David Yang

John Ellington

At the last weekly Monday morning meeting,

2 any additional data they would, based on data available in each department. The ABC report was supplemented by a range of operational and financial datasets collected by the consultants for the past period of two years, called 'XYP ABC Datasets excel files'.

Yang and Everington were expecting that the 'New Yoyo Project' business cases presented by the project teams include some propositions for strategic repositioning if necessary and operations improvement of Xiao Yoyo Plastics' operations, however they were also convinced that the new strategy would highly benefit from using advanced data analytics software solutions. They were convinced that a new 'operating model' would be necessary in order to align the company's operations with new strategic priorities. The new operational model would take advantage of data analytics technologies to create a sustainable competitive advantage for Xiao Yoyo Plastics. Three consecutive meetings were going to take place during the 'Strategy Away Week' for each project team to present to the top management of XYP a strategic plan for the company as well as some practical advice for implementation.

A total budget of 30 million yuan had already been agreed 'in principle' by the board of XYP, therefore the 'New Yoyo' project teams were not expected to investigate the details of the cost and budget of the implementation of their strategic plan at first stage. Instead, they were expected to perform a thorough business analysis to solve XYP's business problems and explore strategic opportunities, review a range of strategic options available and focus on one best scenario, give advice on the implementation of their strategy, and propose solutions for monitoring of XYP's performance in the post implementation phase. It was agreed from the beginning that considerations over the costs of the project would not need to be discussed during the Strategy Away Week, as far as project teams were judging that their proposal would fit the total budget estimate (which indeed was still be flexible if the project team could successfully manage to convince the top management of XYP to give their approval to the business case). Project teams were also expected to recommend solutions for designing a KPI Dashboard (Key Performance Indicators) using a data analytics software package and create a showcase using the datasets contained in the ABC Report (or data collected in any other department of XYP, or even externally).

Each project team will be composed of a group of five executives from XYP, supervised by one member of the Accounting & Finance department. The discussions with the top management team of XYP would need to be completed in three steps. The first presentation is aimed to explain the new strategic plan, what strategic priorities would be, and how the 'New Yoyo' project would help the company succeed. Each project team was expected to give a short, five-minute 'keynote speech' 3 about their strategic vision of XYP according to their strategic plan. For the second presentation, each project team had to propose a number of performance indicators (a number of 8 indicators was judged 'reasonable'), to propose what a KPI dashboard of performance indicators would look like according to their strategic plan. Such KPI dashboard is intended to be an effective tool for the management of the company to the implementation of the strategy at the various levels of the organization, in order to guarantee the achievement of new targets. For the third presentation, the project teams need to demonstrate to what extent the use of data analytics software solutions would help to implement the strategy and KPI dashboard. The management team of XYP was expecting 'showcase' examples of live-simulations of such software during the presentation.

Xiao Yoyo Plastics Products and Markets

XYP, a family-owned company, manufactures and sells a range of products made of polyurethane. The company has grown steadily over the past ten years following a series of mergers with smaller family-run businesses in the plastics industry throughout China. The company has its headquarters located in Suzhou Industrial Park. Its main manufacturing site is also located in Jiangsu province and employs 1,145 staff. XYP also operates a smaller manufacturing site at close distance of its main manufacturing facility for the production of plastic bags.

In 2018 the company recorded total revenue of 1,600 million Chinese yuan. XYP manufactures and sells three main types of products: plastic rolls, rolls of plastics films, and plastic bags (Appendix 1).

• Plastic rolls are used in construction and agriculture, as for example to cover large areas of lands, plantation fields, or construction sites. Plastic rolls are mainly undifferentiated products, and do not need to meet high-quality requirements. • Rolls of plastic films are used in the consumer goods or retail for packaging (like for packaging of bottles of mineral water, or for frozen food items …); customers of those products (as for example leading brands of Chinese consumer goods) have strong expectations on quality standards. • Plastics bags and rolls of plastic films are both sold to the same clients. XYP was said by its customers that the quality of the plastic films and bags vehiculates the brand and reputation of XYP's customers.

XYP has encountered several changes in the market demand for its products recently due to news trends in the plastic manufacturing industry in China and worldwide. Competitors rivalry in the market for plastic rolls has become more and more intense in recent years because of new entrants, which resulted in over supply capacity and practices of price-dumping. In particular, market demand is increasingly driven by product customization (color, logo printing…) and several companies have implemented Just-in-Time systems in order to reduce the time-to-delivery and decrease the size of each onetime delivery. In a recent interview, David Yang summarized the challenges faced by XYP in an increasingly competitive market: "If you want to have a sustainable competitive on China market, you need to take each of those two market segments separately: plastic rolls, and rolls of plastic films or plastic bags. Plastic rolls are undifferentiated products, they can be customized to clients requests to a minor extent only, as for example may be for the size of the product, thickness, quality standards...But for rolls of plastic films and plastic bags, there are many ways you can differentiate your products from your competitors! That is where we can make a difference.' 'It is quite fortunate indeed that while our income from the sales of traditional products like plastic rolls constantly diminished over the past ten years, hopefully the demand for value-added products like plastic bags has continuously increased. In 2017, the demand for specialized products has reached a total revenue of 450 million Chinese yuans for XYP, which represents 30 % of the total revenue of the company'

As compared to Plastic Rolls, the production of rolls of plastic films and plastic bags is more human capital-intensive, with a diverse range of customers in various industries and markets worldwide. However, this market segment requires much more efforts in terms of product customization, service delivery, and supply chain capabilities. A large proportion of customers for those products have implemented Just-in-Time systems which contributed to greater variability in demand for those products, as illustrated for example by the case of plastic bags for frozen food products. Customers of plastic bags do not only have strong expectations for the timely delivery of products, but they are also willing to buy more services from the plastics manufacturers, as for example services for the design of their packaging or for the development of new innovative products to fulfill their needs (like for example design, prototyping and other services supposed to improve the brand image towards end-customers)

Xiao Yoyo Plastics Operational Performance

In 2018, XYP's operating profit decreased by 9 % as compared to 2017. According to the management letter from XYP's auditors, the combined effects of a decrease in sales volumes and lower gross operating margins are the main reasons of the poor financial performance.

Even if XYP had successfully reacted to adapt its products and services to a more complex demand, XYP nowadays serves a wider customer base for the rolls of plastic films, as well as plastic bags, most of those clients placing small, customized orders, and expecting shorter and expecting shorter response times (less than two weeks as compared to two months ten years ago). XYP's factory is now processing short batches of a few hundred items on expensive machines, specifically designed for customized runs, instead of batches of more than 10,000 items on efficient, high volume machines. Beyond the normal operations of extrusion, cutting and welding, XYP also has more and more often to provide assistance to customers for customer administration and technical support, and product design.

In the management letter from XYP's auditors, several issues had been evidenced which affect the normal day-to-day operations of the company:

• several complaints from customers resulting in loss of market share, • significant increase in wages and salaries due to overtime working hours in the factory, • maintenance costs pointed out as some of the reasons of the erosion of profit margins • frequent and unanticipated changes in the production planning incurred by customers' rush orders and ad hoc shipments

It was obvious that XYP's management team had to address several important issues: How should Yoyo Plastics improve its operational model in order to stay competitive in the marketplace? Could Yoyo Plastics really maintain a strategic competitive advantage?

ABC Business Improvement Project

David Yang's introduction to Activity Based Costing (ABC) came two years ago, when XYP's shareholders told him of an initial project undertaken from their external auditors to identify weaknesses in the operational efficiency and processes at XYP's factory. When the ABC concept was explained, Yang agreed that XYP's factory was an ideal candidate to undertake an ABC analysis project. XYP was using a traditional job cost accounting system. Given the many variables that were so tough to manage, and the rapidly evolving and customer base of the business, the Accounting & Finance department needed more knowledge and control of the cost structure.

For example, XYP's administrative expenses had been rising steadily, from 4,5% of sales in 2016 to an estimated 5.9 % of sales in 2018. Also, inventory, which in 2016 used just under 100,000 square feet of storage, was projected to require nearly 250,000 square feet in 2018. Some of this inventory was products held on consignment for specific customers and work in process more than one year old. Indeed, the costing systems at XYP was very traditional. All machines were in a separate cost center. The maintenance cost of those machines, which most of them had extended their life expectancy and were fully amortized, were allocated to each department using traditional cost absorption basis. This was including the cost of the 2 to 15 persons crew burden rate per hour, which included direct wages, fringe benefit costs, shift and overtime premiums, plus an allocated share of plant salaried expense. A work ticket system assigned direct material, direct labor, and crew and machine time burden rates to individual jobs.

