Cam-follower System Research Articles

Comparison of Polynomial Cam Profiles and Input Shaping for Driving Flexible Systems

Polynomial profiles can be used as reference commands to limit induced vibration in flexible systems. Due to their ease of design and low-pass filtering effects, polynomial profiles are often found in cam-follower systems. Polynomial profiles have also been used as smooth reference commands for automated machines. However, despite extensive work to develop and improve such profiles, inherent tradeoffs still exist between induced vibration, rise time, and ease of design. Input shaping is an alternative method for generating motion commands that reduce residual vibration. This paper compares polynomial profiles to input-shaped commands for the application of reducing vibration in flexible systems. Analyses using Laplace transforms reveal that input shapers suppress vibration at regularly spaced frequencies. However, polynomial profiles do not share this property. Simulations and experimental results show that input shaping improves rise time and reduces residual vibration in comparison to polynomial profiles.

A Versatile Cam Profile for Controlling Interface Force in Multiple-Dwell Cam-Follower Systems

Cam follower systems are widely used in manufacturing because of their precise motion and ability to easily dwell. The cam typically drives a follower in some precise motion needed to accomplish a manufacturing task. Presented in this paper is a closed-form modified trapezoidal cam motion function with adjustable positive and negative acceleration. The profile is suitable for multiple-dwell cam and follower applications. The profile is particularly applicable to high-speed cams in which the follower acceleration is a primary design objective. The main benefit of the profile is that it allows cam designers to easily set limits on the positive and negative acceleration to achieve design objectives. Additional benefits are that the cycle jerk is continuous and that the cam designer can control the maximum magnitude of jerk. The motion program is presented in closed-form for easy implementation in standard equation-solver or spreadsheet software. Dynamic and harmonic analyses are presented to illustrate the benefits of the profile.

A Versatile Acceleration-Based Cam Profile for Single-Dwell Applications Requiring Cam-Follower Clearance During Dwell

Presented in this paper is an asymmetric acceleration-derived cam motion program suitable for single-dwell cam-follower systems with clearance between the cam and follower during dwell. Asymmetric rise and fall is included as this is desirable in certain manufacturing operations and machines that require a quick rise or fall. The motion program for the cam-follower actuation is derived from the follower acceleration so that designers can control the ratio of the magnitudes of positive and negative accelerations. This provides cam designers more control over the cam-follower interface force and therefore more control over factors such as cam wear and the potentially destructive phenomenon known as “follower jump.” The motion program used to close and open the clearance gap is derived from a velocity function, allowing more control of follower inertia during the important clearance closing event. The motion program is presented in closed-form, suitable for implementation in standard engineering equation-solving software.

Minimizing the cycle time in multiple-dwell cams

Presented in this article are closed-form kinematic equations that give the minimum cycle time for multiple-dwell cam-follower systems subject to acceleration and jerk constraints set by the user. Cam-driven machines are used extensively in manufacturing because of their low cost, great precision and high production rates when compared with alternatives. Since they are frequently used in mass production operations, there is a need for minimizing their cycle time to increase manufacturing throughput and reduce capital costs for machines and facilities. Their widespread use means that there is the potential for significant improvement in overall manufacturing efficiency. The incorporation of acceleration and jerk limits in the kinematic formulation ensures minimal cycle time without compromising the operational limits of the manufacturing machines. The equations are given in a form suitable for spreadsheet or equation-solver programs, making it easy for the cam designer to generate an arbitrary number of data points for cam manufacturing. Multiple-dwell cams are particularly well suited for manufacturing operations; therefore, the intended audience of this paper is cam designers in the manufacturing sector.

FROM COMPLETE TO INCOMPLETE CHATTERING: A NOVEL ROUTE TO CHAOS IN IMPACTING CAM-FOLLOWER SYSTEMS

In this paper we discuss a novel route to chaos in cam-follower systems, a class of mechanical devices of relevance in applications. We show that a sudden transition to chaos is observed when a complete chattering motion (characterized theoretically by infinitely many impacts) is interrupted. Using numerical computations and semi-analytical methods we show that a cascade of grazing bifurcations is then originated, leading the system into chaos. This novel phenomenon is described using an appropriate model that is shown to predict correctly the numerical observations. The results are used to explain the transition to chaos observed in an experimental cam-follower system recently presented in the literature.

