Optimization of CAM
Optimization of CAM Follower Mechanism Linkage to Drive with Given Trajectory
Introduction
The cam follower mechanisms can be used to convert a rotary motion into controllable or oscillating motions. Automotive companies embrace the CAM and ECU (follower) technologies to lift actuation systems used in synchronizing intake and exhaust of gases in a combustion engine. The cam follower has been applied in cutting shapes and power transmission in manufacturing industries. Though various studies have been conducted on cam follower mechanisms, many efforts have been directed towards conventional mechanism also known as constant lift. Scholars such as Brown, Rong, and Boyle (2011) have been the masterminds of the lift mechanism with cam and electric powered actuator. Aspects to do with design are yet to be explored. These include; kinematic of the cam and performance characteristics. The next sections will deal with studies relating to existing lift mechanism variable, cam characteristics, follower synthesis and dynamic performance (Kumar & Michael, 2012).
Variable lift mechanisms
Variable lift valve plays a pivotal role in the performance of an engine. In 1975, General Motors Company carried methods on how to vary valve lift and reduce emission. It was established that to vary the valve lift; there was a need to minimize the amount of the load carried by the lift to keep the intake velocity high. In 1989, Honda invested in the variable technology system by designing low-speed engine valves (Zhu, Snyder, Wang & Guo, 2012). These engines were assumed to have positively contributed to the transport industry since good road manners were achieved, there was low fuel consumption, and the emission rate was low safeguarding the environment. Variable lift mechanism also includes a high lift that operates at high engine speeds to increase power output. This profile is applicable where high engine performance is needed. It requires as much air as possible. Automobile industries use different types of cam follower mechanism for variable valve lift. Codecogs (2017) presented the mechanism of infinitely variable transmission (IVT) which had some followers that rotatable mounted to a carrier plate.
Salient features of cam follower mechanism
The cam system is noncontinuous in nature and operates different profiles and shifts for each valve to produces an oscillation. The two cam follower is less electro-hydraulic and operates under low pressure. The valve lifts change by pressure variation. The electronic sensors operate the high and low-pressure lines as per the speed. Its cost is high, there is more friction and requires additional linkages. (Zhu, Snyder, Wang & Guo, 2012P). The oscillating cam follower requires electric powered actuator to help in motion and adjust power transmission to the camshaft. The conical cam is designed with a movable follower, DC motor, and a gear train. The cam system works by oscillation motion and has more friction; it is complex in construction and needs additional power transmission to adjust the camshaft (Paden& Moehlis, 2013).
Synthesis and design of cam follower mechanism
The cam follower design involves the synthesis of mechanisms to meet the kinematic requirements. Various mechanisms have been proposed for selecting and scaling mechanical devices. Authors De jalon and Bayo (2012) proposed graphical methods of synthesis when dealing with a limited number of precision points. Likaj and Shala (2013) developed an analytical approach to synthesis. Goris (2004) used the cam mechanism of motion and path generation that based on complex loop closure method to define a general approach for the synthesis of combined cam linkage systems to establish exact paths or motion. Mali, Maskar, Gawande, and Bagi (2012) cited computerization of numerical as a synthesis method.
The above methods guide rigid objects through a series of specified positions, obtain a specified output and input (functional generation), and force a linkage to move along a specified trajectory (path generation). However, these methods restrict the number of precision points. The radius of the curvature of the cam and the kinematics are paramount in designing a corresponding motion. Literally, issues that have been addressed by these authors range from design of cams with various side conditions such as interpolation, constant diameter, minimal acceleration or jerk, and constant dwells, curvature analysis of the roller follower cam mechanism, revolutionary and hyperboloidal surfaces, and general coordinated systems, geometric parameters of follower motion, the cam angles, velocity, the cam profile, the path of cutter, the pressure angle and the radius of curvature of the cam having concave, convex and flat portions. Kumar and Michael (2012) proposed ways of optimization of palar cams that run under high pressure. In this study, it was established that cam area minimization is reduced to solve nonlinear motion. Equations of cam contour show that motion curves are chosen arbitrarily by the designer to avoid replication impulse throughout the whole cycle.
Synthesis of cam profiles
Cam technology is widespread due to its nature of supporting various motions. Cam profiles are designed in a way that the standard motions such as cycloid, harmonic, modified harmonic, polynomial and trapezoidal are easy for the effective working process to accomplish tasks and projects (Zhu, Snyder, Wang & Guo, 2012). This works best when the approach selected is not extremely difficult. Mathematically, the cam profile was generated by the cubic periodicals and developed geometrical relations between optimum parameters and displacement profiles.
