Taking the machining of a new engine cylinder head as an example, this study investigates the manufacturing process regarding positional accuracy requirements for gear mounting/locating holes and dual camshaft holes. By comparing various control methods, a new approach to positional accuracy control is proposed; NC macro-programming is utilized to calculate machining coordinates for the locating holes, effectively ensuring the required center-to-center distance accuracy between the gear mounting/locating holes and the two camshaft holes.
PART 1
Introduction
The factory is developing a brand-new engine targeting "China VII" emission standards, aiming for superior emissions performance and leading technical specifications. To achieve precise control over intake and exhaust airflow within the combustion chamber, the engine employs a dual-overhead-camshaft (DOHC) structure. The new product imposes stringent installation requirements on the gears that interface with the dual-camshaft drive system; consequently, effectively ensuring the positional accuracy of the gear mounting/locating holes is a critical challenge in the trial production and machining of the cylinder head.
PART 2
Part Machining Requirements and Process Analysis
2.1 Common Machining Processes for Camshaft Holes and Gear Mounting/Locating Holes
The positional accuracy requirements for the camshaft holes and gear mounting/locating holes are illustrated in Figure 1. The positional tolerance for the dual-overhead-camshaft holes is specified as φ0.2 mm, while the accuracy requirement for the center-to-center distance between the gear mounting/locating holes and the camshaft holes is ±0.03 mm.
Figure 1: Positional accuracy requirements for camshaft holes and gear mounting/locating holes
Machining both the dual camshaft holes and the gear mounting/locating holes in a single setup (clamping) effectively ensures their relative positional accuracy. Two established machining solutions are commonly used:
1) Using specialized multi-spindle-head equipment: With a single setup and a dedicated boring jig [1], the camshaft holes and gear mounting/locating holes are machined simultaneously from either the same side or opposite sides of the workpiece. However, this equipment involves a high capital investment (exceeding 10 million RMB) and offers poor versatility.
2) Using a large horizontal machining center: With a single setup and a dedicated boring jig, the machine spindle automatically engages a line-boring bar [2]. The camshaft holes are machined first from one side of the workpiece; subsequently, the workpiece and the line-boring tool are rotated 180° together, and a drill jig is used to machine the gear mounting/locating holes. This machining scheme requires the equipment to have a large safe swing radius within the machining zone; furthermore, the spacing between the dual camshaft bores imposes specific requirements on the external dimensions of the spindle box. The increased swing radius and the specific spindle box requirements lead to a sharp rise in the equipment's procurement cost.
Both of the aforementioned schemes entail high equipment investment costs, and the difficulty of adjusting the precision of specialized tooling and fixtures increases exponentially. Current equipment capabilities cannot satisfy the requirement to simultaneously machine the dual camshaft bores and the gear mounting/locating holes in a single setup.
2.2 Analysis of Hole-to-Hole Spacing Precision Control
As current technical capabilities do not allow for the simultaneous machining of the dual camshaft bores and the gear mounting/locating holes in a single setup, a process flow must be adopted wherein the dual camshaft bores are machined first, followed by a process change to machine the gear mounting/locating holes. Positioning errors and shifts in the actual location of the dual camshaft bores during the process transition can cause the spacing between the gear mounting/locating holes and the dual camshaft bores to exceed tolerance limits.
To meet the positional relationship requirements between the gear mounting/locating holes and the dual camshaft bores, the feasibility of the following common machining methods is analyzed.
(1) Fixed Coordinate Method (Tolerance Allocation Method): The fixed coordinate method involves machining the gear mounting/locating holes based on coordinate values specified in the engineering drawings or process documentation after the dual camshaft bores have been machined. To ensure the required hole-to-hole spacing precision of ±0.03 mm between the gear mounting/locating holes and the dual camshaft bores, the machining datum for the gear mounting/locating holes must be aligned with that of the dual camshaft bores during process planning, and the final spacing tolerance must be allocated via a positional dimension chain [3]. The sum of the positional tolerances for the dual camshaft bores and the gear mounting/locating holes is 0.06 mm; the tolerance allocation is illustrated in Figure 2.
Figure 2: Schematic of positional tolerance allocation for dual camshaft bores and gear mounting/locating holes
The positional tolerance for the dual camshaft bores is φ0.03 mm, and the positional tolerance for the gear mounting/locating holes is φ0.03 mm. Based on the results of the positional dimension chain allocation, the dual camshaft bores and the gear mounting location holes require high positional accuracy during their respective machining operations. An analysis of the positioning errors for each operation reveals that datum shift error is the primary issue. The workpiece is positioned using a "one-face, two-pin" method; the maximum clearance between the locating pins and the corresponding holes on the workpiece is φ0.035 mm [4], and the machining equipment has a repeatability of φ0.01 mm. When considering only the effects of workpiece positioning error and machine repeatability, the positional accuracy requirements for the individual operations-machining the dual camshaft bores and the gear mounting location holes-cannot be met; consequently, the accuracy of the center-to-center distance between the gear mounting location holes and the camshaft bores fails to satisfy design specifications.
