To meet the demand for high-efficiency, high-precision machining of C-EPS worm gear profiles, this study systematically investigates key technical aspects-such as process selection, milling optimization, and grinding control-to determine the optimal processing scheme. Improvements are proposed across several areas: equipment selection, workholding methods, cutting tool parameters, cooling systems, and process parameters. Specific solutions include enhancing the rigidity of high-precision CNC whirling machines, optimizing efficiency through hydraulic clamping and automated loading/unloading, designing parameters for ultra-fine coated carbide tools, and controlling high-pressure air-mist cooling and profile grinding processes. The optimized process ensures stable IT7-grade accuracy for the worm profile, significantly improves surface quality and machining efficiency, and substantially reduces production costs.
1
Introduction
Column-type electric power steering (C-EPS) systems are widely used in passenger vehicles ranging from Class A0 to Class B due to their compact structure and manageable costs. The involute worm (see Figure 1) serves as the core torque-transmitting component of the C-EPS; if the tooth profile error exceeds 0.01 mm, issues such as steering lag or abnormal noise are likely to occur [1]. Consequently, the machining process demands strict IT7-grade precision while also meeting the efficiency requirements of mass production.
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Figure 1: Involute worm
Current worm machining processes face three major challenges: ① Traditional turning and grinding processes suffer from low efficiency, with single-shift output falling below 500 units. ② Hobbing and rolling processes yield poor profile consistency; accuracy relies heavily on hob precision, and error fluctuations reach ±0.02 mm as the tool wears. ③ Conventional milling processes fail to meet surface quality requirements, resulting in surface roughness (Ra) values of 1.6 μm or higher. Developing a C-EPS worm machining technology that balances high precision with high efficiency is of significant practical importance for enhancing the market competitiveness of C-EPS products.
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Current State of Research (Domestic and International)
Internationally, efforts to improve worm machining precision often rely on high-end equipment-such as the CNC worm grinding machine developed by the German company KAPP. By utilizing thermal error compensation technology, this equipment controls cumulative helix error to within 0.005 mm; however, the cost per unit exceeds 8 million RMB, creating an extremely high barrier to entry. Domestic research has primarily focused on process optimization; while some automakers utilize a hobbing-plus-rolling process for the mass production of worms, the machining accuracy only reaches the IT8 grade, failing to meet the requirements for high-end vehicle models.
Existing research has yet to establish an integrated machining solution that combines high-efficiency roughing with high-precision finishing. Based on a combined process of whirling and form grinding, this paper constructs a comprehensive optimization system-encompassing equipment, cutting tools, and process parameters-to bridge the gap in high-efficiency, high-precision machining technology for C-EPS worms.
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Selection of Worm Tooth Profile Machining Process
3.1 Comparison of Process Schemes
A quantitative comparison was conducted among three mainstream processes for worm tooth profile machining: turning plus grinding, hobbing plus rolling, and milling (whirling) plus grinding. The comparison evaluated core indicators-such as surface roughness, accuracy grade, and tooth profile consistency-as well as production metrics like machining efficiency and changeover time. Table 1 compares the core indicators of the different processes, while Table 2 compares their efficiencies.
Table 1 Comparison of Core Indicators for Different Processes
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Note: Data derived from actual measurements on an automaker's production line; sample size n=500.
Table 2 Comparison of Efficiency for Different Processes
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Note: Single-shift output is based on measurements of a φ30mm × 120mm worm; equipment features a single-spindle configuration.
3.2 Determination of the Optimal Process
As shown in Tables 1 and 2, the milling-plus-grinding process (whirling for roughing/semi-finishing followed by finish grinding) significantly outperforms the other schemes in both core machining indicators and production efficiency. Furthermore, it eliminates the need for a dedicated hobbing machine process, reducing machining costs by approximately 40%. Consequently, this paper focuses on this process for further in-depth research.
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Optimization of Worm Milling
Milling serves as the roughing and semi-finishing stage for the worm; its machining accuracy and efficiency directly determine the reference quality and production cycle time for the subsequent finish grinding process. This study conducts optimization design across five aspects: equipment selection, workholding methods, cutting tool parameters, cooling systems, and process parameters. 4.1 Equipment Selection and Stiffness Enhancement
(1) Selection of High-Precision CNC Whirling Machine: To meet IT7 precision requirements, a CNC whirling machine equipped with high-precision feed and spindle systems was selected. The key technical specifications are as follows:
1) Feed system: Resolution ≤ 0.0001 mm; full-stroke positioning accuracy of ±0.002 mm.
2) Spindle system: Radial runout ≤ 0.001 mm; axial runout ≤ 0.0005 mm; rotational speed stability of ±5 r/min.
Experimental data indicate that when the machine tool's positioning accuracy improved from ±0.01 mm to ±0.002 mm, the cumulative error of the worm helix decreased from 0.025 mm to 0.008 mm, representing a direct improvement in machining precision by two grades.
