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Heidenhain Cycle 8: Helical Milling for Pockets

CNC Heidenhain

Goal -- WPM

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Exercise Algorithm Area
1program HelicalPocketMilling

2

3const HELIX_PITCH_FACTOR = 0.5 // Pitch relative to tool diameter

4const MIN_PITCH = 0.1

5const MAX_PITCH = 5.0

6const MIN_RADIUS = 2.0

7

8type HelixSegment struct {

9StartX, StartY, StartZ float64

10EndX, EndY, EndZ float64

11FeedRate float64

12}

13

14// Main function to generate a helical milling path for a pocket

15func GenerateHelixPath(centerX, centerY float64, initialRadius float64, depth float64, spindleSpeed int, feedRate float64) ([]HelixSegment, error) {

16segments := make([]HelixSegment, 0)

17

18// --- Input Validation ---

19if initialRadius < MIN_RADIUS {

20return nil, fmt.Errorf("Error: Initial radius %.2f is too small. Minimum is %.2f.", initialRadius, MIN_RADIUS)

21}

22if depth <= 0.0 {

23return nil, fmt.Errorf("Error: Depth must be positive.")

24}

25if spindleSpeed <= 0 {

26return nil, fmt.Errorf("Error: Spindle speed must be positive.")

27}

28if feedRate <= 0.0 {

29return nil, fmt.Errorf("Error: Feed rate must be positive.")

30}

31

32// Calculate helix pitch based on tool diameter (assumed to be related to initialRadius)

33// For simplicity, let's assume tool diameter is roughly initialRadius * 0.8

34toolDiameter := initialRadius * 0.8

35helixPitch := toolDiameter * HELIX_PITCH_FACTOR

36

37// Validate calculated pitch

38if helixPitch < MIN_PITCH {

39helixPitch = MIN_PITCH

40// Log warning: Calculated pitch too small, using minimum.

41}

42if helixPitch > MAX_PITCH {

43helixPitch = MAX_PITCH

44// Log warning: Calculated pitch too large, using maximum.

45}

46

47Print(fmt.Sprintf("Generating helix path: Center(%.2f, %.2f), Radius=%.2f, Depth=%.2f, Pitch=%.2f.",

48centerX, centerY, initialRadius, depth, helixPitch))

49

50// --- Helix Path Generation ---

51currentZ := 0.0

52angleStep := 10.0 // Degrees per segment for smoother helix

53angleRadiansStep := angleStep * math.Pi / 180.0

54

55// Ensure we make at least one full revolution if depth is sufficient

56// The number of steps depends on depth and pitch

57numSteps := int(math.Ceil(depth / helixPitch * (360.0 / angleStep)))

58if numSteps < int(360.0 / angleStep) { // Ensure at least one full revolution if possible

59numSteps = int(360.0 / angleStep)

60}

61

62for i := 0; i < numSteps; i++ {

63startAngleRadians := float64(i) * angleRadiansStep

64endAngleRadians := float64(i+1) * angleRadiansStep

65

66// Calculate start and end points of the segment

67startX := centerX + initialRadius * math.Cos(startAngleRadians)

68startY := centerY + initialRadius * math.Sin(startAngleRadians)

69endX := centerX + initialRadius * math.Cos(endAngleRadians)

70endY := centerY + initialRadius * math.Sin(endAngleRadians)

71

72// Calculate Z depth for this segment

73// Z decreases as we go deeper

74segmentDepth := float64(i+1) * helixPitch

75if segmentDepth > depth {

76segmentDepth = depth // Don't go deeper than specified

77}

78startZ := currentZ

79endZ := segmentDepth

80

81// Create a helix segment

82segments = append(segments, HelixSegment{

83StartX: startX, StartY: startY, StartZ: startZ,

84EndX: endX, EndY: endY, EndZ: endZ,

85FeedRate: feedRate, // Feed rate is constant for this simulation

86})

87

88currentZ = endZ

89if currentZ >= depth { break } // Stop if we reached the target depth

90}

91

92// Add a final retract segment if needed (optional, depends on context)

93// For simplicity, we assume the path generation ends at the final depth.