Data Analytics

During the meetings with Analytics Consulting, John Ellington had increasingly realized the benefits of data analytics software to implement a new operational model at XYP. Several competitors had already implemented 'performance analytics' solutions in overseas markets. John Ellington was convinced that data analytics was essential to be able to align operation with new strategic priorities, 'rationalize' core operations, while keeping a degree of flexibility in responding to a changing market demand. According to the Institute of Chartered Accountant of England and Wales (ICAEW), Performance Analytics is defined as:

'The discovery and communication of meaningful patterns in data to manage performance. Especially valuable in areas rich with recorded information, analytics relies on the simultaneous application of statistics, computer programming and operations research to quantify performance. Analytics often favors data visualization to communicate insight.'.

Indeed, the auditors of XYP had already used data analytics to collect and aggregate data last year, in order 'to get a better perception of the operational health and whether nothing was wrong which could jeopardize the company's well-being. In their report, the auditors had already created a very impressive dashboard of risk profiles, containing for example some information about the full-time to delivery to customers, which was the main source of clients' complaints. John Ellington asked the 'New Yoyo' project teams to exemplify software solutions that could be used to take advantages of integrating performance analytics and create a short software simulation of a few performance indicators for their business case.

Making Strategic Decisions

David Yang and John Ellington were still hesitating on strategic priorities for XYP in the coming years. Although several improvements were made identifiable, it was not clear enough where the company had to focus on, which main priorities it had to pursue and where resources had to be allocated. Considering the importance of the purchasing process (accounting for 56% of the full cost in average for each product line), it was decided to appoint one experienced purchaser to coordinate between the Planning and Procurement department and the Production department to adjust procurement policies (including scheduling and standards of order quantities) against suppliers conditions, then increasing XYP;s negotiating power towards the major suppliers of polyurethane and other suppliers of raw materials in China. But the management team of XYP was still not sure about the strategic priorities and key performance indicators for XYP.

If a new organization and factory layout were to be implemented, and logistics operations reorganized, management would need to be informed very quickly when objectives were not to going to be met, then critical decisions would need to be made in order to restore profitability and ensure that the new operational model would be kept sustainable. This was critical for the company if it wanted to be able to generate the cash needed to enter a new period of growth within one or two years. David Yang knew that this was also a matter of survival. XYP's auditors were already examining some of the key risk operational indicators which they were considering 'could be of crucial importance to the XYP's ability to operate as a going concern'.

David Yang wanted to avoid XYP to experience any drastic restructuring or layoff of employees. Such options were not considered at the moment, even if they could have represented a more comfortable solution for the top management team and the shareholders of XYP. As he was announcing the Strategy Away Week, David Yang said: 'Business improvement is our way to success. We have attractive, growing markets, we have a large portfolio of products, an established customers base with growing needs, and we have skills, an experienced workforce. Our success will depend on operational performance, whether we can set up operational objectives which are reasonable and feasible to us, and make sure that we can achieve those targets'. This had resonated in many debates and discussions among XYP's employees, especially in the Production and Planning/procurements departments, then raising several concerns: What are the most important things XYP should aim to achieve? Which key factors of success should it pursue? How will XYP's management team know that they can succeed in achieving operational targets?

The ABC report prepared by the consultants team of Analytics Consulting was definitely a good starting point, but many questions were still pending: which critical success factors, which business processes should be improved and which performance indicators should be chosen in order to monitor the performance of XYP? Would the management team be able to successfully monitor operational performance on monthly, weekly or daily basis? David Yang knew that if it wanted to succeed, XYP had to build on its strengths. Policy-makers and local governments in the environment of XYP had created suitable conditions to encourage business innovation and successful use of technologies. Then XYP had to find a way to take advantage of it. XYP, as a family-run medium-size Chinese firm, could also learn from successful Chinese firms on building their presence on foreign markets. As requested, we have summarized below the key highlights about XYP performance following the completion a few months ago by the Analytics Consulting consultants' teams of XYP's ABC Business Performance Improvement project. We hope this document will be useful to XYP's 'New Yoyo' projects teams engaged in the 'Strategy Away Week' to make some propositions for business improvements at XYP.

1

MEMO

The conclusions of this report are the results of a series of interviews and analysis conducted by our consultants. Data files of full datasets collected during the project are also available in excel format according to the list in appendix 5. (XYP ABC Datasets excel file)

At current stage, it is still not clear which performance indicators need to be designed and which business improvements to be made. We would like to highlight the fact that the 'ABC Business Performance Improvement Report' only aims to identify potential business improvement opportunities but does not aim to propose any strategic business priorities or explore strategic alternatives.

We believe that information and data contained in this ABC report would be very useful to XYP's 'New Yoyo' project teams to build their business case during the 'Strategy Away Week' at XYP. However, we also recommend that each 'New Yoyo' project team coordinates with some departments of XYP for any additional operational, financial or strategic data that they may need in accordance to their strategic plan. Also. we recommend that data contained in this 'ABC Report' and XYP ABC Datasets excel files could be advantageously supplemented by secondary data collected in the public domain (as for example related to the plastic manufacturing sector).

We suggest that 'New Yoyo' project teams try to 'make sense' of the information and data contained in this ABC report. As we have been informed that the KPI dashboard to be proposed by the project teams should contain no more than eight performance indicators, we believe that an integrated performance management system would have to balance between several (sometimes contradictory) business priorities. Making use of the Balanced Scorecard could then reveal to be as a useful tool to balance between various business objectives.

Xiao Yoyo Plastics -ABC Report 2

Profitability Analysis

In the past three years, Xiao Yoyo Plastics' financial and operational performance has deteriorated. In 2018, net profit decreased by 9.1 % as compared to previous year. According to the management letter from XYP's auditors, the combined effects of a decrease in sales volumes and lower gross operating margins are the main reasons of the poor financial performance. Key financial data is provided in Appendix 2.

It is still difficult to know the underlying causes of the deterioration of the profit margins based on the review of standard budgets, but some important facts clearly came to the attention of the consultants team:

• a significant increase in wages and salaries due to overtime working hours in the factory, as well as maintenance costs had been pointed out as some of the reasons of the erosion of profit margins; • the consultant team had investigated the costs engendered by the preparation of the machine during each production shift from one product batch to another, which seemed to be happening more and more frequently; each new batch entry into the production process requires a certain amount of time for the preparation of the machines.

Based on data available, the consultant team had started to estimate the profitability of each product line of XYP (Appendix 2). This might be very useful to understand where the hidden costs come from. Still, some questions remain about the costs of maintenance: what were the factors influencing those costs?

Competitors Analysis

The consultants team investigated performance indicators used by several key players in the plastic manufacturing sector and found six categories of indicators in relation to the customer dimension (Appendix 1). One member of the Marketing & Sales department of XYP commented about the performance of XYP's competitors:

"In recent years, we have responded to market demand for rolls of plastics film with specific design, higher quality and strict time-to delivery conditions. The average size per order for rolls of plastics film has now dropped to an around 1,400 or 1,500 units per order as compared to an average of 2,000 units per order three years ago. Most of our clients operate nowadays under a Just-in-Time systems; therefore, it is difficult for us to anticipate market demand... It is becoming more and more very volatile and difficult to predict. Our department is currently preparing to publish a new catalogue of our products in order to respond to the need for variety in our products design (thickness, resistance, color, appearance…). We observe similar trends in the market demand for plastics bags, which in addition are more labor-intensive to produce as compared to rolls of plastics film.' Despite the challenges faced by Xiao Yoyo Plastics in responding to ever-changing market conditions, our interviews with the Marketing & Sales department team concluded that the market for rolls of plastic films and plastic bags was still quite attractive and could represent a significant source of growth for XYP, based on current available market data4 .

The data collected from competitors of XYP in the plastic rolls segment showed that the main source of competitive advantage was based on cost leadership. XYPs' Head of Marketing commented: "Plastic rolls products easily be differentiated: those are standard products, and the only source of competitive advantage is based on cost. Although we have paid a lot of attention to cost reduction initiatives and renegotiating with your suppliers of raw materials, we still cannot manage to beat most of our competitors on price…'.

ABC Data Analysis

The ABC consultants' team has collected data and aggregated operational data based on the Process Map5 which had been created by several managers of XYP in several workshop sessions. It was found an average time of 2 to 8 hours for preparation of machines only depending on products in each production shift.

Moreover, the information collected during the interviews revealed that several activities in the Planning Department to prepare for new batches to enter the production process were very time-consuming, which was summarized in a process analysis (Appendix 3). Similarly, the ABC consultants' team compiled data to measure the cost of activities to be conducted for the process 'Develop a new product'. It was discovered that the production planning was very often changed in order to respond to urgent orders requests from customer; also, the production process was very often interrupted by unplanned batches entering the production process for very small order quantities.

