure angles and fillets accordingly. In the modification design of the gear, the pressure angle modification of rack-cutter was conducted firstly and then the corresponding modified involute gear profile was obtained. The geometric model of spur gears was developed using computer-aided design, and the meshing process was analyzed using finite element simulation method. Furthermore, the transmission error and load sharing ratio of unmodified and modified asymmetric spur gears were investigated. Research results showed that the proposed gear design method was feasible and desired spur gear can be obtained through one time rapid machining by the method. Asymmetric spur gear with better transmission characteristic can be obtained via involute modification.

scholarly journals A Method of Selecting Grid Size to Account for Hertz Deformation in Finite Element Analysis of Spur Gears

1982 ◽  
Vol 104 (4) ◽  
pp. 759-764 ◽  
Author(s):  
J. J. Coy ◽  
C. Hu-Chih Chao
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Gear Tooth ◽  
Spur Gear ◽  
Grid Size ◽  
Spur Gears ◽  
Element Analysis ◽  
Element Size ◽  
Full Effect ◽  
The Finite Element Analysis

A method of selecting grid size for the finite element analysis of gear tooth deflection is presented. The method is based on a finite element study of two cylinders in line contact, where the criterion for establishing element size was that there be agreement with the classic Hertzian solution for deflection. Many previous finite element studies of gear tooth deflection have not included the full effect of the Hertzian deflection. The present results are applied to calculate deflection for the gear specimen used in the NASA spur gear test rig. Comparisons are made between the present results and the results of two other methods of calculation. The results have application in design of gear tooth profile modifications to reduce noise and dynamic loads.

Mathematical model of the artificial muscle with two actuators

2020 ◽  
pp. 095440622094156
Author(s):  
Ljubinko B Kevac ◽  
Mirjana M Filipovic ◽  
Ana M Djuric
Keyword(s):  
Mathematical Model ◽  
Control Structure ◽  
Artificial Muscle ◽  
Parallel Robot ◽  
Simulation Results ◽  
Proportional Derivative Controller ◽  
Definition Of ◽  
The Mathematical Model ◽  
The Given ◽  
Very High

Characteristic construction of cable-suspended parallel robot of artificial muscle, which presents an artificial forearm, is analyzed and synthesized. Novel results were achieved and presented. Results presented in this paper were initially driven to recognize and mathematically define undefined geometric relations of the artificial forearm since it was found that they strongly affect the dynamic response of this system. It gets more complicated when one has more complex system, which uses more artificial muscle subsystems, since these subsystems couple and system becomes more unstable. Unmodeled or insufficiently modeled dynamics can strongly affect the system’s instability. Because of that, the construction of this system and its new mathematical model are defined and presented in this paper. Generally, it can be said that the analysis of geometry of selected mechanism is the first step and very important step to establish the structural stability of these systems. This system is driven with two actuators, which need to work in a coordinated fashion. The aim of this paper is to show the importance of the geometry of this solution, which then strongly affects the system’s kinematics and dynamics. To determine the complexity of this system, it was presumed that system has rigid cables. Idea is to show the importance of good defined geometry of the system, which gives good basis for the definition of mathematical model of the system. Novel program package AMCO, artificial muscle contribution, was defined for the validation of the mathematical model of the system and for choice of its parameters. Sensitivity of the system to certain parameters is very high and hence analysis of this system needs to be done with a lot of caution. Some parameters are very influential on the possible implementation of the given task of the system. Only after choosing the parameters and checking the system through certain simulation results, control structure can be defined. In this paper, proportional–derivative controller was chosen.

scholarly journals Modeling and Optimization of Bidirectional Clamping Forces in Drilling of Stacked Aluminum Alloy Plates

Materials ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 2866
Author(s):  
Jintong Liu ◽  
Anan Zhao ◽  
Piao Wan ◽  
Huiyue Dong ◽  
Yunbo Bi
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Aluminum Alloy ◽  
Clamping Force ◽  
Practical Application ◽  
Element Simulation ◽  
Theory Of Plates ◽  
Plates And Shells ◽  
The Mathematical Model ◽  
The Relationship

Interlayer burrs formation during drilling of stacked plates is a common problem in the field of aircraft assembly. Burrs elimination requires extra deburring operations which is time-consuming and costly. An effective way to inhibit interlayer burrs is to reduce the interlayer gap by preloading clamping force. In this paper, based on the theory of plates and shells, a mathematical model of interlayer gap with bidirectional clamping forces was established. The relationship between the upper and lower clamping forces was investigated when the interlayer gap reaches zero. The optimization of the bidirectional clamping forces was performed to reduce the degree and non-uniformity of the deflections of the stacked plates. Then, the finite element simulation was conducted to verify the mathematical model. Finally, drilling experiments were carried out on 2024-T3 aluminum alloy stacked plates based on the dual-machine-based automatic drilling and riveting system. The experimental results show that the optimized bidirectional clamping forces can significantly reduce the burr heights. The work in this paper enables us to understand the effect of bidirectional clamping forces on the interlayer gap and paves the way for the practical application.

Dynamic Transmission Error Measurements From Spur Gear Pairs Having Tooth Indexing Errors

2017 ◽  
Author(s):  
Brian Anichowski ◽  
Ahmet Kahraman ◽  
David Talbot
Keyword(s):  
High Speed ◽  
Transient Behavior ◽  
Transmission Error ◽  
Spur Gear ◽  
Spur Gears ◽  
Transient Effects ◽  
Dynamic Factors ◽  
Frequency Domains ◽  
Error Dynamic ◽  
Dynamic Transmission Error

This paper complements recent investigations [Handschuh et al (2014), Talbot et al (2016)] of the influences of tooth indexing errors on dynamic factors of spur gears by presenting data on changes to the dynamic transmission error. An experimental study is performed using an accelerometer-based dynamic transmission error measurement system incorporated into a high-speed gear tester to establish baseline dynamic behavior of gears having negligible indexing errors, and to characterize changes to this baseline due to application of tightly-controlled intentional indexing errors. Spur test gears having different forms of indexing errors are paired with a gear having negligible indexing error. Dynamic transmission error of gear pairs under these error conditions is measured and examined in both time and frequency domains to quantify the transient effects induced by these indexing errors. Both measurements indicate clearly that the baseline dynamic response, dominated by well-defined resonance peaks and mesh harmonics, are complemented by non-mesh orders of transmission error due the transient behavior induced by indexing errors.

The Mathematical Model of Simulative Calculation for the Process of Airbag Landing

2014 ◽  
Vol 635-637 ◽  
pp. 228-232
Author(s):  
Jian He ◽  
Ji Sheng Ma ◽  
Da Lin Wu
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Finite Element Simulation ◽  
Calculation Method ◽  
Low Cost ◽  
Analytical Analysis ◽  
Heavy Equipment ◽  
Element Simulation ◽  
The Mathematical Model

Airbag is widely used in heavy equipment dropped field with its efficient cushion performance and low cost. The calculation method used now for the process of airbag landing mainly is simulative calculation: analytical analysis and finite element simulation, but there are less systematic introduction for the mathematical model behind these methods in past papers. This paper mainly does the summary for the mathematical model of vented airbag which is usually used.

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