Secondary Inertia Research Articles

A new closed-form method for inertia force and moment calculation in reciprocating piston engine design

The piston crank mechanism is an important component of a reciprocating piston engine. It is an inherent vibration system, and as such, the calculation of unbalance quantity is a critical procedure in balancing mechanism design, which is adopted to balance inertia loading. The traditional method usually applies a Taylor series expansion with the crank-conrod ratio, then a Fourier transform with the crank angle. The Taylor expansion generally ignores the influence on calculations resulting from the high order terms. However, the high order terms of the Taylor expansion will also contribute to the low order terms in the Fourier series. This will induce poor precision in the inertia loading calculation, especially in a high crank-conrod ratio engine. Thus, this paper proposes a new closed-form method, which only adopts a Fourier transformation for the calculation. The coefficients of the Fourier transformation terms contain the contributions of all order terms of the crank-conrod ratio. Therefore, we named it as a closed-form method. Compared with the traditional method, the closed-form method improves the numerical accuracy of the secondary reciprocating inertia force by 1.5%–4%, when the crank-conrod ratio varies from 0.25 to 0.4. Using this new closed-form method to design a balancing mechanism, the primary and secondary reciprocating inertia forces can be completely balanced. For an engine, where the primary and secondary inertia forces are balanced, the ratio of the residual inertia force to the total inertia force using the traditional method is 1.5%, while the ratio decreases to 0.5% using the closed-form method. The closed-form method is independent of engine configurations, including centric and eccentric engines, and single and multi-cylinder engines. Examples of applications using the proposed method are provided.

An extended Reynold equation applicable to high reduced Reynolds number operation of journal bearings

The introduction of this paper serves as a review of previous studies on extending the Reynolds equation. This paper develops an extended Reynolds equation and includes turbulence and inertia effects. Use of low viscosity lubricants and/or high rotational speed applications yield high Reynolds and high reduced Reynolds numbers. Our approach fully realizes the convective inertia effects on the static and dynamic properties of journal bearings as nonlinear with reduced Reynolds number. Two types of temporal inertia terms are identified for the first time: primary and secondary, in both laminar and turbulent regimes. The contribution of the secondary inertia effects can be up to 30% of the lubricant added mass coefficients. Lubricant added mass coefficients are potentially comparable to journal mass.

Dynamics of a 3dof torsional system with a dry friction controlled path

A three-degrees of freedom semi-definite torsional system representing an automotive driveline is studied in presence of a torque converter clutch that manifests itself as a dry friction path. An analytical procedure based on the linear system theory is proposed first to establish the stick-to-slip boundaries. Smoothened and discontinuous Coulomb friction formulations are then applied to the nonlinear system, and the differential governing equations are numerically solved given harmonic torque excitation and a mean load. Time domain histories illustrating dry friction-induced stick–slip motions are predicted for different saturation torques and system parameters. Approximate analytical solutions based on distinct states are also developed and successfully compared with numerical studies. Analysis shows that the conditioning factor associated with the smoothened friction model (hyperbolic tangent) must be carefully selected. Then nonlinear frequency responses are constructed from cyclic time histories and the stick–slip boundaries predictions (as yielded by the linear system theory) are confirmed. In particular, the effect of secondary inertia is analytically and numerically investigated. Results show that the secondary inertia has a significant influence on the dynamic response. A quasi-discontinuous oscillation is found with the conventional bi-linear friction model in which the secondary inertia is ignored. Finally, our methods are successfully compared with two benchmark analytical and experimental studies, as available in the literature on two-degrees of freedom translational systems.

Effect of Gas Forces on Parametrically Excited Torsional Vibrations of Reciprocating Engines

In the past the effects of ignoring the variable inertia characteristics of reciprocating engines on the accuracy of torsional vibration calculations were considered to be negligible. The associated secondary resonances tended to be dismissed by most engineers as interesting but of no importance. The situation changed in recent years, since there was evidence of the existence of the secondary inertia effects, which could have contributed to a number of otherwise inexplicable crankshaft failures in large multi-cylinder marine diesel engine systems. In view of these facts, a mathematical model is derived with key nondimensional parameters for the analysis of the effect of gas forces on the motion of the variable inertia system. The complex waveform responses are examined in detail within the range of speeds of engine rotation at which adverse effects are known to have occurred in practice. The effects on the parametrically excited motion of the system are investigated at a particular speed of the crankshaft rotation due to the action of external excitations with respect to changes in phase angle and inertia ratio. It is shown that under certain circumstances, interaction of secondary resonance effects with the excitations can be serious for torsional vibration. General comments on Draminsky's work in the light of present investigations are included.

The influence of prepregnancy body mass index on labor complications

To investigate the influence of Body Mass Index on the incidence of labor complications in a population of women with a normal pregnancy. From a local database, information on maternal weight and height was extracted concerning 4258 women who had an uncomplicated pregnancy. After calculation and stratification with respect to Body Mass Index, this was retrospectively related to labor interventions and complications. High Body Mass Index was related to more oxytocin infusion and early amniotomy, but not to vacuum extraction or cesarean section. Primary inertia and, to a minor degree, cephalopelvic disproportion and secondary inertia were seen more often in women with high Body Mass Index. Overweight (25.0<=BMI<30.0) and obesity (BMI>=30.0) are only weak predictors of labor complications, given a normal pregnancy. However, the heavy use of labor augmentation indicates that obese women should not be recommended to give birth in an ABC-clinic or at home.

