Noise Characteristics Analysis of Medical Electric Leg Compression Machine Using Multibody Dynamic Simulation

Abstract

Conventional medical equipment used for treating patients with ischemic heart disease relies on pneumatic compression to achieve intense and instantaneous compression of the legs. Because the pneumatic operation of a compressor inevitably produces noise, the treatment is given to a patient in a separate room to avoid causing discomfort to other patients. This need for a dedicated treatment room could be another source of increased medical costs. In this study, a new electrical motor-driven system was developed to address the noise problem of existing pneumatic compression devices. Additionally, the new system features a reduced footprint and weight, and can be carried by medical staff. To develop a low-noise leg compression machine, the noise level at the surface of the structure was estimated using multibody dynamics simulation. Based on the initial design of the electric leg compression machine, parameters including assembly tolerance, component material, and shape of the structure were adjusted to prepare variations of the initial design, and their noise characteristics were analyzed. It was found that by applying the design variables, the noise levels were reduced by 7.2–11.7% compared with the initial design. The most significant reduction in noise levels was 11.7% and was achieved by reinforcing the section surrounding the gearbox enclosing a noise source.

1. Introduction

Ischemic heart disease is closely associated with atherosclerosis and is a condition of insufficient blood flow to the heart through the three major coronary arteries. Hyperlipidemia, diabetes, obesity, high blood pressure, and smoking are well-known risk factors that facilitate the buildup of fats, cholesterols, and blood clots on the walls of the blood vessels. These plaques damage the endothelial cells and reduce or even block the blood flow. Ischemic heart disease is commonly treated in three stages.

The first therapeutic approach includes exercise, diet, medications, percutaneous transluminal coronary angioplasty (PTCA), and stent insertion. As a next step, when medical stent insertion is not available, coronary artery bypass grafting (CABG) surgery can be performed. Lastly, if the treatment effects or symptom improvements achieved by the previous medical and surgical procedures are not sufficient and additional surgery is not a viable option, or the effect of pharmacological treatment is limited, an enhanced external counter pulsation (EECP) procedure is applied to the patient.

In the EECP procedure, a patient lies on the bed wearing cuffs on the legs at the calves and thighs, and buttocks (or upper thighs). The cuffs are inflated during diastole, applying external pressure on the body, and deflated during systole, releasing the applied pressure.

The timing of sequential inflation and deflation is synchronized with the cardiac cycle. During diastole, the pressure exerted by the cuffs facilitates the blood flow from the legs to the upper body; during systole, the blood flow to the lower body increases as the cuffs deflate, strengthening the myocardium and facilitating new blood vessel formation. With these benefits alone, EECP can have therapeutic effects on patients with angina or myocardial infarction [1,2,3,4,5]. Furthermore, the therapeutic effects of EECP include vascular endothelial cell activation, aging prevention through enhanced blood circulation and oxygen supply, increased blood flow to the brain and kidneys, blood vessel regeneration, toxins, blood plaque clearance, and regeneration of new blood vessels [6].

A typical EECP treatment consisting of 35 one-hour sessions (five days a week over seven weeks) can increase blood flow around clogged blood vessels by activating the surrounding dormant blood vessels [7]. Based on these benefits, EECP treatment is recommended for cases where medical or surgical treatments cannot be considered [8]. As shown in Figure 1, traditional EECP treatment uses a pneumatic system where two to three air compressors are placed under the bed. Compressed air is instantaneously injected into the cuffs wrapped around the patient’s legs during the diastole phase of the patient’s cardiac cycle.

Since its initial development in the 1960s, EECP technology has not seen much progress [9].

The machine tends to generate operational noise and heat, and physical impact on the patient’s body, but the technology to address these issues has not yet been developed. The operational noise causes discomfort to both patients and medical staff, and persistent exposure to this noise can cause noise-induced hearing loss.

In this study, an electric EECP machine was developed to overcome the shortcomings (noise and shocks on the body) of conventional EECP machines. In general, hospital noise levels need to be controlled and limited to 50 dB or lower to prevent the noise from discomforting and disturbing other patients [10,11,12,13,14].