The ABC team also identified a large number of extra, non-planned activities necessary to process clients urgent order requests. Those requests were engendering additional activities in the Production and Planning departments and sometimes the Sales department as well. It was estimated that the cost of the process 'To prepare machines' was equivalent to 316 full time employees workload.

The preparation of the machines is under the responsibility of the Maintenance department and Production department together. Several batches of products can enter into the production line however most of new entries in the production line necessitate productions shifts (i.e. preparation of the machines), and longer time production shifts could also negatively affect the occupancy rate of the machines and/or increase the time that employees of the Maintenance department need to spend on each machine. The ABC consultants team recommended the introduction of SMED 6 methods. The performance of the production processes is measured against standards of Ideal Cycle Time 7 .

Supply Chain

Historically, materials handling at XYP's factory has been managed by the Planning department but the ABC team evidenced that several other departments of XYP were involved in completing many activities aiming to optimize logistics inside the factory and to prepare production plans, which resulted in no clear line of responsibility towards the overall efficiency of the production planning. The production planning is changed very frequently due to unstable priority levels in batches to enter into the production process. The ABC team recommended that a process 'Manage the production plan' be further solely examined and that another process ''Manage the production plan for urgent orders' (rush mode) be identified and further analyzed. The results of the cost analysis of those processes are included in Appendix 3.

Customer Complaints

The management letter from the auditors to the board of Yoyo Plastics noticed several complaints from XYP's customers in relation to quality issues or late deliveries which explains that XYP is losing market share. A short review of customer surveys revealed that one of the main reasons of customer's' dissatisfaction is related to delays in product delivery.

Quality measures

It was difficult for the consultant teams to identify any suitable measures for the quality of XYP's products based on data available. First-yield pass 8 was identified as the main indicator used by the Production department to measure quality performance.

Negotiating with suppliers

6 SMED: https://en.wikipedia.org/wiki/Single-minute_exchange_of_die 7 Ideal Cycle Time is the fastest cycle time that your process can achieve in optimal circumstances. Therefore, when it is multiplied by Total Count the result is Net Run Time (the fastest possible time to manufacture the parts). 8 First pass yield. First pass yield (FPY), also known as throughput yield (TPY), is defined as the number of units coming out of a process divided by the number of units going into that process over a specified period of time. Only good units with no rework or scrap are counted as coming out of an individual process.

Considering the large proportion of the cost of raw materials, the ABC team examined the procurement process at XYP in order to find out if any improvement could be made to reduce the cost of raw materials process (accounting for 56% of the full cost in average for each product line). Considering the impact of purchasing of raw materials on profitability, it was decided to appoint one experienced purchaser to coordinate between the Planning and Procurement department and the Production department to review XYP's procurement policies (including scheduling and standards of order quantities) against suppliers' conditions. A workshop organized by the ABC team helped to identify potential improvements in the purchasing process. More information is provided in Appendix 4.

The workforce

The ABC team has conducted an interview with Jane Eyre, Human Resources (HR) manager of XYP. From the point of point or the HR department, XYP is facing a critical issue in attracting and retaining experienced technical workforce, which may explain for the operational problems. Jane Eyre commented:

'Specific competencies are needed in our business; the lack of experienced professional staff is the main reason for weak planning and low efficiency. We need a strong incentive policy to train and retain our personnel'

The plastic manufacturing sector in China is facing a shortage for specific technical skills in extrusion and wielding, which are very specific to the plastic manufacturing industry.

Web Analytics

In our last meeting with John Everington, the ABC consultant team suggested that operational improvements at XYP could also leverage on Big Data, especially in the field of customer analytics and predictive business analytics, or HR analytics. Analytics Consulting suggested that making use of external data could also be a source of business opportunities for XYP to improve its operational model and performance.

To

A keynote in public speaking is a talk that establishes the main underlying theme. In corporate or commercial settings, greater importance is attached to the delivery of a keynote speech or keynote address.

More information about the market forecast for rolls of plastic films can be found on: https://www.marketresearchfuture.com/reports/plastic-films-market-3002

See Process Map (List of Activities) in the document 'Business Case Introduction'

 (End)

Notes:

(1) Sales volumes are split equally between three types of products: plastic rolls, rolls of plastic films and plastics bags for around one third for each category over the period (2) Machines and equipment are amortised over a period of five years and were purchased more than ten years ago (3) Sales Breakdown can be decomposed as follows:

• Annual volume of production: 130 000 tons (1 ton = 1000 kgs.)

• Number of customer order placed in one year: 125 000


A Fillon
email: fillonalicia@gmail.com

M E Mathieu

Y Boirie
email: yves.boirie@inra.fr

D Thivel
email: thiveldavid@hotmail.com

Mathieu Me
email: me.mathieu@umontreal.caboirie

Melle Fillon

Appetite control and exercise: Does the timing of exercise play a role?

Keywords: Exercise, Timing, appetite control Running head: Exercise timing and appetite

The prevention and management of chronic diseases, particularly overweight and obesity, relies on multidisciplinary strategies mainly combining dietary approaches with physical activity. Recently, the timing of exercise (time of the day as well as delay/position relative to a meal) has been suggested as an important parameter to consider when prescribing physical activity. Some studies have for instance shown the interest of the timing of exercise on the glycemia, sleep and body composition regulation. However, the impact of exercise-timing on appetite control and energy intake remains unclear. This is why, the present paper questions whether physical exercise, depending on its timing during the day and related to a meal, can affect energy intake, appetite sensations and food reward.

Although evidences remain actually limited, exercising during the morning; and particularly close to lunch, might have a better impact on overall energy balance through reduced subsequent energy intake, without leading to compensatory intakes at the following meals. Importantly, dealing with the timing of exercise to optimize energy balance (and affect energy intake and appetite) does not only require to consider its time during the day (morning vs. afternoon or evening), but also and maybe mainly its order/position (pre vs. post) and delay regarding meals. While the actual literature remains limited in this area, the present paper tends to highlight the importance of considering the timing of exercise to optimize our impact on the overall energy balance, and to encourage the elaboration of further studies to better understand and determine the potential effect of this timing of exercise, in order to find the best combination between the different exercise characteristics, intensity, duration, modality, to empower these effects.

1

Highlights :

 Exercise differently affect energy intake and appetite depending on its timing  Morning exercise seems to have better effect on energy intake  The closer exercise is to the meal, the greater are the beneficial effects

Introduction

Physical activity programs are nowadays recognized as a core component of multidisciplinary weight loss strategies. Physical activity interventions are elaborated through the selection of the best and adapted exercise's intensity, duration, modality or frequency, among others, in order to optimize their effects. Recently, the timing of exercise (time of the day as well as delay/position relative to a meal) has been suggested as an important parameter to consider when prescribing physical activity [START_REF] Reid | Understanding the potential contribution of a third "T" to FITT exercise prescription: the case of timing in exercise for obesity and cardiometabolic management in children[END_REF]. Some studies have for instance shown a better glycemic control when exercise is performed within one to three hours after food intake in patients with type II diabetes [START_REF] Borror | The Effects of Postprandial Exercise on Glucose Control in Individuals with Type 2 Diabetes: A Systematic Review[END_REF][START_REF] Chacko | Exercising Tactically for Taming Postmeal Glucose Surges[END_REF][START_REF] Haxhi | Exercising for Metabolic Control: Is Timing Important[END_REF][START_REF] Teo | Exercise Timing in Type 2 Diabetes Mellitus: A Systematic Review[END_REF]. However, a better lipemia response to a meal has been shown when exercise is performed before the meal compared with after [START_REF] Petitt | Effects of prior exercise on postprandial lipemia: A quantitative review[END_REF][START_REF] Zhang | Effect of exercise timing on postprandial lipemia in hypertriglyceridemic men[END_REF][START_REF] Zhang | Effect of exercise timing on postprandial lipemia and HDL cholesterol subfractions[END_REF]. Other studies have questioned the interest of the timing of exercise on sleep [START_REF] Buxton | Exercise elicits phase shifts and acute alterations of melatonin that vary with circadian phase[END_REF][START_REF] Yamanaka | Morning and evening physical exercise differentially regulate the autonomic nervous system during nocturnal sleep in humans[END_REF][START_REF] Yoshida | Effects of the timing of exercise on the night sleep[END_REF],

with an evening exercise allowing a better subjective feeling of sleep quality [START_REF] Yoshida | Effects of the timing of exercise on the night sleep[END_REF] , a decrease in daytime sleepiness [START_REF] Yoshida | Effects of the timing of exercise on the night sleep[END_REF], a relevant sleep phase progression [START_REF] Buxton | Exercise elicits phase shifts and acute alterations of melatonin that vary with circadian phase[END_REF] and a better sympathetic regulation (HR and body temperature) [START_REF] Yamanaka | Morning and evening physical exercise differentially regulate the autonomic nervous system during nocturnal sleep in humans[END_REF]. The exercise-meal timing was also investigated in relation to body composition, with regular pre-meal exercise favoring greater weight loss [START_REF] Alizadeh | Comparison between the effect of 6 weeks of morning or evening aerobic exercise on appetite and anthropometric indices: a randomized controlled trial[END_REF][START_REF] Willis | The effects of exercise session timing on weight loss and components of energy balance: midwest exercise trial 2[END_REF], decreased BMI and abdominal circumference [START_REF] Alizadeh | Comparison between the effect of 6 weeks of morning or evening aerobic exercise on appetite and anthropometric indices: a randomized controlled trial[END_REF] and then reducing obesity risks [START_REF] Chomistek | The Relationship Between Time of Day of Physical Activity and Obesity in Older Women[END_REF].