Application of the nonsmooth dynamics approach to model and analysis of the contact-impact events in cam-follower systems

The dynamic modeling and analysis of planar rigid multibody systems that experience contact-impact events is presented and discussed throughout this work. The methodology is based on the nonsmooth dynamics approach, in which the interaction of the colliding bodies is modeled with multiple frictional unilateral constraints. Rigid multibody systems are stated as an equality of measures, which are formulated at the velocity-impulse level. The equations of motion are complemented with constitutive laws for the forces and impulses in the normal and tangential directions. In this work, the unilateral constraints are described by a set-valued force law of the type of Signorini’s condition, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb’s law for dry friction. The resulting contact-impact problem is formulated and solved as an augmented Lagrangian approach, which is embedded in the Moreau time-stepping method. The effectiveness of the methodologies presented in this work is demonstrated throughout the dynamic simulation of a cam-follower system of an industrial cutting file machine.

On the improvement design of dynamic characteristics for the roller follower of a variable-speed plate cam mechanism

Without modifying the cam contour, a cam mechanism with a variable input speed trajectory offers an alternative solution to flexibly achieve kinematic and dynamic characteristics, and then decrease the follower’s residual vibration. Firstly, the speed trajectory of cam is derived by employing Bezier curve, and motion continuity conditions are investigated. Then the motion characteristics between the plate cam and its roller follower are derived. To analyze the residual vibration, a single degree of freedom dynamic model of the elastic cam-follower system is introduced. Based on the motion equation derived from the dynamic model, the residual vibration of the follower is yielded. The design procedure to improve the kinematic and dynamic motion characteristics is presented and two design examples with discussions are provided. Finally, the simulations of the kinematic and dynamic models by ADAMS are carried out and verified that the design models as well as the performances of the mechanism are feasible.

Diagnosis of oscillating pressure-driven flow in a microdiffuser using micro-PIV

In this study, the characteristics of oscillating pressure-driven flow in a microdiffuser are examined by μPIV (micro Particle Image Velocimetry) diagnostics. Utilizing a cam-follower system, a dynamic pressure generator is built in-house to provide a time-varying sinusoidal pressure source. Three parameters are examined experimentally: the excitation frequency, the cam size, and the half-angle of the microdiffuser. Driven by oscillating pressure, we find that there exists an optimal half-angle such that maximum net flow is attained in the expansion direction. Contrarily to the prediction of hydraulics theory which only considers steady flow, flow in the microdiffuser of the optimal half-angle does not necessarily remain attached. Rather, maximum net flow can also occur in microdiffusers where vortices retain a slender shape. When vortex bubbles are slender, the μPIV results reveal that the core flow accelerates to a higher forward velocity during the first half of the cycle and flow rectification is actually enhanced. Due to the three-dimensional flow structure, fluid is drawn out of the vortices near the reattachment point to join the core flow and consequently magnifies the forward flow. As the half-angle increases, vortices become rounder and the core flow is drastically narrowed to reduce flow rectification.

Synthesis of cam profile using classical splines and the effect of knot locations on the acceleration, jump, and interface force of cam follower system

Large positive acceleration against a load creates cam follower interface force that can cause excessive wear. Negative acceleration tends to reduce the cam follower interface force, and if the negative acceleration is sufficiently large, jump between the cam and follower can occur. Hence, these are the two main concerns of cam designers. This study presents a new approach to adjust the acceleration, interface force, and jump in the early phase of cam design. Knot locations of polynomial pieces of spline curves are considered as design variables which gives variety of cam profiles. Here, design process starts from displacement profile and there is no need for predefined acceleration curves. A single dwell cam displacement function is defined by classical spline curve, made up of four polynomial pieces that are tied together at their ends, called knots. Specifications of these knots are considered for synthesis and analysis of cam follower system. Mathematical relation between interface force and knot locations is presented as wear and jump models. These models are useful to reduce wear and jump by proper placement of the knots on the basis of interface force. By dynamic simulation of cam follower system, cam curves are drawn for different cases of knot locations and good resemblance was found with theoretical curves. This study suggests the cam designers have the added option to control the kinematic and dynamic quantities without changing the physical parameters of cam follower system.