By replacing the air compressors with electrical motors, the disturbing noise and physical impact on the body were resolved. In addition, the motors can be electronically controlled for each compression target (calves, thighs, buttocks), which means that the compression timings and pressures can be set individually. This capability is essential for the development of a treatment scheme that is optimized for the patient’s cardiac state and cuff locations.

Since the effect of each cuff on the blood flow can be analyzed, the cuff locations, number of cuffs, and compression timing in relation to other cuffs can be fine-tuned for each patient to achieve the maximum EECP effect. By removing the air compressors, a core component of the pneumatic system, the electric leg compression machine developed in this study, was designed to produce lower levels of operating noise and to allow easy transportation of the entire machine, as shown in Figure 2.

In the new electric leg compression machine, electrical motors, replacing the air compressors, apply pressure on the legs by repeatedly inflating and deflating the cuffs. The motors need to repeat clockwise and counter-clockwise rotations in a short period, and accordingly, the gears should mesh and rotate.

2. Gear and Motor Selection

2.1. Specifications of the Gears and Motor

For noise reduction, helical gears were selected instead of spur gears. In helical gears, meshing starts in a point, expands in width, and then decreases and completes in a point again. Therefore, compared with spur gears, elastic deformation is minimized, resulting in lower noise levels and vibration. Information on the helical gears used in this study is summarized in

Table 1. Specifications of the gears.

	Gear 1: Driver Gear	Gear 2: Driven Gear
Module	1	1
Press angle [°]	20	20
Helix angle [°]	15	15
Number of teeth	19	76
Face width [mm]	8	8
Center distance [mm]	49.175

.

A fixed single gear ratio of 4 was chosen to minimize the volume of the machine as shown in Table 1.

Motor specifications are given in

Table 2. Specifications of the motor.

	Motor Specifications
Power supply capacity [kVA]	0.9
Rated output [W]	400
Rated torque [N·m]	1.3
Rated rotational velocity [RPM]	3000
Maximum rotational velocity [RPM]	5000

. Based on the chosen gear ratio (Table 1), the target pressure was calculated before selecting a motor.

2.2. Calculations for Selecting an Appropriate Motor

The motor selection process was as follows. The pressure required to achieve a therapeutic effect by compressing the body is 40 kPa [15,16]. Assuming the target area of the body to be a cylinder of 0.22 m in diameter and 0.15 m in height, the area to be pressed and required force (FA) can be calculated using Equation (1).

Required pressure [Pa] × Contact area [m²] = 4146.9 N

(1)

The torque of the selected motor is 1.3 N/m, and the gear ratio is 4. In this configuration, the torque of the gear can be estimated using Equation (2).

Motor torque [N/m] × Gear ratio = 5.2 N/m

(2)

The radius of the motor axis is 0.05 m, and consequently, the force applied to the area (FB) is determined using Equation (3).

Gear torque [N/m] ÷ Motor shaft radius [m] = 104 N

(3)

The diameter of the cuffs is designed to be 0.05 m, and the travel distance per one turn of the large gear is calculated using Equation (4).

Diameter of cuff drum [m] × pi = 0.157 m

(4)

The rotational velocity of the driver gear directly connected to the motor is 3000 RPM (rated RPM of the motor), and then, the gear ratio sets the rotational velocity of the driven gear to 750 RPM. Based on this consideration, the stroke per second is determined by Equation (5).

The rotational velocity of driven motor [RPM] × Distance when cuff rotates one turn [m] ÷ 60 = 1.964 m/s

(5)

The gears operate in a 1:2 ratio to inflate and deflate the cuffs per second. That is, it takes 0.33 s to deflate the cuffs. The stroke required to achieve the therapeutic pressure of 40 kPa is 0.06 cm. Based on this, the stroke per second is determined by Equation (6).

Required stroke [m] ÷ Operating time for shrinkage [s] = 0.18 m/s

(6)

The product of the RPM and torque of the selected motor needs to be larger than that of the required RPM and torque to meet the specification established for this study. First, the product of the RPM and torque of the selected motor are determined using Equation (7).