While the effects of exercise, depending on its duration [START_REF] Masurier | Effect of Exercise Duration on Subsequent Appetite and Energy Intake in Obese Adolescent Girls[END_REF][START_REF] Tamam | Overweight and obese boys reduce food intake in response to a glucose drink but fail to increase intake in response to exercise of short duration[END_REF], intensity [START_REF] Thivel | The 24-h Energy Intake of Obese Adolescents Is Spontaneously Reduced after Intensive Exercise: A Randomized Controlled Trial in Calorimetric Chambers[END_REF][START_REF] Thivel | Intensive exercise: A remedy for childhood obesity?[END_REF][START_REF] Thivel | Obese but not lean adolescents spontaneously decrease energy intake after intensive exercise[END_REF], modality [START_REF] Balaguera-Cortes | Energy intake and appetite-related hormones following acute aerobic and resistance exercise[END_REF][START_REF] Broom | Influence of resistance and aerobic exercise on hunger, circulating levels of acylated ghrelin, and peptide YY in healthy males[END_REF][START_REF] Laan | Effects and reproducibility of aerobic and resistance exercise on appetite and energy intake in young, physically active adults[END_REF] or induced-energy expenditure [START_REF] Thivel | Daily energy balance in children and adolescents. Does energy expenditure predict subsequent energy intake?[END_REF] on the control and regulation of appetite and energy intake have received a lot of attention for the last decade, the impact of exercise-timing remains unclear. Since we recently suggested "Timing" as a third "T" to the FITT exercise prescription method (Frequency, Intensity, Time (duration), and Type of exercise) [START_REF] Reid | Understanding the potential contribution of a third "T" to FITT exercise prescription: the case of timing in exercise for obesity and cardiometabolic management in children[END_REF], it seems important to further question the potential effects of the timing of exercise on appetite control to optimize the impact of our interventions on both sides of the energy balance (expenditures and intake). In that context, the present commentary tends to highlight the available evidence regarding the potential effects of the exercise timing on appetite control.

Time of the day

Although Maraki et al. were among the first to specifically question the appetitive responses to exercise (1 hour of aerobic + muscle conditioning exercises) depending on its timing during the day (morning vs. afternoon) [START_REF] Maraki | Acute effects of a single exercise class on appetite, energy intake and mood. Is there a time of day effect?[END_REF], their results failed to show any effect of both exercise conditions on self-reported energy intake, with a similar increase in hunger and PFC as well as a similar fullness and satiety decline, compared with their non-exercise group, among heathy normal weight women. To date, we found only two studies whose main aim was to compare the acute effect of morning versus afternoon exercises on appetite and energy intake [START_REF] Alizadeh | Acute Effect of Morning and Afternoon Aerobic Exercise on Appetite of Overweight Women[END_REF][START_REF] Larsen | Evening high-intensity interval exercise does not disrupt sleep or alter energy intake despite changes in acylated ghrelin in middle-aged men[END_REF]. In their work, Alizadeh and collaborators asked adult women with overweight to perform a 30-minute acute bout of exercise (treadmill running) set at their individually determined ventilatory threshold, whether between 08:00 and 10:00 am (morning condition) or 02:00 and 04:00 pm (afternoon condition). Although the authors did not observe any difference between conditions for the subsequent energy intake, they used selfreported dietary recalls whose sensitivity might not be enough to detect significant changes, and that have been also shown to favor under-reporting [START_REF] Alizadeh | Acute Effect of Morning and Afternoon Aerobic Exercise on Appetite of Overweight Women[END_REF]. Interestingly, the authors found a greater level of satiety in response to the morning session [START_REF] Alizadeh | Acute Effect of Morning and Afternoon Aerobic Exercise on Appetite of Overweight Women[END_REF], suggesting once more the potential beneficial effect of exercising during the morning when it comes to the control of appetite and energy intake. Moreover, Larsen et al. recently observed a higher ghrelin concentration in inactive men after a 30minute acute high intensity intermittent cycling exercise performed during the afternoon compared to the same exercise performed in the morning or evening, while perceived hunger and fullness as well as self-reported energy intake appeared unaffected by the timing of the exercise [START_REF] Larsen | Evening high-intensity interval exercise does not disrupt sleep or alter energy intake despite changes in acylated ghrelin in middle-aged men[END_REF].

In their chronic study, Alizadeth et al. (2017) found reduced dietary intake in women with overweight, including carbohydrate and fat consumption in response to a 6-week intervention when exercise (30 minutes treadmill running at the ventilatory threshold, three-times a week) was performed in the morning but not in the afternoon, despite unchanged appetite feelings [START_REF] Alizadeh | Comparison between the effect of 6 weeks of morning or evening aerobic exercise on appetite and anthropometric indices: a randomized controlled trial[END_REF]. These results have been reinforced by later studies who failed to find any energy intake modifications in response to a 12-week program where adolescents girls performed 30 minutes exercise sessions (composed of various activities such as running, cycling, team games, dancing, etc.) between 03:30 pm and 04:30 pm, three times a week [START_REF] Massie | Effects of a 12-Week Exercise Intervention on Subsequent Compensatory Behaviors in Adolescent Girls: An Exploratory Study[END_REF]. Some authors even observed a 80 to 230 Kcal/day increase in food consumption in response to an afternoon exercise intervention (walking/running on a treadmill), but not when the exercise was set during the morning, in adults with overweight and obesity (noting that these differences did not reach significance) [START_REF] Willis | The effects of exercise session timing on weight loss and components of energy balance: midwest exercise trial 2[END_REF]. Such an increase in energy intake after exercise is of main importance to consider since it might decrease the amount of energy expended during the exercise and, in the long term, if the energy expended is overcompensated, this could favor counterproductive results such as weight gain. Importantly, future studies comparing the effect of morning vs. afternoon exercise should also consider the potential existence of different eating patterns between lunch and dinner, with individuals who might be susceptible to overeat at dinner compare to lunch, independently of exercise.

Exercising before or after a meal?

In 2016, Heden and colleagues questioned for the first time the importance of exercising just before or 45 minute after a meal, to improve appetite control [START_REF] Heden | Impact of Exercise Timing on Appetite Regulation in Individuals with Type 2 Diabetes[END_REF]. They then asked patients with type II diabetes to perform resistance exercise (45-minute session) prior or 45-minute following diner.

According to their results, exercising right before a meal favored increased pre-meal perceived fullness, reduced hunger and reduced acylated ghrelin concentrations compared with their post-meal exercise session and control condition [START_REF] Heden | Impact of Exercise Timing on Appetite Regulation in Individuals with Type 2 Diabetes[END_REF]. These results are in line with those from Cheng et al. who also obtained decreased appetite, despite increased plasma ghrelin concentrations, when healthy adult males cycled before a meal (50 minutes at 60% of their maximal capacities) compared with after [START_REF] Cheng | Appetite regulation via exercise prior or subsequent to high-fat meal consumption[END_REF]. Interestingly these studies also suggest the interest of exercising after a meal as a way to potentially extend the suppressive effects of meal consumption on appetite [START_REF] Heden | Impact of Exercise Timing on Appetite Regulation in Individuals with Type 2 Diabetes[END_REF][START_REF] Cheng | Appetite regulation via exercise prior or subsequent to high-fat meal consumption[END_REF], which definitely warrants further investigations.

