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WOLFRAM SYSTEM MODELER

SpurGear

Spur gear with mass, rotations and visualization

Diagram

Wolfram Language

In[1]:=

SystemModel["RotatingMachinery.Gears.SpurGear"]

Out[1]:=

Information

Spur gear

This component contains the mechanical properties of a spur gearwheel, as well as the visualization.

A circle involute, or simply involute, is a curve defined by the endpoint of a tangent that is rolled up from a circle. The circle involute is used to generate the profile of the teeth on the gear.

Figure 1: Gear teeth.

z = Number of teeth
m = Gear module ( = circular pitch/π])
alpha0 = Reference profile angle (normally 20°)
x = Profile shift coefficient

Figure 2 shows the gear parameter tab the parameters above are set.

Figure 2: Gear parameters tab.

The two frames frame_a and frame_b should be connected to either a fixed point or some kind of beam. They do not have to be connected at both ends.

The two frames frame_to_GearForceCalculation and frame_to_GearForceCalculation1 can be connected to a GearForceCalculation, [1, 2], component if the forces between two outer spur gears need to be calculated.

The spur gear is turned into an inner spur gear by setting isInnerGear to true. By default, it is set to false.

Turning Animation to On in the fixedFrame component will attach a coordinate system at the center of the gearwheel in the animation.

References

[1] Dahl, M., H. Wettergren, and H. Tidefelt. "Modelica Spur Gears with Hertzian Contact Forces." Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017. Linköping Electronic Conference Proceedings 132, no. 82 (2017): 755-763. http://dx.doi.org/10.3384/ecp17132755.

[2] Van der Lunden, F. L. J. and P. H. Vazques de Souza Silva. "Modelling and Simulating the Efficiency and Elasticity of Gearboxes." Proceedings of the 7th International Modelica Conference, Como; Italy, Sep 20-22, 2009. Linköping Electronic Conference Proceedings 43, no. 29 (2009): 270-277. http://dx.doi.org/10.3384/ecp09430052.

Parameters (8)

m	Value: Type: Module (m) Description: Gear module
z	Value: Type: Integer Description: No of teeth
rf	Value: m * z / 2 - 1.25 * m Type: Length (m) Description: Root radius
width	Value: Type: Length (m) Description: Width of gearwheel
gearWheelDensity	Value: 7850 Type: Density (kg/m³) Description: Density
isInnerGear	Value: false Type: Boolean Description: = true if internal gear wheel, otherwise external
profileShift	Value: Type: Real Description: Profile shift for animation object
initialRotationGearWheel	Value: 0 Type: Angle_deg (°) Description: Gear wheel initial angle of rotation

Connectors (4)

	frame_a	Type: Frame_a Description: Coordinate system fixed to the component with one cut-force and cut-torque (filled rectangular icon)
	frame_b	Type: Frame_b Description: Coordinate system fixed to the component with one cut-force and cut-torque (non-filled rectangular icon)
	frame_to_GearForceCalculation	Type: Frame_b Description: Coordinate system fixed to the component with one cut-force and cut-torque (non-filled rectangular icon)
	frame_to_GearForceCalculation1	Type: Frame_b Description: Coordinate system fixed to the component with one cut-force and cut-torque (non-filled rectangular icon)

Components (6)

	spurGearVisualizer	Type: SpurGearVisualizer Description: Visualizer for a spur gear
	fixedFrame	Type: FixedFrame Description: Visualizing a coordinate system including axes labels (visualization data may vary dynamically)
	bodyCylinder1	Type: BodyCylinder Description: Rigid body with cylinder shape. Mass and animation properties are computed from cylinder data and density (12 potential states)
	bodyCylinder	Type: BodyCylinder Description: Rigid body with cylinder shape. Mass and animation properties are computed from cylinder data and density (12 potential states)
	fixedRotation_Frame_b	Type: FixedRotation Description: Fixed translation followed by a fixed rotation of frame_b with respect to frame_a
	fixedRotation_Frame_a	Type: FixedRotation Description: Fixed translation followed by a fixed rotation of frame_b with respect to frame_a

Used in Examples (7)

	ShaftOnFlexibleSeatings RotatingMachinery.Examples.BearingAnalysis Two roller bearings on flexible supports
	FrequencyAnalysis RotatingMachinery.Examples.BearingAnalysis Frequency analysis of a bearing defect on a simple shaft mounted on a structure
	GearTrain RotatingMachinery.Examples.Gears.SpurGears Building a two-wheeled gear train on shafts
	ProfileShift RotatingMachinery.Examples.Gears.SpurGears Analyzing the clearance between gears
	TripleGearTransmission RotatingMachinery.Examples.Gears.SpurGears Construction of triple gearbox on three shafts
	InternalGear RotatingMachinery.Examples.Gears.SpurGears Application of a driven internal gearwheel
	InnerToOuterDrive RotatingMachinery.Examples.Gears.SpurGears Study of a driving internal gear