### Preliminary gear design

Preliminary gear design makes it possible to quickly and simply create gearbox models for subsequent calculation in the FVA-Workbench. After specifying the load data and the gearbox structure, the number of gear stages and the gear geometry are automatically determined. The user can modify the proposed geometry data before the model is created. Once the data is accepted, the FVA-Workbench provides the user with a calculable gear model with all gear stages, shafts, and bearings with no additional input.

#### Load data and gearbox structure

In the first preliminary gear design step, the gearbox load can be defined by specifying the power and rotational speed at the gear unit input or output, or by specifying the torque and rotational speed. The required total gear ratio and whether the speed should be increased or reduced must also be specified. The following gear structures are available:

Single or multi-stage cylindrical gear unit with a maximum of 5 stages, for ratios between 2.5 and 400

Single or multi-stage planetary gear unit (minus gearing) with a maximum of 3 planetary stages, for ratios between 1 and 150

Single-stage bevel gear unit, for ratios between 1 and 8

Combined bevel-cylindrical gear unit with a single bevel stage and a maximum of 2 cylindrical stages, for ratios between 5.5 and 150

Combined planetary-cylindrical gear unit with a single cylindrical stage and a maximum of 2 planetary stages, for ratios between 7.3 and 50

Combined planetary-cylindrical gear unit with a single planetary stage and a maximum of 4 cylindrical stages, for ratios between 4.5 and 1000

Combined bevel gear-planetary gear unit with a single bevel gear stage and a maximum of 2 planetary stages, for ratios between 7.3 and 150

##### Number of stages and gear ratio

The required number of gear stages as well as the gear reduction ratio are determined according to the method developed in FVA Research Project 421 "Getriebevorauslegungsprogramm - GAP" (Preliminary Gear Design Program), under the condition that the weight of the gears is minimized. In addition to automatic calculation of the number of gear stages, the user can also select a number of stages that differs from the automatically determined number by a maximum of one stage.

##### Determination of the gear geometry

The proposed geometry for the gear stages is determined so that the torque can be transmitted with the required minimum safeties according to ISO 6336:2019 (for cylindrical gears) or ISO 10300:2014 (for bevel gears). As several factors for the calculation can only be approximated in this first design step, the safeties calculated in the next step may deviate from the required minimum safeties. In particular, the minimum safeties of the flank and root cannot be approximated equally well for all geometries, so that relatively high tooth root safeties may result, especially for large-modulus gears.

The preset values described below are used to determine the proposed geometry. These apply for all gear stages. Only the material and, for planetary stages, the number of planets can be selected separately for the individual gear stages in the overview.

#### Preset parameters

##### General

The following preset values for the preliminary design of the gear geometries and for calculation of the load capacities can be modified by the user. The last used values are saved in the FVA-Workbench user settings and are used as default values for further calculations. They can be reset to their initial values with the corresponding button. It should be noted that the preset values for the load capacity calculation are applied to the Workbench model.

###### Application factor

The application factor is used for the geometry design of all stage types.

###### Required flank safety

The minimum required flank safety determines the required pinion diameter for transmitting the specified torque.

###### Required tooth root safety

The minimum required tooth root safety determines the required modulus of the gear for transmitting the specified torque from the pinion diameter. It also determines the number of teeth of the pinion. In general, the higher the required tooth root safety, the greater the modulus and the smaller the number of pinion teeth (see: minimum and maximum number of pinion teeth).

###### Operating time

The operating time influences the preliminary design of the gear via the life factors. Specifying a higher operating time tends to result in larger gears. A reduction of the life factors to 0.85 in the endurance limit range at 10^{10} load cycles is considered for both cylindrical and bevel gears.

###### Material

The default gear material. Only ferrous materials are considered. The materials can then be changed for each individual stage.

###### Avoid equal divisors for number of teeth

Activating this switch avoids combinations of the number of teeth with the same divisor in each stage. This also applies to the determination of the number of teeth in the variation calculation. In planetary stages, the sun-planet and planet-ring gear meshes are considered individually.

##### Cylindrical gear stages

###### Face load factor

As a system analysis based on the deformation is required for a meaningful determination of the face load factor, a user-specified value is used for the preliminary design. This is then used as a fixed value in the model. A user-defined face load factor cannot be considered for the preliminary design of bevel gears.

###### Minimum number of pinion teeth

This specification sets a limit for the smallest number of teeth for the pinion of cylindrical gear stages. Furthermore, the shear strength of the material is used to check whether the torque can be transferred over a shaft diameter resulting from the number of pinion teeth and the modulus. If this is not the case, the number of pinion teeth is increased accordingly.

###### Maximum number of pinion teeth

For materials with a low load carrying capacity, a relatively large pinion diameter is required to transmit the torque. The required tooth root safety resulting from the specified modulus leads to a very large number of teeth. The user can limit the number of pinion teeth by specifying a maximum value. This then leads to a larger modulus and thus to high tooth root safeties.

###### Width/diameter ratio

For cylindrical gears, the gear width results from the specified ratio of pinion width to pinion diameter. The greater the pinion diameter in relation to the tooth width, the more difficult it is to ensure even load distribution along the gear width. The following influences must be considered:

Running-in behavior of the material (normalized, hardened and tempered, case-hardened, nitrided)

Bearing formation (symmetrical/asymmetrical, rigid/soft)

Gear quality

Flank modifications

Typical values are between 0.6 and 1.2. For bevel gears, the gear width is determined according to ISO 23509 (2016) Annex B.