(2) Datum compensation method: This method involves using the actual center coordinates of the camshaft bores as the machining datum for the gear mounting location holes-effectively aligning the machining datum with the design datum. This approach eliminates errors caused by datum misalignment and datum shift [5] and has proven effective for single overhead camshaft (SOHC) applications. For dual overhead camshaft (DOHC) applications, positional compensation for both camshaft bores is required. The compensation method involves setting the origin of the machining coordinate system for the gear mounting location holes at the midpoint of the X and Y coordinates of the two camshaft bores (X1, Y1 and X2, Y2); specifically, the origin coordinates are defined as X = (X1 + X2) / 2 and Y = (Y1 + Y2) / 2. The datum compensation method entails quality risks. For instance, if the actual center coordinates of both camshaft bore 1 and camshaft bore 2 shift outward by 0.1 mm along the X-axis while remaining unchanged along the Y-axis, the center coordinates become (X1 − 0.1, Y1) for bore 1 and (X2 + 0.1, Y2) for bore 2; the positional tolerance of the dual camshaft bores remains within specifications. In this scenario, although the calculated origin for the gear mounting/locating hole's machining coordinate system-and the hole's actual machining position-remain unchanged, the actual positions of the dual camshaft bores have shifted, thereby altering the distance between the gear mounting/locating hole and the two camshaft bores. Thus, for a dual-camshaft-bore configuration, using the datum compensation method to control the positional accuracy between the gear mounting/locating hole and the camshaft bores poses a quality risk.
PART 3
Positional Accuracy Control for the Gear Mounting/Locating Hole
3.1 Establishing a Mathematical-Geometric Model
The position of the gear mounting/locating hole is defined as the intersection of two arcs: one centered at the axis of camshaft bore 1 and the other at the axis of camshaft bore 2, with radii corresponding to the specified distances between the gear mounting/locating hole and the respective camshaft bores. Physical analysis confirms there is only one such intersection point; the actual coordinate position of the gear mounting/locating hole varies in response to changes in the center coordinates of the two camshaft bores. Based on this, a new machining method was developed. By utilizing in-process measurement technology, geometric principles, and NC programming-and incorporating the actual center coordinates of the dual camshaft bores alongside the required distances to the gear mounting/locating hole-the system automatically calculates and executes the machining coordinates for the gear mounting/locating hole, thereby meeting the positional accuracy requirements relative to the dual camshaft bores.
Figure 3 illustrates the geometric model showing the positional relationship between the dual camshaft bores and the gear mounting/locating hole. Here, CA and BA represent the design distances (in mm) between the gear mounting/locating hole and the camshaft bores (with CA = BA), and the machining coordinate system (calculation coordinate system) is established with the center of camshaft bore 2 as the origin. Figure 3: Geometric model showing the positional relationship between the dual camshaft bores and the gear mounting locating hole
3.2 Mathematical calculation process
After the workpiece is positioned and mounted, in-process inspection technology is used to determine the coordinates of the centers of camshaft bore 1 and camshaft bore 2 within the machine tool coordinate system-denoted as (XB, YB) and (XC, YC), respectively-and to calculate the coordinates (XA, YA) for the center (point A) of the gear mounting locating hole. The calculation process is as follows: ∠2 = ∠1; CE = BC/2; ∠3 = ∠4 − ∠2. From this, the coordinates of point A (the center of the gear mounting locating hole) relative to the origin of the machining coordinate system can be derived. 3.3 NC program conversion
During actual machining, the mathematical calculation process must be converted into an NC program. Using a Siemens CNC system as an example [6], the coordinates (XB, YB) and (XC, YC) of the centers of camshaft bore 1 and camshaft bore 2-obtained via in-process inspection or other technical means-are read into machine variables R201, R202, R301, and R302; the required center-to-center distances BA (between the gear mounting locating hole and camshaft bore 1) and CA (between the gear mounting locating hole and camshaft bore 2) are read into variables R401 and R402. The program for calculating the machining coordinates of the gear mounting locating hole center is as follows. R201=XB; Write the X-coordinate of the center of camshaft hole 1 to machine user variable R201. R202=YB; Write the Y-coordinate of the center of camshaft hole 1 to machine user variable R202. R301=XC; Write the X-coordinate of the center of camshaft hole 2 to machine user variable R301. R302=YC; Write the Y-coordinate of the center of camshaft hole 2 to machine user variable R302. R401=BA; Write the center-to-center distance between the gear mounting locating hole and camshaft hole 1 to machine user variable R401. R402=CA; Write the center-to-center distance between the gear mounting locating hole and camshaft hole 2 to machine user variable R402. R501=R301-R201; Calculate the distance between the centers of camshaft hole 1 and camshaft hole 2 along the X-axis. R502=R202-R302; Calculate the distance between the centers of camshaft hole 1 and camshaft hole 2 along the Y-axis. R503=ATAN2(R502, R501); Calculate the value of ∠1 (in degrees). R504=SQRT(R501* R501+ R502* R502); calculate the length of line segment BC (mm) R506=R504/2; calculate the length of line segment CE (mm) R507=ACOS(R506/R402); calculate the value of ∠4 (°) R508=R507-R503; calculate the value of ∠3 (°) R509=SIN(R508)*R402; calculate the length of line segment AF (mm) R510=COS(R508)*R402; calculate the length of line segment CF (mm) R101=R301-R510; calculate the X-axis coordinate of the gear mounting locating hole center relative to the center of camshaft hole 2 R102=R302-R509; calculate the Y-axis coordinate of the gear mounting locating hole center relative to the center of camshaft hole 2.
