齿轮翻译

Description:

The model type Gear stage can be used for the conversion of rotational speed and torque during the transmission process. It models the meshing of the gears, taking the tooth stiffness and rotary backlash into account. It is suitable for modeling spur and helical gears. If required, the gear contact can be modeled as rigid.

The radial and axial support behavior can be modeled externally and thus can be rigid or elastic. Force, spring, and pre-load models are possible.

Figure 1: Coordinate systems of the Gear stage model

The gear element transforms displacements, velocities, accelerations, and forces (torques) between the red connector coordinate systems and the green inner coordinate system at the tooth contact (indicated by I). The tooth contact model is described in the chapter Tooth Contact.

Furthermore, the element is able to represent losses. The losses can be considered in the tooth contact and / or in the gear supports (at the rotational connectors).

Parameters:

Geometry

It is possible to use only constructional data for the parameterization of the gear (see Figure 1). These are in particular:

∙the Normal Modulus,

∙the Tooth Width ,

∙the Number of Teeth z1 and z2 for the two gears,

∙the Helix Angle (measured with respect to gear 1, see Figure 1),

∙the Pressure Angle ,

∙and the Rotary Backlash j t.

All the mechanical parameters (stiffness, damping, overlap) can be calculated internally, if nothing else is specified. In addition each parameter (if known) can be altered manually in further parameter groups in order to precisely adjust the model to the situation to be simulated.

Tooth Contact

The tooth contact can be modeled as rigid (see below) or elastic. If no values are given, SimulationX computes the tooth stiffness by an internal approach. Otherwise you can choose between an elastic or a rigid tooth contact model. Further information for parameterization, calculation and results of the tooth contact can be found in chapter Tooth Contact.

The principal model of the gear stage is defined by the Rigid checkbox. It can behave as

∙Spring-Damper-Backlash: The Rigid checkbox is deselected. The behavior is defined by the given or computed stiffness, damping, and backlash parameters. Within the backlash the stiffness and damping are always zero.

∙Rigid End Stop: If the Rigid checkbox is selected, the model behaves as rigid. I.e., it consists of an ideal transformation with rigid connection between all connectors

(kindR == "without Backlash") or an ideal transformation combined with a rigid end stop. The kind of impact can be specified by the user via the Tooth Contact parameter - in the same way as for the rigid end stop in the Linear Mechanics library. If a

backlash is present, it is set via the Rotary Backlash parameter.

∙If the checkbox Rigid is selected and if the Contact enumeration kindR is switched to "without Backlash", the gear stage as a transformer (transmission). In this case,

forces will only be transferred via the right tooth flanks, no matter in which direction the power is transmitted. So, the right tooth flanks transfer tensile and compressive forces (tensile forces have a negative sign). In this case, the result variables for the forces of the left tooth flanks Fbnl and Ftl are deactivated.

∙If Consideration of Stiffness Change is selected (only possible if Rigid is deselected) the element computes a variable toothing stiffness by an internal approach (see

chapter Tooth Contact).

Stiffness of Toothing and Damping of Toothing

∙If Rigid is deselected, the properties dialog page Free Definition 1 provides parameters to define the elastic tooth contact model. Read more about the

parameters and the calculation in the chapter Tooth Contact.

Modified Profile / Contact Ratio

This group provides further geometry parameters of the gear. If Consideration of Modified Profile is selected, it is possible to enter

∙profile offset factors x1 and x2 for every gear. Based on this the effective radii for the force and motion quantity transformation between Tooth Contact and connector

coordinate systems will be computed.

∙the center distance a of the gears. Together with the tooth numbers, the effective transformation radii can be computed.

∙Furthermore, the Input of an Addendum Modification is possible. The Addendum Modification kmn in the element Gear is an absolute value. If only an relative value k mn,rel is given, the absolute value can be computed using the normal modulus m n by:

∙Finally the Total Contact Ratio can be specified. By default it is computed internally,

but it is possible to enter a constant value for epsilon (, see chapter Tooth

Contact) in order to consider different kinds of modified profiles. The total contact

ratio is used for the computation of the total stiffness by the specific stiffness of one pair of teeth (see also chapter Tooth Contact). Thus, this parameter is redundant if Summated Meshing Spring Stiffness is selected for kindS on page Free Definition 1.

If you decide to enter a value for the total contact ratio, the addendum modification