In 2017, Mathieu et al. published a well-controlled free-living study designed to compare the effect of two different lunchtime organizations : i) exercise then meal or ii) meal then exercise, on overall energy balance, also considering the importance of the intensity of exercise [START_REF] Mathieu | Optimal timing of exercise for influencing energy intake in children during school lunch[END_REF]. Twenty-one primary school children were then asked to exercise for 40 minutes (ball games as well as running and chasing games) right before their lunch meal either at low or moderate-to-high intensity; or to perform the 40-minute moderate-to-high intensity exercise right after their lunch, on three separate occasions. While their results confirm the interest of prescribing higher intensity exercises to benefit from a subsequent transient anorexigenic effect (with a significantly higher energy intake after the low intensity exercise compared with the moderate-to-high intensity one), they failed to observe any difference in energy intake when exercise was performed before or right after the meal [START_REF] Mathieu | Optimal timing of exercise for influencing energy intake in children during school lunch[END_REF]. More recently, similar results were obtained among adolescents with obesity whose energy intake and food reward remained unchanged whether the adolescents performed a 30-minute cycling exercise (65%VO2 peak ) right before or after their lunch meal [START_REF] Fillon | Does exercising before or after a meal optimize overall energy balance in adolescents with obesity?[END_REF] . Pre-and post-meal hunger feelings were however found reduced when the exercise was performed right before the meal [START_REF] Fillon | Does exercising before or after a meal optimize overall energy balance in adolescents with obesity?[END_REF] . To our knowledge, only one chronic study questioned the effect of exercising right before or after meals among patients with overweight and obesity. In this study, participants were asked to exercise twice a day for 15 minutes at high intensity for 4 consecutive weeks [START_REF] Damour | Exercise training in the free-living environment and its impact on energy intake and anthropometric outcomes: A pilot study on exercise timing around meals[END_REF]. According to their results, the authors failed to find any effect on energy intake, except a slight increase in the percentage of protein intake when exercise was performed just before meal [START_REF] Damour | Exercise training in the free-living environment and its impact on energy intake and anthropometric outcomes: A pilot study on exercise timing around meals[END_REF].

Interestingly, [START_REF] Gustafson | Exercise and the Timing of Snack Choice: Healthy Snack Choice is Reduced in the Post-Exercise State[END_REF] highlighted the importance of the cognitive and hedonic control of energy intake that must be considered when comparing pre and post meal exercise [START_REF] Gustafson | Exercise and the Timing of Snack Choice: Healthy Snack Choice is Reduced in the Post-Exercise State[END_REF]. They indeed pointed out that individuals' free food selection differs in quality when realized before or after an acute exercise. According to their study, people show a 33.5% higher probability of choosing healthy food items when the choice is made before exercising; while they are about 39% more likely to select "unhealthy" items after exercise [START_REF] Gustafson | Exercise and the Timing of Snack Choice: Healthy Snack Choice is Reduced in the Post-Exercise State[END_REF]. Although the participants of this later study were proposed apples or brownies only, which certainly composes its main limitation; such hedonic compensatory responses to exercise have to be considered when prescribing exercise before or after a meal in order to avoid any compensatory consumption that might attenuate the beneficial effects of exercise.

The exercise-meal delay

While not specially designed and focused on the effect of the exercise-timing, results from studies using similar exercises and conducted among similar populations tend to suggest potentially different energy intake responses depending on the delay between exercise and the subsequent meal. In their work, Fearnbach et al. for instance showed reduced ad libitum energy intake in 12-15 years old adolescents with obesity 30 minutes after an acute bout of moderate intensity cycling exercise [START_REF] Fearnbach | Reduced neural response to food cues following exercise is accompanied by decreased energy intake in obese adolescents[END_REF][START_REF] Fearnbach | Impact of imposed exercise on energy intake in children at risk for overweight[END_REF] while others failed to observe any food consumption modification in a similar population when the same exercise is performed 60 minutes before lunch [START_REF] Thivel | Acute post-exercise energy and macronutrient intake in lean and obese youth: a systematic review and metaanalysis[END_REF]. Some studies have been specifically conducted to compare some nutritional outcomes in response to exercise depending on its delay with a meal. In their work, Josaphat and collaborators asked healthy men to perform an acute 30-minute exercise set at 70% of their maximal aerobic capacities either 90 minutes or right before a lunch test meal [START_REF] Josaphat | Impact of exercise timing on chemosensory response, appetite and energy intake in lean males[END_REF]. According to their results, there was no difference between the two conditions regarding total ad libitum energy intake, appetite feelings and the taste or smell sensations [START_REF] Josaphat | Impact of exercise timing on chemosensory response, appetite and energy intake in lean males[END_REF]. Interestingly, using a similar design, Albert et al. observed a reduction of 11% of the post-exercise energy intake (with a 23% decrease in ingested fat) when the exercise ( 30minutes treadmill running at 70% VO 2max ) is performed just before the meal compared with 165 minutes before, with no difference regarding appetite feelings, in normal-weight adolescents [START_REF] Albert | Timing of moderate-to-vigorous exercise and its impact on subsequent energy intake in young males[END_REF]. This reduced food intake was moreover not compensated for by an increase of the following snack or dinner intake [START_REF] Albert | Timing of moderate-to-vigorous exercise and its impact on subsequent energy intake in young males[END_REF]. Our team recently obtained similar results in adolescents with obesity who show a decrease of their relative energy intake after an acute bout of moderate intensity cycling exercise (65% VO2 peak ) set 30 minutes before lunch compared with 180 minutes before, without any compensation at the following meal (dinner) [START_REF] Fillon | Effect of exercise-meal timing on energy intake, appetite and food reward in adolescents with obesity: the TIMEX study[END_REF]. This was accompanied by a significantly reduced intake of proteins and lipids after the control session (rest) or both the control and exercise + 180 minutes sessions respectively [START_REF] Fillon | Effect of exercise-meal timing on energy intake, appetite and food reward in adolescents with obesity: the TIMEX study[END_REF]. Interestingly, none of the appetite feelings (hunger, fullness, desire to eat and prospective food consumption) were found different between conditions, suggesting an optimized effect on overall energy balance when exercise is realized close to a meal, without creating any food frustration or hunger. These results are in line with those from Panissa et al. (2019) who recently showed that intermittent high intensity exercise performed one hour before an ad libitum meal reduces appetite and energy intake in overweight inactive men [START_REF] Panissa | Timing of high-intensity intermittent exercise affects ad libitum energy intake in overweight inactive men[END_REF]. Moreover, Fillon et al. showed a significantly lower pre-meal explicit liking for high-fat relative to low-fat foods when the exercise is close to the meal [START_REF] Fillon | Effect of exercise-meal timing on energy intake, appetite and food reward in adolescents with obesity: the TIMEX study[END_REF]. Importantly, all the studies conducted so far questioned the potential effect of the exercise-meal delay implementing exercises between 30 to 150 minutes after the breakfast and testing the energy intake response at a fixed meal (usually 12:00pm). However, by doing so, these studies compared the appetitive responses to exercise of different metabolic load and activities. Indeed, it has been showed that performing the same exercise, in terms of duration and intensity, 60 or 180 minutes after a standardized breakfast, leads to different substrate use in children, which in turns can differently affect subsequent energy intake and appetite [START_REF] Aucouturier | Effect of time interval between food intake and exercise on substrate oxidation during exercise in obese and lean children[END_REF]. In that sense, ad libitum energy intake has been compared at a test meal settled 30 or 90 minutes after an acute exercise (30 minutes cycling at 65% VO2 peak ) fixed 150 minutes after a standardized breakfast on both conditions (modifying then the timing of the lunch meal) [START_REF] Fillon | Effect of the exercise timing on energy intake and appetite sensations in adolescents with obesity[END_REF] .

Interestingly, energy intake was found lower on both exercise conditions compared to the control one, with a greater decrease when the lunch was consumed 90 minutes after the exercise, without any difference in terms of food reward [START_REF] Fillon | Effect of the exercise timing on energy intake and appetite sensations in adolescents with obesity[END_REF].

