Milling bevel rack
A helical rack is a rack with a tooth profile that forms a fixed angle with the axis. Used in conjunction with helical gears, it can transmit motion and power between intersecting axes. It features smooth transmission, high load capacity, and high contact ratio. It is widely used in machine tool feed mechanisms, automated production lines, and other equipment. Helical racks have an involute tooth profile, with the tooth direction forming an angle β (helix angle) with the length of the rack. The difficulty in milling lies in ensuring the accuracy of the helix angle, tooth direction, and tooth profile. This requires specialized fixtures and a gear mechanism to achieve the combined motion of the tool and workpiece to ensure the correct helix angle of the tooth profile.
Helical rack design parameters include module m, pressure angle α, helix angle β, pitch p, and tooth height h. The helix angle β is a key parameter for helical racks and is typically between 8° and 20°. A larger helix angle improves transmission smoothness but also increases machining difficulty. The module and pressure angle must match those of the mating helical gear, with a standard pressure angle of 20°. The module series is the same as for spur racks (1mm, 1.25mm, 1.5mm, etc.). For example, a helical rack with a module m = 2mm, a pressure angle α = 20°, and a helix angle β = 15° has normal pitch pn = πm = 6.283mm, face pitch pt = pn/cosβ ≈ 6.283/cos15° ≈ 6.506mm, and tooth height h = 2.25m = 4.5mm. These parameters must be accurately calculated before machining to serve as a basis for tool selection and machine tool adjustment.
When selecting a tool for milling helical racks, the influence of the helix angle must be considered. A gear milling cutter that matches the normal tooth profile parameters should be selected. This means the cutter’s module and pressure angle are normal parameters and should be consistent with the normal module and normal pressure angle of the helical rack. For example, to machine a helical rack with a normal module of 2mm and a normal pressure angle of 20°, a size 2 (module 2mm) gear milling cutter with a 20° pressure angle should be selected. The tooth profile accuracy of the milling cutter should be higher than the workpiece accuracy grade. An M-grade cutter should be used for rough milling, while an A-grade cutter should be used for fine milling. During tool installation, the angle between the cutter axis and the work surface must be adjusted to align the cutter’s helix angle with the helix angle of the helical rack. This can be achieved by using angle shims. The angular deviation should be ≤±5°; otherwise, the tooth profile error will increase.
Helical rack clamping and machine tool adjustment are critical to ensuring tooth profile accuracy. They are typically clamped with flat-nose pliers or specialized fixtures. The workpiece bottom surface must be tightly aligned with the worktable surface, checked with a dial indicator. Flatness deviation should be ≤0.02 mm/m to prevent workpiece tilt from causing tooth profile errors. To achieve the helical profile of the rack, a pulley is installed between the milling machine’s table’s longitudinal feed and the indexing head. This pulley’s transmission ratio controls the additional rotation of the workpiece. The pulley ratio, i = tanβ/π. For example, for β = 15°, i = tan15°/π, which is approximately 0.2679/3.1416, which is approximately 0.0853. Select an appropriate pulley combination based on the milling machine’s transmission ratio. The worktable’s lateral offset is adjusted to align the cutter’s line of symmetry with the workpiece’s axis. The offset, s = mZ/2 (where Z is the number of rack teeth), ensures uniform tooth thickness. Before machining, a trial cut is required to mill shallow teeth on the end face of the workpiece, measure the tooth direction and helix angle, and only after confirmation can formal machining be carried out.
Milling process parameters should be adjusted based on the helix angle and tool material. For rough milling, the cutting speed should be 15-25 m/min (for high-speed steel cutters) or 40-60 m/min (for carbide cutters), with a feed rate of 0.1-0.2 mm/r and a depth of cut of two-thirds of the tooth height. A 0.5-1 mm allowance should be reserved for finishing. Due to the inclined tooth profile of the helical rack, the axial component of the cutting force is greater, so the feed rate should be reduced appropriately to prevent workpiece vibration. For finishing milling, the cutting speed should be increased to 25-35 m/min (for high-speed steel cutters), the feed rate reduced to 0.05-0.1 mm/r, and the depth of cut should be the remaining allowance. Down-milling should be used to reduce tooth surface roughness. Cutting fluid should be used during milling, and extreme pressure emulsions should be used when machining steel parts to cool and lubricate the tool to prevent excessive tool wear due to high cutting temperatures. After each rack section is milled, the tooth thickness and tooth pitch need to be measured. The tooth thickness deviation is controlled within ±0.02mm, and the cumulative error of tooth pitch is ≤0.05mm/1000mm.
Quality inspection includes testing of tooth profile, tooth direction, pitch, and surface quality. Tooth profile accuracy is tested using an involute tester, with a profile error of ≤0.015mm. Tooth direction accuracy is tested using a tooth gauge or dial indicator, with a tooth direction error of ≤0.01mm over a length of 100mm. Tooth pitch is measured using a pitch gauge, with an error of ≤0.02mm between adjacent teeth. Surface roughness Ra is ≤1.6μm. For long helical racks (length > 1000mm), rack straightness is also tested, with an error of ≤0.05mm/m to ensure good meshing with the helical gear. Through strict process control and precise measurement, the transmission accuracy and smoothness of the helical rack are guaranteed to meet the operational requirements of mechanical equipment.