The values stored in macro variables R101 and R102 represent the coordinates of the gear mounting locating hole center point A; in the subsequent machining program, machining will be performed based on the calculated center coordinates A (R101, R102). The machining coordinates for the gear mounting locating hole are calculated using the actual mechanical coordinates of camshaft hole 1 and camshaft hole 2 as references during the specific machining operation for that hole; this eliminates errors caused by datum misalignment or displacement. Consequently, the entire 0.06 mm positional tolerance for the distance between the gear mounting locating hole and camshaft holes 1 and 2 is accounted for within this single operation, without needing to consider the positional accuracy of camshaft holes 1 and 2 from preceding operations. When machining different workpieces, the actual position coordinates (R101, R102) of the gear mounting locating hole will vary in accordance with changes in the actual center coordinates of camshaft holes 1 and 2, rather than remaining fixed. Practical machining verification demonstrates that the center-to-center distance tolerance between the gear mounting/locating hole and the dual camshaft holes can be controlled within ±0.01 mm, fully meeting design specifications.
3.4 Innovations
The key innovations of this machining method are as follows:
1) It provides a novel machining strategy that resolves the challenge of controlling the positional accuracy between the gear mounting/locating hole and the dual camshaft holes. When machining the gear mounting/locating hole, the machining coordinates are calculated based on the actual positions of the camshaft holes and the required positional relationship between the gear mounting/locating hole and the camshaft holes; machining is then performed using these calculated coordinates. The actual machining coordinates for the gear mounting/locating hole adjust dynamically according to the actual positions of camshaft hole 1 and camshaft hole 2, thereby ensuring the required accuracy of the distance between the gear mounting/locating hole and the camshaft holes.
2) It integrates geometric principles with NC macro programming to enable the automatic calculation of machining coordinates for the gear mounting/locating hole. A geometric model defining the positional relationship between the gear mounting/locating hole and the two camshaft holes was established, and the calculation process for the center coordinates of the gear mounting/locating hole was derived; NC macro programming is then utilized to automate this coordinate calculation.
3) It employs flexible in-process measurement technology to align the machining datum with the design datum, thereby eliminating positioning errors. During the machining of the gear mounting/locating hole, a probe automatically measures the coordinates of camshaft hole 1 and camshaft hole 2 within the machine tool coordinate system. These measured values are then input into the calculation process to determine the machining coordinates for the gear mounting/locating hole. This integrated process simultaneously aligns the machining datum with the design datum, effectively eliminating positioning errors.
4) It reduces the machining difficulty associated with the preceding operation of producing camshaft hole 1 and camshaft hole 2. The machining coordinates for the gear mounting locating hole are calculated based on the actual positions of camshaft hole 1 and camshaft hole 2. This approach imposes no special requirements regarding the positional accuracy or consistency of the camshaft holes processed in the preceding stage, thereby reducing the difficulty of adjusting and controlling machining precision for that stage.
PART 4
Conclusion
This paper investigates the manufacturing process regarding positional accuracy requirements for the gear mounting locating hole and the dual camshaft holes. Through an innovative machining scheme, the establishment of a mathematical-geometric model, and the proposal of a new positional accuracy control method, the machining coordinates for the locating hole are calculated using an NC macro program based on the spatial relationship between the locating hole and the two camshaft holes. This effectively resolves the challenge of meeting strict hole-spacing accuracy requirements-which are otherwise difficult to guarantee-and provides a solution for machining similar gear train hole configurations.