###### Helix angle

Specification of the helix angle for cylindrical gears (refer to "Axial force balancing on intermediate shafts").

###### Determination of the addendum modification

The profile shift sum is determined according to DIN 3962. The distribution of the profile shift between the pinion and wheel can be done according to the following criteria:

Acc. to DIN 3962

Equal maximum sliding speeds according to Niemann/Winter

Equal addendum modification amounts for pinion and wheel

For bevel gears, the addendum modification is determined according to Niemann/Winter.

###### Planet carrier design

Specification of whether a single or double-plate planet carrier should be added. This specification has no influence on the gear geometry.

###### Axial force balancing on intermediate shafts

For gearboxes with cylindrical gear stages, activating this switch determines the helix angle of the gear stages such that the axial forces are balanced for intermediate shafts. Angles are rounded to 0.5°. Helix angles less than 1° are set to 0°.

##### Bevel gear stages

###### Helix angle

Specification of the helix angle for bevel gears. For intermediate shafts with cylindrical and bevel gears, the helix angle is not automatically determined such that axial forces are balanced.

##### Planetary stages

###### Planet carrier design

Specification of whether a single or double-plate planet carrier should be added. This specification has no influence on the gear geometry.

##### Load capacity calculation

The load capacity calculation includes additional preset values which can be modified by the user. They only influence the calculation of the safeties, not the preliminary design of the gear geometries.

###### Addendum coefficient

Specification of the addendum coefficient of the basic profile of the gear.

###### Dedendum coefficient

Specification of the dedendum coefficient of the basic profile of the gear.

###### Root fillet radius coefficient

Specification of the root fillet radius coefficient of the basic profile of the gear.

###### Gear quality

Specification of the gear quality, based on ISO 1328 (2013) for cylindrical gear stages and DIN 3965 (1986) for bevel gear stages.

###### Arithmetic mean roughness of the flank

For calculations that use the mean roughness, these values are multiplied by a factor of 6.

###### Arithmetic mean roughness of the root

For calculations that use the mean roughness, these values are multiplied by a factor of 6.

###### Lubricant

Selection of the lubricant used from the FVA-Workbench lubricant database.

###### Oil temperature

This value is not used in the preliminary gear design itself, it is only transferred to the Workbench model for further calculations.

#### Geometry modification and load capacity calculation

The results are shown in the second preliminary design input window. The torques and speeds resulting from the current total gear ratio are visible in the gearbox data section. For gear designs without bevel gear stages, the total center distance between the input and output shafts is also shown here. The calculation of the center distance also considers the respective shaft angle of the stages, which indicates the angle of the center distance in the v-w plane to the w-axis about the negative u-axis of the pinion shaft.

##### Modification of geometry values

The geometry values of the gearbox stages can be modified by the user. To specify locked values (e.g., normal pressure angle, modulus, helix angle, or addendum modification of a gear in a stage), the center distance must first be deleted and an addendum modification specified for the gear. This ensures that the specified geometry always leads to a suitable gear.

##### Variation of the number of teeth

The number of teeth can be varied in a separate window to make it possible for the user to change the number without deviating too far from the desired total gear ratio. Variation ranges can be defined for all numbers of teeth in this window. By clicking "next," all possible combinations are calculated and sorted according to their proximity to the desired total gear ratio. The total weight of the gears and, for gearboxes without bevel gear stages, the total center distance are also output. The variation results can also be sorted according to these two criteria. A suitable combination of the number of teeth can then be selected and applied by clicking "next."

##### Calculation of the gear safeties

By clicking "calculate safeties," all gear safeties according to ISO 6336 (2019) are calculated and displayed for the cylindrical and planetary stages. The lower of the two safeties for the pinion and wheel of a stage is shown. For planetary stages, the lowest safety from the sun-planet and planet-ring gear meshes is displayed. For an initial estimation of the dynamic behavior, the transverse contact ratio, overlap ratio, and the total contact ratio as well as the ratio of the current stage speed to the resonant stage speed are also output. To evaluate whether the axial forces on the intermediate shaft are balanced, the axial forces of the stage are also output. For bevel gear stages, the gear safety is calculated according to ISO 10300 (2014). Here, the axial force is not output, and the axial forces for intermediate shafts with bevel gears are not automatically balanced.

If no geometry can be calculated from the predimensioning, no gear tooth safeties are displayed. Further information is shown in the message window.

Calculated safetys that are below the specified minimum safetys are highlighted in red.

#### Model creation

Clicking the "finish" button completes the preliminary gear design and a model is created in the FVA-Workbench with the generated data. Models created in this way include all required data for the calculation of the gear safeties according to ISO 6336 (2019) or ISO 10300 (2014). The specified calculation parameters (e.g., application and face load factors or the basic profile data) should be checked in advance and adjusted if necessary. The local gear stresses of cylindrical gear stages can also be calculated without any additional input. For bevel gear stages, the required machine settings data must be generated in the Workbench model via the "geometry design according to ISO 23509 (2016)" calculation.