The optimization also aims at minimizing the cam disk area and increase acceleration. Valve trains can also be optimized using logarithms. Optimal control theory is applied in this case to create a framework that helps to control cam mechanism (Likaj & Shala, 2013). Applying kinematics, the motion characteristics of the follower can be improved using the optimal control to the cam speed. The smoothing of curves in the creation of cam profiles, requirements such as displacement, velocity and acceleration are paramount. In synthesizing the cam profile, kinematic quantities are minimized by manipulation of parameters in the intermediate knots (Flores 2013). The outlined studies do not track dynamic parameters such as force, jump, and wear at the cam follower interface. To achieve this, an acceleration profile is highly recommended to offer flexibility to follower accelerations that allow value minimization with regards to force and jump. The cam profile synthesis is henceforth based on a trajectory which comprises the cam follower mechanism. The dynamic stability of cam follower is stimulated by Matlab tool.
Dynamic performance of cam follower
There is a negligible deviation between machine displacement profiles and can follower displacement due to system dynamics. Cam wear is promotional to interface force. Traditionally, cam profiles have reduced the influence on the dynamic response (Zhu, Snyder, Wang & Guo, 2012). This has been minimized through the sensitivity of mass motion output. The system parameters considered in cam follower dynamics are mass, damping, coefficient, and the speed of the cam rotation. To eliminate static errors, adjusting the cam profile would substantially help. Additionally, to achieve a significant improvement in residual vibrations, designing a cam spring would help in compensating the variations in the load in a mechanical transmission process. Flores (2013) designed motor engine cams for valve trains using constrained optimization algorithm. He found out that the imposed constraints were products of maximum valve lift and timings that demanded maximization of time integrals of the valve area opened to allow gas flow.
Analytically, accelerations are imposed to control the profile through variables to optimize operations and motion. Using springs that are elastic create contact between can followers for a circular motion. In 2005, an automotive company created a hybrid valve lifter that composed of composite and steel. This engine was tested in train to determine the rate of automotive combustion in the internal engine (Likaj & Shala, 2013). The company saw the need of emphasizing on the reduction of mass of the valve lifter to achieve a higher fuel efficiency level. This experiment further revealed that cam driven mechanisms were possible during the initial design stages to obtain a rough estimate of natural frequency from values of masses, inertia, and stiffness of the links.
The frequencies of cam mechanism are paramount in designing follower systems. According to studies conducted by Industries and Motors in 1976, it was established that in cam follower systems, high-speed engines amount to noise and vibration. This causes wearing of engines calling for manufacturers to design follower systems with closure springs to avoid this menace (Rizzo, Hernandez, Leonardo, Toro, Zhao, Santoros & Lin, 2011). A large enough spring and preload must be applied to cam follower joint to keep them intact throughout the entire rotational period. However, measures should be taken to control the force that comes in contact with the machines since the larger the force, the larger the stress-induced leading to system failure and destruction of contact objects. The inertia force of the spring must be calculated as well. In cases where inertia force is larger than the spring force, a jump occurs. When these forces are balanced, it is referred to as cusp. These are the two main concerns when designing a cam follower. A single cam displacement function is defined by the classic spline curve made from polynomial pieces that are tied together at the ends by knots. These knots form design variables of synthesis and analysis. Significantly, this method helps in the adjustment of acceleration and jerk. Jump and can be reduced by placing the knots properly in the spline curves.
Experimental studies
Dynamic responses are meant to record velocity, displacement, acceleration, and jerk. The match between a response and its predicted outcome depends on some factors. These are trajectory for reducing the peak values of the follower motion characteristics, constraints and systematic design procedures for selecting a substantial trajectory of the cam velocities developed. The setup used the accelerometer to record acceleration, and displacement of the cam follower. The jerk and velocity were computed via square method from acceleration and displacement data. Experimentally, cam follower wear mechanism in a diesel valve gear created conditions necessary for routinely activities on a valve gear. Sahu, Kedia, and Sahu (2016) experimented on cam wear and arrived at a conclusion that cam wear can be defined by comparing profile lifts of the cam. These experiments, however, had some errors to do with the performance of the cam follower, experimental analysis of measuring responses of the jerk optimization, and stress optimization.