Conclusion

Although the actual literature remains limited to date, available results seems to encourage the consideration of the timing of exercise when prescribing physical activity, as an interesting way to empower energy balance by affecting both energy expenditure and energy intake. The available literature discussed in the present work seems to indicate that regularly exercising during the morning would have beneficial effects on subsequent energy intake when compared to afternoon interventions. While it remains difficult to draw any conclusion regarding the effect of exercising right before or after a meal (due to the reduced and heterogeneous evidences); available results suggest that the closer to the lunch is the exercise, the greater might be the impact on overall energy balance through reduced subsequent energy intake, without leading to compensatory intakes at the following meals, which remains obviously to be confirmed. Importantly, dealing with the timing of exercise to optimize energy balance (and affect energy intake and appetite) does not only require to consider its time during the day (morning vs. afternoon or evening), but also and maybe mainly its order/position (pre vs. post) and delay regarding meals. These results remain however to be confirmed since the actual body of literature rests on studies that present a high level of methodological heterogeneity, suggesting the need for a more consensual and standardized method to facilitate our actual understanding and help future exercise prescriptions. Similarly, this high degree of methodological disparity limits any interpretation regarding the potential effect of the exercise timing on food preference and macronutrients intake, which should be better considered in future studies. While the present work highlights the importance of considering the timing of exercise to optimize our impact on the overall energy balance, further studies are needed to find the best combination between the different exercise characteristics, intensity, duration, modality, to empower these effects. Further studies questioning the effect of the timing of exercise on food reward are also required since the few available results come from the same research group and were obtained in adolescents with obesity only. Not only the appetitive and behavioral responses to exercise, depending on its timing, should be further explored, future studies should also investigate the potentially involved physiological and neurocognitive mechanisms, including the potential role of some eating traits such as the eating profile (cognitive restriction, disinhibition, food craving, etc.). Indeed, the beneficial effects (and their extent) of the exercise timing might also depend on these parameters (certainly mainly its intensity). Although encouraging results exist in both lean and children with overweight/and obesity, further long-term investigations and especially free-living school-based studies are required. Indeed, while the elaboration of daily schedules that respect the chronobiology of children has created a lots of debate for the last couple of years, especially regarding the introduction and organization of physical education and physical activities, there is a clear need to better explore and understand the exact effects and interests of the exercise-meal timing to improve both our public health prevention strategies and treatment programs.


Jean-Claude Bermond

Marie-Claude Heydemann

Dominique Sotteau

Line graphs of hypergraphs I

come   L'archive ouverte pluridisciplinaire


C A F Silva

L Manin

R G Rinaldi

E Besnier

D Remond

Dynamics of Torsional Vibration Damper (TVD) pulley, implementation of a rubber elastomeric behavior, simulations and experiments

In this work, the Torsional Vibration Damper (TVD) rubber ring viscoelastic-material properties are determined based on Dynamical Mechanical Analysis (DMA) measurements and master curves reconstructions using thermo-simplicity principle. The elastomeric constitutive behavior is then implemented in the torsional vibration damper's equation of motion and the frequency response is simulated so that enhanced physical representation of the TVD dynamics can be achieved. Major differences in the TVD frequency response are highlighted and analyzed whether or not the viscoelastic material properties (elasticity modulus and damping) are considered constant or frequency and temperature dependent.

Introduction

The Torsional Vibration Damper (TVD) is an essential component of power transmission systems such as the Front Engine Accessory Drives (FEAD). The FEAD of a vehicle is a system composed of individual accessories such as compressor, alternator, water and steering pumps, etc. These accessories are coupled to pulleys which are driven in rotation by a poly-V belt driven itself by the crankshaft pulley (Fig. 1). This driving pulley is commonly used as a torsional vibration damper for the crankshaft since rotational vibrations are harmful to the system performance and may cause fatigue. The TVD is usually tuned so that to dampen the first torsional mode of the crankshaft and therefore provide rotational speed stability. The pulley (outer ring) is used as an inertia (I1, Fig. 2) which is coupled to the crankshaft (CS) by a rubber-ring. Hence, TVD is composed of an inner ring (hub) mounted on the crankshaft extremity, an intermediate viscoelastic rubber ring and an outer ring used as a poly-V pulley (Fig. 1). Generally, in simulation and for sake of simplification, the TVD dynamic properties -stiffness and damping -are chosen to be constant [START_REF] Ewins | Encyclopedia of Vibration[END_REF]. However, these properties depend on the operating temperature, the shear strain amplitude and the frequency to which the TVD is subjected since the rubber ring is made of a viscoelastic material [START_REF] Lakes | Viscoelastic Materials[END_REF]. The viscoelasticity of the rubber layer embedded within the vibration dampers such as the TVD has rarely been explored. Recently, Bhatti (2012) indirectly compared viscoelastic dampers with Magnetorheological dampers. Also, the TVD behavior was investigated by [START_REF] Jauregui | Viscoelastic torsional damper model[END_REF] through a case study of a complicated model. A particularity of these studies is that they consider rheological models such as Maxwell [START_REF] Bhatti | Comparison between the visco-elastic dampers and magnetorheological dampers and study the effect of temperature on the damping properties[END_REF], Kelvin [START_REF] Jauregui | Viscoelastic torsional damper model[END_REF][START_REF] Kelly | Moving load problems in the theory of viscoelasticity[END_REF], etc. Such rheological models significantly increase the complexity of the differential equations of motion which are usually solved using complex numerical schemes.

Some other authors analyzed the dynamic characteristics of the stiffness and the damping from an experimental point of view [START_REF] Kinoshita | An experimental study of a torsional/bending damper pulley for an engine crankshaft[END_REF][START_REF] Wakabayashi | Torsional vibration damping of diesel engine with rubber damper pulley[END_REF]. However, in the Wakabayashi's work, the results were fitted to a specific engine case. Recently, [START_REF] Manin | Pulley torsional vibration damper characterization[END_REF] proposed a methodology to easily characterize the pulley torsional vibration damper.

The objectives of this paper are: [START_REF] Bhatti | Comparison between the visco-elastic dampers and magnetorheological dampers and study the effect of temperature on the damping properties[END_REF] to propose a methodology based on the master curves of the TVD elastomeric layer, (2) then to simply and directly consider the viscoelastic properties of the constituting rubber-ring in the damper's equation of motion; (3) to highlight the influence of taking into consideration the viscoelastic properties of the elastomer when computing the TVD dynamic response; (4) to evaluate the coefficients of the equation of motion, stiffness and damping, as a function of the operating conditions.

This research aims at accurately calculating the viscoelastic TVD response in order to provide a realistic representation of the system dynamics, which is in accordance with Jauregui (1996)'s work and conclusions.

2 Torsional Vibration Damper modelling

Torsional damper dynamics

The torsional vibration damper can be modeled by a one degree-of-freedom (DOF) massspring-damper system [START_REF] Blanc | Dynamique des rotors en torsion Etude des amortisseurs de torsion[END_REF], it is also similar to the one DOF base excited vibrating system [START_REF] Jazar | Advanced Vibrations -A Modern Approach[END_REF], however in this case, the single DOF is the rotation around z-axis as shown in Fig. 2.

Figure 2. Torsional vibration damper and its schematic diagrams.

Assuming the engine at idling, the driving torque fluctuation usually contains 2 harmonics (ω, 2ω). However, in this paper, only the prevailing harmonic (ω) and its amplitude (θ ) generally represented as θ = θ sin(ω t) is considered to represent the acyclism on the crankshaft (θ , Fig. 2). The difference between the torque experienced by the TVD outer-ring and the driving torque imposed by the crankshaft results in an angular lag of θ with respect to the excitation θ , and is due to the viscoelastic properties of the TVD intermediate rubber-ring.

To evaluate the impact of considering the intermediate rubber-ring temperature and frequency dependent viscoelastic properties leading to varying TVD stiffness K and viscous damping C coefficients, one considers the equation of motion of the system shown in Fig. 2, (Eq. 1):

I θ + C θ + K θ = C θ ω cos(ω t) + K θ sin(ω t) ( 1
)
Where I is the outer-ring inertia, angle θ is the DOF considered, θ and ω are, respectively, the amplitude and the excitation pulsation of the fluctuations (engine acyclism).

The steady-state response of θ has an amplitude and phase as detailed in Eq. ( 2) [START_REF] Jazar | Advanced Vibrations -A Modern Approach[END_REF]. This represents the Frequency Response Function (FRF) of one DOF base excited vibrating system with the frequency ratio r, natural frequency ω and damping ratio ξ as in Eq. [START_REF] Chen | Steady-state transverse response in coupled planar vibration of axially moving viscoelastic beams[END_REF].

FRF ∶ " θ θ = #1 + (2 ξ r) $ #(1 -r $ ) $ + (2 ξ r) $ & φ ( ) = tan + , 2 ξ r - 1 -r $ + (2 ξ r) $ . / (2)
r = ω ω ω = 0 K I ξ = C 2 #K I (3)
The equations ( 2) and ( 3) are considered because they are adapted from a classical formulation in the frequency-domain, which is consistent with the TVD elastomer DMA characterization presented in 3.1.

TVD rubber-ring viscoelastic model

The TVD intermediate ring is made of rubber which can be described as a viscoelastic material. A complex modulus E * is usually defined to describe its response to a small strain oscillatory loading (Eq. 4).