Secondary Inertia Effects in the Torsional Vibration of Reciprocating Engines—A Literature Review

It has been known for some time that the torsional vibration of reciprocating engines and pumps cannot be modelled accurately by representing the reciprocating mechanism by a constant inertia. There have been many publications describing better models than those that use constant inertia and these indicate that the effective inertia of a reciprocating mechanism varies with angular position. The major component of this variation is a twice per revolution cyclic effect—hence the term ‘secondary inertia’. The consequences of this secondary inertia effect can be serious for torsional vibration causing ‘secondary resonance,’ and even instability. This paper contains a review of the current literature on the subject and introduces some recent work by the authors.

Parturition and Pelvic Fracture

Thirty-four women with a history of pelvic fracture gave birth. Ten had experienced increasing or recurrent pain during the course of their pregnancy. Twenty-seven women gave birth without complications, including 13 patients with displaced pelvis. In only one patient was cesarean section carried out on suspicion of disproportion. Cesarean section was carried out in another case because of resymphysiolysis and in one because of other complications to the pregnancy. Two underwent vacuum extraction because of secondary inertia, but subsequently they gave birth by the vaginal route without complications. In connection with pregnancy and birth, 2 patients had resymphysiolysis. They were the only patients of 8 with symphysiolysis who had undergone osteosynthesis, and both had had the material removed before pregnancy. It is concluded that separation of the symphysis in a pelvic fracture is a more serious complication in subsequent parturition than is displacement of the bony birth canal.

Parturition and pelvic fracture. Follow-up of 34 obstetric patients with a history of pelvic fracture.

Thirty-four women with a history of pelvic fracture gave birth. Ten had experienced increasing or recurrent pain during the course of their pregnancy. Twenty-seven women gave birth without complications, including 13 patients with displaced pelvis. In only one patient was cesarean section carried out on suspicion of disproportion. Cesarean section was carried out in another case because of resymphysiolysis and in one because of other complications to the pregnancy. Two underwent vacuum extraction because of secondary inertia, but subsequently they gave birth by the vaginal route without complications. In connection with pregnancy and birth, 2 patients had resymphysiolysis. They were the only patients of 8 with symphysiolysis who had undergone osteosynthesis, and both had had the material removed before pregnancy. It is concluded that separation of the symphysis in a pelvic fracture is a more serious complication in subsequent parturition than is displacement of the bony birth canal.

Natural vibrations of shear wall buildings on flexible supports

AbstractA shear wall building is considered as an assembly of plane and curvilinear shear walls tied together by floor slabs to act as a composite unit. Based on this conception and the continuous medium approach, the governing dynamic equations and boundary conditions are derived from energy principles, using Vlasov's theory of thin‐walled beams. All primary and secondary inertia forces, as well as the influence of elastic foundation flexibility, have been taken into consideration. A numerical solution of the dynamic equations is achieved by employing the Ritz‐Galerkin technique, yielding both natural frequencies and mode shapes. The technique is applicable to buildings containing coupled and non‐coupled, open section shear walls oriented in plan in any arbitrary manner. The use of the method is illustrated by the example of a complex building with unsymmetric plan, and the analytical natural frequencies of two shear wall building models are compared with those obtained experimentally by other investigators.

Free vibrations of open‐section shear walls

AbstractThe coupled torsional‐flexural vibration of open‐section shear walls, braced by connecting beams at each floor level, is analysed on the basis of Vlasov's theory of thin‐walled beams. The basic dynamic equations and boundary conditions are derived from Hamilton's principle, and a numerical solution obtained by the Ritz‐Galerkin method. In addition to the primary torsional and flexural inertias, secondary effects due to rotatory and warping inertia forces have also been taken into account. The method is suitable for both rigid and flexible base conditions.A series of numerical examples is presented in which analytical results are compared with available experimental data, and the effects of secondary inertia forces, base flexibility and connecting beams upon the vibration characteristics of such shear walls are examined for two different structural forms.

Intranasal oxytocin in obstetrics.

Brief exposures to synthetic oxytocin, applied intranasally as a spray, were used in 74 cases of induced labor, 138 cases for enhancement of labor, 39 cases for testing sensitivity to oxytocin, and 15 cases for enhancement of prelabor. The purpose was to obtain a mild stimulation of uterine activity, usually for 15 to 20 minutes. The method of application is remarkably simple, and the authors recommend it as having a wide degree of safety in determining the degree of labor readiness of a patient at term, in inducing labor (in combination with amniotomy), and especially in combating mild degrees of secondary inertia which appear during labor.

Influence of Secondary Inertia Terms on Natural Frequencies of Rotating Beams

Abstract The equations of small motion of a straight cantilever beam attached to the rim of a rotating disk are determined assuming the Bernoulli-Euler theory of bending and the Saint Venant theory of torsion are valid, the mass and elastic axes coinciding and retaining all inertia terms. Influence of the secondary inertia terms on the fundamental torsional and lateral frequencies is then examined at two angular settings for a uniform beam having a length to disk-radius ratio in the range usually encountered in gas-turbine buckets and axial-flow compressor blades.

The graphic analysis of labor

1. The efficacy of plotting cervical dilatation against time as a method of graphically analyzing labor is demonstrated.2. The sigmoid characteristics of the curves thus obtained in primiparas at term are illustrated.3. The first stage of labor is divided into four phases based on the graphic alterations noted. Their respective limits are defined.4. Primary and secondary inertia are redefined in terms of deviation from the “normal.”5. The application of this method to the study of the effects of sedation, stimulation, anesthesia, etc., upon the course of labor is indicated.6. The value of this method for the study of individual labors, in progress, is stressed.