Centrifugal actuation
The centrifugal actuation based on methods of governing devices that are automated in speed such as engines to prevent damage. Centrifugal governor plays an important role in safeguarding rotational engines subjected to external disturbances ranging from a diesel engine, steam engine and others (Likaj & Shala, 2013). Mechanical governors work on the principle of the centrifugal force of rotating weights that are counterbalanced by springs. In cases where the speed of the engine increases, the weight stretches outward changing the setting of the control rod. The governor creates a linkage to the injection pump moving the control mechanism towards the fuel position (Vanderborght, Tsagarakis, Van, Thorson, & Caldwell, 2011).
Summary of literature review
This section has effectively dealt with variable lift mechanism, synthesis and design of cam profile, cam dynamics, and experimental studies. From the discussions presented, some studies have been conducted with regards to cam follower technology and established that cam follower mechanism in automotive and industrial applications are very complex regarding construction and design, power actuators, sensors and electronic control units. However, none of the studies have emphasized performance characteristics. Citing from the previous studies, acceleration, jump, internal force, and pressure angle have been well addressed. These studies are important in predicting characteristics of cam followers.
References
Brown, D. C., Rong, Y., & Boyle, I. (2011). A review and analysis of current computer-aided fixture design approach. Robotics and computer integrated manufacturing, 27(1), 1-12.
Codecogs. (2017). Cams. Retrieved from codecogs.com: http://www.codecogs.com/library/engineering/theory_of_machines/cams.php
De jalon, J. G., & Bayo, E. (2012). Kinematics and dynamic simulation of multibody systems: the real-time challenge. Springer Science & Business Media.
Flores, P. (2013, November 5). A computational approach for cam size optimization of disc cam follower mechanisms with translating roller followers. Journal of mechanisms and robotics, 5.
Goris, K. (2004). Autonomous mobile robot mechanical design. Vrije University, Scientia Vincere Tenebras. Brussels: Vrije Universiteit Brussel. Retrieved September 21, 2017, from http://mech.vub.ac.be/multibody/final_works/ThesisKristofGoris.pdf
Kumar, V., & Michael, N. (2012). Opportunities and challenges with autonomous micro aerial vehicles. The International Journal of Robotics Research, 31(11), 1279-1291.
Likaj, R., & Shala, A. (2013). An analytical method for synthesis of the cam mechanism. International Journal of Current Engineering and Technology, 432-435.
Mali, M., Maskar, P., Gawande, S., & Bagi, J. (2012). Design optimization of cam & follower mechanism of an internal combustion engine for improving the engine efficiency. Modern Mechanical Engineering, 2(3), 114.
Malil, M., Maskar, P. D., Gawande, S., & Bagi, J. (2012). Design Optimization of Cam & Follower Mechanism of an Internal Combustion Engine for Improving the Engine Efficiency. Retrieved September 21, 2017, from https://file.scirp.org/pdf/MME20120300006_92300689.pdf
Paden, B. A., & Moehlis, J. (2013). Point-to-point control near heteroclinic orbits: Plant and controller optimality conditions. Automatica, 49(12), 3562-3570.
Rizzo, A., Hernandez, L. F., Leonardo, B., Toro, C., Zhao, X., Santoros, F., & Lin, N. (2011). Computational challenges in simulating and analyzing experimental linear and non linear circular dichronism spectra . American Chemical Society, 811-824.
Sahu, L. K., Kedia, V. K., & Sahu, M. (2016, February). Design of cam and follower system using basic and synthetic curves: A review. International Journal of Innovative Science, Engineering & Technology, 3(2). Retrieved September 21, 2017, from http://ijiset.com/vol3/v3s2/IJISET_V3_I2_51.pdf
Vanderborght, B., Tsagarakis, N., Van, H. R., Thorson, I., & Caldwell, D. G. (2011). MACCEPA 2.0 compliant actuator used for energy efficient hopping robot Chobino 1D. Autonomous Robots, 31(1), 55-65. Retrieved September 21, 2017, from https://www.researchgate.net/profile/Bram_Vanderborght/publication/225896451_MACCEPA_20_Compliant_actuator_used_for_energy_efficient_hopping_robot_Chobino1D/links/5797572508aed51475e69316/MACCEPA-20-Compliant-actuator-used-for-energy-efficient-hopping-rob
Zhu, L., Xu, W., Snyder, J., Liu, Y., Wang, G., & Guo, B. (2012, November). Motion guided toy modeling. ACM Transactions of graphics, 31(6). Retrieved September 21, 2017, from https://pdfs.semanticscholar.org/1359/606e641857325042849946061a728b70cab2.pdf