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CDS – Spline-Based Motion Design for Valve Trains

From Motion Design to Dynamic Simulation

CDS was developed by Dipl.-Math. Dieter Zuck as a specialized engineering tool for the design and calculation of valve trains. At its core is a spline-based approach for defining valve motion, generating the corresponding cam profile and evaluating the key mechanical parameters of the valve train.

Over many years of cooperation, CDS and RecurDyn were used together to connect the initial motion and cam design with the nonlinear dynamic analysis of the complete valve train. This combination made it possible to evaluate a design not only from a kinematic perspective, but also with respect to contact forces, component flexibility, valve lift-off and spring dynamics.

Today, the central spline methodology developed by Dieter Zuck has been integrated directly into RecurDyn. This preserves the engineering approach behind CDS while bringing motion design and dynamic simulation into a single environment.

In memory of Dipl.-Math. Dieter Zuck († 2025), we will continue the CDS name and his approach to valve train design as part of our RecurDyn development and engineering work.

CDS Cam Shaft Design Systems

Cam Design

The design of a valve train starts with the required valve motion. Based on valve lift, opening duration and the geometry of the valve train, CDS calculates the corresponding cam profile.

The resulting design can be evaluated with respect to the key mechanical parameters, including:

  • Cam profile and radius of curvature
  • Contact forces and Hertzian contact pressure
  • Spring and inertia forces
  • Entrainment velocity and lubrication conditions
  • Manufacturing and geometric constraints

Different valve train concepts – from direct acting systems to finger followers, rocker arms or desmodromic mechanisms – can be treated within the same design approach.

Cam Design by CDS
CDS Cam Spline

Spline-Based Motion Generation

The central element of CDS is the definition of the valve acceleration as a spline function over the cam angle:
 

B(φ) = S″(φ)

Velocity and valve lift are obtained by integration. By modifying the spline control points and boundary conditions, engineers can systematically influence:

  • Opening and closing ramps
  • Maximum valve lift
  • Peak acceleration and deceleration
  • Transition behavior between individual motion sections
  • Valve opening duration
  • Dynamic excitation of the valve train

The spline representation produces smooth and mathematically consistent motion curves. This helps to avoid artificial high-frequency excitation and provides a reliable basis for cam profile generation and dynamic contact simulation.

CDS Valve Graph

Dynamic Valve Train Analysis

Nonlinear Contact & System Dynamics

The interaction between cam and follower is at the core of the valve train dynamics. While the kinematic design defines the nominal valve motion, the actual motion depends on inertia forces, spring forces and the nonlinear contact between the individual components.

RecurDyn directly simulates these interactions in the complete mechanical system. This makes it possible to analyze:

  • Cam/follower contact forces
  • Valve lift-off and rebounce
  • Valve seating velocity
  • Contact loss at high engine speeds
  • Influence of clearances and contact stiffness
  • Dynamic behavior over the complete engine speed range

A purely kinematic force balance can provide a first estimate of the critical engine speed, but it cannot capture the dynamic interaction of the complete system. In the CDS example, the kinematic analysis predicted valve lift-off at approximately 9,660 rpm, while the dynamic simulation showed lift-off already at approximately 9,100 rpm.

Valve Simulation
CDS RecurDyn Kinematic vs Dynamic Model

Flexible Valve Train Components

At high engine speeds, the deformation of valve train components can significantly influence the actual valve motion and the resulting contact forces. Treating components such as rocker arms, finger followers or valves as flexible bodies allows these effects to be included directly in the system dynamics.

RecurDyn combines multibody dynamics with flexible body simulation within the same model. This allows the influence of structural flexibility to be evaluated with respect to:

  • Dynamic deformation of valve train components
  • Cam/follower and other contact forces
  • Valve motion and timing
  • Component stresses under operating conditions
  • Structural vibrations and resonances

Flexible components can be introduced where they are relevant, while the remaining valve train stays represented by efficient rigid-body models.

Lever CAD
Lever FEM

Dynamic Valve Spring Simulation

Valve springs are highly dynamic components. At increasing engine speed, their distributed mass and structural flexibility can lead to spring surge, resonances and significant deviations from the quasi-static spring force.

RecurDyn allows the valve spring to be included directly in the dynamic valve train model. Depending on the required level of detail, the spring can be represented from a simple force element up to a fully flexible FE model.

This enables the analysis of:

  • Spring surge and resonances
  • Dynamic spring forces
  • Coil-to-coil contact and coil clash
  • Local deformation and stresses
  • Spring modes during operation
  • Influence of spring dynamics on valve lift-off and seating behavior

The spring dynamics are evaluated as part of the complete valve train rather than as an isolated component. This makes it possible to directly assess their influence on cam/follower contact and the actual valve motion.

Vale Train Spring Dynamics
Vale Train Spring Dynamics Simulation