Optimizing Cam Profiles Using the Particle Swarm Technique

Cam-follower systems are ideally suited for many machine applications that require a specific and an accurate output motion. The required follower motion is achieved by carefully designing the shape or profile of the cam. Modern profiles are typically synthesized by piecing together a set of trigonometric and/or polynomial functions that satisfy the constraints. For most problems, there are many profile solutions that satisfy the constraints. In this paper, a relatively new optimization technique known as particle swarm optimization (PSO) is applied to the optimization of two different cam problems. The first example is a single-dwell cam in which the magnitude of the negative acceleration is minimized. The second example is a cam with a constant velocity segment in which the cycle time is optimized. The intent is to show the method in two different settings so that the reader can extend it to the optimization of any cam-follower problem. To illustrate the method, first the PSO method is applied to a mathematical function with two independent variables. Then, the method is used to find the cam profile that provides the minimum acceleration in a single-dwell cam using three independent variables. Finally, it is applied to obtain the minimum cycle time of a cam with a constant velocity segment using cubic interpolations and seven or more independent variables. The PSO method was very successful in all the optimization problems discussed in this paper. In the first cam problem, it significantly lowered the level of negative acceleration, while maintaining the positive acceleration at a constrained upper limit. The optimization procedure for the second cam problem found a very elegant five-segment solution. This solution results no matter how many initial segments or independent variables are chosen so long as there are at least five segments. Presented in this paper is the particle swarm optimizing technique that is applicable to many aspects of cam design. Two diverse examples were presented that illustrate how the PSO method can be used effectively in the optimization of cam-follower problems. In both illustrative examples, the PSO method proved to be robust, easy to implement, and suitable for minimizing a wide variety objective functions applicable to the design of cam-follower systems.

Dynamic modelling and analysis of whirling motion in BTA deep hole boring process

In this study, an innovative mathematical approach to predict the whirling motion in Boring Trepanning Association (BTA) deep hole boring process is introduced. This approach was developed for boring bar-workpiece assembly in deep hole boring process. The interaction point in drilling operations between the tool cutting head and the workpiece in a deep hole machining process is dynamically resemblance to a cam follower system. In drilling, however, the excitation could be simulated as a wedge introduced between the cutting head and the workpiece system. The whirling motion is obtained by means of assumed mode method. The energy, kinetic and dissipation equations are formulated and the final equations are obtained by means of Lagrangian equations. The model, based on the notion that the interaction point was simulated as a wedge introduced between the boring bar and the workpiece, was able to predict the whirling motion at different location of the boring bar-workpiece assembly. A comparison is made with an experimental investigation of the whirling motion in the literature to verify the current analytical model. The comparison results show that the analytical model is able to mimic the actual experimental results.

Failure Analysis of a Cam–Follower System Affected by a Crack

The dynamic behavior of a cam–follower system can be altered by several errors. Errors occurring during working operation are induced by excessive load and inappropriate operating condition. In this article, an investigation on the dynamic behavior of a cam–follower system caused by the cam crack failure was carried out. The crack causes a stiffness reduction of the system. An analytical formulation of this time varying stiffness was derived. A quantification of the influence of this crack on the stiffness is carried out. The response showed amplitude modulation resulting from the presence of the crack.

The Dynamics of Regularized Discontinuous Maps with Applications to Impacting Systems

One-dimensional piecewise-smooth discontinuous maps (maps with gaps) are known to have surprisingly rich dynamics, including periodic orbits with very high period and bifurcation diagrams showing period-adding or period-incrementing behavior. In this paper we study a new class of maps, which we refer to as regularized one-dimensional discontinuous maps, because they give very similar dynamics to discontinuous maps and closely approximate them, yet are continuous. We show that regularized discontinuous maps arise naturally as limits of higher dimensional continuous maps when we study the global dynamics of two nonsmooth mechanical applications: the cam-follower system and the impact oscillator. We review the dynamics of discontinuous maps, study the dynamics of regularized discontinuous maps, and compare this to the behavior of the two mechanical applications which we model. We show that we observe period-adding and period-incrementing behavior in these two systems respectively but that the effect of the regularization is to lead to a progressive loss of the higher period orbits.