E * = E ʹ + i E " = f (T 78 , f 78 , ε 78 ) (4)
The real part of E * , the storage modulus E ʹ relates to the elastic behavior of the rubber, it defines the capacity to store energy upon deformation. The imaginary part of E * , the loss modulus E " defines the energy dissipative ability of the material. For the problem considered, the rubber-ring shall permit dampening the crankshaft torque fluctuations. The complex modulus E * is determined via DMA characterization and, for polymers, is known to vary as a function of the temperature T 78 , , the loading frequency f 78 and the dynamic strain ε 78 experienced by the rubber. Hence, the TVD intermediate ring material properties shall be determined in accordance with the engine-range of operating conditions (speed, temperature). Interestingly, for the material considered, the thermo-simplicity principle can be used [START_REF] Silva | Modeling of power losses in poly-V belt transmissions: hysteresis phenomena (enhanced analysis)[END_REF] to predict the viscoelastic behavior of the rubberring at a given temperature T :7; (Fig. 5), i.e. the temperature in the engine room over a broad range of frequencies, which couldn't be assessed by DMA measurements otherwise. Practically, the DMA response curves measured for different temperatures and a limited frequency domain are horizontally shifted to form a unique/master curve (the vertical shift related to thermal expansion is often neglected). To a given temperature corresponds a shift factor a < (Fig. 5, left). As a result, a master curve is constructed (Fig. 5, right). It will be further fitted (Tab.2) in order to be used in the TVD viscoelastic model as explained in the next paragraphs.

Viscoelastic torsional damper model

When the viscoelasticity of the TVD rubber-ring is considered the equation of motion Eq.( 1) becomes Eq.( 5) with stiffness K = : and damping C = : which both depend on the temperature, the frequency and the dynamic strain similarly to the complex modulus E * in Eq. ( 4).

I θ + C = : θ + K = : θ = C = : θ ω cos(ω t) + K = : θ sin(ω t) (5)
Indeed, K = : and C = : are calculated from E * . Let us examine the dependency of these terms on E * and point out the way to determine them. The torsional stiffness K of the torsional vibration damper (TVD) in Figs. 1 and 3 can be estimated by Eq. ( 6) which was demonstrated by [START_REF] Blanc | Dynamique des rotors en torsion Etude des amortisseurs de torsion[END_REF].

Figure 3. Geometrical parameters used to calculate the stiffness of the TVD.

K = 2 π R -L G ʹ e (6)
Where R , L , e are respectively the rubber-ring radius, width and thickness. The rubberring is assumed to be a homogeneous and isotropic material of shear modulus G ʹ . Thus, Eq. ( 7) is valid for calculating G ʹ from E ʹ obtained via DMA with the Poisson ratio of the rubber B 1 2 ⁄ .

G ʹ = E ʹ 2 (1 + B) (7)
Replacing G ʹ by Eq. ( 7) in Eq. ( 6) the stiffness K = : can be calculated by Eq. [START_REF] Jazar | Advanced Vibrations -A Modern Approach[END_REF].

K = : = π R -L e (1 + B) E ʹ (8)
As E ʹ in Eq. ( 4), K = : varies as a function of the temperature T 78 , the frequency f 78 and the strain ε 78 experienced by the TVD rubber-ring. The viscous damping coefficient C can be calculated using the third term of Eq. ( 3) where the only unknown is the damping ratio ξ (Eq. ( 9)).

C = 2 #K I ξ (9)
Moreover, according to several authors (Piersol and Paez, 2010; Hujare and Sahasrabudhe, 2014) the structural loss factor η can be approximated as twice the damping ratio ξ, i.e. η = 2ξ at resonance (Thomas and Laville, 2007) and η = E " E ʹ ⁄ for viscoelastic materials (rubber-ring) leading to Eq. [START_REF] Kinoshita | An experimental study of a torsional/bending damper pulley for an engine crankshaft[END_REF].

C = : = #K = : I E " E ʹ (10)
Similarly, C = : depends on the temperature T 78 , , the frequency f 78 and the strain ε 78 experienced by the TVD rubber-ring.

In the next paragraphs, the differences between Eqs. ( 1) and ( 5) are evaluated thanks to the TVD response (FRFs) for several operating conditions (temperature, frequency). The differences between the constant (K, C) and varying (K = : , C = : ) stiffness and damping are also discussed.

Results

Results are presented for the TVD with the inertia and geometric parameters as detailed in Tab. [START_REF] Bhatti | Comparison between the visco-elastic dampers and magnetorheological dampers and study the effect of temperature on the damping properties[END_REF]. This is the crankshaft TVD used in the FEAD of a six-cylinder truck engine (Fig. 1).

Dynamic Mechanical Analysis

The two components of the viscoelastic complex modulus E * , namely the storage E ʹ and loss E " moduli, are used in Eqs. ( 7), ( 8) and ( 9) and thus need to be determined. To do so, Dynamic Mechanical Analysis measurements in tensile mode are performed on samples cut out of the TVD rubber-ring (Fig. 4). More precisely, a forced periodic strain profile is imposed and the associated force is recorded. It is worth noting that the phase shift between the two time signals (strain and force) evidences the viscoelastic behavior of the tested sample. Furthermore, in order to explore the time temperature dependence, several frequencies and temperatures are considered. Finally, providing thermoreological simplicity of the material, the associated master curves can be determined for a given temperature of interest (the engine operating temperature).

In this work, three different frequencies (0.2, 2, 20Hz) and testing temperatures ranging from -10 to 120°C, were considered as evidenced in Fig. 5 (left). The resulting master curve at T :7; = 20°C is plotted in Fig. 5(right), it permits predicting the mechanical behavior of the TVD rubber-ring at 20°C over a large frenquency range that can not be experimentally measured. In this study, master curves were obtained and fitted (Tab. ( 2)) for the engine operating temperatures of 20, 40, 60, 80 and 100°C. The TVD geometric parameters from Tab. (1) with its rubber-ring material properties (stiffness, damping) calculated from DMA characterization (Eqs. ( 8) and ( 10)) are then used in Eqs. ( 2) and (3) for several operating conditions of the torsional vibration damper producing the FRF plotted in Figs. ( 6), ( 7), ( 8) and (9). 2) and ( 3). Thus, both the FRFs and the rubber-ring properties from DMA vary with the TVD operating conditions (temperature, frequency) and the empirical equations in Tab. [START_REF] Blanc | Dynamique des rotors en torsion Etude des amortisseurs de torsion[END_REF]. In Fig. 6 when the TVD working temperature is changed, e.g. from T 78 = 60°C to 80°C, the maximum amplitude (peak) value of its FRF slightly changes (Fig. 10), which means that it changes by a few percent with a maximum of 3.3% at T 78 = 20°C when compared to the constant case in Tab. (3) (T 78 = 60°C).

Assuming constant values for K and C (FRF `a bc c in Fig. 6) with the same temperature (T 78 = 60°C) seems to be good approximations of the realistic K = : and C = : (FRF WS d7e in Fig. 6) with a maximum relative error of around 12.3 % (Fig. 11). However, throughout the engine range of operation, f 78 from 0Hz (engine at rest) to 2 times the TVD resonant frequency (~430Hz) in Fig. 11, the relative error increases substantially when the temperature is changed. For example, comparing the FRF $S d7e obtained at T 78 = 20°C (K = : and C = : as in Eqs. [START_REF] Jazar | Advanced Vibrations -A Modern Approach[END_REF][START_REF] Kinoshita | An experimental study of a torsional/bending damper pulley for an engine crankshaft[END_REF]) and FRF `a bc c (K and C as in Tab. ( 3)) at T 78 = 60°C the relative error gFRF $S d7e -FRF `a bc c h FRF $S d7e i between these responses can reach around one hundred percent, see Fig. 11. The range of the testing temperatures is chosen to be representative of the TVD working conditions, even in severe conditions of use, and the range of the excitation frequency is chosen to be equal in size to two times the TVD resonance frequency. Although, in practice, the resonance frequency corresponds to an operating point to be avoided, here, it permits analyzing clearly the change (viscoelasticity effects) in the frequency responses of the TVD thanks to the symmetry of the FRFs and shifting in relation to each other. The differences between the results obtained with constant and varying coefficients for several temperatures and the frequency domain equal to two times the TVD resonance frequency are also presented in Figs. [START_REF] Kinoshita | An experimental study of a torsional/bending damper pulley for an engine crankshaft[END_REF] and [START_REF] Lakes | Viscoelastic Materials[END_REF].

Experimental analysis

After generating numerical results for the case study (Tab. ( 1)) of the TVD in Fig. 1, one aimed at verifying experimentally the effectiveness of the TVD modeling as a single DOF system (Fig. 2) with varying stiffness and damping.