Rotation velocity of Motor × Motor torque = 3900 N/m∙RPM

(7)

The product of the RPM and torque required to obtain the therapeutic effect by compressing the body is determined using Equation (8).

Required stroke per sec × Rotational velocity of driven motor ÷ Stroke per sec × Motor torque ÷ (F_B/F_a) = 3564 N/m∙RPM

(8)

The results of Equations (7) and (8) indicate that the selected motor satisfied the specification, as the product of the RPM and torque of the selected motor exceeds that of the required RPM and torque required to obtain the therapeutic effect by compressing the body.

3. Multibody Dynamics Simulation

3.1. Simulation Model

Using the multi-body dynamics software ANSYS DAFUL, the noise levels generated by the structures with different assembly tolerances, materials, and reinforcement were estimated under a given operating condition. Operational noise is transmitted via the gears, the axis connected to the gears, bearings, and the structure cover. The trembling of the structure cover is radiated through the vibration in the air and finally perceived as noise by humans. Because the noise generated at the cover travels through the air, the noise levels perceived by patients and medical staff are lower than the level at the cover. In this study, multi-body dynamic analysis was used to analyze the noise level at the cover of the structures with different assembly tolerances, materials, and configurations. The noise level at the cover surface of the body compression machine was determined using the multi-body dynamics software ANSYS DAFUL. The schematic calculation flow is shown in Figure 3.

The sound pressure and sound pressure level in Figure 3 are calculated using Equations (9) and (10) [17].

P(t) = (ρ₀/2π) × a × (t − r/c) ÷ r × A

(9)

where P(t) refers to sound pressure (N/m²), ρ0 is the density of air (kg/m³), a is the acceleration of the element (m/s²), r is the distance to the cover (m), c is the velocity of sound (m/s), and A is an area of the element (m²). The air density and sound velocity were set to 1.21 kg/m³ and 343 m/s, respectively.

SPL = 20 × log(P/P₀)

(10)

In Equation (10), SPL stands for sound pressure level (dB) and P₀ represents reference sound pressure. The reference of sound pressure was set to be 20 × 10⁻⁵ N/m².

Short time Fourier transform (STFT) in Figure 3 was used to analyze the time-frequency distribution of the sound pressure level [18].

The medical electric leg compression machine developed in this study is shown in Figure 4. Motor-driven repeated sequential inflation and deflation of the cuffs applies pressure to the target area of the body.

The multi-body dynamic analysis model for the medical compression machine is shown in Figure 5. The inside and outside of the model are shown in Figure 5a,b, respectively. The inside of the structure consists of a frame, motor, gears (driver and driven), gear cover, main shaft, idle shaft, and connectors. The exterior of the structure consists of the main cover and top cover. Two types of ball bearings are connected to the main shaft as shown in Figure 6, and their specifications are summarized in

Table 3. Specifications of the bearings.

	Bearing 1	Bearing 2
Bore [mm]	10	17
Outer diameter [mm]	22	30
Width [mm]	6	7
Designation number	6900	6903

.

The inside of the structure consists of a frame, motor, gears (driver and driven), gear cover, main shaft, idle shaft, and connectors.

The exterior of the structure consists of the main cover and top cover. Two types of ball bearings are connected to the main shaft as shown in Figure 6 and their specifications are summarized in Table 3. The structural properties used for multi-body dynamic analysis are presented in

Table 4. Material properties.

Part	Material	Young’s Modulus [GPa]	Poisson’s Ratio	Density [kg/m3]
External cover	Polycarbonate	2.2	0.37	1210
	Polyacetal	3.3	0.35	1420
Gear	S45C	210	0.3	7865
Etc.	Al6061-T6	68.9	0.33	2698

.

