Shape Optimization of Cam Profiles Using a B-Spline Representation

1989 ◽  
Vol 111 (2) ◽  
pp. 195-201 ◽  
Author(s):  
E. Sandgren ◽  
R. L. West

An arbitrary acceleration profile for the cam follower acceleration is generated using a B-spline representation. The control point locations for the B-spline become the design variables in the nonlinear programming problem. The B-spline representation provides for local control of the acceleration profile which is required in order to generate reliable optimization results. Constraints are imposed in order to place appropriate limits on the contact stress, lift, duration, acceleration, jerk, radius of curvature, manufacturing requirements, and to avoid cam-follower separation. The objective function may take on a number of forms depending upon the design requirements. The optimization is carried out with a gradient based penalty function algorithm. A specific example is presented in which the flow area is maximized for an internal combustion engine.

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
J. K. Jiang ◽  
Y. R. Iwai

This paper presents an improved method for dynamically-compensated (tuned) cam design by minimizing or restricting vibrations in high-speed cam-follower systems. Using this approach, cams can be synthesized with a variety of design requirements and reduced residual vibrations. An example of the dynamically-compensated B-spline method illustrates the application process and demonstrates the improvement effect. While preserving the features of the B-spline method, the improved design method allows the cams to satisfy requirements, such as pressure angle, radius of curvature, and contact stress, and also reduces the residual vibrations caused by deviations in actual cam speed or system damping ratio from their design values.


Author(s):  
Eleftherios I. Amoiralis ◽  
Ioannis K. Nikolos

In this work FFD technique is compared to the classical parameterization technique using B-Spline curves by performing inverse airfoil design tests, with a Differential Evolution (DE) algorithm to serve as the optimizer. The criteria of the comparison between the two techniques are the achieved accuracy in the approximation of the reference pressure distribution and the convergence behavior of the optimization algorithm. Experiments are presented, comparing FFD to B-Spline techniques under the same flow conditions, for various numbers of design variables.


2018 ◽  
Vol 57 (2) ◽  
pp. 931-937 ◽  
Author(s):  
Samreen Abbas ◽  
Malik Zawwar Hussain ◽  
Misbah Irshad

2015 ◽  
Vol 119 (1222) ◽  
pp. 1513-1539 ◽  
Author(s):  
J. W. Lim

AbstractThis design study applied parameterisation to rotor blade for improved performance. In the design, parametric equations were used to represent blade planform changes over the existing rotor blade model. Design variables included blade twist, sweep, dihedral, and radial control point. Updates to the blade structural properties with changes in the design variables allowed accurate evaluation of performance objectives and realistic structural constraints – blade stability, steady moments (flap bending, chord bending, and torsion), and the high g manoeuvring pitch link loads. Performance improvement was demonstrated with multiple parametric designs. Using a parametric design with advanced aerofoils, the predicted power reduction was 1·0% in hover, 10·0% at μ = 0·30, and 17·0% at μ = 0·40 relative to the baseline UH-60A rotor, but these were obtained with a 35% increase in the steady chord bending moment at μ = 0·30 and a 20% increase in the half peak-to-peak pitch link load during the UH-60A UTTAS manoeuvre Low vibration was maintained for this design. More rigorous design efforts, such as chord tapering and/or structural redesign of the blade cross section, would enlarge the feasible design space and likely provide significant performance improvement.


Author(s):  
Sriram Shankaran ◽  
Brian Barr

The objective of this study is to develop and assess a gradient-based algorithm that efficiently traverses the Pareto front for multi-objective problems. We use high-fidelity, computationally intensive simulation tools (for eg: Computational Fluid Dynamics (CFD) and Finite Element (FE) structural analysis) for function and gradient evaluations. The use of evolutionary algorithms with these high-fidelity simulation tools results in prohibitive computational costs. Hence, in this study we use an alternate gradient-based approach. We first outline an algorithm that can be proven to recover Pareto fronts. The performance of this algorithm is then tested on three academic problems: a convex front with uniform spacing of Pareto points, a convex front with non-uniform spacing and a concave front. The algorithm is shown to be able to retrieve the Pareto front in all three cases hence overcoming a common deficiency in gradient-based methods that use the idea of scalarization. Then the algorithm is applied to a practical problem in concurrent design for aerodynamic and structural performance of an axial turbine blade. For this problem, with 5 design variables, and for 10 points to approximate the front, the computational cost of the gradient-based method was roughly the same as that of a method that builds the front from a sampling approach. However, as the sampling approach involves building a surrogate model to identify the Pareto front, there is the possibility that validation of this predicted front with CFD and FE analysis results in a different location of the “Pareto” points. This can be avoided with the gradient-based method. Additionally, as the number of design variables increases and/or the number of required points on the Pareto front is reduced, the computational cost favors the gradient-based approach.


