Keywords

1 Introduction

Distance learning in higher studies is a challenge that requires the use of additional techniques and skills to address similar studies in the face-to-face mode. The use of new communication technologies, adapted computer media and the application of more attractive and effective teaching methods, especially in the teaching of STEM subjects, represent a necessary aid for the achievement of teaching objectives [1].

There are numerous computer programs and platforms for mechanical design and calculation in the field of mechanical engineering, some of which are specifically dedicated to the calculation of cams [2,3,4]. It is absolutely essential to put it into practice gradually because the correct use of it requires knowledge and understanding of all related theoretical concepts. In this context, this article describes a teaching experience that involved the creation of a group project by the students to improve the teaching of the kinematic and dynamic analysis of cams using the creation of an Excel computer application. This application must facilitate obtaining the most relevant and important results in this kind of system, producing visual and numerical results.

the project’s main goals can be summarized as follows:

  • User-friendly, intuitive, adaptable, and versatile.

  • Easily expandable to other needs or calculation requirements.

  • Easily adaptable to other spreadsheets of machine elements.

  • Didactic approach: support for students and teachers.

  • Follow the calculation scheme and nomenclature of the basic bibliography [5].

  • Open access without programming requirements.

  • A first Spanish version. Upcoming English versions.

Due to its accessibility, ease of use, and capability to perform matrix calculations, Microsoft Excel spreadsheets [6] were chosen as the base for the software application being created to achieve these goals.

2 Theoretical Basis on the Calculation of Cams

2.1 Introduction, Working Principle, and Applications

A cam-follower system is essentially a four-bar linkage with variable-length links. Because of this fundamental difference, cams are particularly advantageous for producing specific output functions in a flexible manner, as they can produce a wide range of output movements [7]. By causing the output element, or follower, to roll or slide on the atypical profile of the input element, or cam, cams are mechanical components that enable the conversion of rotary motion into oscillating motion. There is some sort of spring used to ensure that the contact between the cam and follower is always maintained.

2.2 Terminology and Classification of Cam Systems

The mechanism under study is that of a cam, which performs a uniform movement, and the follower, which performs a periodic movement. Depending on the movements of these components and according to their geometric characteristics, the types of cam-follower systems are classified: according to the spatial configuration, depending on the output movement of the follower, according to the geometry of the follower, depending on the type of closure of the joint, according to the restrictions and the movement program, etc. The reader is advised to consult the standard literature on cam design [7] for further details on each of these types of cams.

2.3 Fundamental Law of Cam Design and Kinematic Diagrams

The next design challenge is to define the mathematical function with which the follower moves as a function of cam rotation, in accordance with the Fundamental Law of Design of Cams, once the foundations for the operation of cam mechanisms have been established. The above Law is equivalent to matching the value of the boundary functions for displacement, velocity, and acceleration, making the functions of displacement parts have continuity of third degree, and making the jerk function finite by subdividing the cam motion functions into several parts.

2.4 Follower Displacement Math Functions

Simple harmonic movement, cycloidal displacement, modified trapezoidal acceleration, modified sinusoidal acceleration, polynomial 3-4-5, polynomial 4-5-6-7, double harmonic movement, 3-4-5-6 polynomial, critical path motion, and constant velocity motion are among the common mathematical functions used in the design of cams.

2.5 Cam Size

The functions to be used in each section are chosen based on the type of cam and follower. The program’s SVAJ functions are then generated, and the design’s suitability is checked. It is necessary to provide information on the cam size in order to be able to size the cam profile based on the follower type and the SVAJ diagrams. The eccentricity, the primitive curve, the base circumference, and the main circumference are all defined for this. The pressure angle and the radius of curvature are two crucial cam design elements that are examined from these geometrical elements.

3 Cam Profile Analysis and Design Validation

The steps in the design and validation of a cam are logically ordered: choose the type of cam and follower, create SVAJ diagrams, size the cam and its profile, determine the pressure angle and radius of curvature, and validate the cam design to prevent curve radii that are either negative or larger than the follower radius. The system’s dynamic forces, damping ratio, critical damping, and damped and undamped natural frequencies are then calculated using a lumped parameter model to perform a dynamic analysis of the system.