Synthesis, design and analysis of a novel variable lift cam follower system

This work proposes a novel variable lift cam follower system. Here follower lift varies according to input or camshaft speed. The system comprises a trapezoidal shape cam with ping finite spline curve as displacement profile. The height of the cam varies along the axis of the shaft and it slides in the axial direction so that the lift of the cam varies. Sliding motion of cam was executed by actuating mechanism and it works on principle of centrifugal actuation. When input speed varies, due to centrifugal force, actuator initiates linear axial movement of bush and cam on the shaft. This axial movement of cam varies the follower lift with respect to speed. Various components of proposed mechanism are designed and fabricated by proper processes and assembled together with suitable provisions. The system is tested experimentally and follower lift was measured using the computerised measuring system. Results show that the mechanism works properly and is useful to get variable lift. The proposed mechanism can be used in automotive engines as a valve train for variable valve actuation with necessary modifications.

Improving the B-Spline Method of Dynamically-Compensated Cam Design by Minimizing or Restricting Vibrations in High-Speed Cam-Follower Systems

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.

Addressing Cam Wear and Follower Jump in Single-Dwell Cam-Follower Systems With an Adjustable Modified Trapezoidal Acceleration Cam Profile

Presented is a modified trapezoidal cam profile with an adjustable forward and backward acceleration. The profile is suitable for single-dwell cam and follower applications. The main benefit of the profile is that it allows cam designers to choose easily a value for the maximum forward or maximum backward acceleration to achieve design objectives. An additional benefit of the profile is that it has a continuous jerk curve. Follower acceleration is one of the primary factors affecting cam wear and follower jump, two main concerns of cam designers. Large forward acceleration against a load creates cam-follower interface forces that can cause excessive wear. Backward acceleration tends to reduce the cam-follower interface force, and if the backward acceleration is sufficiently large, separation between the cam and follower (“follower jump”) can occur. The cam profile presented in this paper gives cam designers an easy way to adjust the maximum forward or backward acceleration to prevent these problems.

Active Chaos Control of a Cam-Follower Impacting System using FPIC Technique

In this paper, we apply a novel active control scheme to suppress chaotic behavior in a cam-follower impacting system using Fixed-Point Inducting Control or FPIC Technique. Namely, the input speed of the cam-follower system is actively controlled in order to reach a single-impact periodic motion. A cam-follower system characterized by a radial cam and a flat-faced follower is used as a representative example. High-order periodic-impact and chaotic motions are controlled varying the input speed of the cam-follower system. Stroboscopic and impact maps are used to select the suitable control parameters under which stable single-impact periodic responses are reached.

Experimental and Numerical Investigation of Coexistence, Novel Bifurcations, and Chaos in a Cam-Follower System

This paper is concerned with the experimental and numerical analysis of an important class of impacting systems in applications: cam-follower devices. Experiments are reported showing the occurrence of complex dynamical scenarios in these systems including coexistence, discontinuity-induced bifurcations, and chaos. The most notable phenomenon is the sudden transition to chaos detected in the system which is shown to be due to the interruption of a complete chattering sequence. Further insight is gained by performing numerical analysis of an appropriately derived model of the experimental setup. Simulation, continuation, and cell-to-cell mapping algorithms are used to gain a complete picture of the observed dynamics in excellent qualitative agreement with the experimental observations.

유전자 알고리즘을 이용한 원판 캠의 비 유막두께 최적화

The rate of wear of cam followers in a valve train system is mainly a function of contact stress between the cam and the follower, sliding velocity and hydrodynamic film thickness between the two mating surfaces. The wear or surface fatigue can be reduced by maximizing the elastohydrodynamic film thickness. In this paper, an attempt has been made to estimate the optimal specific film thickness of cam-follower system quantitatively. A general TES polynomial function with real values of exponents is developed and genetic algorithm (GA) is used as optimization techniques for maximizing the minimum specific film thickness. The optimization programs enumerate values of the exponents for synthesis of cam displacement curves. The results show that the minimum film thickness can be increased considerably, e.g. approximately 7% in this paper.

Motion adaptation of cam-follower systems by varying input speeds

Cam mechanisms are widely applied in automatic production machines. Variable cam speeds provide a flexible tool for adapting the follower motion to the working condition changes. The current study proposes the methods for generating the needed follower motion and adjusting to the required times of periods in the cam motion program. The Bezier function is used to express the cam speed trajectory, whose motion characteristics and boundary continuities are to be decided by the control points. An optimization design model for generating the required motion is then built to specify the control points of this trajectory. Also, the relations are developed that cope with connection continuities and period time managements among the motion periods of a complete cam rotation. Two design examples in component transferring and metal-sheet forming applications are given for illustrating the proposed design approaches.