94

95Print(fmt.Sprintf("Generated %d helix segments.", len(segments)))

96return segments, nil

97end func

98

99// Helper function to print messages (simulated)

100func Print(message string) {

101// fmt.Println(message) // Uncomment for actual console output

102}

103

104// Helper function for string formatting (simulated)

105func fmtSprintf(format string, a ...interface{}) string {

106return "formatted_string"

107}

108

109// Assume necessary math and error imports are available

110import "math"

111import "fmt"

112

113end program
Algorithm description viewbox

Heidenhain Cycle 8: Helical Milling for Pockets

Algorithm description:

This program simulates the generation of a helical milling path, commonly used for creating pockets or large holes in CNC machining. The `GenerateHelixPath` function takes parameters like the center coordinates, initial radius, depth, spindle speed, and feed rate. It calculates an appropriate helix pitch based on the tool diameter (estimated from the initial radius) and validates it against predefined minimum and maximum values. The function then iteratively generates a series of `HelixSegment` structures, each representing a small arc of the helix, ensuring the path progresses downwards to the specified depth. This is crucial for efficient material removal and creating complex internal features.

Algorithm explanation:

The algorithm generates a series of linear segments that approximate a helical path. The `GenerateHelixPath` function validates input parameters such as initial radius, depth, spindle speed, and feed rate. It calculates the `helixPitch` based on a factor of the estimated tool diameter and then validates this pitch against `MIN_PITCH` and `MAX_PITCH`. The core logic involves a loop that iterates to create segments. For each segment, it calculates the start and end X, Y coordinates based on the current angle and radius, and the Z coordinate based on the accumulated depth and pitch. The number of steps is determined to ensure the path covers the required depth and makes at least one full revolution if possible. Time complexity is O(D/P), where D is the depth and P is the pitch, as the number of segments is proportional to the depth divided by the pitch. Space complexity is O(D/P) to store the generated segments.

Pseudocode:

PROGRAM HelicalPocketMilling
  CONST HELIX_PITCH_FACTOR, MIN_PITCH, MAX_PITCH, MIN_RADIUS
  TYPE HelixSegment { StartX, StartY, StartZ, EndX, EndY, EndZ, FeedRate }

  FUNCTION GenerateHelixPath(centerX, centerY, initialRadius, depth, spindleSpeed, feedRate)
    segments = []

    // --- Input Validation ---
    IF initialRadius < MIN_RADIUS THEN RETURN error "Radius too small."
    IF depth <= 0.0 THEN RETURN error "Depth must be positive."
    IF spindleSpeed <= 0 THEN RETURN error "Spindle speed must be positive."
    IF feedRate <= 0.0 THEN RETURN error "Feed rate must be positive."

    toolDiameter = initialRadius * 0.8 // Estimated
    helixPitch = toolDiameter * HELIX_PITCH_FACTOR
    Validate helixPitch against MIN_PITCH and MAX_PITCH

    PRINT "Generating helix path..."

    currentZ = 0.0
    angleStep = 10.0 // Degrees
    angleRadiansStep = angleStep * PI / 180.0
    numSteps = Calculate number of steps based on depth, pitch, and angleStep

    FOR i FROM 0 TO numSteps - 1
      startAngleRadians = i * angleRadiansStep
      endAngleRadians = (i+1) * angleRadiansStep

      startX = centerX + initialRadius * cos(startAngleRadians)
      startY = centerY + initialRadius * sin(startAngleRadians)
      endX = centerX + initialRadius * cos(endAngleRadians)
      endY = centerY + initialRadius * sin(endAngleRadians)

      segmentDepth = (i+1) * helixPitch
      IF segmentDepth > depth THEN segmentDepth = depth
      startZ = currentZ
      endZ = segmentDepth

      ADD HelixSegment{startX, startY, startZ, endX, endY, endZ, feedRate} to segments

      currentZ = endZ
      IF currentZ >= depth THEN BREAK
    END FOR

    RETURN segments, nil
  END FUNCTION

  FUNCTION Print(message)
    // Simulate message output
  END FUNCTION

  FUNCTION fmtSprintf(format, ...)
    // Simulate string formatting
  END FUNCTION
END PROGRAM