Program Chordal Height and Tooth Thickness

Transcription

1 Program Chordal Height and Tooth Thickness Introduction The purpose of this model is to enable you to calculate the tooth thickness at the reference pitch diameter from the chordal caliper dimensions usually found on shaper cutter tool drawings and sometimes found on gear drawings. Of course, with the back solving capability of TK Solver, you may solve for the caliper dimensions from the tooth thickness as well. The model is primarily set up for shaper cutters but may also be used for gears. Examples Suppose we have a manufacturer s tool drawing of a shaper cutter we wish to consider for machining a gear. We then need, along with other data, the tooth thickness of the cutter at the reference pitch diameter and the true involute form diameter to allow us to do further calculations to determine the suitability of the cutter. (The reference pitch diameter is found by dividing the number of teeth by the transverse diametral pitch.) Figure 1 shows the wizard data input form with the data at hand. 1

2 UTS Integrated Gear Software Fig. 1 Be careful that the outside diameter you use is in the plane where the chordal dimensions are given. On many shaper cutter drawings two outside diameters are given, the outside diameter when new and the design outside diameter. The linear offset is the distance from the base circle to the lowest point on the cutter with true involute form measured along a tangent to the base circle. (It is not necessary to enter the linear offset if only the tooth thickness is wanted.) The linear offset must be in the same plane as the chordal dimensions. NOTE: The model calculates two values for the normal chordal tooth thickness of the tooth. The Exact value is in accordance with the method in The Geometry of Involute Gears, by J.R. Colbourne, published by Springer-Verlag, New York, (This excellent book is recommended to all those who wish to study the geometry of involute gears for both design and manufacturing purposes.) The AGMA value is calculated in accordance with ANSI/AGMA Standard 2002-B88, Tooth Thickness Specification and Measurement. The AGMA value is approximate but quite accurate. 2

3 Chordal Height and Tooth Thickness Report 1 shows the solved model. Report 1 Plot tooth? 'y/'n Default='y Number of Teeth 21 NORMAL PLANE y Diametral Pitch Module Pressure Angle Tooth Ref PD Helix Ref PD Base Helix Angle Axial Pitch Lead TRANSVERSE PLANE Diametral Pitch Module Pressure Angle Tooth Ref PD Base Tooth Thickness Base Tooth Thickness Semi Angle /in ` mm ` deg in deg deg in in /in ` mm ` deg in in rad 3

4 UTS Integrated Gear Software Outside Diameter Roll Outside Diameter Reference Pitch Diameter Base Diameter (Projected) True Involute Form Diameter Roll TIF Diameter Linear Offset (Base Circle to TIF) CALIPER CONTACT DATA Chordal Height from Outside Diameter Normal Chordal Tooth Thickness-Exact Normal Chordal Tooth Thickness-AGMA Helix Angle at Caliper Contact Points Trans PA at Caliper Contact Points Caliper Contact Diameter Normal TT at Contact Diameter Transverse TT at Contact Diameter in deg in in in deg in in in in deg deg in in in We now have the tooth thickness at the reference pitch diameter along with the diameter and roll angle at the lowest point with true involute form. The variable tau is the angle from the center line of the tooth to the tooth involute on the base circle. This angle is sometimes given on the cutter drawing. The base circle diameter given by the model will not be the same as the base diameter on the cutter drawing. The base diameter on the drawing has been reduced slightly to counter the effect of the rake angle on the cutting face of the cutter and bring the projected tooth form into conformance with the required involute. The projected base diameter should be used for all subsequent calculations. A plot of the tooth and caliper is available. The TIF diameter is marked on the plot. Figure 2 is a copy of the plot. 4

5 Chordal Height and Tooth Thickness Fig. 2 The wizard data input form can also be used in the event that you are designing a shaper cutter (or gear) and wish the caliper dimensions and/or the linear offset and roll angle at the TIF. Figure 3 shows the data input form with the information usually at hand for this case. Report 2 shows the solved model. 5

6 UTS Integrated Gear Software Fig. 3 Report 2 Plot tooth? 'y/'n Default='y Number of Teeth 21 NORMAL PLANE y Diametral Pitch /in ` 6

7 Chordal Height and Tooth Thickness Module Pressure Angle Tooth Ref PD Helix Ref PD Base Helix Angle Axial Pitch Lead TRANSVERSE PLANE mm ` deg in deg deg in in Diametral Pitch Module Pressure Angle Tooth Ref PD Base Tooth Thickness Base Tooth Thickness Semi Angle Outside Diameter Roll Outside Diameter Reference Pitch Diameter Base Diameter (Projected) True Involute Form Diameter Roll TIF Diameter Linear Offset (Base Circle to TIF) CALIPER CONTACT DATA Chordal Height from Outside Diameter Normal Chordal Tooth Thickness-Exact /in ` mm ` deg in in rad in deg in in in deg in in in 7

8 UTS Integrated Gear Software Normal Chordal Tooth Thickness-AGMA Helix Angle at Caliper Contact Points Trans PA at Caliper Contact Points Caliper Contact Diameter Normal TT at Contact Diameter Transverse TT at Contact Diameter in deg deg in in in We now have the chordal tooth thickness for the (arbitrary) chordal height of.168 inches and the tau dimension. For a TIF of inches we have the roll angle and the linear offset. Because a shaper cutter is a gear with varying tooth thickness and addendum from the cutting edge to the back, the various dimensions (but not the base diameter) will change as the cutter is sharpened. This model is useful in the investigation of the change in performance of the cutter throughout its useful life. For internal gear cutters see UTS Models and For external gear cutters see UTS Program 500 and UTS Model