Vibratory Finishing Formulas

• Labor time standard: specified as the machine property Labor Time Standard. This multiplier is used to account for otherwise unaccounted for factors that affect labor time, such as operator fatigue or time spent by the operator for cleaning or maintenance.

• Labor Handling time: this is 0 if the machine property Automatic Part Separator is Yes. Otherwise, it is the value of the cost model variable mediaSiftTime (900 seconds in starting point VPEs), amortized over the parts in a machine batch (see Vibratory Finishing Batch Size):

Labor Handling Time = Media Sift Time / Vibratory Finishing Batch Size

Cycle Time and Process Time for Vibratory Finishing

Cycle time and process time are given by the following formulas:

Cycle Time = Process Time * Cycle Time Adjustment Factor

Cycle time is the product of the following

• Process time: this is the sum of the child operation, Tumble Deburr. See formula for Tumble Deburr Cycle Time, below.

• Cycle time adjustment factor: specified by the cost model variable cycleTimeAdjustmentFactor (1 in starting point VPEs). Administrators can customize this value in order to globally adjust cycle times for Assembly Molding.

Tumble Deburr Cycle Time = Media Deburr Time / Vibratory Finishing Batch Size

Process time for the Vibratory Finishing process is the cycle time for the Tumble Deburr operation. This the time for one machine cycle, amortized over the number of parts that the machine can handle at one time. It depends on the following:

• Media deburr time: this is the time for one machine cycle. It is looked up by Media Material Type in the tool shop table Media for Vibratory Finishing.

• Vibratory Finishing Batch Size

Media Material Type

By default, media material type is looked up by part material cut code family in lookup table vibratoryFinishingMediaCompatibility. Cut code family is the integer part of the value of the material property Cut Code.

If cut code family does not appear in this lookup table, or if the material does not have a cut code, the cost model uses the cost model variable defaultMediaNoMaterialCutCode (Plastic in starting point VPEs).

Users can override the default media type with the setup option Type of Media Used.

Vibratory Finishing Batch Size

Vibratory finishing batch size is the number of parts processed in one machine cycle. It is the maximum number of parts that the machine can accommodate, provided that it does not exceed the size of a production batch (specified in the Production Scenario tab of the Cost Guide). So the vibratory finishing batch size is the smallest of the following three values:

• Batch size (the size of a production batch, specified in the Production Scenario tab of the Cost Guide)

• Machine batch size volume: this is the largest number of parts that, when combined with the required media, does not exceed the machine's maximum volume capacity. See the formula below.

• Machine batch size weight: this is the largest number of parts that, when combined with the required media, does not exceed the machine's maximum volume capacity. See the formula below.

Machine Batch Size Volume = rounddown(Machine Container Volume /

(Part Volume + Media Volume Per Part))

This depends on the following:

• Machine container volume (see formula)

• Part volume (specified by the geometric property Volume)

• Media volume per part (see formula)

Machine Container Volume = Container Volume * Container Fill Percentage

This is the product of the following:

• Container volume: this specified by the machine property Container Volume.

• Container fill percentage: this is the maximum fraction of the Container Volume (specified by the machine property) that should be occupied by the parts and media together. By default in starting point VPEs, this 0.95. VPE administrators can customize the default with the cost model variable vibratoryFinishingContainerFillPercent (which specifies a percentage--95 in starting point VPEs). Users can override the default with the setup option Fill Percentage of Container.

Media Volume Per Part = Media Fill Ratio * Part Volume

Media volume per part is the product of the following:

• Media fill ratio: the ratio of the total volume of media to the total volume of parts in a vibratory finishing batch. By default, this is the value of the cost model variable defaultVibratoryFinishingMediaRatio (3 in starting point VPEs). Users can override the default with the setup option Volume ratio of Media to Parts Being Utilized.

• Part volume (specified by the geometric property Volume)

Machine Batch Size Weight = rounddown(Machine Weight Limit /

(Part Mass + Media Mass Per Part))

This depends on the following:

• Machine weight limit (specified by the machine property Weight Limit)

• Part mass (the product of the geometric property Volume and the material property Density)

• Media mass per part (see formula)

Media Mass Per Part = Media Density * Media Volume Per Part

Media mass per part is the product of the following:

• Media density: by default, this is the value of the toolshop property Density for the current Media Material Type. This value is based on the assumption that the media size is larger than 3/8".

