Presets
Playback
Cam profile
Choose the lift law and set lift, ramps, dwell and base circle.
Valve spring
Wire, coil diameter and number of coils set the spring rate; preload and mass set the jump speed.
Drive
Real engine speed drives the dynamics; slow motion only slows the picture.
Layers
Model checks
The science
Cam and follower
A flat bucket follower rides on a cam whose base-circle radius is rb. The valve lift equals the cam lift function h(phi): a rise over the opening ramp, a dwell and a fall. The ramps use f(s) with s = phi / beta: cycloidal s - sin(2 pi s)/(2 pi), 3-4-5 polynomial 10 s^3 - 15 s^4 + 6 s^5, or simple harmonic (1 - cos(pi s))/2. The acceleration is h'' w^2; simple harmonic has a jump in acceleration at the ends, which excites vibration. A flat follower needs the radius of curvature rb + h + h'' to stay positive (otherwise the profile has a cusp).
Valve and spring
The valve, retainer, rocker and one third of the spring mass form an equivalent mass m on a spring of rate k = G d^4 / (8 D^3 n) with preload F0. If the follower never leaves the cam, the force between them is N = m h'' w^2 + k h + F0. Where N would become negative the cam cannot pull: the valve jumps (valve float). The page finds the first speed at which the minimum of N reaches zero and compares it with a time-domain simulation of the same train with compliant cam and seat contacts.
Spring surge
The spring is itself a continuous elastic body. Its first natural frequency with fixed-free ends is f = d / (2 pi n D^2) * sqrt(G / (2 rho)) (about 400 Hz for the default spring). When a harmonic of the cam acceleration coincides with it, coil surge can start. The page shows the cam acceleration harmonics against this frequency.
What is simplified
One degree of freedom: the rocker, bucket and valve are rigid and lumped into one mass; the spring is a linear spring with a lumped damper; cam and seat contacts are stiff one-sided springs; the oil film, gas force on the valve, cam deflection and the spring surge itself are not simulated. Spring coil mass is included as one third of its mass. The cam speed is half the engine speed (four-stroke). The geometry is drawn eight times real size in the 3D view.
What to try
- Raise the engine speed until the valve state changes to FLOAT: the cam force goes to zero on the closing flank.
- Pick the Weak spring preset, then raise the preload or the wire diameter: the jump speed moves up.
- Compare the three cam families at the same lift: simple harmonic is the harshest at the dwell junctions.
- Make the opening ramp short and watch the cam curvature readout turn negative (a cusp).