Multibody Diagrams

Introduction

Since version 4.0, Bladed uses a multibody dynamics approach. This approach consists of connecting many independent “bodies” or “components” together to represent the dynamics of a complex system. Each component has one or more of the following properties:

• Rotational or translational flexibility
• Rigid rotation and translation
• Mass and Inertia

Components are connected to one another with “nodes”. Each node has fully defined kinematics at all times. Structural motion is typically outputted at the nodes. The multibody formulation in Bladed is a tree structure, which means that it has no closed loops. Each component has:

• One proximal node on the inboard side of the component.
• Any number of distal nodes on the outboard side of the component.

The mathematical descriptions of the components describe the physical relationships between the proximal and distal nodes of each component.

Figure 1: A multibody component in Bladed has one proximal and any numbers of distal nodes.

Legend

Components

Table 1: Components used in this article

Symbol	Description
	Fixes the inertial frame reference for the structure. The only component with no proximal node.
	Connects different components together. Each node has fully defined kinematics and orientation.
	A rigid translation and orientation offset between the component’s proximal node and its distal nodes.
	Mass and inertia are defined in relation to a single point (node).
	Single degree of freedom rotational flexibility.
	Single degree of freedom translational
	Six degrees of freedom (3 translational and 3 rotational) flexibility.
	A single rotational degree of freedom between the mounting and one distal node. The first and second distal nodes (low-speed and high-speed shafts) have kinematics related by a fixed (gear)
	The most complex component is used to represent towers and blades, which is made up of a system of linear finite element beams each with full stiffness and mass definitions. Modal reduction is used to reduce the number of degrees of freedom of the complete component.
	Dashed perimeter indicates that the component may or may not exist dependent on an option in the Bladed user interface. E.g. Low speed shaft torsional flexibility in the power train screen adds the LSS Flexibility hinge component. The colour depends on what type of component is selected.

Applied Loads and Outputs

Table 2: Inputs and outputs

Symbol	Description
	An external force applied on the structural system
	An external torque applied on the structural system
	Output kinematics or loads. These can either come from a node, or from a flexibility within a component. In the latter it is the stress or relative kinematics across the flexibility.

Loads can be applied either:

• Between a component and a node
• As a stress across a component flexibility, which is defined as an action and equal reaction load on each side of the flexibility

Turbine Diagram

This is the complete model (excluding blades) of a typical turbine configuration with many optional features disabled.

Figure 2: Complete turbine model in a typical configuration (blades not shown).

Blade Diagram

This is a detailed diagram of one blade including the pitch actuator system:

Figure 3: A detailed diagram of one blade including the pitch rotary actuator system.

Drivetrain

This is a complete diagram of the (geared) drivetrain with all available options. See the subsections below for more detailed diagrams:

Figure 4: An overview of the drivetrain with all available options.

Low-Speed Shaft Options

1-dof Low-Speed Shaft

Figure 5: Basic LSS with torsional flexibility.

3-dof Low-Speed Shaft

Figure 6: Advanced LSS with torsional and bending flexibilities.

Yaw System and Mounting Options

Figure 7: An overview of the drivetrain mounting options including the yaw system.

High-Speed Shaft Options

Rigid High-Speed Shaft

Figure 8: Rigid HSS

Flexible High-Speed Shaft

Figure 9: HSS with torsional flexibility. The HSS inertia is connected to the node on the right.

Rigid High-Speed Shaft + Slipping Clutch

Figure 10: Rigid HSS with additional slipping clutch. The HSS inertia is connected to the node on the left.

Flexible High-Speed Shaft + Slipping Clutch

Figure 11: HSS with torsional flexibility and additional slipping clutch. The HSS inertia is connected to the node on the right.

Direct-Drive Drivetrain

Direct-drive transmission is modelled using a GearboxRatio = 1.

Figure 12: Diagram of a direct-drive transmission without a HSS.