Users can specify a smaller media size (<=3/8") by setting the setup option Media Size to false. In this case, media density is the product of the toolshop property Density and the cost model variable smallMediaDensityMultiplier (1.15 in starting point VPEs).

• Media volume per part (see formula)

Expendable Tooling for Vibratory Finishing

Expendable tooling costs are incurred for consumption of the abrasive additive and a certain fraction of media. Cost is given by the following formulas:

Expendable Tooling Cost Per Part =

(Abrasive Additive Cost + Media Cost) / Final Yield

Expendable tooling cost per part depends on the following:

• Abrasive additive cost (see formula)

• Media cost (see formula)

• Final yield (see the section on Yields in the chapter for the primary process group)

Abrasive Additive Cost = (Abrasive Additive Usage Rate * Process Time *

Abrasive Additive Cost Per Volume) / Vibratory Finishing Batch Size

Cost per part for abrasive additive depends on the following:

• Abrasive additive usage rate (see formula)

• Process time: see the formula Tumble Deburr Cycle Time in Cycle Time and Process Time for Vibratory Finishing.

• Abrasive additive cost per volume (see formula)

• Vibratory Finishing Batch Size

Note that abrasive additive cost is 0 if the setup option Abrasive Additive Utilized is set to None.

Abrasive Additive Usage Rate =

Machine Container Volume * Default Abrasive Additive Ratio

The consumption rate (unit volume per unit time) for abrasive additive is the product of the following:

• Machine container volume: see the formula for Machine Container Volume in Vibratory Finishing Batch Size.

• Default abrasive additive ratio: this is the volume of additive that is consumed per unit time, expressed as a fraction of the usable container volume per unit time. It is specified by the cost model variable defaultAbrasiveAdditiveRatio (0.001hour-1 in starting point VPEs). So, for example, in starting point VPEs, the cost model assumes that the volume of additive consumed per hour is equal to 1/1000th of the usable container volume. aPriori converts this value to a per-second value, so that abrasive additive usage rate uses standard units (mm3/sec).

Abrasive Additive Cost Per Volume = Abrasive Cost / Abrasive Purchase Volume

Abrasive additive unit cost is 0 if the current additive name is None (see below). Otherwise, it is the quotient of values looked up by abrasive name in the lookup table vibratoryFinishingAbrasiveAdditive:

• Cost

• Purchase Volume

By default, the current additive name is specified by the cost model variable defaultAbrasiveAdditive (whose value is Default Abrasive Additive in starting point VPEs). Users can override the default with the setup option Abrasive Additive Utilized.

Media Cost = Media Mass Per Part *

Media Cost Per Unit Mass * (Media Attrition Rate/100) * Process Time

Media cost per part is the product of the following:

• Media mass per part: see the formula for Media Mass Per Part in Vibratory Finishing Batch Size.

• Media cost per unit mass: this is the value of the toolshop property Cost for the current Media Material Type.

• Media attrition rate: this is the percent of in-use media consumed per hour. By default, this is the value of the toolshop property Attrition Rate Percent for the current Media Material Type. This value is based on the assumption that the media size is larger than 3/8".

Users can specify a smaller media size (<=3/8") by setting the setup option Media Size. In this case, media attrition rate is the product of the toolshop property Attrition Rate Percent and the cost model variable smallMediaAttritionMultiplier (1.25 in starting point VPEs).

Note that aPriori converts this value from percent per hour to percent per second, since process time is expressed using seconds.

• Process time: see the formula Tumble Deburr Cycle Time in Cycle Time and Process Time for Vibratory Finishing.

Setup Time for Vibratory Finishing

Setup time per part is given by the following formula:

Amortized Batch Setup = (Setup Time * (Labor Rate + Direct Overhead Rate)) /

Vibratory Finishing Batch Size

Batch setup cost per part depends on the following:

• Setup time (specified as the machine property Setup Time)

• Labor rate (specified by the machine property Labor Rate)

• Direct overhead rate (see Direct and Indirect Overhead)

• Vibratory finishing batch size (see Vibratory Finishing Batch Size)