Set up description

An experimental setup has been designed to enable the measurment of the TVD frequency response when subjected to a torsional excitation under specific operating conditions, i. e. temperatures (Fig. 12). The temperature range was chosen to be representative of the TVD working conditions (25°C to 100°C) and according to the heating system capabilities. The range of the excitation frequency is chosen so that to be almost centred on the torsional resonance frequency (150 Hz -350 Hz). The principle of the experiment consists in exciting the TVD outer inertia with constant force of 5N applied by a shaker during a frequency sweep from 150Hz to 350 Hz. The response to this excitation is measured by accelerometers placed on the outer inertia so that to be sensitive to angular acceleration and therefore to permit analysing the torsional behavior. The hub of the TVD is bolted to a rigid frame, the outer-ring of the TVD is harmonically excited by a shaker through a push-rod system connecting the shaker head with the TVD outer ring. Since the excitation force is tangent to the pulley, it is also a torque/angular excitation for the outer ring with respect to its center. A hot air blower and a temperature controlled box (closed during the tests) are also used to increase the temperature from the ambiant environment to the desired temperature. This testing temperature is measured by a thermocouple inserted in the TVD rubber-ring. Once the target temperature is reached, a stabilisation time of five minutes is applied before performing the frequency sweep. The input force is controlled and measured with a force sensor placed between the shaker head and the push-rod. The shaker and the excitation force are controlled by an M+P® control and acquisition system. Due to lack of time, the measurements have been done once for each temperature, therefore the variability of the experimental results are not discussed. The trends, consistency and agreement with simulations are analysed in next section.

Experimental results

The FRFs amplitudes and phases represented in Figs. [START_REF] Marynowski | Non-Linear Dynamic Analysis of an Axially Moving Viscoelastic Beam[END_REF] and 14 are obtained from the signals of the left accelerometer and the force sensor. As a result of the experiments, the stiffness and damping obtained experimentally through the half power bandwidth (3dB) method (Hujare and Sahasrabudhe, 2014) (Fig. 15 and Eq. ( 11)) show good agreement (j 11% of error) with those obtained via simulations Eqs. ( 8) and [START_REF] Kinoshita | An experimental study of a torsional/bending damper pulley for an engine crankshaft[END_REF] for the temperature of 60°C (Tab. ( 4)).

ξ = f $ -f 2 f (11)
The frequency responses (Figs. 13 and14), obtained experimentally, confirm some interesting points observed in simulations: when the TVD working temperature is increased the resonance frequency is decreased and the FRFs are shifted to the left which coresponds to a softening behavior(Tab. ( 5)). It is observed that simulations results are in good agreement (j 4.7% of error, Tab. ( 5)) with experimental results for several temperatures. The variability of the experimental results being not accessible since the tests were done once, the relative error has to be considered with some criticism even if it is satifactory. The small difference between the peaks obtained numerically and experimentally may be due to the 3dB method which introduces a constant error. However, the absolute value of the shifts when the temperature is changed are equivalent validating experimentally the results predicted numerically. For temperatures up to 80°C the frequency response curves change shape and a secondary peak appears (Fig. 13). At 100°C the torsional resonance is observed experimentally for 206,9 Hz (0,6g) but the peak amplitude is smaller than that at 182 Hz (0,86g). The corresponding phase curve shows two inflections at these later frequencies (Fig. 14). This phenomenon may be due to the emergence of a structural vibration mode of the test apparatus that is no more negligible since the rubber ring becomes softer. This shows the limits of the experimental set up for high temperatures.

Discussion and Conclusions

In this paper, the TVD response is analyzed as a function of its operating conditions (temperature, frequency) because it is assumed here that the moduli in Eq. ( 4) and, consequently, the torsional stiffness K = : and damping C = : depend exclusively on the temperature and the frequency [START_REF] Silva | Modeling of power losses in poly-V belt transmissions: hysteresis phenomena (enhanced analysis)[END_REF], i.e. no Payne effect. Thus, for the constant strain ε 78 = 0.2%, different operating conditions lead to different responses as in Figs. 6 and7.

An interesting point when considering the viscoelasticity of the TVD rubber-ring is the different resonant frequencies in Tab. ( 5) accordingly with the operating conditions. When the temperature is increased the TVD resonance peak is shifted to the left. This is because the stiffness K in Eq. ( 6) depends on G ʹ which depends on E ʹ (Eq. ( 7)). Thus, as the stiffness K is operating conditions dependent (Eq. ( 4)), the resonance frequency of the TVD calculated by the second term of Eq. (3) also depends on its operating conditions.

Finally, the comparisons between simulations and experiments show good agreement with small relative error (Tab. ( 5)). However, when the temperature is increased the FRFs are more dampened (smoothing, Fig. 13) and there are some side-effects (SE, Fig. 14). These may be due to the complex viscoelastic material behavior and due to the fact of not being able to impose a pure torsional mechanical excitation to the TVD experimentally. It means that there are also the response of other modes (directions) in the experimental FRFs.

Figure 1 .

 1 Figure 1. Serpentine poly-v belt of a FEAD with its TVD pulley.

Figure 4 .

 4 Figure 4. Experimental setup, principle and rubber-ring samples for the DMA tests.

Figure 5 .

 5 Figure 5. TVD rubber-ring DMA data (left) and correspondent master curve (right).

Figure 6 .

 6 Figure 6. TVD amplitude, frequency response for several temperatures.

Figure 7 .

 7 Figure 7. TVD phase, frequency response for several temperatures.

Figure 8 .

 8 Figure 8. TVD rubber-ring stiffness K = : for several temperatures.

Figure 9 .

 9 Figure 9. TVD rubber-ring damping C = : for several temperatures.

Figure 10 .

 10 Figure 10. FRFs maximum peaks provided by K = : and C = : .

Figure 11 .

 11 Figure 11. FRFs (relative) error made when K and C are used instead of K = : and C = : . These results are summarized, discussed and verified experimentally in the next sections.

Figure 12 .

 12 Figure 12. Experimental set-up used to test the TVD under specific operating conditions.

Figure 13 .

 13 Figure 13. Experimental FRF (amplitude) of the TVD for several temperatures.

Figure 14 .

 14 Figure 14. Experimental FRF (phase) of the TVD for several temperatures.

Table 1 .

 1 Inertia and geometric parameters of the TVD considered.

	I (Kg mm $ ) R (mm) L (mm) e (mm) 31344.2 90 35 7

Table 2 .

 2 Empirical equations describing the TVD rubber-ring moduli as F(T :7; , f

	T :7; (°C) 20 40 60 80 100	0.002) modulus E ʹ (MPa) Storage 6.55 R :7Q S.ST U 5.68 R :7Q S.ST V 5.02 R :7Q S.ST$S 4.49 R :7Q S.STST 4.27 R :7Q S.ST-V	Loss modulus E " (MPa) 5.79 R :7Q S.S VW -4.81 5.41 R :7Q S.S W--4.58 6.17 R :7Q S.S U -5.47 6.07 R :7Q S.S -X -5.49 6.34 R :7Q S.S -Y -5.81	:7Q , ε =
	3.2 Simulations

Table ( 3

 ( ) gives data on stiffness and damping for the TVD which dimensions are given in Tab.[START_REF] Bhatti | Comparison between the visco-elastic dampers and magnetorheological dampers and study the effect of temperature on the damping properties[END_REF]. Both constant values K and C are used to simulate the constant FRF (dashed curves in Figs.6 and 7) resulting in the resonance frequency of 216.5 Hz and damping ratio of 0.075 (Tab. (3)).

Table 3 .

 3 TVD constant characteristics at T 78 = 60°C used to determine the FRF

	K (N m rad ⁄ ) C (N m s rad ⁄ ) Resonance (Hz) Damping ratio ξ 58000 6.4 216.5 0.075

Table 4 .

 4 Comparison between TVD stiffness and damping, simulated and measured at 60°C Stiffness [Nm/rad] Damping [N ms/rad] Resonance [Hz] Damping ratio

	Simulations	58000	6.4	216.5	0.075
	Experiments	60526	5.8	221.2	0.067
	Rel. error [%]	4.4	9.2	2.2	11.0

Figure 15. 3dB method applied to obtain the damping from the experimental FRFs.

Table 5 .

 5 Comparison of resonance peaks from simulations and experiments.

	Temperature [°C] Amplification [g]	Peak [Hz] experiments	Peak [Hz] simulations	Relative error [%]
	25/20	1.5	263.6	251.6	4.7
	40	1.5	243.8	233.7	4.2
	60	1.3	221.2	219.5	0.8
	80	1.1	209.2	206.3	1.4
	100	0.6	206.9	202.6	2.1

Acknowledgement

The authors are very grateful to the Auvergne Rhone Alpes council, Volvo-Renault Trucks and the FEDER fund who supported this work.