(2) Machine Tool Stiffness Enhancement Strategy: Insufficient machine tool stiffness tends to induce cutting vibrations, causing an increase of over 30% in worm tooth trace errors. Machine tool stiffness can be enhanced through the following two measures:
1) Foundation Anchoring: A machine tool base with a thickness of ≥500 mm is cast using C30 concrete and rigidly connected to the floor via M30 expansion bolts; the base's levelness is maintained within 0.02 mm/m.
2) Structural Optimization: A wedge-type locking mechanism is employed at the connection between the tool rest and the machine bed, increasing the contact area by 40% and raising the machine tool's static stiffness to 250 N/μm.
4.2 Optimization of Clamping and Loading/Unloading Methods
(1) Precision Control of Hydraulic Clamping: Traditional manual clamping results in axial positioning errors of up to ±0.1 mm, causing significant fluctuations in the axial positional accuracy of the worm tooth profile. By utilizing a hydraulic self-centering chuck with a clamping force of 5–8 kN-in conjunction with an end-face positioning datum and an axial thrust ring-the clamping positioning error is controlled within ±0.03 mm. This improves the worm's axial positional accuracy threefold, providing a stable machining datum for subsequent finish-grinding processes. (2) Efficiency improvement through automated loading and unloading: A truss robot was adopted to replace manual labor for the automated loading and unloading of worm shafts [2]. Clamping time was reduced from 20 s/piece to 5 s/piece, equipment utilization increased from 65% to 90%, and single-shift output increased by over 300 pieces.
4.3 Cutting Tool Parameter Design and Wear Control
High-quality alloy steel was selected as the raw material for the C-EPS worm shaft, achieving a hardness of 28–32 HRC after quenching and tempering [3]. Based on the material's characteristics, the design process addressed tool material selection, geometric parameter optimization, and wear control during installation.
(1) Tool material selection: A comparison of the cutting performance of high-speed steel (W18Cr4V), standard cemented carbide (WC-Co), and ultrafine-grained coated carbide (YBG series) [4] is shown in Table 3. YBG ultrafine-grained coated carbide was ultimately selected as the tool substrate.
Table 3 Comparison of cutting performance for different tool materials
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Note: Cutting conditions were a feed rate of 0.15 mm/r and a depth of cut of 1.2 mm.
The tool features a WC-Co substrate with added Niobium (Nb) and a 3–5 μm thick TiAlN nano-coating. The coating hardness reaches 3200 HV, and the hot hardness remains stable up to 800°C, meeting the process requirements for high-speed cutting.
(2) Tool geometric parameter optimization: Based on the involute tooth profile characteristics of the worm shaft,
specialized geometric parameters were designed for the rough milling cutter (ZA-type form cutter) and the finish milling cutter (ZI-type form cutter) (see Table 4), balancing cutting forces, cutting edge strength, and machined surface quality.
Table 4 Design of specialized tool geometric parameters
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(3) Tool installation and wear monitoring: Tool installation and wear monitoring must adhere to the following technical requirements. 1) Cutter head configuration: A precision cutter head with a dynamic balance grade of G2.5 is employed. As shown in Figure 2, the cutter head features six mounting positions arranged to alternate between three rough-milling cutters and three finish-milling cutters. The rough-milling cutters extend 0.12–0.20 mm further than the finish-milling cutters, enabling both rough and semi-finish machining to be completed in a single pass.
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Figure 2: Schematic of cutter head installation
2) Helix angle matching: The cutter head is tilted and rotated to align the cutter's helix angle with the worm's lead angle (γ). The formula for calculating the lead angle is:
tanγ = Pz / (πd1) (1)
Where γ is the lead angle (°), Pz is the axial lead (mm), and d is the pitch circle diameter (mm).
3) Wear monitoring: A worm inspection instrument is used to monitor tooth profile errors in real-time. Cutters are replaced promptly when wear reaches 0.005 mm; the inserts can be reused three or four times after regrinding.
4.4 Optimization of cooling system and process parameters
(1) High-pressure air-mist cooling design: The cutting speed for whirling milling reaches 260–360 m/min, with temperatures in the cutting zone rising to 600–800°C. A high-pressure air-mist cooling system [5] operating at 0.80–1.38 MPa is employed. The cooling medium consists of a mixture of 5% extreme-pressure emulsion and compressed air, delivered via four symmetrically arranged fan-shaped nozzles (1.5 mm diameter) to directly flush the cutting zone. This system improves cooling efficiency by 60% compared to traditional flood cooling and reduces the chip residue rate to below 0.5%.
(2) Milling parameter optimization: The orthogonal test method is used to determine the optimal combination of process parameters for worm milling, balancing machining efficiency with machining quality. 1) Depth of cut: The total depth of cut for gear milling is calculated based on the full tooth height, *h*:
*h* = [(d1 + 2mx) - (d1 - 2.4mx)] / 2 (2)
Where *h* is the full tooth height (mm), representing the total depth of cut; *d1* is the gear pitch circle diameter (mm); *m* is the axial module (mm); the factor of 2 in "2m" corresponds to the addendum coefficient (standard addendum is 1*m*, so both sides total 2*m**x*); and 2.4 is the dedendum-related coefficient (standard dedendum is 1.2*m*, so both sides total 2.4*m*).