Author(s):  
Snegdha Gupta ◽  
Harish Hirani

Quick response and rheological properties as a function of magnetic field are well known features of MR fluids which inspire their usage as brake materials. Controllable torque and minimum weight of brake system are the deciding functions based on which the viability of the MR brake against the conventional hydraulic brake system can be judged. The aim of this study is to optimize a multi-disk magneto-rheological brake system considering torque and weight as objective functions and geometric dimensions of conventional hydraulic brake as constraints. The electric current accounting magnetic saturation, MR gap, number of disk, thickness of disk, and outer diameter of disk have been considered as design variables. To model the behavior of MR Fluid, Bingham and Herschel Bulkley models have been compared. To implement these models in estimating the braking torque a modification in shear rate dependent component has been proposed. The overall design of MR brake has been optimized using a hybrid (Genetic algorithm plus gradient based) optimization scheme of MATLAB software.


Author(s):  
Hartmut Prautzsch ◽  
Wolfgang Boehm ◽  
Marco Paluszny

Author(s):  
F. Zhang ◽  
B. J. Gilmore ◽  
A. Sinha

Abstract Tolerance allocation standards do not exist for mechanical systems whose response are time varying and are subjected to discontinuous forcing functions. Previous approaches based on optimization and numerical integration of the dynamic equations of motion encounter difficulty with determining sensitivities around the force discontinuity. The Alternating Frequency/Time approach is applied here to capture the effect of the discontinuity. The effective link length model is used to model the system and to account for the uncertainties in the link length, radial clearance and pin location. Since the effective link length model is applied, the equations of motion for the nominal system can be applied for the entire analysis. Optimization procedure is applied to the problem where the objective is to minimize the manufacturing costs and satisfy the constraints imposed on mechanical errors and design variables. Examples of tolerance allocation are presented for a single cylinder internal combustion engine.


2021 ◽  
pp. 41-47
Author(s):  
Vladimir Tupov ◽  
O. Matasova

Insertion losses as the main characteristic that mathematically describes the acoustic efficiency of a noise silencer has been considered. This characteristic shows the reduction of noise generated by its source, in particular by the internal combustion engine’s exhaust system, at the control point as a silencer use result. Has been presented a mathematical description of the insertion losses, and have been considered parameters necessary for calculating this characteristic. Has been demonstrated the analytical dependence of impedance for the sound emission by the exhaust system’s end hole from the coefficient of acoustic waves reflection by this hole. The performed analysis of the widely used formulas for calculating the coefficient of sound reflection by the end hole has showed their insufficient accuracy for project designs performing. Have been proposed calculation dependences providing high accuracy for calculations of the reflection coefficient modulus, and the attached length of the channel end hole without a flange in the entire range of the existence of plane waves in it. It has been shown that the end correction of this hole at ka = 0 is 0.6127, and not 0.6133, as it was mistakenly believed until now in world acoustics. Has been proposed a method for calculation the exhaust noise source internal impedance. This method more accurately, in comparison with the already known ones, describes the acoustic processes in the internal combustion engine’s exhaust manifold, thanks to increases the accuracy of calculation the silencer acoustic efficiency, that allows develop the silencer at the early stages of the design of an automotive internal combustion engine.


2021 ◽  
pp. 1-25
Author(s):  
S. Shitrit

Abstract The aerodynamic performance of conventional aircraft configurations are mainly affected by the wing and horizontal tail. Drag reduction by shape optimisation of the wing, while taking into account the aircraft trimmed constraint, has more benefit than focusing solely on the wing. So in order to evaluate this approach, the following study presents results of a single and multipoint aerodynamic shape optimisation of the wing-body-tail configuration, defined by the Aerodynamic Design Discussion Group (ADODG). Most of the aerodynamic shape optimisation problems published in the last years are focused mainly on the wing as the main driver for performance improvement, with no trim constraint and/or excess drag obtained from the fuselage, fins or other parts. This work partially fills this gap by an investigation of RANS-based aerodynamic optimisation for transonic trimmed flight. Mesh warping and geometry parametrisation is accomplished by fitting the multi-block structured grid to a B-spline volumes and performing the mesh movement by using surface control points embedded within the free-form deformation (FFD) volumes. A gradient-based optimisation algorithm is used with an adjoint method in order to compute the derivatives of the objective and constraint functions with respect to the design variables. In this work the aerodynamic shape optimisation of the CRM wing-body-tail configuration is investigated, including a trim constraint that is satisfied by rotating the horizontal tail. The shape optimisation is driven by 432 design variables that envelope the wing surface, and 120 shape variables for the tail, as well as the angle of attack and tail rotation angles. The constraints are the lift coefficient, wing’s thickness controlled by 1,000 control points, and the wing’s volume. For the untrimmed configuration the drag coefficient is reduced by 5.76%. Optimising the wing with a trim condition by tail rotation results in shock-free design with a considerably improved drag, even better than the untrimmed-optimised case. The second optimisation problem studied is a single and multi-point lift constraint drag minimisation of a gliding configuration wing in transonic viscous flow. The shock is eliminated, reducing the drag of the untrimmed configuration by more than 60%, using 192 design variables. Further robustness is achieved through a multi-point optimisation with more than 45% drag reduction.


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