OPTIMUM SYNTHESIS OF FUNCTION-GENERATING SLIDER-CRANK MECHANISM BASED ON CLOSED-FORM SOLUTION USING FIVE DESIGN PARAMETERS

Serpentine belt drive systems with spring-loaded tensioners are now widely used in automotive engine accessory drive design. The steady state tension in each belt span is a major factor affecting belt slip and vibration. These tensions are determined by the accessory loads, the accessory drive geometry, and the tensioner properties. This paper focuses on the design parameters that determine how effectively the tensioner maintains a constant tractive belt tension, despite belt stretch due to accessory loads and belt speed. A nonlinear model predicting the operating state of the belt/tensioner system is derived, and solved using (1) numerical, and (2) approximate, closed-form methods. Inspection of the closed-form solution reveals a single design parameter, referred to as the “tensioner constant,” that measures the effectiveness of the tensioner. Tension measurements on an experimental drive system confirm the theoretical predictions.

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A New Accurate Closed-Form Analytical Solution for Junction Temperature of High-Powered Devices

Journal of Electronic Packaging ◽

10.1115/1.4026352 ◽

2014 ◽

Vol 136 (1) ◽

Cited By ~ 3

Author(s):

J. H. L. Ling ◽

A. A. O. Tay

Keyword(s):

Analytical Solution ◽

Closed Form ◽

Material Properties ◽

Heat Dissipation ◽

Field Effect Transistors ◽

Closed Form Solution ◽

Form Solution ◽

Junction Temperature ◽

Design Parameters ◽

Closed Form Analytical Solution

The peak junction temperature has a profound effect on the operational lifetime and performance of high powered microwave devices. Although numerical analysis can help to estimate the peak junction temperature, it can be computationally expensive and time consuming when investigating the effect of the device geometry and material properties on the performance of the device. On the other hand, a closed-form analytical method will allow similar studies to be done easily and quickly. Although some previous analytical solutions have been proposed, the solutions either require over-long computational times or are not so accurate. In this paper, an accurate closed-form analytical solution for the junction temperature of power amplifier field effect transistors (FETs) or monolithic microwave integrated circuits (MMICs) is presented. Its derivation is based on the Green's function integral method on a point heat source developed through the method of images. Unlike most previous works, the location of the heat dissipation region is assumed to be embedded under the gate. Since it is a closed-form solution, the junction temperature as well as the temperature distribution around the gate can be easily calculated. Consequently, the effect of various design parameters and material properties affecting the junction temperature of the device can be easily investigated. This work is also applicable to multifinger devices by employing superposition techniques and has been shown to agree well with both numerical and experimental results.

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A Closed-Form Solution to the Crank Position Corresponding to the Maximum Velocity of the Slider in a Centric Slider-Crank Mechanism

Journal of Mechanical Design ◽

10.1115/1.2181997 ◽

2005 ◽

Vol 128 (3) ◽

pp. 654-656 ◽

Cited By ~ 4

Author(s):

W. J. Zhang ◽

Q. Li

Keyword(s):

Closed Form ◽

Classical Problem ◽

Closed Form Solution ◽

Maximum Velocity ◽

Form Solution ◽

Machine Design ◽

Rotary Engine ◽

Engine Systems ◽

Crank Mechanism

This paper revisits a classical problem in kinematics, specifically determination of the crank position corresponding to the maximum velocity of the slider in the centric slider-crank mechanism. This position is often critical in designing products constructed using the slider-crank mechanism, e.g., industrial sewing machinery, rotary engine systems, etc. In current literature, the numerical, graphical, or approximate closed-form solution to this problem is available. In this paper, an exact closed-form solution is derived. With this new closed-form solution, it is found that there exist significant errors in an approximate closed-form solution which can be found from many machine design text books for a practica1 use.

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Closed-Form Steady-State Response Solution of the Twin Rotor Damper and Experimental Validation

Journal of Vibration and Acoustics ◽

10.1115/1.4035134 ◽

2017 ◽

Vol 139 (2) ◽

Cited By ~ 3

Author(s):

Richard Bäumer ◽

Uwe Starossek

Keyword(s):

Steady State ◽

Closed Form ◽

Closed Form Solution ◽

Form Solution ◽

Design Parameters ◽

Control Force ◽

Steady State Response ◽

Active Mass ◽

State Response ◽

Twin Rotor

In previous research, the twin rotor damper (TRD), an active mass damper, was presented including control algorithms for monofrequent vibrations. In a preferred mode of operation, the continuous rotation mode, two eccentric masses rotate in opposite directions about two parallel axes with a mostly constant angular velocity. The resulting control force is harmonic. Within this paper, the steady-state response of a single-degree-of-freedom (SDOF) oscillator subjected to a harmonic excitation force with and without the TRD is studied. A closed-form solution is presented and validated experimentally. It is shown that the TRD provides damping to the SDOF oscillator until a certain frequency ratio is reached. The provided damping is not only dependent on the design parameters of the TRD but also depends on the steady-state vibration amplitude. The solution serves as a powerful design tool for dimensioning the TRD. The analytical closed-form solution is applicable for other active mass dampers.

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Finite Kinematic Synthesis of a Cycloidal-Crank Mechanism for Function Generation

Journal of Engineering for Industry ◽

10.1115/1.3427800 ◽

1970 ◽

Vol 92 (3) ◽

pp. 531-535 ◽

Cited By ~ 5

Author(s):

S. N. Kramer ◽

G. N. Sandor

Keyword(s):

Closed Form ◽

Closed Form Solution ◽

Optimization Method ◽

Gear Ratio ◽

Form Solution ◽

Complex Numbers ◽

Kinematic Synthesis ◽

Function Generation ◽

Approximate Function ◽

Crank Mechanism

The method of complex numbers is applied towards the kinematic synthesis of a planar geared five-bar cycloidal-crank mechanism for approximate function generation with finitely separated precision points. It is shown that up to 10 precision points can be obtained, and a closed-form solution is presented which yields up to 6 different mechanisms with a 6-point approximation. In this method, the designer has control over the design of the cycloidal crank regarding gear ratio and configuration. The method has been programmed for automatic digital computation on the IBM-360 system, and the program is made available to interested readers. An optimization method utilizing iterative application of the closed-form solution is outlined.

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