The contact force must then be consistently positive in order to prevent the follower from jumping, and the operating speed must be such as to minimise any potential resonance effects. Finally, the required torque is obtained on the camshaft to be able to drive the cam. The contact efforts made by the cam and follower are examined after the contact force has been determined in order to look for any potential contact surface cracks. In order to achieve this, the Hertz contact theory between parallel cylinders is used, and graphs of the main stresses and Von Mises stresses in the proximity of the contact are obtained.

4 Computer Application Design

The application is being developed with its two primary uses in mind: as a teaching tool and as a professional work tool. In this first version, the application’s scope is defined for the following design variants: flat rotational cams, programmes with any sequence of up to eight rising, stopping, or falling segments, roller or flat face followers, and varying sorts of closure of form or force.

The Excel application is organised using a spreadsheet for each of its 14 sections, where the design and operation requirements are examined and the set of results’ graphs are created. There are two distinct categories of spreadsheet. For application users, an external spreadsheet. To avoid accidental editing or change, the internal spreadsheets for the developer are hidden. A user manual is created to make the application easier to use or to clarify any usage questions (Fig. 1).

Fig. 1.
figure 1

Kinematic analysis. User interface [8].

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4.1 First Part: Kinematic Analysis

The screen is divided into five zones to make it easier to use; numerical data is entered in cells of various colours, and non-numerical data is chosen from drop-down menus:

  • Zone 1: contains simple operating instructions.

  • Zone 2: list the type of cam programme and the design that will be examined.

  • Zone 3: specify the distances and lengths of each segment.

  • Zone 4: numerous checks produce error or warning messages.

  • Zone 5: the most significant results are summarised and shown (Fig. 2).

Fig. 2.
figure 2

Menu for choosing application results graphically [8].

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4.2 Second Part: Dynamic Analysis

The structure and format remain the same as the kinematic analysis part.

  • Zone 1: introduce the parameters of the concentrated model for the dynamic analysis, as well as the preload deflection.

  • Zone 2: introduction of material properties and cam width, required to perform contact force calculations.

  • Zone 3: validate the values needed to continue with the calculations.

  • Zone 4: displays a summary of the most important results.

Calc. A section hidden in the user’s working file that is destined for internal developer use. The Technical Manual explains how it works.

4.3 Spreadsheets of Results

  • S-V-A-J: SVAJ graphs, with maximum and minimum values for each variable.

  • Zoom_S-V-A-J: expands the SVAJ graphs, and in the comparative case, five functions are drawn at the same time.

  • Phi_ρ: pressure angle and radius of curvature over a rotation period.

  • Perf_leva: the cam’s profile, including the base and primary circumferences.

  • POLAR_perf_φ: cam profile in polar coordinates next to the pressure angle.

  • POLAR_perf_ρ: cam profile in polar coordinates next to radius of curvature.

  • Fuerzas: preload force, dynamic force and maximum contact pressure.

  • Esfuerzos: preload force, dynamic force and maximum contact pressure.

  • VM_ρ: curvature radius and contact pressure graph.

  • Par_torsion: torque and the force of contact between the cam and the follower.

  • Selec. Internal developer section. As a result, it is hidden in the user’s work file. The Technical Manual explains how to use it (Fig. 3).

Fig. 3.
figure 3

Results. SVAJ diagrams. [8].

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4.4 Technical Manual

The application includes the preparation of a detailed technical manual that explains the operation of the computer application from the developer’s perspective. This section is relevant if you want to modify, adapt, or complete the application with a calculation or additional result.

5 Conclusions

As part of a collaborative project carried out by the subject’s students, a computer application for the design and calculation of cams was developed, with the following properties: versatile, intuitive, simple, adaptable, and accessible. The goal is to improve the teaching task of the project’s developers and student users of the application. It is also a useful tool for teachers in terms of exercise proposal and resolution. Professionals or specialists in cam design can also benefit from the application.

The project is designed to be open to new students’ continuous participation in the expansion and improvement of the same, in advanced topics of cams study such as: dynamic study of complete mechanical assemblies, dynamic study of vibrations, study of failure to superficial fatigue, study of wear phenomena, and connection with other axle calculation sheets.