last update: 7/11/05

Virtual Turning

[Part I] [Part II] [Part III] [Part IV]

Introduction

This webpage briefly summarizes the methodology of simulating manufacturing errors for rotational part given machine and fixture capability and the software VTurning developed by ICAMS.

In Part I, a sample rotational part and its setup plan are introduced, along with machine and fixture capability involved; In Part II, implementation of simulation using MATLAB is introduced, focusing on sample point generation for a number of features commonly encountered in rotational part. Geometry modeling steps and output of the program are provided; In Part III, measuring methods for dimensional and geometric tolerance based on generated sample points are introduced; In Part IV, interface and usage of VTurning are briefly introduced.

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Part I.  Sample Part and Setup Plan

The sample part is a simplified version of Delta Spindle from Delphi Company.  Note that in the drawing below, the key geometric tolerance is the runout of feature F in relation to feature A. 

Sample Part Drawing

Setups and Machining Operations

Face A;

Face E;

Turn B;

Turn D;

Bore F;

Machine Capability

Three operations are used, namely, facing, turning and boring.

Operation         Index                            Distribution

Facing              Z-Axis Deviation            N (0, σ₁²)

Turning Radius Deviation                       N (0, σ₂²)

Boring              Radius Deviation           N (0, σ₃²)

Fixture Capability

Three indexes are sufficient for describing fixture capability of manufacturing rotational part. They are,

1)      rotational  deviation from nominal Z axis;

2)      translational deviation in Z axis from nominal origin;

3)      translational deviation in X axis from nominal origin.

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Part II.  Sample Points Generation

SETUP 1:

1, Set up Machine Coordinate System 1 (MCS_1) as followed,

    Set spindle axis as Z axis, the main locating surface in the machine as XOY plane

2, Given MCS,

Surface A:       

for each sample point,                         

X = R cosθ,  Y = R sinθ, Z = A_OperDim + Z_Error                        

Where, R ~ U(H_Diameter, B_Diameter), θ ~ U(0, 2PI),  Z_Error ~ N (0, σ₁²).  See Figure 1.

Figure 1,  Feature A in MCS_1

 3,  Transform generated sample points from MCS to Workpiece Coordinate System (WCS_1), which has the newly machined feature A as XOY plane, and the Z axis direction opposite to previous MCS_1.   See Figure 2.

Figure 2,  Feature A in WCS_1

SETUP 2:

1, Set up MCS_2 as followed,

    Set spindle axis as Z axis, the main locating surface in the machine as XOY plane

2, Given MCS_2,

Surface E:         for each sample point, 

                        X = R cosθ,  Y = R sinθ, Z = E_OperDim + Z_Error

                        Where, R ~ U(0, D_Diameter), θ ~ U(0, 2PI), Z_Error ~ N(0, σ₁²).

Surface D:        for each sample point,

                        X = (D_Diameter + r_Error)cosθ,  Y = (D_Diameter + r_Error) sinθ,

Z = Length

                        Where, Length ~ U(L_D1, L_D2), θ ~ U(0, 2PI), r_Error ~ N(0, σ₂²).

Surface F:         for each sample point,

                        X = (F_Diameter + r_Error)cosθ,  Y = (F_Diameter + r_Error) sinθ,

Z = Length

                        Where, Length ~ U(L_F1, L_F2), θ ~ U(0, 2PI), r_Error ~ N(0, σ₃²).

See Figure 3.

Figure 3.  Feature D,E,F in MCS_2.

3. Based on the given Fixturing Capability, generate translation and rotation deviation of WCS_1 from MCS_2. Then, transform sample points in MCS_2 into WCS_1 based on generated deviation.  See Figure 4.

Figure 4, Feature D, E, F, A in WCS_1.

Up till now, all features of interest have been represented by their own sample points.

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Part III.  Virtual Inspection

In preceding section, sample points for all features of interest have been generated. Based those sample points, virtual inspection is then conducted. Different geometric tolerance will generally have different algorithm for inspection.  The runout tolerance inspection is explored for our case since it is of the most interest. Referring to sample part drawing, the runout relation is between feature F--a thou hole, and datum A—a flat round surface.  The practical way of inspecting this kind of tolerance will be, first, to establish an axis from datum A, then revolve the part around the established axis, then use indicator to touch inner cylindrical surface of feature F, and then the full indicator movement (FIM) will be the runout tolerance. Referring to Figure 4, it is easy to find that the deviation of distances of sample points in feature F to Z axis is the counterpart of runout tolerance in real inspection.  It is fairly simple to get the deviation since all sample points are already available.

Figure 5 shows the output of a simulation run, given the machine capability of Radius Error as Normal(0, 0.0015²) for boring; Rotational Error as 2*pi/180000, and Translation Error as 0.001 and 0.001 for Z axis and X axis, respectively, for fixturing error.

Figure 5, Runout Tolerance 

The runout is 0.0105 based on this particular run.