2) Feed rate: The feed rate is 0.13–0.20 mm/r, adjusted dynamically based on material hardness.
3) Rotational speed: The workpiece spindle speed is 12–18 r/min, and the cutter head speed is 6000–8000 r/min (cutting linear speed of 300–400 m/min).
4) Finish grinding allowance: The allowance is 0.5–0.7 mm, balancing grinding efficiency with final machining accuracy.
Using the parameters above, the production cycle time for a single whirling machine reaches 90–105 pieces/h; the surface roughness (Ra) of the worm after milling is 0.8–1.2 μm, and the tooth profile error is ±0.004 mm [6].
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Control of worm tooth profile grinding
Grinding is the finishing process for the C-EPS worm and directly determines the final machining accuracy. This study implements process control regarding grinding equipment/grinding wheel selection and grinding parameters/cooling control to ensure the worm's accuracy consistently meets the IT7 grade.
5.1 Selection of grinding equipment and grinding wheels
A CNC worm grinding machine with an automatic tooth-alignment function is selected; the machine's positioning accuracy is ±0.001 mm. A form grinding method [7] is employed, using a CNC dresser to dress the grinding wheel into an involute shape matching the worm, thereby ensuring consistency in tooth profile machining. A white fused alumina (WA) grinding wheel is selected, featuring a hardness of H5, a grit size of F80, and a resin bond (offering excellent impact resistance); the wheel diameter is 405 mm, and the operating linear speed is 45 m/s. White fused alumina wheels possess good self-sharpening properties and effectively minimize grinding heat generation-producing less heat than silicon carbide wheels-thereby preventing grinding burns on the workpiece.
5.2 Grinding Parameters and Cooling Control
(1) Grinding process parameters: Based on the reference datum established after worm milling and the final precision requirements, the optimal grinding parameters were determined as follows:
1) Rotational speed: Workpiece spindle speed is 5–8 r/min; grinding wheel speed is 1800–2000 r/min (wheel linear speed is 2289–2543 m/min).
2) Feed rate: Rough grinding feed rate is 180–200 mm/min; finish grinding feed rate is 50–80 mm/min.
3) Wheel dressing cycle: The grinding wheel is dressed after every 5–8 worms to ensure the accuracy of the wheel profile.
(2) Grinding cooling control: Extreme-pressure cutting oil with a viscosity of 20–30 mm²/s at 40°C is used as the cooling medium. Forced cooling is achieved via a 2 MPa high-pressure pump with a flow rate of ≥50 L/min [7]. This ensures adequate cooling of the grinding zone and effectively removes grinding chips, preventing abrasive grain clogging that could compromise machining quality.
5.3 Verification of Grinding Results
Inspection using a high-precision worm tester confirms that worms machined with the optimized form-grinding process achieve stable tooth profile accuracy of IT7 grade, a surface roughness (Ra) of 0.2–0.4 μm, and a tooth alignment error of ≤0.008 mm. The production cycle time is 60–72 pieces/hour, meeting the process requirements for the mass production of C-EPS worms. The dressing profile and profile retention of the grinding wheel are critical control points in the grinding process; any deviation in the wheel profile directly leads to excessive errors in the worm's lead and tooth profile. Therefore, wheel dressing and inspection must be strictly executed in accordance with process requirements.
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Conclusion
This paper establishes a high-efficiency, high-precision manufacturing technology system for C-EPS worms through the optimization of processes and multi-dimensional parameters, yielding the following key research results:
1) The combination of whirling (for roughing/semi-finishing) and form grinding (for finishing) was identified as the optimal manufacturing process for C-EPS worms. Compared to traditional turning and grinding methods, this approach increases efficiency by 10–13 times, achieves IT7-grade machining accuracy, and reduces production costs by approximately 40%.
2) A stiffness enhancement scheme and a hydraulic clamping strategy for high-precision CNC whirling machines were proposed; these measures increased the machine tool's static stiffness to 250 N/μm and reduced clamping positioning error from ±0.1 mm to ±0.03 mm.
3) YBG ultra-fine coated carbide tools (suitable for alloy steel worms) and a high-pressure (0.80–1.38 MPa) air-mist cooling system were developed, enabling high-speed cutting at 300–400 m/min and achieving a post-milling surface roughness of Ra ≤ 0.8 μm.
4) Form grinding process parameters were optimized, establishing a wheel dressing interval of 5–8 parts. Post-grinding surface roughness was reduced to Ra 0.2–0.4 μm, and lead error was kept at ≤ 0.008 mm, meeting the accuracy and stability requirements for mass production.
Future research could integrate artificial intelligence technologies to realize intelligent manufacturing for C-EPS worms: utilizing machine vision systems to monitor tool wear in real-time and deep learning models to dynamically adjust cutting parameters; and developing thermal error compensation algorithms for machine tools to further improve worm grinding accuracy to IT6 grade. These advancements would provide technical support for the R&D and production of high-end C-EPS products and expand their market applications.