3.2. Design Variables

In this study, the effects of assembly tolerance, material, and structural configuration on noise levels were determined using multibody dynamic analysis. First, the effects of assembly tolerance on noise levels were analyzed. Case 1 was designed to allow the main shaft which is connected to the driven gear to be displaceable by a maximum of 0.3 mm in the axial direction. Case 2 was prepared with a bearing tolerance of 0.02 mm. These design variations are represented in Figure 7. Two additional cases were prepared to test the effects of the materials. For Case 3, the top cover material was changed from polycarbonate to Al6061-T6. Aluminum has a better sound absorption property than engineering plastic polycarbonate and was expected to reduce the gear noise level. For case 4, the material for the driven gear was changed from S45C to polycarbonate. In general, plastic gears produce less noise than metal gears, but the durability issue needs to be considered [19]. Polyacetal has a small wear and friction coefficient and is also wear-resistant with good mechanical properties compared to ordinary plastics [20]. Because the driver gear is exposed to a fatigue load four times higher than that of the driven gear, the material for the driver gear was fixed with S45C. The components tested with different materials are shown in Figure 8.

The effects of structure on noise levels were tested with four additional cases. The purpose of structural modifications is to reduce noise levels by enhancing structural rigidity within the scope of the basic design. For Case 5, the structural frame next to the gear case was changed to a solid type (Figure 9a). Gears are the major source of noise, and as such enhanced rigidity of the frame close to the gears may reduce noise generation. For Case 6, an arch-shaped reinforcement was added transversely in the middle of the frame without interfering with other internal components (Figure 9b). For Case 7, the thickness of the top cover was increased from 1 mm to 2 mm (Figure 9c). This was the maximum thickness increase allowed without interfering with other structural components. For Case 8, the gear thickness was reduced from 8 mm to 6 mm (Figure 9d). The lower the thickness of the gears, the smaller the contact area, resulting in lower noise levels.

3.3. Mesh Generation

Meshes were generated for each component needed for multi-body dynamic analysis. The generated meshes are shown in Figure 10. The mesh was tetrahedral in shape and 1 mm~3 mm in size.

3.4. Loading Condition

Analysis conditions are determined by the motor specifications. Figure 11 shows the shape of the gear and motor. The input value is the rated rotational velocity of 3000 RPM (Table 2). Considering the rated torque of 1.2 N·m and the gear ratio, the output torque becomes 5.2 N·m. The input rotational velocity and output torque over time are shown in Figure 12.

In Figure 12, the input rotational velocity and output torque were set to be stabilized after 1 s and 0.5 s, respectively, giving a time difference of 0.5 s for an initial load of analysis and analysis stabilization. Vibration or impact may occur in the early stage of analysis if the same time zone is set for both velocity and torque without applying this time difference when analyzing the gear operation. In addition, it is highly likely to cause issues regarding the time efficiency of analysis and convergence of the numerical method.

The vibration of the gearbox originates from the gear mesh frequency (GMF). The GMF can be calculated using Equation (11).

Number of gear teeth × Rotational velocity of gear [RPM] ÷ 60 = 950 Hz

(11)

In Equation (11), the gear ratio of the driver gear to driven gear is 4, and consequently, the rotational velocity also has a 4-fold difference, resulting in the same GMF values.

4. Noise Level Analysis Results

The level of noise generated by rotating gears was measured at the top cover of the medical compression machine.

The main cover is in contact with the body, so it does not propagate noise. The results of an analysis of the eight cases are summarized in Figure 13. In Figure 13, the noise patterns were represented with STFT plots. In the STFT plots, the time and frequency were shown on the horizontal and vertical axis, respectively, and the color contour indicates the amplitude (dB) of the frequency component.

The plots were generated by sequentially overlapping frequency transformations for a specific time interval (0.05 s). Figure 12a shows the analysis results of the initial model. In all cases, the noise level peaks at 950 Hz, which is the GMF component of the gear pairs calculated using Equation (11).

This result suggests that the GMF component generated from the pair of gears has the most significant impact on the system.

The STFT results in Figure 12 show the typical whine noise pattern caused by the meshing of the toothed gears. Whine noise is excited by the transmission error of mating gears and can be described as a resonance due to gear mesh frequency.

The highest noise level at the top cover and the weight of each case are summarized in

Table 5. Noise level by case.

