Follower Max Velocity (SHM)
Calculate the maximum velocity of a simple-harmonic-motion cam follower, v_max = (π·h·ω) ÷ (2·β), from the total lift h (mm), the cam angular velocity ω (rad/s) and the rise angle β (rad). In simple harmonic motion, the follower velocity starts from zero (rest), rises to a MAXIMUM at mid-rise (when the follower passes mid-height) and returns to zero at the top. This peak matters for several reasons: it sets the speed the follower — and the coupled mass (valve, tool, part) — moves at, affecting inertia and dynamic forces; it influences cam-follower contact wear; and, with acceleration, it decides whether the follower can follow the cam without 'floating' (losing contact, jump, at high speeds). Maximum velocity grows linearly with the cam rotation ω and the lift h, and decreases with the rise angle β (more 'spread-out' rises are smoother). Comparing SHM with other motion laws (parabolic, cycloidal) by maximum velocity and acceleration is how the right law is chosen per application. Enter the lift, the cam angular velocity and the rise angle.
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Velocidade máxima do seguidor (MHS)
A velocidade máxima do seguidor de um came com movimento harmônico simples é v_max = (π·h·ω) ÷ (2·β), a partir da elevação total h, da velocidade angular do came ω e do ângulo de subida β. No MHS, a velocidade do seguidor parte de zero (repouso), cresce até um máximo no meio da subida (quando o seguidor passa pela meia-altura) e volta a zero no topo. Esse valor de pico é importante por várias razões: define a velocidade com que o seguidor — e a massa a ele acoplada (válvula, ferramenta, peça) — se move, o que afeta a inércia e as forças dinâmicas; influencia o desgaste do contato came-seguidor; e, junto com a aceleração, determina se o seguidor consegue acompanhar o came sem 'flutuar' (perder contato, o jump, em altas rotações). A velocidade máxima cresce linearmente com a rotação do came ω e com a elevação h, e diminui com o ângulo de subida β (subidas mais 'espalhadas' são mais suaves). Comparar o MHS com outras leis de movimento (parabólica, cicloidal) pela velocidade e aceleração máximas é como se escolhe a lei adequada a cada aplicação. Informe a elevação, a velocidade angular do came e o ângulo de subida.
Related Tools
Max Velocity (Cycloidal Cam)
Calculate the maximum velocity of a cycloidal-motion cam follower, v_max = (2·h·ω) ÷ β, from the total lift h (mm), the cam angular velocity ω (rad/s) and the rise angle β (rad). In cycloidal motion, the follower velocity follows a smooth (1 − cosine) curve, starting from zero, reaching the MAXIMUM at mid-rise and returning to zero at the top — similar in shape to SHM, but with a slightly different profile ensuring acceleration continuity. The cycloidal maximum velocity (factor 2) is slightly HIGHER than SHM's (factor π/2 ≈ 1.57), reflecting that, to 'fit' the same lift in the same angle with smoother end accelerations, the mid velocity must be higher. Knowing the maximum velocity matters for the mechanism dynamics (the follower-mass kinetic energy, supplied then absorbed each cycle), for friction and wear at the cam-follower contact, and to check the system can follow the cam at high rpm. Comparing the maximum velocities and accelerations of the three classic laws (parabolic, SHM, cycloidal) is the basis of choosing the right cam profile per combination of load, speed and smoothness requirement. Enter the lift, the angular velocity and the rise angle.
Follower Max Acceleration (SHM)
Calculate the maximum acceleration of a simple-harmonic-motion cam follower, a_max = (π²·h·ω²) ÷ (2·β²), from the total lift h (mm), the cam angular velocity ω (rad/s) and the rise angle β (rad). Follower acceleration is perhaps the MOST important parameter in high-speed cam design, since it generates the INERTIA FORCES (F = m·a): the higher the acceleration, the greater the force the cam must apply to the follower (and the reaction back on the cam and bearings), the greater the tendency to vibration and follower 'jump', and the greater the contact stresses. In SHM, maximum acceleration occurs at the ENDS (start and finish of the rise), and — crucially — it has a DISCONTINUITY there (jumping from zero to maximum instantly), causing a shock and exciting vibrations. So for very high speeds, CYCLOIDAL motion is preferred (its acceleration is continuous, starting and ending at zero), despite cycloidal having a slightly higher peak acceleration. Acceleration grows with the SQUARE of the rotation ω — so doubling the rotation quadruples the inertia forces, and high-rpm engine cams are a design challenge. Enter the lift, the angular velocity and the rise angle.
Follower Displacement (SHM)
Calculate the displacement of a simple-harmonic-motion (SHM) cam follower, s = (h/2)·(1 − cos(π·θ/β)), from the total lift h (mm), the cam angle θ (rad, current position) and the rise cam angle β (rad, ramp duration). A cam is a special-profiled mechanical element that, rotating, imposes a programmed motion on a FOLLOWER sliding or pivoting on it — the heart of engine valve trains, automatic machines, textile, printing and packaging equipment. Simple harmonic motion is a classic follower motion law: displacement follows a cosine, starting smoothly from rest, accelerating to mid-height and decelerating smoothly to rest at the top. It has continuous velocity and acceleration (no jumps), but acceleration is discontinuous at the ends (start and finish), causing a small shock — so SHM suits moderate speeds. The follower displacement diagram (s vs θ) is the starting point of cam-profile design: from it derive velocity, acceleration and jerk, which set the forces, vibrations and accuracy of the mechanism. Enter the lift, the current angle and the rise angle.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.