Abstract
This article discusses the principles of gear shaving and the determination of cutting parameters. It calculates the cycle times for different gear shaving methods based on actual operational work cycles. By comparing the process routes of axial gear shaving and radial gear shaving, significant differences in processing efficiency between different processes are identified. This paper analyzes the causes of these differences and determines the suitable method for gear finishing.
Keywords: Gear shaving principles; Cutting parameters; Machining methods; Cycle time
Gear shaving is an economical and efficient method for gear finishing. To optimize production scheduling and improve production efficiency, it is necessary to estimate the processing time for gear shaving operations. Determining the processing time for each operation is fundamental to production management and cost accounting. Based on the feeding method during the machining process, gear shaving is typically divided into four types: axial gear shaving, diagonal gear shaving, tangential gear shaving, and radial gear shaving. This article focuses on the most common two methods: axial gear shaving and radial gear shaving.
1. Principles of Gear Shaving
During gear shaving, the main motion between the disk-shaped shaving cutter and the workpiece is actually the meshing of a pair of spiral gears with no backlash and a small shaft intersection angle (typically 10° to 20°). In addition to rolling and sliding along the tooth height direction, there is also relative sliding along the tooth flank direction between the gear teeth during the motion of the spiral gear pair. For gear transmission, this sliding along the tooth flank is harmful, accelerating tooth flank wear. However, for gear shaving, this sliding is utilized to achieve shaving of the workpiece tooth flank.
2. Gear Shaving Operations
(1) Cutting Speed v
The tooth flank sliding between the shaving cutter and the workpiece gear teeth constitutes the cutting motion of gear shaving. The relative speed of this sliding is the cutting speed of gear shaving. The cutting speed v at the meshing node P is typically considered. The normal component v_on and tangential component v_ot of the velocity v_o of the shaving cutter at node P are:
v_on = v_o cos β_o
v_ot = v_o sin β_o
The normal component v_wn and tangential component v_wt of the velocity v_w of the workpiece at node P are:
v_wn = v_w cos β_w
v_wt = v_w sin β_w
Since the normal components of the two velocities are equal, v_w = v_o cos β_o / cos β_w. The vector difference between the tangential components of the two velocities is the cutting speed v, calculated as:
v = v_w ± v_o = v_o sin Σ / cos β_w
where Σ = β_w ± β_o, β_o is the spiral angle at the pitch circle of the shaving cutter, β_w is the spiral angle at the pitch circle of the workpiece, d_o is the diameter of the pitch circle of the shaving cutter, and n_o is the rotational speed of the shaving cutter.
(2) Axial Feed f_x and Radial Feed f_r
When the axial shaving cutter meshes with the workpiece, the contact points of the two tooth surfaces move along the line of action, which is a spatial straight line passing through the node and tangent to the two base cylinders. Without axial movement, only a narrow shallow groove can be shaved on the tooth surface of the workpiece. Therefore, to shave the entire tooth surface, the workpiece must move axially. The axial feed f_x is measured by the axial movement length per revolution of the workpiece (see Table 1).
Table 1: Axial Feed Based on Shaft Intersection Angle and Workpiece Tooth Number
After selecting the axial feed f_x from Table 1, it can be adjusted based on factors such as workpiece rigidity, hardness, and surface roughness requirements. Once the axial feed f_x is selected, the axial feed speed v_x of the workpiece can be calculated as:
v_x = f_x n_w
Radial feed involves moving the shaving cutter along the radius of the workpiece towards the workpiece’s axis of rotation. Both axial and radial gear shaving require radial feed to machine the tooth thickness of the workpiece to the specified size. Axial gear shaving involves radial feed in 4 to 6 increments during the entire cutting stroke, with each radial feed f_r ranging from 0.02 to 0.06 mm. To improve efficiency and tooth surface quality, unequal feed increments are often used. The tooth surface of the radial shaving cutter is not a theoretical involute spiral surface but a special tooth surface conjugate to the tooth surface of the workpiece. Therefore, the workpiece does not need axial movement to process the entire tooth surface. In principle, the tool and workpiece are in point contact during axial gear shaving, while they are in line contact during radial gear shaving. To reduce the pressure on the tooth surface contact and lighten the load on the machine tool, the radial feed speed v_r for radial gear shaving is typically lower than that for axial gear shaving.
3. Calculating the Cycle Time for Axial Gear Shaving
Axial gear shaving involves both radial and axial feeds.
The cycle time t for axial gear shaving includes times for rapid tool advancement t_s, radial feed t_r, axial feed t_x, slight return t_m, finishing t_f, and rapid tool retraction t_b. The calculations for these times are as follows:
t = t_s + t_r + t_x + t_m + t_f + t_b
where:
t_s = L_s / v_q
t_r = (L_r1 + L_r2 + … + L_rn) / v_r
t_x = nL_x / v_x
t_m = L_m / v_q
t_f = NL_x / v_f
t_b = (L_s + L_r – L_rn) / v_q
Here, v_q is the rapid advancement and retraction speed of the shaving cutter, v_f is the axial feed speed of the workpiece during finishing (about 2/3 of v_x), L_r1, L_r2, …, L_rn are the radial feed increments, L_m is the slight return distance (typically 0.02 to 0.04 mm), n is the number of radial feed increments (usually 4 to 6), and N is the number of finishing cycles (typically 2 to 4).
Processing Example
- Workpiece: Modulus 2.5, tooth number 23, pressure angle 20°, straight tooth, tooth width 18 mm, material 20CrMnTi, hardness ≤ 217 HBW, surface roughness after shaving R_a = 1.6 μm, machining allowance on the common normal line 0.07 mm.
- Axial shaving cutter: Tooth number 67, spiral angle 15°.
- Machine: YWA4232 universal gear shaving machine.
Based on these conditions, the following process parameters are determined:
- The initial cutting speed is selected as 30 m/min. The rotational speed of the shaving cutter n_o is calculated as 212.77 r/min using equations (4) to (6), and 225 r/min is selected from the available spindle speeds. Therefore, the rotational speed of the workpiece n_w is 655.43 r/min according to equation (7).
- The axial feed f_x of the workpiece is initially selected as 0.15 mm/r, and the feed speed is calculated as 98.32 mm/min using equation (8). Hence, the table feed speed v_x of 100/60 mm/min (100 mm/min for axial feed after radial feed and 60 mm/min for finishing) is selected.
- The cutting stroke L_r and working stroke L_x are calculated as 0.102 mm and 23 mm, respectively, using equations (9) and (10).
- The air stroke L_s is set to 0.2 mm, and the slight return distance L_m is set to 0.02 mm. The entire processing cycle involves 4 feeds and 2 finishing operations. Since the YWA4232 universal gear shaving machine does not have rapid advancement and retraction functions during axial gear shaving, the radial movement speed of the tool is fixed at 3.75 mm/min.