A NOVEL DESIGN OF AN ELECTRIC POWER-ASSISTED BIKE BASED ON HELICAL GEARS

2017 ◽  
Vol 41 (5) ◽  
pp. 845-854
Author(s):  
Chung-Yu Tsai*
Keyword(s):  
Mathematical Model ◽  
Electric Power ◽  
Force Sensor ◽  
Helical Gear ◽  
Design Rule ◽  
Force Distribution ◽  
Electric Power Output ◽  
Helical Gears ◽  
Parameter Values ◽  
Novel Design

An electric power-assisted bike (EPAB) is a bicycle with an attached electric motor to assist with human pedaling, where the electric power output of the motor is provided in accordance with the pedaling-force. This makes the pedaling-force sensor (PFS), which is used to sense the human pedaling force, the critical device in the EPAB. Accordingly, the present study proposes a novel design for the PFS, comprising of a helical gear system and an annular magnet device. The study then develops a mathematical model for the force distribution on the helical gears, and provides a general design rule to determine the parameter values of the PFS which will prevent a self-lock situation. A prototype is produced to verify and demonstrate the proposed approach.

Structure Analysis of a Pre-Stressed Six-Axis Force Sensor

2014 ◽  
Vol 635-637 ◽  
pp. 772-775
Author(s):  
Zhi Jun Wang ◽  
Jing He ◽  
Wan Yu Liu ◽  
Li Zhan Xian
Keyword(s):  
Mathematical Model ◽  
Structure Analysis ◽  
Homogeneous Solution ◽  
Force Sensor ◽  
Force Distribution ◽  
Distribution Analysis ◽  
Structure Characteristics ◽  
Force Mapping ◽  
Particular Solution ◽  
The Mathematical Model

This study proposes a pre-stressed dual-layer six-axis force sensor with eight limbs, and discusses the structure analysis of the sensor. The number of measuring limbs is determined and the structure characteristics are introduced. Force distribution analysis of the sensor is presented based on the mathematical model and force mapping matrix. The forces on the measuring limbs are decomposed into particular solution and homogeneous solution. The results of the paper are useful for the development and further research of the pre-stressed six-axis force sensor.

Analysis of Plastic Helical Gear

2006 ◽  
Author(s):  
Toni Jabbour ◽  
Ghazi Asmar ◽  
Chadi Ghaith
Keyword(s):  
Mathematical Model ◽  
Real Number ◽  
Modulus Of Elasticity ◽  
Load Distribution ◽  
Large Deformations ◽  
Tooth Wear ◽  
Helical Gear ◽  
Contact Ratio ◽  
Helical Gears ◽  
The Real

The objective of this work is to present a mathematical model which studies helical gears made of a material with a small modulus of elasticity, when one or more pairs of teeth mesh prematurely during engagement. This phenomenon may lead to the modification of the load distribution on the teeth which are initially in contact and to a kind of interference causing additional tooth wear of the gear. In this case, the calculation of the contact ratio must account for the real number of pairs of teeth in contact. This is especially important when large deformations occur as is confirmed in the results presented to confirm the validity of the proposed method.

Development of the Dressing Software for Form Grinding Wheel Used for Grinding Involute Helical Gears

2010 ◽  
Vol 97-101 ◽  
pp. 3556-3559
Author(s):  
Jian Xin Su ◽  
Xiao Zhong Deng ◽  
Xiao Zhong Ren ◽  
Kai Xu
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Helical Gear ◽  
Grinding Wheel ◽  
Analytic Method ◽  
Factors Affecting ◽  
Helical Gears ◽  
Form Grinding ◽  
Wheel Profile ◽  
The Mathematical Model

On the basis of establishing the mathematical model of grinding wheel profile by means of analytic method, the grinding wheel profile was determined. Different factors affecting gear form grinding was analyzed by means of numerical simulation. The form grinding wheel dressing software for grinding helical gear was developed, and the instruction for dressing grinding wheel profile was generated. Wheel dressing results show that the dressing software is correct and feasible.

Gear transmission error outside the normal path of contact due to corner and top contact

1999 ◽  
Vol 213 (4) ◽  
pp. 389-400 ◽  
Author(s):  
R. G. Munro ◽  
L Morrish ◽  
D Palmer
Keyword(s):  
Dynamic Test ◽  
Theoretical Models ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear Transmission ◽  
The Novel ◽  
Transmission Systems ◽  
Helical Gears ◽  
Tooth Stiffness ◽  
Top Contact

This paper is devoted to a phenomenon known as corner contact, or contact outside the normal path of contact, which can occur in spur and helical gear transmission systems under certain conditions. In this case, a change in position of the driven gear with respect to its theoretical position takes place, thus inducing a transmission error referred to here as the transmission error outside the normal path of contact (TEo.p.c). The paper deals with spur gears only, but the results are directly applicable to helical gears. It systematizes previous knowledge on this subject, suggests some further developments of the theory and introduces the novel phenomenon of top contact. The theoretical results are compared with experimental measurements using a single flank tester and a back-to-back dynamic test rig for spur and helical gears, and they are in good agreement. Convenient approximate equations for calculation of TEo.p.c suggested here are important for analysis of experimental data collected in the form of Harris maps. This will make possible the calculation of tooth stiffness values needed for use in theoretical models for spur and helical gear transmission systems.

scholarly journals MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN INTERACTION WITH MIXED FUNCTIONAL RESPONSE

2012 ◽  
Vol 09 ◽  
pp. 334-340 ◽  
Author(s):  
MADA SANJAYA WS ◽  
ISMAIL BIN MOHD ◽  
MUSTAFA MAMAT ◽  
ZABIDIN SALLEH
Keyword(s):  
Mathematical Model ◽  
Functional Response ◽  
Food Chain ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Bifurcation Points ◽  
Dynamical Behaviors ◽  
Practical Life ◽  
Parameter Values ◽  
Chain Interaction

In this paper, we study mathematical model of ecology with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III functional response for predator and super predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviors of this model are investigated. Models for biologically reasonable parameter values, exhibits stable, unstable periodic and limit cycles. The dynamical behavior is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

Condition Monitoring Technology for Connecting Part and Sliding Part of Reciprocating Compressor

2017 ◽  
Author(s):  
Yoshifumi Mori ◽  
Takashi Saito ◽  
Yu Mizobe
Keyword(s):  
Mathematical Model ◽  
Natural Frequencies ◽  
Error Function ◽  
Connecting Rod ◽  
Value Analysis ◽  
Before And After ◽  
The Difference ◽  
Bending Modes ◽  
Parameter Values ◽  
The Mathematical Model

We focused on vibration characteristics of reciprocating compressors and constructed the mathematical model to calculate the natural frequencies and modes for crank angles and proposed a method to estimate the degree and the suspicious portion of failure by difference of temporal parameter values obtained using measuring data in operation and the mathematical model. In this paper, according to the proposed method, a case study is carried out using the field data, where the data were acquired before and after the failures occurred in the connecting parts of connecting rod, to prospect the difference between each parameter value for two operating states. Inspecting resonant characteristics each in the frequency response data relating to the natural frequencies for bending modes of the piston rod, we determined two resonant frequencies, which could correspond to the 1st and 2nd mode about bending of the piston rod. To equate the calculated each natural frequency from eigen value analysis based on the proposed model with each resonant frequency, we define the error function for the identified problem, namely optimum problem. In the identified results, it is found that some parameter values have much difference and the corresponding failure could occur around the connecting rod. We could show the possibility to detect both the change of the parameter values and the deterioration parts for two different kinds of the operating states by our proposed method.

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