ID	Maximum Noise [dB]	Compared with Reference [%]
Reference	171.6	-
Case 1	173.9	1.3
Case 2	176.2	2.7
Case 3	157.6	−8.2
Case 4	158.7	−7.5
Case 5	151.4	−11.8
Case 6	159.2	−7.2
Case 7	159.2	−7.2
Case 8	158.7	−7.5

and

Table 6. Weight by case.

ID	Weight [kg]	Compared with Reference [%]
Reference	2.82	-
Case 1	2.82	-
Case 2	2.82	-
Case 3	3.06	8.4
Case 4	2.58	−8.5
Case 5	3.42	21.5
Case 6	2.87	1.9
Case 7	2.88	2.1
Case 8	2.74	−2.7

.

The initial tolerance applied in Cases 1 and 2 increased the noise level to 1.3% and 2.7%, respectively. Poor bearing assembly was found to have a more significant effect.

Combining Table 5 and Table 6, the following results can be obtained. In Case 3, where the cover material was changed from polycarbonate to aluminum, a material with a better sound absorption property, the weight increased by 8.4% while the noise level was reduced by 8.2%. For Case 4, where the driven gear material was changed from S45C to polyacetal, the noise level and weight were reduced by 7.5% and 8.5%, respectively. Both the weight and noise level could be reduced by changing the material for the driven gear. The fatigue strength of S45C and polyacetal are 307.7 [21] and 40~45 MPa [22], respectively. The polyacetal gears are vulnerable to fatigue because gears are exposed to repeated loads. For Cases 5–7, structural reinforcement increased the weight, but the noise levels were lowered. For Case 5, the gear cover was enclosed with the solid frame, the weight increased by 21.5% (600 g), and the most significant level of noise reduction was achieved—11.8%.

This result could be attributed to the sealed gear cover, through which significant noise is propagated. The arch-shaped reinforcement also increased the weight of Case 6 by 1.9%, but the noise level was reduced by 7.2%. Increased cover thickness in Case 7 also increased the weight by 2.1%, with a noise reduction of 7.2%. Based on these results, structural reinforcement (Case 6) and increased cover thickness (Case 7) are preferred for noise reduction while keeping the weight increase minimal. Reduced gear thickness and a consequent decrease in weight and contact area of the gears led to noise reduction (Case 8). However, as described earlier, the pressure required for therapeutic body compression is 40 kPa.

The load required to achieve this pressure level is applied to the gears in contact, and therefore, increased stress due to a smaller contact area may cause fatigue problems.

5. Conclusions

This study was carried out to develop a new electrical motor-driven EECP machine by addressing the shortcomings of the pneumatic EECP used to treat ischemic heart disease patients. To suppress noise generation to a level suitable for operation in general multi-bed rooms in hospitals, the effects of assembly tolerance, material, and shape of the structure on noise generation were investigated using multi-body dynamic analysis. Using STFT, the acceleration over time and frequency was converted into dB to represent noise levels. Based on the STFT results, parameters affecting the noise levels during the operation were analyzed. The major findings are as follows.

• The noise level increases due to axial assembly tolerance of the main shaft and bearing assembly tolerance that may be generated during processing and assembly processes. Therefore, it is necessary to strictly ensure the required tolerance levels of the main shaft and bearing are achieved when manufacturing a product.
• For the cover material, the noise level could be reduced by replacing the plastic with aluminum, which has higher sound-absorbing power than plastics, but this increases the weight of the structure. Plastic-driven gears significantly reduce the noise level. However, additional safety research is necessary due to the potential fatigue damage in gears.
• In general, a noise reduction effect is proportional to the weight of a given structural reinforcement. Although simulation results suggested that both the weight of the machine and the noise level could be reduced by decreasing the thickness of the gears, additional experimental validation studies are needed to investigate the effects of increased stress applied to the gears.

In summary, this study developed a simulation approach that could be used to estimate the noise from an operating gear unit, and based on the simulation results, an efficient design method for electric EECP machines was proposed. The proposed simulation approach is expected to reduce development time and cost significantly by replacing the experimental validation process performed during the design phase.